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TE NIVERSITY LIBRARIES

Itfiiiiixiim WWW I

3 1293 00880 2880

 

 

 

 

 

 

 

 

 

 

 

 

 

This is to certify that the

dissertation entitled

CONTINUOUS PROCESSING OF
UNIDIRECTIONAL PREPREG

presented by

Shridhar R. Iyer

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in Chemical Engineering

 

 

Wifl/M

 

Date flCfé/J/efl/ 0137,/970

MS U i: an Affirmative Action/Eq ual Opportunity Institution 0-12771

 

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| LIBRARY
Michigan State
i University

 

 

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TO AVOID FINES return on or before date due.

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MSU is An Affirmative ActioNEqual Opportunity Institution
chIm—pd

CONTINUOUS PROCESSING OF
UNIDIRECTIONAL PREPREG

by

Shridhar R. Iyer

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemical Engineering
1990

ABSTRACT

CONTINUOUS PROCESSING OF
UNIDIRECTIONAL PREPREG

By

Shridhar R. Iyer

The use of thermoplastic composites has been limited by the lack of reliable
techniques to make prepreg tapes of consistent quality. The intractability of
thermoplastic matrices leads to problems such as the manufacture of stiff and boardy
tape, solution or carrier devolatilization leading to the formation of voids with its
attendant loss in mechanical properties and high resin content. Dry powder
impregnation methods offer a clean inexpensive solution to this problem. The
objectives of this investigation were to explore the viability of dry powder processes
and to study the fundamental physical phenomena associated with the manufacture of
powder-impregnated thermoplastic composites.

A novel powder prepregging process suitable for the manufacture of high
quality powder-impregnated tapes was successfully developed as a result of this
investigation. The important components of the process are an acoustic spreader to
spread narrow fiber tows to expose individual filaments, an acoustic aerosolizer
which delivers a controlled concentration of fine particles to the spread fiber tow and
a heater where the particles are sintered on the fibers. It is shown that the powder-
prepregging process can achieve fine control over both fiber-matrix composition in
the prepreg tape and intimate wetting between individual fibers and the thermoplastic

matrix. The coalescence of polymer particles on fibers is a sequential process which
is comprised of heat transfer to the impregnated tow, interparticle sintering, formation
of a polymer film and its subsequent retraction to form droplets on the fibers. The
consolidation of powder-impregnated tapes under heat and pressure to form void-free
parts is also discussed. Consolidation cycles are shown to be simple and require the
use of temperatures above the softening or melting point of the polymer, and
optimum pressure which depends on fiber volume fraction in the composite and a
contact time that allows for intimate wetting between interfaces and interdiffusion of
polymer chains across the interface.

Copyright by
SHRIDHAR R. IYER
1990

' ACKNOWLEDGEMENT

My sincere appreciation goes to Dr. L. T. Drzal for his guidance, support and
encouragement throughout the duration of the project. It has been a pleasure to work
with him and I have learned a great deal during my stay at Michigan State

University.

i I wish to thank all members of the "Composites Group" past and present - Raj
Agrawal, Javad Kalantar, Tesh Rao, Craig Chmielewski, Jim Dounis, Brent Larson
and many others for their assistance and friendship and for making my sojourn here a
pleasant one. In addition, I wish to thank Mike Rich and Madhu Madhukar for their
help in the project. My thanks are also due to Dr. K. J ayaraman for his technical

assistance in the development of the process.

I wish to acknowledge the excellent fabrication skills of Tom Palazzolo, Jim
Muns and Tom Hudson of the Physics Machine Shop; and Dan Shakespear and
Frank Palazzolo for their role in the automation of the process.

I am grateful to the other members of my committee - Dr. J. V. Beck, Dr. B.
W. Wilkinson, Dr. Selim Yalvac and Dr. J. L. Dye for many discussions and for the
time that they dedicated to this dissertation. '

I thank my parents for their continual support and encouragement throughout
my educational career.

Finally, I thank my wife Rupa for her love and support in enabling me to

complete this work and for enduring my long irregular work hours over the years.

iv

Table of Contents

1. introduction

 

2. Background

 

2.1 Slurry Processing

 

2.2 Solution Processing

 

 

2.3 Melt Impregnation
2.4 Film Stacking

 

2.5 Fiber Co-mingling '

 

2.6 Dry Powder Impregnation

 

2.7 Process Design

 

 

3. Theory
3.1 Tape Manufactme

 

 

3.1.1 Spreading
3.1.2 Impregnation

 

 

3.1.3 Coalescence
3.2 Consolidation

 

4. Preposcd Process

 

4.1 Fiber Motion

 

4.2 Aerosolizer

 

 

4.3 Spreader
4.4 Heater

 

4.5 ProcessDescription

 

4.6 Automation

 

4.6.1 Fiber Motion

 

 

4.6.2 Oven Temperature
4.6.3 Data Acqutlvition

 

4.7 Ancillary Equipment

 

5. Material Characterization

 

5.1 Particle Size Analysis

 

 

5.2 Differential Scanning Calorimetry
5.3 Viscosity

 

 

5.4 Summary of Properties
6. Tape Manufacture

 

6.1 Fiuidized Bed Behavior of Cohesive Powders
6.1.1 Experimental

 

 

6.1.2 Fluidized Bed Behavior

 

6.2 Pulsed Gas Flow

 

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6.3 Aerosolization

 

6.3.1 Determination of Natural Frequency

 

6.3.2 Aerosolizer Behavior at the Natural Frequency
6.3.3 Future Improvements

 

 

 

6.3.4 Discussion - Aerosolizer Performance

6.4 Speeding

 

6.4.1 Discussion - Spreader Performance

 

6.5Coalescence

 

6.5.1 Heat Transfer

 

 

6.5.2 Interparticle Sintering and Coalescence
6.5.3 Droplet Formation

 

6.5.4 Spreading of Polymer Droplets on Fibers

 

 

6.5.5 Discussion of Coalescence Phenomena
6.6 Process

 

6.6.1 Discussion - Process Performance

 

7. Consolidation

 

7.1 Experimental

 

 

7.2 Optimum Cycles for Void-Free Consolidation
7.3 Intimate Contact and Autohesion

 

7.4 Crystallinity

 

 

7.5 Fracture Toughness and Failure Mode
7.6 Discussion of Consolidation Experiments

 

8. Unified Approach

 

8.] Fiber Motion

 

8.2 Spreader

 

8.3 Aerosolizcr

 

8.4 Heater

 

9. Conclusions And Future Work

 

 

Appendix A : Engineering Drawings
Appendix B : Automation

 

 

Appendix C : Contact Angle Program
Bibliography

 

vi

111
111
115
119
120
121
124
124
128
132
133
140
141
143
151
154
154
158
164
165
166
171
173
173
173
174
174
176
182
203
237

 

LIST OF FIGURES

Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8.
Figure 9.
Figure 10.

Figure 11.
Figure 12.
Figure 13.

Figure 14.
Figure 15.
Figure 16.
Figure 17.
Figure 18.
Figure 19.
Figure 20.
Figure 21.
Figure 22.
Figure 23.
Figure 24.
Figure 25.
Figure 26.
Figure 27.
Figure 28.
Figure 29.

Slurry processing [8].

Melt impregnation process [18].

Electrostatic fluidized bed process [18].

Recirculating powder deposition chamber.

Design of powder prepregging process.

Flowchart for the manufacture of thermoplastic composites.
Coalescence in the heater.

Heat transfer to the impregnated tow.

Sintering between adjacent equal-sized spherical particles (initial radius = a).
Spreading of a liquid on a planar surface.

Unduloidal droplet on a cylindrical fiber.

Non-symmetric perturbation of an axisymmeu'ic droplet.

Transition from axisymmetry to non-symmetry for a droplet on a cylindrical
fiber.

Consolidation of powder-impregnated tapes.

Fiber motion in the powder prepregging process.
Aerosolizer.

Momentum balance inside the aerosolizer.
Spreader.

Fiber spreading operation.

Schematic of powder prepregging process.

Data acquisition and control of powder prepregging process.
Temperature control of oven.

Hot stage for coalescence experiments.
Consolidation mold.

Experimental investigation.

Plot of length vs breadth for each particle.

SEM photograph of polyamide particles.

Particle size distribution of Orgasol 2001 Ex D Nat.
DSC thermogram of as-received polyamide.

vii

Figure 30.
Figure 31.
Figure 32.
Figure 33.
Figure 34.
Figure 35.
Figure 36.
Figure 37.
Figure 38.
Figure 39.
Figure 40.
Figure 41.
Figure 42.
Figure 43.
Figure 44.
Figure 45.
Figure 46.
Figure 47.
Figure 48.

Figure 49.

Figure 50.
Figure 51.

Figure 52.
Figure 53.
Figure 54.
Figure 55.

Figure 56.
Figure 57.
Figure 58.
Figure 59.
Figure 60.
Figure 61.

Figure 62.
Figure 63.

Figure 64.

Estimation of relative crystallinity of polyamide.

DSC thermogram of polyamide quenched in liquid nitrogen.
Viscosity-temperature plot of polyamide at a shear rate of 0.1 sec“.
Distributor pressure drop as a function of gas velocity.

Particle size distributions of the fine, medium and coarse powders.
Bed pressure drop vs velocity, fine powder.

Bed pressure drop vs time, fine powder.

Fluidized bed profiles.

Bed pressure drop vs velocity, medium powder.

Bed pressure drop vs time, medium powder.

Bed height vs velocity, medium and coarse powders.

Bed pressure drOp vs velocity, coarse powder.

Bed pressure drop vs time, coarse powder.

Effect of gas pulsing.

Experimental scheme to determine natural frequency of aerosolizer.
Weight of particles collected in filter vs frequency.

Sound pressure level vs time, two hour experiment.

SPL and particle concenuation vs time.

SEM photographs of coalescence in the heater - (a) and (b) show heat transfer to
the impregnated tow, the particles initially adhering to the fiber surface. (c)
shows interparticle sintering and coalescence into a film, droplet formation. ((1)
shows the formation of droplets and (e) the formation of axisymmetric
thermodynamically droplets at long times.

Cross section of prepreg tapes of different widths. Bar at bottom right represents
50 microns.

SEM photograph of a polyamide particle showing the presence of nodules.

Plot of K vs L for the polyamide droplets on carbon fibers. The solid line is the
prediction by the model [45] for 6 = 23°. .

Residual error for different contact angles.
Histogram of droplet sizes.
Axisymmetric droplets on a fiber at equilibrium, S < 3,.

SEM photographs of prepreg tapes. (a) 90.9% V;, (b) 77.5% Vf, (c)70.2% V,,
and (d) 33.2% V,.

Prepreg tapes of different widths. Bar at bottom right represents 1 cm.

Turning angles, fiber tow over spreader.

Consolidation cycle, specimen 2.

ENF test, loading pins and specimen geometry.

Operating curve for optimum consolidation of polyarnide-AS4 composites.
Optical micrographs of polyamide-A84 composites. (a) Specimen 3, and (b)
specimen 7.

Mode 11 fracture energy vs fiber volume fraction, polyamide-A84.

SEM photographs of fractured specimens. (3) and (b) specimen 15,
(c) and (d) specimen 9.
Mode 11 fracture energy vs void fraction, V; = 70%.

viii

 

LIST OF TABLES

Table I.

' Table II.
Table 111.
Table IV.
Table V.
Table VI.
Table VII.

Table VIII.

Table IX.
Table X.
Table XI.
Table XII.

Table XIII.

Table XIV.
Table XV.
Table XVI.

Table XVII.

High performance polymers.

Behavior of cohesive powders.

Definitions of mean diameters.

Specific heats of polyamide.

Crystallinity of polyamide.

Material properties.

Properties of powders.

Sound pressure.

Spreading experiments - constant amplitude, varying fiequency.
Spreading experiments - constant frequency, varying amplitude.
Coalescence experiments.

Calculated heating times for clusters of different sizes.
Predictions of sintering times for selected thermoplastics.
Prepregging experiments - identical conditions.

Prepregging experiments - different conditions.

Prepreg tape widths.

Consolidation and ONVFA experiments.

Table XVIII. Unified approach - powder prepregging process.

Chapter I
INTRODUCTION

 

A composite material can be defined as a material system consisting of two
or more physically distinct and mechanically separable components one of which has
distinctly superior properties. The dispersion of the different components in a
composite material can usually be controlled to achieve optimum properties, which in
many cases, are superior to that of the individual components [1]. Composite
materials may be broadly classified as fibrous composites (which consist of fibers in a
matrix), laminated composites (which consist of layers of various materials) and
particulate composites (which consist of particles in a matrix). The discussion in this
investigation will be restricted to fibrous composites, specifically to the manufacture
of unidirectional prepreg tapes and their subsequent consolidation to form void-free
composite parts.

Unidirectional prepreg tapes are precursors of composites composed of fibers
aligned in one direction and embedded in an unconsolidated polymer matrix. The
fibers themselves can be of various types, the most prominent among them being
glass, carbon and Kevlar fibers. Fiber diameters usually vary from 5 to 15 microns,
e.g., Magnamite AS4 Graphite fibers made by Hercules have a diameter of 8
microns. All polymers are potential candidates for matrix materials but limitations
such as processability and desired end use properties dictate the final' choice.

Polymer matrices can be either thermoset or thermoplastic in nature.

The finished composite part is formed by consolidating unidirectional prepreg
tapes which have been stacked in a predetermined sequence of orientations, e.g., 0°,
45°, 90° as specified by the end application. The physical phenomena which occur
during consolidation are different for thermoset and thermoplastic materials.
Thermosets undergo a chemical reaction with curing during consolidation to their
final crosslinkcd form. Curing is the process of polymerization of the resin to form a
crosslinked network between fibers in the composite part. Curing is accomplished by
the application of heat and/or pressure during processes such as vacuum bagging,
autoclave molding, hot press molding etc. Thermoplastic matrices are usually in
their final polymerized form and the consolidation step primarily ensures that the
polymer interfaces within and between adjacent prepreg tapes fuse into each other to
form a homogeneous part. If a solvent or liquid carrier is used in the prepregging
step, then devolatilization is carried out prior to actual consolidation to prevent

volatiles from being trapped within the composite part.

Thermoset matrices such as epoxy resins are widely used in the composites
industry. Their advantages include low shrinkage, excellent adhesion, good chemical
resistance and easy processability [1]. Prepreg tapes are made by pulling a fiber tow
(fiber bundle wound on a spool, available commercially in numbers ranging from 30
fibers/tow to 250,000 fibers/tow) through a heated pot containing liquid matrix and
then through a die. The fibers are individually coated with the matrix and aligned in .
one direction. This process is called hot melt impregnation. Since the resin is
partially cured during the impregnation step, the tape is said to be B-staged.
Thermoset tapes have a limited shelf life and are stored at low temperatures to
prevent unwanted additional curing. Among the drawbacks of these resins are the
tendency to degrade at high temperatures (usually above 175°C), low resin strength

and fracture toughness and a high degree of brittleness.

Thermoplastic matrices offer many advantages [2,3] over thermosetting resins.
These include short molding cycle time, infinite shelf life of prepreg, capability of
fusion bonding, recyclability and repairability, reduced storage and handling
problems, increased moisture resistance and better fracture toughness. However,
their use has been limited by the lack of good processing techniques to make flexible
prepreg tapes. The general intractability of these matrices due to their high viscosity
gives rise to a host of problems such as the manufacture of stiff and boardy tape,
solution devolatilization leading to the formation of voids with its attendant loss in
mechanical properties and prepreg tapes with high resin content.

The desire for improved properties of matrix materials led to the quest for
polymers with improved toughness and strain capability along with good chemical
resistance, stiffness, strength and the ability to withstand high temperatures. Many
high temperature resins (a high temperature resin has the ability to retain its
mechanical properties for thousands of hours at 232°C, hundreds of hours at 316°C,
and/or rrrinutes at 538°C [4]) were developed. Most of these failed to be
incorporated into composite materials for advanced su'uctural applications primarily
due to their poor processability. Hergenrother and Johnston [4] proposed the
following requirements for an ideal high temperature polymeric system to be used as
a composite matrix : easy prepreg preparation, good shelf life, acceptable tack
(stickiness) and drape (shape relaxation), acceptable quality control procedures, low
processin g temperature and pressure, no volatile evolution, dense void-free matrix,
good mechanical performance over the desired temperature range, time, and
BnVironmental conditions, acceptable repairability and cost-effectiveness. No
available matrix conforms to all these properties and hence the choice of a matrix

usually represents a compromise.

High temperature polymers have highly stable structural units in the polymer
chain such as aromatic rings and/or heterocyclic rings [5]. These units absorb
thermal energy and contain a minimum number of oxidizable hydrogen atoms, thus
lending thermo-oxidative stability to the resin matrix. Also, they degrade at a very
slow rate at elevated temperatures into thermally stable residues which retain
structural integrity. The structural units, which lend thermal stability to the matrix
also serve to make processing of these polymers, most of which are thermoplastic,
exu'emely difficult. They are not easily soluble and they melt or soften at very high
temperatures. Their viscosities are very high, usually of the order of 1000 to 10,000
Pa.s. Table I lists the properties of some popular high temperature polymers which

are being investigated for advanced structural applications.

The primary objective of this investigation was to explore the possibility of
developing a viable technique to prepreg reinforcing fibers with thermoplastic
matrices to form flexible prepreg tapes. The basic premise can be summarized as
follows :

If polymers can be synthesized and/or pulverized to sufficiently fine

powders (of the order of 1-20 microns) and suspended in a fiuidizing

medium inside a chamber, then fiber tows can be passed through this

chamber so that the fine polymer particles would impact and adhere to

the fibers. This impregnated fiber tow can be subsequently heated to

sinter the particles without consolidation and thereby form flexible

prepreg tapes.
Such a process would be solvent-free and offer complete control over the final
configuration of the prepreg tapes, i.e., fiber-matrix volume fractions, prepreg tape
width and hence flexibility. The secondary objective was to couple this process with
a fundamental investigation into the different aspects of powder adhesion,

coalescence and the consolidation of the prepreg tapes to form void- free parts.

TABLE I. HIGH PERFORMANCE POLYMERS [6]

 

 

Polymer/Source Type of Polymer? Tg (Tm), °C Processing T, °C
Polyetherether Ketone SCT 143 (343) 360-400
(PEEK) ICI

Polyether Ketone SCT 165 (365) 400-450
(PEK) BASF

Poly (EKEKK) BASF SCT 173 (370) 420-450
Polyimide (LaRC-TPI) APT 250 (325) 350
Mitsui Toatsui

Polyether Sulfone AT 260 400-450
(HTA) ICI

Polyetherimide AT 21 350-400
(Ultem) GE

Polyetherimide SCI 270 (3 80) 380-420
(P-IP) Mitsui Toatsui

Polyirrride ATS 320 315
(PMR- 15) Hysol

Polyimide 2080 APT 280 350
Lensin g i

Polyirrride APT 265 350
(Matramide 9725)

Ciba-Geigy

 

 

 

 

 

 

1 AT :Amorphous Thermoplastic
APT: Amorphous Pseudothermoplastic
SCI‘ : Semi-crystalline Thermoplastic
ATS: Amorphous Thermoset
T : Glass transition temperature
T; : Melting temperature
The chapters in this thesis are arranged as follows :
(1) Chapter 2 reviews existing techniques for the manufacture of thermoplastic
composites and provides the rationale for the development of a new dry powder
process from fundamental principles.
. (2) Chapter 3 discusses the different unit operations which are integral to a dry
powder prepregging process as well as the theory underlying prepreg tape

consolidation into a composite part.

(3) Chapter 4 discusses the configuration and operation of the components of the
proposed process.

(4) Chapter 5, 6 and 7 describe the experimental and theoretical investigation into
the manufacture of void-free thermoplastic composite parts from its precursor
materials, namely thermoplastic powders and reinforcing fibers using this process.
Chapter 5 describes the characterization of the properties of the fiber and the matrix,
chapter 6 discusses tape manufacture and chapter 7 describes the consolidation of
these tapes to form composite parts.

(5) Chapter 8 is attempts to provide guidelines for the manufacture of thermoplastic
composites from any fiber-matrix precursor.

(5) Chapter 9 enumerates the conclusions that can be drawn as a result of this

investigation and makes suggestions for future work.

The appendices include engineering drawings of the different equipment, the
electrical diagrams and the computer program implemented for the automation of the
process, and a finite difference program used to calculate contact angles from drop
dimensions on fibers.

Chapter 2
BACKGROUND

 

Different methods have been employed in the past to make thermoplastic pre-
impregnated tapes. This chapter enumerates and discusses the salient features of
each of these methods and develops the reasoning for the choice of dry powder

impregnation as a technique ideally suited for the manufacture of flexible prepreg

tapes.

2.1 Slurry Processing :

In this technique, the polymer powder is suspended in a liquid carrier and this
slurry is used to infiltrate the fiber tow. The process is shown in Figure l. The fiber
tow/tows are passed through a roving guide and past a spray nozzle (which sprays a
gas such as air) optionally used to spread the fibers to a limited extent. It passes
through the impregnation tank containing the polymer in suspension and fitted with
several impregnation pins. The impregnated tow is dried in a drying chamber and
then passes through a preheater and die before being wound on a takeup spool.

Taylor [7] outlined a slurry process whereby the particles are suspended in
water thickened with a material such as polyethylene oxide to increase the viscosity
to 40300 Pa.s at 25°C, c.g., 0.5 weight % polyethylene oxide and 0.5 weight %
hydroxyethyl cellulose are mixed in water for 15 hours to produce an aqueous
solution with a viscosity of 0.4 Pa.s at 25°C. 162 g of polysulfone powder less than

177 microns in size is added to 800 g of solution and a carbon fiber cloth

impregnated with this solution. The cloth is then dried at 100°C and heated to 350°C
to fuse the polysulfone around the fibers. O’Connor [8], in a very thorough
discussion in a patent, pointed out potential problems which include finding the right
concentration of slurry, maintaining the optimum concentration in the resin tank and
accumulation of excess resin at the die entrance (where the impregnated tow is
consolidated into a tape or flat sheet). The minimum void content in the slurry-
processed tapes were about 2-4%. Dyksterhouse et a1. [9] impregnated fibers in an
impregnation bath filled with a polymer binder in which the polymer particles are
uniformly suspended. The gelled binder has plastic flow characteristics and shear-
tlrinning behavior. As an example, a PEEK-carbon fiber composite was made by
impregnating 630-500 carbon fibers in a gelled impregnation bath having a viscosity
of 81 Pa.s. In addition to the problems pointed out by O’Connor [8], slurry processes
require a time-consuming drying step prior to consolidation to ensure that there is no
remaining liquid that can lead to voids in the final composite. Also, the

consolidation step has to ensure that fibers are completely wetted by polymer.

2.2 Solution Processing :

Thermoplastic particles are dissolved in a solvent and the fiber tow is
impregnated with the resulting low viscosity solution [10]. The solvent must be
completely removed to eliminate void generation during composite consolidation.
Methylene chloride and N-methyl pyrrolidone are widely used as solvents but
complete removal of solvent after impregnation is often a difficult time- consuming
step. Turton et al. [10] dried the prepreg tapes (carbon fibers impregnated with poly
(phenyleneoxy) polyphonylenesulfonyl) for 16 hours at 120°C to remove methylene
chloride before consolidating them into a part. Polysulfone, polyphonyl sulfone and
polyether sulfone are some of the thermoplastics which have been solution-

impregnated. A major limitation is that some polymers are not soluble in solvents

 

 

 

 

 

 

 

 

 

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Fluorzm BED

Figure 3. Electrostatic fluidized bed process [18].

10

but the solubility of those polymers used in the process also indicates that they will
be prone to solvent attack. The use of toxic corrosive solvents such as methylene
chloride which have to be recovered and recycled is another factor which detracts
from its appeal.

2.3 Melt Impregnation :

In this method, prepreg tapes are produced by the impregnation of fiber tows
with molten polymer. A sketch of this technique is shown in Figure 2. Two
approaches have been used to accomplish this - (a) A crosshead extruder feeds
molten polymer into a die through which the rovings pass [11], and, (b) the fibers
pass through a molten resin bath fitted with impregnation pins to increase the
permeability of the polymer into the tow. The impregnation pins can be heated to
decrease viscosity locally to further improve the impregnation process [12]. In either
case, the forces exerted on the fibers e.g. from the die pressure for the crosshead
extruder are exuemely high and may cause fiber damage. Chung [l3] estimates die
pressures in excess of 1450 psi are required for a Newtonian fluid with a viscosity of
.10 Poise. The resulting prepreg usually lacks tack (stickiness or the ability of the
prepreg tapes to retain their position after they have been laid up for consolidation)
and drape (flexibility). The tapes have to be spot welded in position before

consolidation.

2.4 Film Stacking :

Film stacking is a process where layers of fiber reinforcement either in the
form of unidirectional tows or woven fabrics are stacked with thermoplastic sheets
and consolidated under pressure for long times. Lind et a1. [14] made a 50% fiber
volume fraction composite by interleaving 60 micron thick polycarbonate film with

unidirectional carbon fibers. Film stacking is widely used with low viscosity matrix

ll

materials due to the relative ease of manufacture. Disadvantages include high resin
content, the uneconomic (labor- intensive) nature of the process and difficulty in
impregnating the fiber tow (high pressure forces the fibers together) with high

viscosity matrix material.

2.5 Fiber Co-mingling :

In the fiber co—mingling process, thermoplastic matrix is spun into a fine yarn
and co-mingled with the reinforcing fiber tow to produce a co-mingled hybrid yarn
[15]. These hybrid yarns can be consolidated to form composite parts. An
advantage of this technique is the drapeability of the hybrid yarn while the high cost
involved in producing thermoplastic yarn and weaving it with the reinforcing fibers is
an obvious disadvantage. Clemans et al. [15] spun thermoplastic yarn from high
temperature polymers such as PEEK and PPS and comingled them with carbon fibers
to produce hybrid yarn with fiber volume fractions of upto 61%. A consolidation
step is needed to ensure that the thermoplastic fibers melt and wet the reinforcing

fibers intimately to ensure good adhesion between the two components.

2.6 Dry Powder Impregnation :

Dry thermoplastic powder can be used to produce a prepreg. The powder is
introduced into a fiber tow which is processed by heating to sinter the powder
particles onto the fibers. This technique was first employed by Price [16] who passed
glass roving through a bed (either fluidized or loosely packed) of thermoplastic
powder. Polypropylene particles with an average diameter of 250 microns were used.
The particles stick to the fibers due to natural electrostatic attraction. The tow is then
heated and passed through a die to produce an impregnated tow. The impregnation
is macroscopic, i.e. the particles coat clusters of fibers rather than individual fibers.

Thus, the process is targetted mainly at producing short-fiber reinforced

12

thermoplastics. Ganga [17], fluidized polyamide particles less than 20 microns in
size in a fluidization chamber, impregnated glass rovings and then covered this with
an. outer sheath of a second material of lower melting point than the impregnated
particles. The second sheath is extruded onto the tow. The process offers little or no
control over fiber-matrix volume fractions during the impregnation step. The
possibility of motion of particles within the sheath during handling leads to higher

standard deviations in particle pickup than intended by the manufacturer.

Muzzy et al. [18] demonstrated the ability to manufacture powder prepreg by
passing a spread tow through an electrostatic fluidized bed of PEEK powder (50
microns average particle size). The process is shown in Figure 3. The fiber tow
passes through a spreader and then through an electrostatic fluidized bed of polymer
particles around 10250 microns in size. The electrostatic fluidized bed is based on
the principle of conventional fluidization except for one difference - it has charging
electrodes located under the distributor to charge the fluidizing gas which in turn
charges the particles. It has been primarily used for powders with average particle
sizes greater than 30 microns. In this size range, fluidization can be accomplished by
conventional means. The imposed electrostatics ensures that the particles adhere to
the fibers and is necessary due to the large particle sizes used in the process i.e. the
particles do not inherently have sufficient charge in them to be attracted to the fiber
surface. An electrostatic fluidized bed has to solve the problem of agglomeration and
channeling faced by conventional techniques before it is applied successfully to the
fluidization of lower particle sizes. The impregnated tow then passes through a
heater where the particles are sintered on the fibers. The residence time in the oven
is directly proportional to the flexibility of the prepreg. This is because of capillarity
between ,fibers which causes the polymer to bond adjacent fibers together and hence
reduce flexibility. Muzzy et al. used temperatures in excess of 600°C (PEEK has a

melting point of 343°C) in the heater for short times to sinter the particles and ensure

l3

flexibility. The possibility of thermal degradation of the matrix increases at

temperatures so far above the melting point.

Allen et al. [19] impregnated the fibers in a recirculating powder deposition
chamber with annular walls to aid in powder recovery. The recirculating powder
deposition chamber is a unit which merits more serious consideration in the particle
sizes of interest used in this investigation. The chamber is shown in Figure 4 and
includes powder recovery in its basic design. It consists of a screw feed which drops
particles from the top of the chamber. This "shower" of particles impacts the fibers
and falls down to the base where an exhaust fan recirculates the powder through a
tube to the top of the chamber. Baffles at the sidewalls with a slight vacuum in
between trap any particles that escape from the tow entry and exit slots and
rccirculate them through gaps at the base into the chamber. The humidity of the
environment, material balances in the chamber to decide feed rates, pressure drop in
the recirculating tubes to prevent clogging and the cohesive nature of fine powders all
serve to make this a complex operation which works satisfactorily if conditions are at
their optimum. The particle concentration in the chamber is in excess of 10,000
mg/m3 and good control over this variable is difficult. The response time of this
system to instabilities is of the order of minutes after a change is implemented.
Baucom et a1. [20] used the process to impregnate carbon fibers with PEEK and
LaRC-TPI particles 7-19 microns in size. A resin control monitor which measures
weight fraction matrix in the prepreg tape is mounted before the takeup drum. This
measruement is used in a feedback loop to control the speed of the takeup drum to
account for instabilities in the powder deposition chamber and ensure consistent
particle pickup by the fiber tow. Standard deviations of around 4 weight % fiber are
reported within each prepregging run. The powder processes by both Muzzy et al.

[18] and Allen et a1. [19] were developed concurrently'with this investigation.

l4

 

DIRECTION OF row I m
MOVEMENT / .

/ [IL Ill
I' . N2 WITH

/ POLYMER FEED

 

 

 

 

 

' . .‘I ,i , ’ ,4 " 1 CENTRIFUGAL FAN
AIR TO VACUUM '
THROUGH HOLLOW M070? ROTATES
FAN SHAFT FAN SHAFT

Figure 4. Recirculating powder deposition chamber.

15

2.7 Process Design :

The above review of the different thermoplastic processing techniques leads to
the conclusion that dry powder processes offer several advantages for the
manufacture of thermoplastic prepreg tapes. An ideal dry powder process would
have the following advantages over other processes :

(i) It would be independent of matrix viscosity. Most high performance
thermoplastic matrices are highly viscous (104 to 105 Poise) above their softening
point (amorphous) or melting temperature (semi-crystalline). A good dry powder
process would circumvent this problem by coating fibers individually with fine
particles so that flow occurs over very short distances of the order of microns instead
of millimeters as in a process such as melt impregnation.

(ii) It would avoid the use of solvents or water which have to be removed during
the latter stages of the processing cycle. Incomplete removal may produce voids
which have a deleterious effect on the mechanical properties of the composite.
Binders must also be avoided since they can alter the matrix or fiber-matrix adhesive
properties.

(iii) It would avoid inu'oducing any secondary material processing operations such
as fiber spinning which may increase the cost of the final product.

(iv) It would yield prepreg tapes that are completely wetted by the polymer and are

almost as flexible as unimpregnated fiber tows.

These advantages can be realized through the design of a dry powder process
which possesses the following features :
(i) The average particle size of the material used should be approximately of the
order of the dimensions of the fiber for optimum impregnation. Irnpregnation of
individual fibers becomes more difficult with larger particle size resulting in an
uneven coating and/or a resin-rich composite. The level of precise control over

fiber-matrix volume fractions that can be achieved decreases with increasing particle

16

size. Polymer flow has to occur over larger distances on the fiber surface as particle
size is increased.

(ii) The fiber tow should be spread out to a sufficient width so that each fiber in the
tow is uniformly coated with particles.

(iii) The concentration of powder particles in the "impregnation chamber" where the
particles meet the fibers should be constant and controllable at all times. This
facilitates the manufacture of high quality prepreg tapes in a wide range of volume
fractions.

(iv) The mechanism of adhering the particles to the fibers should be controllable
and well-understood.

(v) The resulting prepreg tape should be flexible so that complex parts can be

formed easily by consolidation.

As a result of this analysis, a powder prepregging process (Figure 5) which
incorporates these components was designed in this thesis. The fiber tow is unwound
from a fiber spool and passes through a device (spreader) which spreads the
collimated fiber tow (or tows) to any desired width. A pretreatment tank may be
used to modify the fiber surface to provide better adhesion with the thermoplastic
matrix or to apply a binder on the fibers. The spread tow enters the impregnation
chamber where it meets a controlled concentration of particles. At this position, the
means of adhering the particles to the fibers is either electrostatic attraction or
through the use of a binder on the fiber surface. The impregnated tow passes through
a heater where the particles are "fixed" on the fiber surface with the help of thermal

energy. The resulting flexible tape is then wound on a takeup drum.

17

.33on wfimwoaoa .8293 we ewmmofl .m onE

conga
scrawamna

 

.830: . . . .. .. “megaphone 832%

 

30%
39E

 

 

 

 

 

 

 

 

 

 

Chapter 3
THEORY

 

There has been no coherent investigation into the manufacture of
thermoplastic composites using dry powder impregnation techniques. This
investigation has been undertaken to elucidate the underlying physical principles
governing the manufacture of a composite part from its precursor materials, namely
thermoplastic powders and reinforcing fibers. The flowchart (Figure 6) lists the
important components in the manufacturing process. The two basic steps are : (1)
tape manufacture which involves the spreading of the fiber tow, the impregnation of
the spread tow with thermoplastic particles and particle coalescence on the fibers to
form a flexible prepreg tape, and ( 2) consolidation which involves the layup of
prepreg tapes in a mold followed by the application of heat and pressure to form

void-free composites.

3.1 Tape Manufacture :

Tape manufacture by powder prepregging processes involves the following
steps : (l) spreading of the fiber tow so that individual fibers are exposed, (2)
impregnation of the spread fiber tow by a controlled concentration of fine particles,

and (3) coalescence of the particles on the fibers to form a prepreg tape.

18

l9

 

MANUFACTURE OF POWDER-IMPREGNATED
THERMOPLASTIC COMPOSITE

 

 

l
i

l FIBER SPREADING

V

IMPREGNATION

 

 

 

 

 

 

 

TAPE
* MANUFACTURE
COALESCENCE
Heat transfer
Interparticle sintering

Film formation
Droplet formation

 

 

 

 

 

 

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

 

 

INTIMATE CONTACT

Surface Approach
Wetting

 

 

] CONSOLIDATION

 

AUT‘OHESION
Difi‘usion

Randomization

 

 

 

 

 

_-‘_‘__ ‘ “ __---
—-‘—_—““_ ““‘—v“"--" v ““‘——““‘-‘——

 

 

Figure 6. Flowchart for the manufacture Of thermoplastic composites.

 

20

3.1.1 Spreading :

The function Of the spreader is tO ensure that the fiber tow is spread to a
width large enough to expose individual fibers so that powder impregnation occurs
throughout the fiber tow. The principle Of Operation of most spreaders is to use a jet
Of air directed at the fibers which forces them to spread apart due to the resulting
drag. Baucom and MarchellO [20] describe a typical spreader in which the tow of
fibers enters at the throat Of a flat expansion region. Air is drawn in from the tow
exit slot and flows out into a vacuum manifold through holes in the side walls of the
chamber. The tow spread angle is a function Of the tow tension and the pressure
drop between the chamber and the surrounding medium. A maximum width Of only
1.87 cm was achieved for a 3000 fiber tow (8 microns/fiber, a tow spread to expose
monofilaments is 2.4 cm wide). Problems with directed air methods include the
drawing Of loose fibers through the holes along the side walls, fiber breakage during
sudden system shutdown and the narrow spreading width that can be attained by such

a system without damage to the fibers.

3.1.2 Impregnation :

The impregnation chamber should be designed such that it delivers a
controlled concentration of particles to the fibers at all times. This is essential in
order to manufacture prepreg tapes Of any desired fiber/matrix volume fraction with a
minimum standard deviation. The degree Of control that can be achieved over the
impregnation process increases with decreasing particle size as discussed in Section

2.7 in the previous chapter.

Interparticle forces which act between adjacent particles are significant for fine
powders less than 30 microns in size. Van der Waal’s forces act over a distance Of
100 Angstroms and interparticle distances in a packed bed at the point Of contact are

Of the order Of 5 Angstroms [2]]. Powder particles also tend tO acquire charge by

21

frictional or sliding contact through a process known as contact electrification or
triboelectrification [22]. The work function or the minimum energy required to
remove an electron from the surface Of a particle to infinity increases with decreasing
particle size. Hence fine particles tend to charge negatively. If there is a broad
particle size distribution, there may be a change in particle charge with decreasing
particle size. Polymer particles also tend to charge easily and retain a charge for
long times because they have high values Of electrical resistivity and low electrical
permittivity. Charge pickup by particles increases with decreasing particle size due
to the increased surface-tO-volume ratio. All Of these effects combine to make

fluidization of fine powders a complex phenomenon.

A fundamental understanding Of particle impregnation requires the
measurement Of particle charge and interparticle cohesive forces to characterize the
behavior Of the powder both in the chamber and its interaction with the reinforcing
fibers. Masui ct al. [23] outline a technique to measure powder charge. A suction-
type Faraday cage is used with an electrometer tO measure the charge-to- mass ratio
for any powder. Interparticle cohesive forces can be gaged by measuring
characteristic angles such as the angle Of repose and tilting angle [24]. A simpler
way is to mourn the Hausner ratio [25] which is the ratio Of the loosely packed (or
aerated) density to tapped density Of a powder (pbtlpblp)° This ratio increases as
interparticle forces become larger because such forces “prevent particles from flowing
smoothly thereby resulting in a more Open structure for a cohesive powder. An
approximate rule of thumb is that the Hausner ratio is l for a powder with negligible

interparticle forces and greater than 1.5 for highly cohesive powders.

External means of electrostatic enhancement Of particle charge is usually not
required for fine particles because the uiboelectric effect is sufficiently large to cause
strong adhesion Of the particles to fiber surfaces on contact. Typically, the particles

are carried to the fibers by the gas stream. Inertial forces make the particles impact

22

the fibers instead Of following the gas streamlines around the fibers. Adhesion Of
particles to the fibers on impact is initially due to electrostatic charging but is
followed by van der Waal’s forces between the fibers and the particles which also

contribute to the adhesion.

Inertial effects are significant for particles greater than 1 micron in size [26].

The collection efficiency Of an isolated fiber, 710 is a function of an inertia parameter

W-

__ Drillpp

‘I’ - 18I1Df [1]

The collection efficiency Of a single fiber, 116 when Other fibers are nearby is given

by
n. = no [1 + 13(1 - ea] [2]

Here, cf is the void fraction Of the fiber bed and the parameter [3 is between 5 and 20
when inertial effects predominate. Baucom and MarchellO [20] derive a relationship
for the particle pickup by a tow and show that the resin- tO-tow weight ratio is
directly proportional to the resin cloud density, the collision cross section and the
average collection efficiency Of each fiber and inversely proportional to the tOw
velocity. Their analysis ignores the fact that particles charge differently depending
on their electrical resistivities and permittivities and the relative humidity Of the
surrounding medium. A transfer Of charge to the particles by external means such as

an electrostatic generator will enhance the particle collection efficiency.

An Obvious method to convey the particles tO the fibers is by fluidization and
entrainment. In conventional fluidization, the particles start to fluidize at a gas

velocity (minimum fluidization velocity) at which the buoyant force overcomes

23

gravitational forces caused by the weight Of the powder. However, interparticle
forces and tribocharging serve to make fluidization difficult for fine powders. Geldart
[27] proposed that fine powders fall into 2 categories - Type A powders fluidize
homogeneously at the minimum fluidization velocity and expand considerably before
bubbling commences. Type C powders are extremely cohesive and difficult to
fluidize and do not have a distinct minimum fluidization velocity. Geldart et al.
[25,28] Observed that the fluidization Of Type C powders leads tO the formation Of
cracks and channels in the fluidized bed. This results in bed expansion without the
true formation Of bubbles. Rietema [29] argued that the border between Type A and
Type C powders depends on particle size, particle density, viscosity Of the fluidizing
gas and interparticle cohesive forces as characterized by a cohesion constant. Geldart

et al. [30] included relative humidity Of the fluidizing gas as an additional variable.

Dry et al. [31] extended the above classification tO include a uansitional group
AC which is characterized by the absence Of a distinct minimum fluidization velocity
and the absence Of a contraction Of the bed when bubbles first pass through.
Chaouki et al. [32] discovered that fine aerogel powders agglomerate to form clusters
at superficial velocities greater than 4 cm/sec. These larger particles retain their
integrity and fluidize homogeneously. They found that these powders form a subset
Of Type C. They proposed a new group, C’, which includes particles which pack
very loosely (extremely low bulk densities, 0.066 gin/cm3 in their experiments) and
form clusters. Properties Of the bed can be predicted from the sizes of these
agglomerated particles. A summary Of major Observations for the behavior Of
cohesive powders in fluidized beds of different diameters is given in Table H. The
bed diameters ranged from 5 to 64 cm and only cursory analyses Of bed behavior
was presented in all these papers. This study attempted to gain some insight into the
behavior Of fine polymer powders during fluidization and thereby design an

impregnation chamber where particle concentrations can be precisely controlled.

24

TABLE II. BEHAVIOR OF COHESIVE POWDERS

 

 

 

Investigators Bed diameter Observations
(cm)
Geldart et al. [30] 15.2 No clear minimum fluidization velocity;

cracking and channeling without sustained
» bubble formation; cohesiveness increases
by decreasing particle size and or
increasing relative humidity (Type C,
Alumina, 5-12 pm)

Geldart et al. [28] 15.2 Few bubbles; cracks, sloping and

vertical channels; decreasing particle

size causes vertical channels to
predominate (properties of Type C powders
listed in Table 2).

Dry et al. [31] 5, 14, 64 No clear minimum fluidization

velocity; anomalous fluidization, i.e.

spread in pressure drop-velocity curves;
bubbles present (Type AC, iron oxide/carbon
mixtures, 12-30 um).

Chaouki et al. [6] S, 10 Fine particles agglomerate to

form clusters at higher velocities and
homogeneous fluidization results; at low
velocities, channeling occurs (Type C’,
bulk density of 0.066 g/cm3).

 

 

 

 

25

3.1.3 Coalescence :

The fiber tow enters the heater after the impregnation step. The sequence of
events which occur in the heater (Figure 7) are : the heating up of fibers and the
particles; interparticle sintering between adjacent particles until a film forms on the
fiber surface; and, finally, the formation of a stable configuration of axisymmetric or
non-symmetric droplets. Development of a process control model therefore requires

consideration of heat transfer, sintering and film and droplet forming mechanisms.

3.1.3 (a) Heat transfer :

The temperature of the powder-impregnated fiber tow is raised by convection
and radiation to a value greater than the melting or softening point of the polymer
particles. The physical situation is shown in Figure 8. Individual impregnated fibers
or clusters of impregnated fibers pass through the heater as a flat porous sheet. The
first step in the development of the processing model is to establish upper and lower
bounds for the time to reach a temperature at which subsequent events begin to
occur. The Biot number measures the significance of internal (heat conduction
within the solid) to external (heat convection to the surface of the solid) heat transfer

resistances is given by
Bi = 111 [3a]
ks

where

h = heat transfer coefficient which includes contributions from
convection and radiation

k3 = thermal conductivity of the solid

L = VslS = volume of body/surface area.

26

 

 

Heat transfer to the impregnated tow Interparticle sintering

   
 

Reinforcing
' fiber

 

Particles

 

Uniform droplets

   

Polymer sheath

 

Figure 7. Coalescence in the heater.

 

27

 

 

Heater

7/ 4’

Theater

 

 

v, tow velocity

 

Impregnated fiber tow

 

Figure 8. Heat transfer to the impregnated tow.

 

28

Bi is extremely low (less than 0.1) for a typical spread fiber tow impregnated with
polymer particles. This implies that external heat transfer resistances are rate-
controlling and hence a lumped model would serve as an adequate representation of
the physical situation. For a lumped system of mass m, specific heat Cp, surface area
A, heat transfer coefficient (which includes contributions from convection and
radiation) h, the time t required to raise its temperature from Ta (ambient

temperature) to T when the temperature of the heater is Th is given by

me
hA

1n

 

t = [3b]

 

Th—Ta
Th-T

Lower and upper bounds can be calculated by considering an isolated particle in a

convective medium and a large-diameter cluster of coated fibers respectively.

3.1.3 (b) Interparticle sintering :

Adjacent particles begin to sinter, i.e., a neck forms between neighboring
particles and grows till the particles coalesce into one. The phenomenon of
interparticle sintering was first studied by Frenkel [33]. He considered the sintering
of two identical amorphous spherical particles (Figure 9). The work required for a
change in shape is equated to a decrease in surface energy. Viscous flow dissipation

accounts for the work done during coalescence.

x2 __3_ 1
at]:

where

X
ll

radius of the interparticle bridge

r = radius of the particle

29

 

 

 

 

 

 

2x

Figure 9. Sintering between adjacent equal-sized spherical
particles (initial radius = a)

30

= polymer melt surface tension

:-<
u

polymer viscosity
t = sintering time

In Frenkel’s model, it is assumed that dimensional changes occur in the radii
of the two amorphous spherical particles during sintering. The analysis is restricted
to the early stages where r is approximately equal to the initial radius of the particles.
Kuczynski et al. [34] studied the sintering of polymethyl methacrylate spheres and
proposed that the sintering process is non- Newtonian, being pseudoplastic at lower
and dilatant at higher temperatures. Experiments were conducted in an oven and the
sintering process stopped from time to time for microscopic observation thereby
increasing the probability for experimental error. Rosenzweig and Narkis [35]
developed a precise experimental technique whereby two pre-sintered equal-sized
spheres are introduced into a hot stage and observed in situ under a microscope.
They observed contradictions to Frenkel’s model i.e. a rounded contour in the neck
region between the two particles (Frenkel assumed a sharp profile as shown in Figure
9) and no dimensional changes in the two spheres during sintering indicating that
flow occurs only in the neck region as opposed to the entire volume. Nevertheless,
the overall behavior predicted by Frenkel was confirmed. A plot of x versus t gives a
straight line with a slope of 1/2. In a subsequent paper [36], Rosenzweig et al.
further demonstrate the applicability of Frenkel’s model by calculating activation
energies for viscosity from sintering data and comparing it favorably to rheological
measurements. Siegman et al. [37] studied the sintering of amorphous and semi-
crystalline materials and found that semi- crystalline materials sintered faster than
that predicted by Frenkel. The increased surface energy of polyethylene was
attributed to its developed internal morphology (nodular and/or fibrillar, less than 1
micron in size) which accelerated the sintering process. In summary, Frenkel’s

theory, though not exact, provides good estimates of sinterin g times for amorphous

31

materials and upper bounds for semi-crystalline materials, with the actual sintering
times being dependent on the internal morphology of the particles. Interparticle

sintering rates are controlled primarily by viscosity and particle size.

3.1.3 (c) Film and Droplet Formation :

Interparticle sintering leads to the formation of a film which breaks up to form
droplets on the fiber. These droplets are of varying shape and symmetry with respect
to the fiber axis. The shape of these droplets changes with time to an equilibrium
configuration which can be axisymmetric or non-symmetric depending on droplet
volume and the influence of gravitational forces [38,39]. In the case of a spread fiber
tow in which the impregnated fibers are in intermittent contact with each other,
capillary forces between adjacent fibers may make film formation thermodynamically
favorable. The final configuration depends on interfiber distances and droplet sizes in

addition to surface tension forces.

The transition from a polymer film on the fiber surface to droplets is driven
by the finite wetting abilities of most thermoplastics. Many investigations have been
made on the spreading of spherical drops on planar surfaces. Van Gene [40]
modified the momentum equations for a liquid film on a planar surface to account for
spreading of polymer droplets and arrived at a result whereby spreading rate is
proportional to y Cos(6)/(r u) where 9 is the contact angle between the polymer
droplet and the solid surface (see Figure 10). The spreading rate depends on the
droplet mass (proportional to 1/(mass)1’3)) which explains why small drops take very
short times to spread to their equilibrium configurations. The rate of capillary

penetration is shown to be proportional to y Cos(9)/t1.

Consider the situation shown in Figure 10. For a liquid film to cover an area
dA of the solid surface, the driving force is the reduction in surface energy as a

result of the spreading (assuming the liquid film to have the same surface area as the

32

YLV

Contact angle, 9

r *

Figure 10. Spreading of a liquid on a planar surface.

33

surface area of the solid it covers), we have

st M 2 (‘YSL + 7) (1A [53]

The spreading coefficient, 8 of any liquid on a planar solid is defined by

S = st - Ysr. " 7 [5b]

where 75v and 73L are the interfacial energies between solid/air and solid/liquid and 'y
is the liquid/air interfacial tension. The units of interfacial energy are ergs/cm2 or
dynes/cm.

S < 0 corresponds to partial wetting. The liquid does not spread to a film but forms
a droplet. The equilibrium contact angle, 6, that the droplet makes with the solid

surface is given by Young’s equation

st = 751. + 7 (305(9) [6]

S > 0 implies complete wetting and the droplet spreads out to form a film on the
surface. The film is stabilized by attractive forces like van der Waal’s interactions

between the solid surface and the liquid and its thickness, e is given by -

21 1/2
e=a[28] [7]

Here, a is a molecular size proportional to the Harnaker constant, A, which is a

measure of van der Waal’s forces

Ya =-— [8]

34

London dispersion forces account for almost all of the van der Waal attraction except
between highly polar materials [41]. London dispersion interactive energy V A
between spherical particles of radius r separated in vacuum by a shortest distance, H,

H << r is given by

 

[9]

 

 

Brochard et al. [42,43] studied the spreading of liquid drops on thin cylinders on a
microscopic level. In the case of a cylindrical fiber, for S > 0, the interfacial area
between the liquid and the solid is less than the surface area of the film due to the
larger diameter of the concentric film (the surface area dA in equation (5a) is no
longer the same on both sides). Hence, a larger value of the spreading coefficient, Sc
is required to achieve complete wetting and form a liquid film on the fiber surface.
Brochard argues that in most cases, the film thicknesses are small compared to the
radius of the cylinders. Therefore curvature can be neglected in the calculation of the
equilibrium film thickness for a cylindrical fiber and equation (7) can be used with

reasonable accuracy. Sc is given by

3 213
8c = —y [3] [10a]

Brochard gives numerical estimates for the molecular size, a, for carbon and Kevlar

fibers.

Carbon fiber : Say 2 0.01, Dir/2a : 103, a = 0.004 [.1 [10b]

Kevlar fiber : SCI? 2 0.005, Dgza = 104, a = 0.0006 n

35

A comparison of the magnitude of a for carbon and Kevlar fibers indicates that van
der Waal’s forces between the polymer film and the fiber surface will be larger for
carbon fibers. This attraction leads to a thicker film as it tends to retard the
spreading of the film. The thickness of the film is usually of the order of lOO-300°A.

If the droplet is not much thicker than the fiber, then the critical spreading

coefficient is 8:,

s; = s, (1 - wk) [11]

where R is the dmplet radius.

In practice, if the spreading coefficient is greater than the critical value, the
droplet flows out from both ends to form the film. If there are two droplets separated
by a finite distance, then the film serves to drain the smaller droplet into the larger

one due to pressure differences as predicted by the Laplace equation.

AP = 7(1/R1+ 1/R2) [12]

where AP is the droplet pressure, R1 and R2 the principal radii of curvature at a point

on the surface of the droplet.

The pressure in the film is smaller than the pressure in the droplet, the
thickness being stabilized by attractive forces between the fiber and the film. At
8 = Sc, the pressure is 0. On the other hand, if S is less than the critical value, a
precursor film forms on either end of the droplet but adjacent droplets will be stable
since the film does not extend along the fiber. The length of the precursor film is
proportional to the difference between S and the critical value for S < Sc. Film
formation is unstable as the pressure in the film is larger than the pressure in the

droplet.

36

The contact angles between a cylindrical filament and a liquid can be
calculated from drop dimensions that are accurately measured under a microscope by
using a method outlined by Carroll [44] and Yamaki et al. [45]. This macroscopic
analysis [44] which is based on the Laplace equation applies to axisymmetric
droplets. Figure 11 shows an unduloidal droplet on a fiber at equilibrium. R1 is the
radius of curvature at a point of the curve y = f(x) which is rotated around the axis to
obtain the Figure of revolution. R1 is given by the analytical relation [46]

2 3/2
R1 = _[ [1+(dy/dx) ] ] [13]

dzy/dx2

R2 is in the plane perpendicular to the paper and for Figures of revolution, it is

obtained by projecting the normal to the axis of revolution
R2 = y/Cos<B> = ySec(B> = y<1 + Tanzp» = y[1 + (dy/dxfl“2 [14]

Substituting equations (13) and (14) in (12), we have

d2 AP d 3’2 1 d 2
e2=7H7§fl VHEH “51

The boundary conditions are
(1) x = O, y = Dr
(2) x = 0, dy/dx = tan(6)
(3) x = U2, dy/dx = 0

These three conditions can be used in a finite difference program (Appendix C) to

iterate for 6 given the two dimensions 1 and k for a droplet.

37

 

 

 

 

 

 

 

 

 

Y
0, I ,
A A3 /*"
x y=ftx1
c , "
\ # T
i 0 B\ "‘ "f
at
lee(T2)
Plone(T.)

Figure 11. Unduloidal droplet on a cylindrical fiber.

’—----

 

 

 

 

Figure 12. Non-symmetric perturbation of an axisymmetric droplet.

 

10

5—-

 

 

 

l I

0 25 0 so 75

Figure 13. Transition from axisymmetry to non-symmetry for a dr0plet on a
cylindrical fiber.

38

The above analysis applies only to axisymmetric droplets. Carroll [38] discusses the
formation of unsymmetric droplets. The transition between axisymmetry and non-
symmetry occurs if the contact angle increases for a given droplet volume or the
volume decreases below a threshold value for a given contact angle. Consider a
axisymmetric perturbation of the drop from its equilibrium conformation. If the drop
volume is kept constant, the effect is to increase one curvature, R1” 1, while decreasing

R51. From the Laplace equation we have
5(AP) = EDI (812.31 + 6R3) [171
f

where R111 and an are 2R1/Df and 2R2/Df respectively.
Rd and an at x = 1/2 can be written in terms of 9 and n (where n = 2k/Df) as

follows [44]

1 = (n2 - 2nCos(6) + 1)
Rm (r1012 - 1))

 

[18a]

_;_ = _ [18b]

If at x = U2, the perturbation causes a change 8x2 in the drop median radius (x2 >

0), then

 

 

 

812,711 2 -[d(:n’:‘l)]5n [19a]
511,31 2 -[d(:n“-2l)]8n [19b]
Substituting equations (18) and (19) in (17), we have
6MP) ___ 21 n4 — 4n3Cos(9) + 4n2 - 1] [20]
Df 112012 - 1)2—(1/n2)

 

39

Here, if 5(AP) < 0, then change in pressure is negative and the resulting conformation
is axisymmetric. But if 5(AP) > 0, then if the perturbation is non-symmetric, there
will be a flow of liquid from the upper to the lower part of the drop due to a pressure
gradient (Frgure 12) resulting in a non-symmetric dr0plet. Hence the transition is at
5(AP) = 0. Equation (20) can be solved to give

2n3Cos(0) - 3n2 + 1 = 0 [21]

WhCI'C n = lef.
Figure 13 shows a plot of n vs 9. In the region above the curve, we have

axisymmetry while the region below the curve corresponds to non-symmeuic

droplets.

Both the above analyses (contact angle measurement and droplet transition)
hold good only in the case of negligible gravity. The effect of gravity for a droplet
can be assessed by considering the basic Bernoulli equation [47] and eliminating the

kinetic energy term, we have

AP, = (mgh 1221

where p is the liquid density, g the acceleration due to gravity and h the distance
between any two points. The largest value of h is 2k. Hence a comparison of AP,
the Laplace pressure in the droplet, with APg is sufficient to determine the

significance of gravity in the spreading process.

3.2. Consolidation :

The powder-impregnated prepreg tapes have to be consolidated under heat and
pressure to form void-free composite parts. The physics of the consolidation process

is shown in Figure 14. If the impregnation of particles in the fiber tow is uniform,

40

 

 

    

(a) Particles coalesced on (b) Intimate contact.
fibers.

Disappearance
of interface

 

(c) Autohesion or polymer-polymer
interdiffusion

 

Figure 14. Consolidation of powder-impregnated tapes.

 

o.

41

this leads to the formation of uniform-sized droplets and a polymer sheath on the
fibers. In such a case, the phenomenon of consolidation broadly involves two steps :-
(i) Intimate contact at the polymer-polymer interface at numerous sites across the
composite. Consolidation is usually performed at temperatures higher than the melt
temperature for semi-crystalline or the softening point for amorphous thermoplastic
polymers. Physical deformation at the polymer-polymer interface is required to
achieve intimate contact. (ii) Autohesion or the interdiffusion of polymer chains

across the interface so as to cause its disappearance.

Wool et al. [48-51] describe healing at the interface for amorphous
thermoplastic polymers as a five step process : (i) surface rearrangement of the
polymer chains before contact (i.e. chain ends diffuse back into the bulk with time
after the creation of a freshly fractured surface), (ii) surface approach (contact of
different surfaces to form an interface), wetting (contact at the microscopic level),
(iii) diffusion (movement of polymer chains across the interface), and (iv)
randomization (disappearance of the interface so that it is no longer distinguishable
from the bulk). The interfacial bond strength is the sum of two components, wetting
and diffusion. The wetting component (strength associated with wetting between the
two surfaces) is constant once complete wetting is achieved at the interface and is
primarily due to van der Waal’s forces. The diffusion component (strength
associated with interdiffusion of polymer chains across the interface) increases with
contact time after wetting is achieved until it reaches a plateau when the diffusion
process is complete. At this point, the interfacial bond strength is as high as that of
the virgin polymer. For an amorphous polymer, the mechanical energy required to
separate the two interfaces is a function of contact time, temperature, pressure and
molecular weight of the polymer chains at the interface. With the help of reptation
theory [52], Wool et al. arrived at relations for the time dependence of mode I

fracture energy (Gk) and stress intensity factor (KIC).

42

(3,, = t“2 [23]

K1, 2 t“4 [24]

These equations are valid only if free chain ends are available at the interface e.g. for
freshly fractured surfaces. The fracture energy at constant contact time decreases
with increasing surface rearrangement time. Two modes of fracture are possible :
chain scission is favored at low temperature, fast testing rate and high molecular
weight; and chain pullout favored at high temperature, low deformation rate and low
molecular weight. The fracture toughness of an amorphous polymer increases with
pressure until a saturation pressure is reached beyond which there is no further
improvement. A high consolidation pressure promotes faster wetting but decreases
the volume available for segmental motion of the polymer molecules thereby
reducing the diffusion coefficient and slowing down the diffusion process. An
increase in temperature accelerates the wetting process while decreasing the

saturation pressure needed for complete wetting.

In contrast to pure polymers, healing at incompatible crystallizable interfaces
(polyethylene [polypropylene (PE/PP» was studied by Wool et al. [51] who found
that the nucleation of PP spherulites coupled with flow of PE across the interface
followed by its subsequent crystallization produced strong mechanical interlocking
(fibrils of PE attached to PP spherulites) up to a depth of several microns and
increased the interfacial strength. The events occuring at a compatible crystallizable
interface of a semi-crystalline polymer are diffusion, homogenous crystallization and

mechanical interlocking to a lesser degree.

Healing in thermoplastic composites is complicated by the fact that the fibers
act like a spring and absorb a part of the applied load. Therefore a specimen with a
high fiber content requires a higher consolidation pressure than a specimen with

lower fiber content for optimum consolidation. Howes et al. [53] studied the healing

43

phenomenon in a thermoplastic composite (polysulfone lgraphite fiber) by performing
double cantilever beam toughness tests to evaluate Mode I fracture toughness on
rehealed specimens. The results were inconclusive because of an inconsistent
interface i.e. fiber breakage, excess resin at the interface after initial fracture and
possibly changing molecular weight distribution at the interface due to chain fracture.
Lee et al. [54] measured bond strength between two crossply AFC-2 laminates (two
flat 0.016" diameter surfaces) and found that the degree of autohesion was roughly
proportional to t1”. They did not see any effect of processing pressure on bond
strength probably because of instantaneous wetting at the interface. Manson et al.
[55] noted that processing pressure did not affect the toughness values significantly.
Lee et al. [54] and Manson et al. [55] reported that fracture toughness values
decrease with increasing crystallinity for PEEK/graphite fiber composites.

In summary, the design of optimum consolidation cycles for powder-
impregnated thermoplastic composites involves the selection of time, temperature,
pressure and cooling rates (for semi-crystalline materials). Another variable which
affects consolidation cycles is the volume fraction of matrix in the composite. The
saturation pressure increases with decreasing matrix volume fraction (time and
temperature constant) due to the ability of the fibers to store elastic energy during

consolidation.

Chapter 4
PROPOSED PROCESS

 

The preceding chapters discussed the rationale for the design of the process
and the fundamental physical phenomena underlying the process. This chapter
describes the design of each of the components constructed to perform the unit
Operations identified in Figure 6 (page 19). They are -

(1) The fiber motion system which performs two functions - (a) It conveys the
fiber tow from the fiber spool to the takeup drum. (b) Rotary and lateral motion of
the takeup drum so that the prepreg tape can be wound across the entire width of the
drum.

(2) The spreader which spreads the collimated fiber tow into its individual
filaments.

(3) The aerosolizer which disperses the particles in the gaseous medium and
delivers a controlled concentration of particles to the spread fiber tow.

(4) The heater in which the particles sinter and coalesce on the fibers to form a
flexible prepreg tape.

(5) The automation scheme which monitors the performance of the different

components and controls the entire process.

The design of two related pieces of equipment, the heated stage used to study
the fundamental phenomena associated with coalescence and the mold used to
consolidate the tapes into a part are also discussed. The engineering drawings of all

the equipment described in this chapter are attached in Appendix A.

45

4.1 Fiber Motion :

A schematic of the fiber motion system is shown in Figure 15. The fiber
spool is mounted on a shaft which is mounted on a block at each end. The bearing
blocks are fitted with precision ball bearings to enable the shaft and consequently the
fiber tow to be rotated with a minimum amount of tension. The fiber tow passes
through a guide ring and is pulled from the spool by a pair of nip rollers (NR1). All
the nip rollers are fabricated with stainless steel case-hardened shafts for the bottom
roller, smooth aluminum shafts for the top roller and are mounted on precision ball
bearings so that the shafts rotate with minimum friction on their axes. The top
rollers can be adjusted to maintain any desired gap between the two rollers. A
second pair of nip rollers (NR2) is mounted downstream and connected by a chain
drive to ensure that they operate at identical speed. A third pair of nip rollers (NR3)
is mounted before the takeup drum. This arrangement ensures that the fiber tow is
devoid of any tension between NR1 and NR3. Nip rollers 1 and 3 are driven by
precision d.c. motors while a gear system with chains links 1 and 2 and drives them

both synchronously.

The takeup drum is mounted similar to the fiber spool on a shaft. It is
powered by a dc. motor to enable it to rotate on its own axis. The mounted drum is
placed on a table which can be moved laterally by a linear motion system. The
prepreg tape is wound on the drum as the drum rasters in a direction perpendicular to
the rotary motion. This ensures that the tape is wound across the entire drum. Limit

switches make the drum change direction as the tape reaches either end.

4.2 Aerosolizer :

Preliminary experiments were done on the fluidized bed behavior of cohesive
powders [56]. These experiments led to the conclusion that enhancement to

conventional fluidization is necessary for good controllable fluidization and

Nip rollers
Guide

. ‘ Linear motion,
r. ’ ‘ :W unmmrumtm:. - . 0
Heater ,

 

 

 

Fiber 1 , , Rotary
spoo Spreader Aerosolizer Tdnaklmeup motion ’
Gear chain th
, connecting e .
Dnven by 3 two nip rollers 22:11:; a

dc. motor

Figure 15. Fiber motion in the powder-prepregging process.

47

entrainment of cohesive polymer powders. Enhancements include the addition of
fluidization promoters such as fumed silica, some form of pulsed energy e.g. pulsed
gas flow (low frequency less than 1 Hz), acoustics (1-20,000 Hz) and ultrasonics
(greater than 20,000 Hz); and electrostatics. The addition of fluidization promoters is
undesirable because it would lead to the presence of impurities in the final part that
could detract from its mechanical performance. Gas flow pulsing with the help of a
solenoid valve did not improve the quality of fluidization significantly compared with
that of a conventional bed (Section 6.2). This led to the selection of the acoustic
aerosolizer as a reliable system for the controlled entrainment of polymer particles

[57].

The principle of operation of the aerosolizer is that the acoustic energy
generated by an audio speaker prevents agglomeration and aids in fluidizing and
entraining the cohesive particles within and out of the fluidizing chamber. The
aerosolizer is packed with particles at the base of a column on a rubber diaphragm.
The speaker is operated at a predetermined frequency and amplitude. The acoustic
energy is absorbed by the vibrating diaphragm which in turn imparts this energy to
the particles. Standing waves are set up between two diaphragms placed at either
end of the chamber. This system consisting of the diaphragms, the chamber
including the slits which allow the fiber tow to pass through and the weight of the
powder resonates with a natural frequency. At this frequency, the aerosolization of
particles attains a concentration which remains constant with time if the amplitude of

the sound wave is kept constant.

A sketch of the aerosolizer is shown in Figure 16. It consists of a speaker
box over which a cylindrical plexiglass column is mounted. Vibrating rubber
diaphragms are placed on a lip between the column and the speaker box and at the
top of the column. There is a gas inlet near the base of the column. Two slits at

either side of the column provide entry and exit means for the spread fiber tow. The

48

Vibrating rubber diaphragm

 

 

O—ring
Unimpregnated Powder-impregnated
tow spread tow
Entrained particles
Nitrogen gas into Packed bed of
aerosolizer powder particles
Vibrating rubber
diaphragm
Plywood casirr{ / Audio speaker
for speaker

 

 

 

 

 

O _

H

To power amplifier
and frequency generatbr

 

 

 

 

Figure 16. Aerosolizer.

49

inside walls are covered by smooth Aluminum foil to reduce particle caking on the
walls. The speaker is powered by an audio amplifier connected to a frequency
generator. The column with its vibrating diaphragms is enclosed in a rectangular
plexiglass housing. The housing has two slits corresponding to the entry and exit
means for the fiber tow. The back wall of the housing is fitted with an air filter and
an exhaust fan (not shown) to trap all the particles which escape from the column
through the slits. The air filter is cleaned between experiments. This arrangement
eliminates particle entrainment to the surrounding environment. The chamber has
two sensing devices - a sound level meter (Type 2231, Bruel and Kjaer) which
measures acoustic pressure in decibels and a Realtime Aerosol Monitor (RAM-S,

MIE Inc.) which measures particle concentrations in the range 0-200 mg/m3.

The aerosolizer is best operated at the natural frequency of the system. The
choice of materials for diaphragms is dictated by their stiffnesses. The magnitude of
acoustic energy that is transferred to the powder particles decreases with increasing
stiffness. The tension with which the diaphragms are stretched over the two ends of
the chamber and the weight of the powder packed on top of the lower diaphragm are
experimental variables which change the compliance for a given material. As shown
in Figure 16, a gas stream is introduced into the chamber at a level greater than the
height of the packed bed. This helps in the entrainment process by providing an
additional steady buoyant force for entrained particles which are thrown up into the

upper regions of the chamber from the packed bed by acoustic energy.

A simple momentum balance around a control volume is shown in Figure 17.
This analysis serves to highlight some of the phenomena which occur in the
aerosolization of particles. If T” is the shear stress and u is the average velocity

(u = u(xty)). then

du dTyx
Pp“ dx dy Ppg [ 5]

51

F = buoyant force, the sum of the acoustic force and any upward gas flow

pp = the particle density

0
ll

volume concentration (m3 of particles/m3 of total volume), C = C(x).

Bagnold [58] considers the flow of powders in two regimes, the graineinertia
region which corresponds to high shear rates and where interparticle interactions
dominate and the macro-viscous region which corresponds to lower shear rates and

where the viscosity of the fluid plays a significant role.

2
Grain-inertia region : TXy at [£67] [26]
Macro—viscous region : TX, (1 [2—3] [27]

Savage [59] also arrived at similar results for the grain-inertia region. Johnson et al.
[60] theorized that interactions between colliding particles can be of two kinds -
fiictional contacts which are characterized by long contact times and collisional-
translational contacts characterized by short contact times. Though they considered a
dense flow of solid particles, these phenomena, especially inelastic collisions of short

contact times also occur in aerosols of low particle concentrations.

When particles in a medium are exposed to sound waves, they experience
hydrodynamic sound pressure [61]. If the radius of a particle is small compared to
the wavelength, 2., of sound, the pressure FM on an isolated spherical particle due to
standing waves is

FM = 3. n2 pg ’3“? sin

 

41cx
T] ”31

wlu:

52

where

p, = density of gas

r1, = radius of particle

U0 = amplitude of vibration of the particle relative to the medium

x = distance of the particle from the nearest node.

As entrainment of particles by the oscillating medium increases, the sound
pressure decreases in proportion and becomes zero for complete entrainment. In an
aerosol, the sound waves undergo scattering, absorption and diffraction. The
scattering of sound by aerosols is negligibly small and is usually neglected. The
absorption of sound depends on particle concentration and on the extent to which the
particles follow the vibration of the sound waves i.e. resonance. The attenuation of
sound pressure due to the presence of aerosol particles is proportional to the
absorption coefficient of sound waves by the aerosol. Other mechanisms for sound
absorption include viscous loss and the irreversible heat transfer between the particle
and the gas which causes an increase in entropy with a subsequent decrease in free

energy.

Another issue which comes up in the operation of the aerosolizer is the
agglomeration of particles in acoustic sound fields [61]. In an acoustic field, different
particles oscillate at different amplitudes due to the competition between acoustic and
gravitational forces. Small particles tend to oscillate along with the sound wave
while larger particles remain relatively stationary. This leads to the collection of
small particles by the larger particles to form agglomerates. This phenomenon
increases in magnitude with sound intensity and is called the mechanism of

orthokinetic interaction. A sonic agglomeration constant, b, is defined such that

bntr“2 pm

53

where I is the sound intensity which is the average rate of flow of energy through a
unit area normal to the direction of wave propagation. In real terms, the intensity

level is usually expressed in decibels and is the same as the sound pressure

I Pe
IL = 10 log? = 20 log!)— [30]
0

where

10 = reference intensity, usually 10'12 watt/m2
P,3 = effective or root mean square pressure = PN2}
P0 = reference pressure, usually .00002 N/m2 which corresponds to a pressure

barely audible to the human car at a frequency of 1000 Hz

I = P3l(poc), c is the velocity of sound in a medium of density p0.
(The intensity level IL is known as the sound pressure level SPL, a reference
pressure of 0.00002 N/m2 is commonly used for computing sound pressure levels in
air.)

The sound intensity in the aerosolizer is proportional to the amplitude of the
sound wave fed to the speakers at the natural frequency of the chamber. Hence the
aerosolizer operates best within a narrow range of amplitudes where b is low. At
very high amplitudes, the polydispersity in particle size causes a variation in particle
oscillations thereby leading to the agglomeration of small particles to larger ones.
The oscillation of particles with the acoustic field also generates multiple collisions
with the reinforcing fibers which pass through the aerosolizer. This increases the
probability of each particle being carried away by the fibers compared to a
conventional entrainment system where particle paths are either Brownian or follow

the profiles dictated by the flow of gas.

54

A rigorous analysis to predict concentration profiles within the aerosolizer
must take all of the above phenomena into account. The instantaneous velocity at
any point is the sum of the average velocity, u and the fluctuating component due to
the sinusoidal nature of sound waves. Equation (25) assumes that the particles and
the gas medium behave as a continuum. This may be adequate as a first
apprOximation but subsequent refinements should incorporate the discrete nature of
the particles and the medium. The bulk cf the shear stresses Tyx are generated by
interparticle collisions which are treated by several workers [57-59]. The two
buoyant forces, gas flow and acoustic force have to be taken into account in the
governing equations. The acoustic force depends on many factors such as diaphragm
tension which includes the weight of the packed bed, the geometry of the chamber,
the operation of the chamber at its natural frequency and the sound absorption
characteristics of the aerosol which cause attenuation of the acoustic force along the
length of the chamber. Concentration profiles and sound pressure profiles measured

within the chamber during each experiment will aid in the development of this

theory.

4.3 Spreader :

The conventional technique for spreading currently used in the composites
industry is elucidated in Section 3.1.1.. This investigation attempted to design a
spreader which would spread fiber tows to a width large enough that individual
filaments are exposed. The design chosen for spreading is an extension of the
principle of operation of the aerosolizer [63] where a pulsating flow of energy
provided by a vibrating speaker cone is used to separate the collimated fiber tow to
its individual filaments. The speaker vibrates at a constant predetermined frequency
and amplitude. The acoustic energy enables the fiber tow to spread to any desired

width. The acoustic pressure generated by the speaker in the region above the

55

spreader is transferred to the filaments in the fiber tow. This energy forces them to
spread apart. For a particular fiber tow, there is a narrow range of frequencies at
which the efficiency of spreading is the maximum. This range is centered around the
natural frequency at which the fibers absorb the most energy. The spreading width is
a function of tow tension in the region over the spreader and the amplitude of the
sound wave once the right frequency is selected. The spreading width increases with
increasing amplitude (frequency and tension constant) to a plateau beyond which
there is no appreciable increase. The spreading width increases with decreasing
tension to a point beyond which there is too much slack which causes uncontrollable
fiber motion and oscillations resulting in fiber damage. A spreading device based on
acoustics was also used by Hall [64] to spread internally wound spools (which are

unwound from the inside and have no tension in the tow).

A sketch of the spreader is shown in Figure 18. It consists of a speaker
mounted in a housing and driven by a frequency. generator and power amplifier.
Adjacent to the speaker are mounted several highly polished shafts. The shafts are
held in place by means of an aluminum block fitted with precision bearings. A fiber
tow of narrow width containing 3000 filaments enters the spreader and is spread to a
width sufficient to expose individual filaments. The function of the shafts is to hold
the tow in its spread form (due to friction) as it is being conveyed forward. The
bearings enable the shafts to rotate along with the fibers whenever there is excessive
friction between the fibers and the shafts. Alternatively, the shafts can be driven by a

motor so that they rotate synchronously with the same velocity as the fiber tow.

A schematic of the spreading operation is shown in Figure 19. The fiber tow
of narrow width is unwound from the spool by a pair of nip rollers. Both externally
and internally wound spools can be used with this process. The fiber tow is held at a
constant level of slack between this pair of nip rollers and a second pair of nip rollers

mounted between the first pair and the takeup drum. This arrangement ensures that

Polished shafts
Narrow fiber [Ow

Bearing block

I Spread fiber tOw
, / \

 

 

 

COO

 

 

 

 

 

 

Speaker

 

 

m

 

 

 

 

 

 

 

Power amplifier

Figure 18' SPmader

57

doggone wfiuaoam 89E .3 25mm

 

 

 

 

O

 

 

oBHHEH

 

 

 

 

 

 

 

 

 

 

 

 

 

58

the tow is held at the desired level of slack over the spreader regardless of the level
of tension of the tow in the fiber spool. Alternatively the speed of the takeup drum
can be regulated to maintain a constant level of slack in the fiber tow as it passes

over the spreader.

4.4 Heater :

The function of the heater is to ensure that the particles which are
electrostatically attracted to the fibers in the aerosolizer sinter, coalesce and adhere to
the fibers so that there is no loss of matrix during subsequent processing operations.
The heater currently used in the process is a natural convection oven (VWR 1300,
750 Watts) capable of heating to a maximum temperature of 250°C. Slits have been
machined at the front and back faces of the oven for the impregnated fibers to pass
through.

4.5 Process Description :

A schematic of the entire powder prepregging process is shown in Figure 20.
A fiber tow 2 is unwound from a spool 1. The tow 2 passes through a guide ring 3
and between nip rollers 4a before passing over the spreader 6. The spreader uses an
audio speaker to separate the tow into its individual filaments. Nip rollers 4a and 4c
maintain a constant level of tension in the spread tow 5 in the region above the
spreader. The spread tow passes through an aerosolizer 9 which coats the fibers in
the tow with a controlled concentration of particles. The impregnated tow 12 then
enters an heater 14 which sinters the particles on the fibers. The resulting prepreg

tape is wound on a takeup drum 15.

59

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4.6 Automation :

The automation scheme for the powder-prepregging process is shown in
Figure 21. It consists of a Hewlett-Packard personal computer QS/ 168 with an
interface card (Data Translation DT2811-PGH), a controller box (Composite Line
Controller or CLC) and various sensors monitoring the process. Each of the tasks
performed by the control system is described conceptually in this section. The
specifications of the various components, the control program and the wiring
diagrams are enclosed in Appendix B. The tasks performed by the control system
are - (1) Frber motion which includes speeds of the nip rollers, a slack controller
which controls the speed of the takeup drum depending on tow tension between the
third nip roller and the takeup drum and the linear motion of the takeup drum; (2)

control of oven temperature; and (3) data acquisition within the process.

4.6.] Fiber motion :

The speeds of the nip rollers are maintained at any desired speed by the
computer. An optical slotted disk is mounted on the drive shaft of nip rollers 4a and
4c (Figure 20). A photosensor placed around the disk keeps track of the number of
slots that pass through in a given time period. This signal is fed to a pulse counter
in CLC which holds this information in 3 data registers as a 12- bit number. The
computer program acCesses these data registers through the interface card, decides the
next control strategy and sends a command to the motor controller within the CLC in
the form of a 12-bit number (0-4095). The motor controller pulses full power to the
motors driving the rollers for a time period proportional to this number e.g. if the
number is 1200, the motor is on for 1200/4095 of one period (1/9.1 seconds). Both
the nip rollers l and 2 are powered by a 20 V dc. power supply. Both the input and
output signals for this control loop use the digital input/output channels in the

interface card.

 

~.,|l~|u
- L L think on.

61

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

won‘t”...

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 21

 

 

 

 

 

 

 

. Data acquisition and control of powder prepregging process.

62

The control scheme used by the program to maintain the speeds at their set points is
a PID algorithm (proportional-integral-derivative control). The ideal PID controller
equation is [65]

t
_— _1_ ' E.
p(t) - p + Kc e(t) + 11 £e(t’)dt +19 dt [31]

where

p(t) = controller output

'p‘ = bias value

Kc = controller gain (proportional constant)
e(t) = U“,‘ - U = set point - measured value
11 = integral constant

ID = derivative constant

The use of this equation for computer control entails its conversion to digital form by

the use of the following approximations

‘ lc=n e + e _

Trapezoidal rule : Ie(t’)dt’ = E (—k—kl)- [32]
o lr=1 2

Backward Difference : '2le = (Egg-3 [33]

where At is the time step.

Substituting equations (31) and (32) in (30)

_ At ck—l T1)
pn=p+chn+E[ck+-2—]+z?(cn-Cn_1) [34]

63

Writing a similar equation for pn_1 and subtracting the two, we have

+ T
A‘ [FL—1‘1] + —" (en — 2e,,_1 + en_2) [35]

Apn=Kc(cn-cn_1)+t—I- 2 At

This is called the velocity form of the PID controller and is the primary equation
used for motor control in the process. The main advantage of this equation over (33)
is that the summation term does not have to be computed. This avoids the problem of
reset windup which occurs when the error summation term grows to a very large

value and exaggerates the fluctuations of the controlled variable about the set point.

If the motors are controlled directly by a dc. power supply, fluctuations in the
power supply cause a fluctuation in motor speed and synchronous control of multiple
motors is extremely difficult. Feedback control by a PD controller such as the one
described above theoretically allows speed regulation to any desired set point. The
role of Kc is to accelerate the system response while 11 eliminates the error and TD
reduces the oscillations of the controlled variable about the set point. Increasing the
value of K6 increases the system response and reduces the offset. Above a certain
value, the response becomes oscillatory and unstable. The addition of 1:1 eliminates
offset but makes the system oscillatory. Reducing 1:1 makes the system sluggish in its
response to any fluctuation about the set point. The derivative constant, 1:0, reduces
oscillation and increases response time but above a certain value, the response
becomes oscillatory. If there is system noise or instantaneous fluctuations in the
measured speeds, then local derivatives will fluctuate wildly and result in an unstable
system. Optimization of the three constants is required for the synchronous control

of speeds by digital computer control.

64

The takeup drum is driven by a dc. motor which is powered by a 20 V power
supply. The drum rotates at a constant base speed throughout each experiment
except when slack is present. A slack sensor is mounted between nip roller 4c and
i the drum. The optical sensor detects slack whenever the tape falls below a certain
height. This switches a transistor in the CLC which accelerates the speed of the
takeup drum by boosting its power supply till the slack is no longer present. This
assembly is mounted on a table which tracks linearly thereby facilitating the takeup
of prepreg tape across the entire width of the drum. The table is fastened to a linear
actuator tube which is powered by a 90 V dc. motor which runs on a 25 % duty
cycle. The computer resets the value of a bit in a data register (0 or 1) in the CLC
to turn the motor off or on in accordance with this duty cycle. Limit switches
mounted at either end of the travel reverse polarity of the voltage supplied to the

motor causing the table to change direction.

4.6.2 Oven Temperature :

The oven is maintained at a desired set point temperature during each
experiment. .The oven temperature is measured by a K-type thermocouple which
converts temperature to a millivolt reading in differential output. A converter
changes this differential signal into a single—ended output which is fed to an analog
channel in the interface card. This voltage is read by the control program which
converts it to temperature. The program changes the status of a bit in a data register
(0 or 1) in the CLC to turn the oven on or off depending on the deviation of the
temperature from its set point. The control scheme utilizes proportional control and

is shown in Figure 22 as a conceptual plot between temperature and % ON time.

65

100

 

%ON

 

I
Set point

TEMPERATURE

Km 22. Temperature control of oven.

4.6.3 Data Acquisition :

Other signals which are acquired by the computer at the present time include
the sound level in decibels and the particle concentration in mg/m3 inside the
aerosolizer. Both signals are analog voltages which are acquired by analog channels

in the interface card at any frequency set within the control program.
4.7 Ancillary Equipment :

A heated stage was designed to simulate the phenomena which occur in the heater
under an optical microscope. An exploded sketch of the stage is shown in Figure 23.
It is a double-walled chamber, the outer wall fabricated out of Teflon and the inner
wall made from aluminum. The side walls of the inner chamber are fitted with two
firerod heaters (500 Watts, Watlow) controlled by a temperature controller (Omega,
CN310 KC). Slits are machined into the chamber to facilitate insertion of the
samples from the sides. The samples consist of a stiff aluminum frame with the
fibers laid across the center and glued to the sides as shown in Figure 23. The top
and bottom panels of the stage have a rectangular hole in the center where a 22 mm

cover slip is inserted to permit observation under the microscope.

A consolidation mold was fabricated to consolidate the prepreg tapes manufactured
by the process into composite specimens. The open-ended mold is shown in Figure
24. The male and female parts are machined to a close tolerance and are kept in
position by means of two locater pins on either side of the mold cavity. Prepreg
tapes are laid up in the mold and consolidated to form specimens which are tested for

their mechanical properties.

67

Top cover

 

 

“ Cover slip

‘- Gasket

  
 
 
 
  
     

Gasket
¢
.<> :

Chamber cover

Inner chamber

Outer chamber
Heat ‘

Chamber floor
Gasket

Cover slip

Gasket

 

Bottom cover

 

Figure 23. Hot stage for coalescence experiments.

 

‘ Locator pin
8.0

 

 

 

 

 

 

 

 

 

Easy slip fit between the two
parts of the mold

Pre-impregnated tape being consolidated
into a test specimen

Figure 24. Consolidation mold (All dimensions in inches).

Chapter 5
MATERIAL CHARACTERIZATION

 

An investigation encompassing the entire manufacturing process was
undertaken to gain an understanding of dry powder impregnation processes. A
flowchart which summarizes the different thrusts of the investigation is shown in
Figure 25. They are - (1) Characterization of the different properties of the
thermoplastic matrix and the reinforcing fiber. (2) Tape manufacture which includes
a study of the powder prepregging process and its different unit operations i.e.
spreading, impregnation and coalescence. (3) Consolidation of the prepreg tapes to
form a void-free part. This chapter describes material characterization while
subsequent chapters discuss tape manufacture, consolidation and an unified approach

for the manufacture of thermOplastic composites.

The fiber and the matrix need to be characterized for their properties in order
to optimize processing. These properties include particle size, fiber diameter,
charge-to—mass ratio of the particles, electrical conductivity of the fiber, interparticle
cohesive forces, matrix viscosity, crystallinity, transition temperatures, fiber-matrix

thermal properties and surface energies.

A model fiber-matrix system was used throughout the investigation. The
thermoplastic matrix chosen for this study is a polyamide called "Orgasol"

manufactured by ATOCHEM, Inc. This material was chosen because of its

69

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availability in the size range of interest - 1 to 30 microns in diameter. Unsized
Carbon fibers in fiber tows of 3000 fibers each with the designation AS4-3K made by

Hercules, Inc. were used as the reinforcement.

5.1 Particle Size Analysis :

The particle sizes of the different powders used in the project were
determined using an image analysis technique (J oyce-Loebl Magiscan Version 2A).
The procedure used involved suspending particles in a beaker filled with acetone. The
beaker was stirred vigorously to break up clumps of powder. A dilute suspension
was then deposited on a slide and the acetone allowed to evaporate. This left a
dispersion of unagglomerated particles on the slide which was protected from dust
particles with the help of a cover slip. The particle size distribution of each powder
was measured by image analysis from a population of 500-600 particles which

consisted of five different samples taken from various locations in the powder bin.
The choice of a liquid carrier such as acetone in the above technique raises
the possibility of swelling of the particles by the acetone. This can be gaged by

comparing solubility parameters 8 and calculating an interaction parameter x

according to the equation [66] -

V1 2
X = Bl + [E] (51 - 52) [36]

where

[31 = Lattice constant, usually 0.35 i 0.1

V1 = Molar volume of solvent, cm3/gmole

R = Gas constant = 1.9872 cal/gmol K

81 = Solubility parameter of solvent, (cal/cm3)m

82 = Solubility parameter of polymer, (cal/cm”,2

72

T = Temperature, K

8 for nylon which is a polyamide is 13.6 (cal/cm”,2 while that for acetone is 10.0. x
for this system is 1.96. A value of 75 greater than 0.5 implies that the polymer-
solvent pair is immiscible and there is no swelling of the polymer. Hence acetone

was chosen as a liquid carrier for the image analysis experiments.

Image analysis involves the digitization of an image and its subsequent
quantification and classification [67]. It consists of five steps - (1) Image capture
involves the digitization of the image. The image is stored as digital information by
dividing it into a square or rectangular grid of elements called pixels each of which
can have 64 (6-bit) or 256 (8-bit) intensity levels (grey scales). (2) Segmentation is
the separation of the regions of interest by thresholding, edge finding and/or region-
growing. These operations result in the distinct separation of the object from the
background e.g. the powder particle from the slide background. (3) Object detection
is a data reduction step which reduces the storage requirements of each image. Each
object is stored either as run-length encoding (the object start point and length along
the raster-scanning horizontal lines) or as boundary chain encoding which stores the
coordinates of the boundary. The latter technique reduces the storage requirements
for each image as compared with run-length encoding. (4) Measurement is the
quantitation of the encoded image in terms of dimensions of interest i.e. lengths and
areas. (5) Analysis of the measurements to arrive at meaningful information such as

particle size distributions.

The measurements on the Orgasol 2001 sample were done on 488 particles.
The length (the longest dimension), breadth (perpendicular to the length) and detected
area were measured for each particle. A plot of length vs breadth of each particle is
shown for the entire sample in Figure 26. The plot results in a linear correlation
between the two dimensions with a slope close to 1. This implies that the particles

are approximately spherical which can also be ascertained from the scanning

an
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74

electron micrograph shown in Figure 27. The particle diameters were therefore

calculated from the detected area of each particle by the formula

 

4 A 1/2
—] [37]

where
D1, = diameter of particle

A = detected area

The mean diameter of a sample can be represented in different ways as tabulated in
Table III [68]. The linear diameter of the Orgasol 2001 Ex D Nat powder was
calculated to be 9.16 i 3.96 microns from equation (37). A histogram of particle
diameters as a function of frequency (number of particles in each size range) is

shown in Figure 28.

5.2 Differential Scanning Calorimetry :

Differential scanning calorimetry was used to estimate transition temperatures,
specific beats and crystallinity of the polyamide. The differential scanning
calorimeter (DSC) measures temperature and heat flow associated with material
transitions and provides qualitative and quantitative information on both endothermic
and exothermic processes. A sample pan containing the material and an empty
reference pan are placed in the DSC cell. The cell is heated or cooled through a
temperature profile. The temperature is monitored by thermocouples placed beneath
the cell. A heater maintains the temperature in the cell according to the profile
whenever there is an instability e.g. exothermic crystallization, endothermic change of
phase etc. This power is recorded as a peak which can be integrated to calculate the
total energy transferred to or from the sample. A DuPont DSC 910 with a ramping

75

 

Figure 27. SEM photograph of polyamide particles.

_ 4 .

“I

.I

TABLE III.

76

DEFINITIONS OF MEAN DIAMETERS.

 

 

 

 

Order _ Other
(p+q) Name of D rymbol Where uaed symbols Alternative nomenclature
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1 . - no it I —- I — um , mean
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3 Volume, nan 0.13... Compariaoa, hydrology d3. 1:”, I -— I Number. volume mean diameter
atomizin; Z d” 2 d”
3 SWIM“ 5 Abaorption E Z d5 23' d” Laugh, surf Mtg
.12 at x = — I — ace mean
' ‘3 2 4!. 2: 41V
_ - m r us
4 Volume-diameter D... p Evaporation. molecular d3. ’1. y = 2.3 3 §'_"” Um. volume mean diameter
diffusion I: 41. Ex 4”
r - - ‘ 2 av Zr’ db!
5 Samar 05... Effie Ieney studies an ’3' a 2 as _ 2:: d” Surface. volume mean I'
7 new“: 5M Combustion. equilibrium 5., 2 4M Zx‘ dN
xv” I m I W Volume. moment mean diameter
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PARTICLE SIZE (microns)
Figure 28. Particle size distribution of Orgasol 2001 Ex D Nat.

78

rate of 5-10°C/min was used for all the experiments.

A typical scan of the as-received material in the DuPont DSC 910 is shown in
Figure 29. The therrnogram shows a melting transition with an onset of 171°C. The
glass transition temperature which is reported to be 42°C [69] for polyamide-12 could
not be identified in the DSC runs. The endothermic heat of fusion was calculated by
peak integration to be approximately 100 Joules/gm for the as-received powder.

The specific heats were estimated by the following procedure -

(1) Perform a baseline run with two empty pans in both the sample and reference

holders.
(2) Repeat with sample pan filled with powder.
(3) Subtract baseline run from sample run.

(4) Calculate specific heat by the formula [70] -

-93:
CP" H.

 

1] [38]

m

where

E = Cell constant, dimensionless (1.1577 for the DSC 910)
H, = Heating rate in °C/min

Y = Absolute value of heat flow in mW after subtraction
m = Weight of the sample in mg

Cp = Specific heat, J/gm°C

The measured values which are listed in Table IV showed a wide degree of
experimental scatter. They ranged from 0.58 i 0.15 at 40°C to 0.81 :1: 0.16
cal/gm/°C at 140°C (average of 5 runs) prior to melting.

 

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TABLE IV. SPECIFIC HEATS OF POLYAMIDE

 

Temperature, °C Cp, cal/gm/°C

 

40 0.58 i 0.15
60 0.63 :l: 0.16
80 0.68 i 0.17
100 0.71 i 0.17
120 0.76 i 0.17
140 0.81 :1: 0.16

 

 

 

 

DSC is the most widely used instrument for the measurement of degree of
crystallinity in polymers. The weight-fraction degree of crystallinity, We)” can be
defined [71] as

AH“-
w :
Ch AHfic'l‘

 

[39]

where
AH“- : Measured heat of fusion referred to temperature T

Aan-r = Heat of fusion of the 100% crystalline polymer determined at T

The degree of crystallinity of the polyamide could not be estimated due to
lack of reliable values for the heat of crystallinity of 100% crystalline polyamide.
However, the endothermic heats associated with melting were computed for different
samples in an attempt to gage relative crystallinity. All the baselines for integration
were constructed as follows - (1) Plot heat flow (J/gm) and the first derivative i.e.
the heat flux (J/gm/°C) as a function of temperature in the same graph. (2)
Determine the temperatures at which the first derivative changes prior to the melting
transition and falls back to a constant value after the melting transition. (3) Draw a

baseline for integration between these two points. This procedure is illustrated in

81

Figure 30.

The relative crystallinities of the polyamide subjected to different thermal
histories i.e. annealing at a constant temperature (165°C) for 2 hours, quenching with
liquid nitrogen and different cooling cycles from 1°C/min to 20°C/min were
estimated by the above procedure. Programmed heating experiments performed in
the DSC show that the endothermic heat of melting of the neat resin does not change
significantly for the different processing conditions. Table V lists the endothermic
heats calculated from the integration of peak areas for all the runs. The average
endothermic heat calculated from the 15 runs is 50.8 :1: 2.9 J/gm. The quenched
samples and the ones cooled at 20°C/min were the only ones which showed an
exotherm associated with crystallization of the amorphous portion of the polyamide

in addition to the melting endotherrn (Figure 31).

TABLE V. CRYSTALLINITY OF POLYAMIDE

 

 

No Thermal History Endothermic Heat (Hm)
I 1°C/min cool 54.7
2 1°C/min cool 52

3 2°C/min cool 51.5
4 5°C/min cool 49.9
5 5°C/min cool 49.9
6 5°C/min cool 48.9
7 5°C/min cool 50.1
8 5°C/min cool 49.6
9 Ambient cool (5-10°Clmin) 50
10 Ambient cool (5-10°C/min) 49.3
11 Ambient cool (5-10°C/min) 46.7
12 Ambient cool (5-10°C/min) 50.3
13 Cooling water (20°C/min) 45.7
14 Quenched sample 55.7
15 Quenched sample 55.6
16 Anneal at 165°C (2 hrs) 52.9

 

 

 

 

 

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84

One feature that the DSC runs bring out is that the as-received powder shows a
single endothermic peak while all samples which have a thermal history i.e. heated
beyond the melting point at least once show two endothermic peaks adjacent to each
other (Figure 30). Though the reason for this is not clear, it is postulated that the
existence of different crystalline states for polyamides [72] may be a contributing
factor. It can also be seen that the as-received powder has a much higher level of
crystallinity than any of the samples which were subjected to different thermal

cycles.

5.3 Viscosity :

The objective of this exercise was to generate a master curve in order to be
able to predict viscosities at any value of shear rate and temperature. Viscosity was
estimated by performing steady shear experiments in a parallel plate rheometer
(RMS 800 Rheometrics Mechanical Specuometer) and a mastercurve generated for
shear rates 0.1-100 sec‘1 for a temperature range from 180°C to 220°C. Parallel
plate or cone and plate experiments can be conducted to measure viscosities. A
parallel plate configuration was chosen because of the availability of disposable plates
since it is very difficult to dissolve and hence clean the polyamide off the plates (the
solvent recommended by ATOCHEM Inc. is m-cresol at 50°C). The torque
transducer of the instrument has a range of 2-2000 gm cm. The lower end of this
range is the one of interest in this set of experiments. 50 mm diameter parallel plates
were used (25 mm plates are also available) as lower shear rates are attainable with
the larger diameter. The lowest attainable shear rate with this dimension (50 mm) is
0.1 sec-1. The experiments were done in the range 0.1-100 sec‘l at different
temperatures between 185-220°C. The material showed signs of degradation at
temperatures above 240°C. The zero shear viscosity could not be predicted because

the lower limit of 2 gm cm of the torque transducer precluded experiments at shear

85

rates below 0.1 sec-1.

Two types of experiments were carried out -

l. Steady shear experiments were done in which the temperature is kept constant
and the shear rate is varied from 0.1 to 100 sec-1. Five readings were taken per
decade (tenfold increase in shear rate) and 30 seconds allowed for the instrument to
reach equilibrium before each reading. Two readings were taken, one each in the
clockwise and counter clockwise directions and an average was computed.

2. A strain sweep was done at l rad/sec and 215°C to determine the region over
which (3’ and G” remain constant with strain rate. It was intended that dynamic

experiments be performed at this strain rate.

Dynamic Experiments :

The strain sweep experiments revealed that the torque values are above 2 gm
cm (the sensitivity of the instrument) only after a strain rate of 30 % or higher. The
G’ and G” values also did not stay constant over this range of strain rates. Hence it
was not possible to determine the linear region over which dynamic experiments
could be performed. This led to the conclusion that steady shear experiments were

the only possibility for this project.

Steady Shear Experiments :

25 mm parallel plates were initially used for the experiments. Torque
readings of 2 gm cm or higher were achieved only at shear rates of 10 sec"1 or more.
The minimum measurable shear rate was lowered to 0.1 sec“1 by using 50 mm
parallel plates. For a particular shear rate, the torque required to keep the upper plate
stationary against the movement of the lower plate and the polymer melt decreased

with increasing temperatures.

86

The problems encountered during the experiments were - (l) Extrusion of the
sample occured at high shear rates. The centrifugal forces at _high shear rates (or
high angular frequencies) caused the melt to squeeze out from the sides. This is
unavoidable and the upper limit of the shear rate for each experiment was determined
by monitoring the experiment and terminating it when extrusion occured. (2) The
presence of bubbles in the melt can reduce the measured torque. This problem was
countered by letting the sample equilibrate on the bottom plate at the desired
temperature before bringing the two plates together to the desired gap width. This
procedure eliminated the presence of bubbles most of the time. Another option tried
out was to extrude the sample (and hence the bubbles) at very high shear rates,
decrease the gap width to account for the decreased volume and then conduct the
experiment. (3) Non-isothermal experiments. There was a variation of 0.2-0.6°C in
the temperatures measured in any particular experiment. This problem was solved by
treating each viscosity-shear rate measurement as a discrete point, conducting many
experiments and grouping together all points i 01°C to obtain an isothermal run.
This scheme also served as a check on the accuracy of different runs conducted at

the same temperature.

Data reduction was done as follows [73] -

(l) Classify data from different experiments into isothermal sets :l: 0.1°C.

(2) Calculate shear stress, 1, which is the product of the viscosity and shear rate at
each point.

(3) Calculate a reduced shear stress, 1,, at a reference temperature of (197.3°C).

1929.

“=4 Td

[40]

where
To = reference temperature in K (197.3+273)

do/d = ratio of reference to actual density (1 for most polymers in the region of

87

interest).

(4) Plot log(1:) vs log(y) where y is the shear rate for each temperature.

(5) Fit a straight line using least squares for each isothermal set of data.

(6) Calculate a1- based on the amount of shifting needed to move each of the
isothermal lines to a reference temperature (197.3°C).

(7) Plot log(a1-) vs log(1000/I‘) and fit a line to this plot.

(8) Determine the reduced shear rate-viscosity master curve.

The prediction of viscosity at any temperature and shear rate from the above
mastercurve consists of the following steps :

(1) Calculate a; for the particular temperature
log(a1~) = 2.664031(1000/1‘) - 5.680173
(2) Calculate t,
log(*t,) = 0.9813163log(y) + 2.702483
(3) Calculate reduced viscosity, u,
u. = vi

(4) Calculate actual viscosity. 11

T
1* = 3r “'[T—o]

A viscosity-temperature plot is shown in Figure 32 along with the relevant
equations for the shift factor, a7 and the reduced shear stress, 1?, (reduced shear stress
in dyne/cm2 reduced to a reference temperature of 197.3°C). In the equations, T is

given in Kelvin and y, the shear rate in sec‘1

. The zero shear viscosity is not
reported since none of the curves of viscosity vs shear rate at constant temperature

reached a plateau for shear rates greater than 0.1 sec-l.

88

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5.4 Summary of Properties :

In addition to the above measured properties, other relevant values were taken
from the data sheets provided by the manufacturers and from references. The
material properties of the polyamide and the carbon fibers are tabulated in Table VI.

TABLE VI. MATERIAL PROPERTIES OF POLYAMIDE AND CARBON FIBERS

 

 

Property Value
Polyamide :
Particle size, microns 9.2 :l: 4
Specific gravity 1.02 ‘
Apparent density (loose), gm/cm3 0.20-0.35 ‘
Apparent density (compact), grrr/cm3 0.35-0.50 ‘
Melt temperature, °C 175
Specific heat, cal/gm/°C

@ 40°C 0.58 :l: 0.15

@ 140°C 0.81 :l: 0.16
Thermal Conductivity, W/m/°C 0.22-0.31 b
Viscosity, Pa-s
(0.1 sec-1, 197.3°C) 52.6
Surface tension, dyne/cm 0.30 °
Carbon Fibers :
Diameter, microns 8.0 d
Specific gravity 1.80 d
Specific heat, cal/ngC

@ 75°C 0.22 d

@ 175°C 027 4
Thermal conductivity, W/m/°C 5.73 °
(parallel to fiber axis)

 

 

 

 

a Manufacurrer’s literatme (ATOCHEM, Inc.)

b Reference 43

c Reference 44

d Manufacurrer’s literature (Hercules Corporation)
e Reference 45

Chapter 6
TAPE MANUFACTURE

 

This chapter describes the experimental and theoretical analyses of the
different unit operations involved in the manufacture of prepreg tapes. The topics
discussed in this chapter are -

(1) The behavior of fine polymer powders in a conventional fluidized bed and in an
aerosolizer.

(2) The operation of spreading and the performance of the spreader in separating
fiber tows into their individual filaments.

(3) The coalescence operation which includes all the physical phenomena which
occur in the heater.

(4) An evaluation of the entire process and its efficacy in manufacturing flexible

prepre g tapes of controlled resin content.

6.1 Fluidized Bed Behavior of Cohesive Polymer Powders :

Section 3.1.2 discussed the classification of fine powders below 30 microns
broadly into Type AC and Type C powders. A fluidization column was built to
investigate the behavior of these powders the results of which are presented in this

section.

91

6.1.1 Experimental:

All experiments were conducted in a 5 cm i.d., 200 cm tall glass column.
Pressure taps were mounted at various points so that the pressure drops across the
distributor and the bed could be measured. The fluidizing medium was Argon, dried
of moisture by passing through a bed of silica gel. The static bed height used for all
the experiments was about 60-65 cm. The distributor used for the study was a fritted
glass disc sandwiched between two pieces of Whatrnan No 5 filter paper. The
pressure drop developed across the distributor as a function of gas velocity is shown
in Figure 33.

The powders studied were all of the same kind - a polyamide (Orgasol 2002
D Nat series, specific gravity 1.02-1.03, manufactured by Atochem Inc.). The
particle size distributions of the three powders, fine, medium and coarse are shown in
Figure 34. The properties of the fine, medium and coarse powders are shown in
Table VII. The particle sizing was done on a Joyce-Loebl Image Analyzer
(Magiscan Version 2A). The particle diameters shown in Figure 34 are the Sauter
diameters which are defined in Table III (page 75). Sauter diameters can be
measured by sieving techniques which are commonly used for particle size
characterization. They are a popular form of particle size representation in the
fiuidization literature and are used in this section to facilitate comparisons with prior

work.

All experiments were performed as follows :

(1) The bed was aerated at approximately 9 cm/s for 1-2 minutes. This was done
to get rid of all cracks and channels which may have developed during the previous
experiment.

(2) The gas flow was then shut off and the bed allowed to contract and settle down.

(3) The gas valve was reopened to the desired velocity of the experiment as

indicated by a fiowmeter.

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TABLE VII. PROPERTIES OF POWDERST

 

 

 

 

 

 

 

 

 

Powder Specific (l.p (microns) r/d.Pm Type of

gravity Powder
This work :
Fine Polyamide 1.02 12.2 0.28 C
Medium Polyamide 1.02 14.9 0.15 AC
Coarse Polyamide 1.02 19.4 0.16 AC
Geldart et a1. [25] :
FRF20 2.43 12 0.55 C
FRF40 2.43 10 0.5 C
FRF85 2.43 5 0.47 C
Corvic/M 1.637 30 0.8 C
CorViCIU 1.637 26 0.65 C
a320—N 3.97 30 0.09 AC
0.360 3.97 24 0.14 - AC

1 r = ((18490 ' dusts)’2
d1“, d3”, = Particle sizes below which there are 16 and 84
weight % particles respectively

(11, = average particle size (Sauter diameter)
dpm =median particlesize(basedon weight)

The bed pressure drop measurements shown in Figures 35, 36, 38, 39, 41 and
42 were all taken 11 minutes after the experiments were begun to allow the pressure
drop to stabilize to a constant value. The values have been normalized with the
weight of the powder packed into the bed divided by the cross sectional area (i.e. the
hydrodynamic pressure drop).

95

6.1.2 Fluidized Bed Behavior :

Fine Powder :

All attempts to sustain the fine powder in a fluidized state for long periods of
time resulted in failure. The formation of cracks of different orientations, lengths
and tortuosities is observed at velocities less than 3.6 cm/sec. The bed is therefore in
an expanded state, though there is no actual fluidization per se. The presence of
cracks results in the development of a sizeable pressure drop across the bed as shown
in Figure 35. The reproducibility of these measurements is poor because each
experiment produces a fresh set of cracks, with their "density", inclinations and

tortuosities determining the pressure drop.

At higher velocities, the bed initially fiuidizes but cracks and vertical channels
are seen to form. These vertical channels extend across the entire bed with time
resulting in defluidization of the bed. Most of the cracks which are present drain into
these vertical channels. This sequence of initial fluidization with crack formation,
followed by vertical channeling eventually leading to defiuidization is observed at all
velocities higher than 3.6 cm/s. The time span of the initial fluidization roughly'
increases with an increase in velocity eg. 5 minutes at 8.9 cm/s as opposed to 1.5
minutes at 4.24 cm/s. Figure 36 shows that the bed pressure drop decreases with
increasing velocity due to increased gas bypassing through vertical channels. It also
shows the variation of bed pressure drop with time at constant velocities. As can be
seen, the reproducibility of bed pressure dr0p is suspect. The primary reason for this
is the presence of cracks as was noted earlier.

A profile of such a bed is shown in Figure 37a. Cracks are the predominant

means for the transport of gas across the bed at low velocities (less than 3.6 cm/s).

The vertical channels shown form only at higher velocities.

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Medium Powder :

The fluidization behavior of the medium powder is different from that of the
fine powder though the difference in particle size is less than 3 microns. A profile of
a typical fluidized bed observed in this case is shown in Figure 37b. There is a
defluidized region near the distributor where only cracks and channels form and there
is no true fluidization. Above the defluidized region, bubbles start forming which
increase in size as they proceed towards the top of the bed. These bubbles keep
disrupting the cracks and channels as they form thus maintaining the bed in a

fluidized state. Hence bubbles lend a measure of stability to the fluidized bed.

At velocities less than 4.6 cm/s, the bed initially fluidizes with a profile as
described above. But the defluidized region grows with time, eventually traversing
the entire length of the bed. The only point in Figure 38 which shows an unusually
high pressure drop ratio (0.65 at a velocity of 3.65 cm/s) defluidized at 13 minutes
dropping down to a pressure drop of 0.37. In most cases, a vertical channel was

seen to form alongside the wall.

At velocities greater than 4.6 cm/s, the bed remained in a fluidized state
indefinitely. The scatter in the data is caused by variations in the depth of the
defluidized region. This trend is more noticeable at lower velocities. At higher
velocities i.e. greater than 6 cm/s, the defluidized region is so small that the scatter in
the data is greatly reduced. Also, at lower velocities, one sees a slightly higher
pressure drop. It is postulated that the defluidized region develops a higher pressure
drop than an equivalent length of the bubbling region. The ability of the
cracks/channels to generate a sizeable pressure drop was amply demonstrated in the
fine powder experiments. Figure 39 shows the variation of the bed pressure drop with
time at constant gas velocity. It is obvious from this Figure that the bed fluidizes
initially at all velocities. The cohesive forces overcome the buoyant forces exerted

by the gas at lower velocities thus resulting in defluidization of the bed. At

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higher velocities, bubbles keep the bed in an agitated state and the depth of the
defluidized region is small. Hence we see a plateau in the measured bed pressure
drop.

It can be seen from Figure 40 that bed expansion of the medium powder is
very high, reaching a maximum of 2.23 (bed height/static bed height) at a velocity of
8.32 cm/s. A variation in the height of the fluidized bed of less than 5 % was
observed during the course of most experiments. This can be attributed to the
periodic bursting of bubbles at the top of the bed. Each time this occurs, there is an

instantaneous drop in bed height.

Coarse Powder :

The coarse powder shows an ability to remain fluidized at velocities greater
than 3.2 cm/s. The scatter in the data is quite widespread between 3.2 to 5.5 cm/s
(Figure 41). This is primarily due to the large fluctuations in the depth of the
defluidized region. The bed fluidizes to attain a certain bed height. The defluidized
region then starts rising, sometimes reaching upto 60 - 70 % of the total bed height.
The bed does not sustain this growth indefinitely and the cracks/channels break up to
reduce the size of the defluidized region. This constant "tussle" between the
interparticle cohesive forces which tend to build a defluidized zone and the
hydrodynamic forces which give rise to bubbling leads to fluctuations in the observed
bed pressure drop and bed height. As the gas velocity increases, the defluidized
region decreases in size and at velocities greater than 5.5 cm/s, it is less than 5-7 cms
tall, thus leading to a more reproducible pressure drop. Figure 42 reflects the
stability of pressure drop measurements at higher velocities compared to that at lower

velocities at which the bed tends to defluidize.

103

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Difi'erences in bed behavior :

Bed expansion of medium and coarse powders at different velocities is shown
in Figure 40. It is evident that medium powders expand more than coarse powders.
It appears that for beds of particles with sustained fluidization, bed expansion
increases with decreasing particle size. This is in keeping with the findings of
Geldart and Wong [25]. They report that bed expansion increases as particle size
goes down for Types A and AC powders.

An inspection of Figures 38 and 41 reveal that the highest pressure drop
attained by the coarse powder is 0.89. At velocities greater than 5.5 cm/s, the bed
routinely achieves pressure drops of 0.86-0.87. The medium powder peaks at 0.88
and achieves average pressure drops of 0.83 at high velocities. There is a decrease
of 4-5 % in the pressure drop between the coarse and medium powders. Geldart et al.
[30] also noticed this decrease in pressure drop as the particles become more

cohesive.

The reason for the high pressure drops seen at velocities where the defluidized
region contributes to the total pressure drop was enunciated in the section on medium
powders. The coarse powder does not show such behavior. This is the result of
crack formation in the defluidized region which is more stable and intricate as
powders decrease in particle size. Hence the defluidized region develops a larger
pressure drop for a more cohesive (in this case a smaller- sized) powder. It must be
noted that in the bubbling region, particle mixing is too vigorous to allow any cracks

to form.

This investigation emphasizes the transitional nature of the change from Type
C to Type A as argued by Dry et al. [31]. Attempts to fluidize the fine powder result
in crack and channel formation, with hardly any bubbling. This is characteristic of
Type C behavior as outlined by Geldart [25]. The medium powder fluidizes at 4.6
calls with the help of bubbles. There is no homogeneous fluidization preceding the

107

bubbling phase and pressure drops attained are less than 1. Crack formation here is
stronger than for the coarse powder which fluidizes at 3.2 curls and achieves higher
pressure drops than the medium powder. Both the medium and coarse powders diplay
Type AC behavior. It is likely that increasing the particle size will cause a gradual
transition into Type A behavior characterized by bed pressure drops close to 1 and
weaker interparticle forces which allow for homogeneous fluidization initially before

bubbling sets in.

Effect of Relative Spread of the Particle Size Distribution :

The width of the particle size distribution can be characterized by the ratio
r/dpm where r is the spread and d.pm the median particle size. It can be seen from
Table VII that the fine powder has a fairly wide particle size distribution while the
medium and coarse powders have a narrow distribution. Figure 32 shows that the
medium powder has a size distribution which lies in between the fine and coarse
powders. Therefore, bed behavior for the medium powder should be transitional with
respect to the behavior of the other two powders. This concurs with the observations
made in this investigation. A large relative spread of a powder might serve to
accentuate the transitional nature of bed behavior i.e. the presence of fines leads to
channeling and cracking (a defluidized region) while the presence of larger particle
sizes results in a larger bubbling region. The precise effects of the relative spread
i.e. differences in bed behavior for different samples of a material with the same
mean particle size and different values for the relative spread remain to be
characterized. Geldart et al. [25] fluidized different powders with r/dpm ranging from
0.47 to 0.8 and 0.09 to 0.14 and found that the powders evinced Type C and Type
AC behavior respectively (listed in Table VII).

108

Influence of Bed Diameter :

Dry et al. [31] found that the dense phase voidage and dense phase velocity
(of transitional Type AC and Type A powders) do not show an equipment
dependence in going from the 5 cm unit to the 14 cm unit. The 64 cm unit however
yielded different values as the gas from the multi-orifice distributor (porous
distributor for the smaller units) had difficulty penetrating the dense phase at
velocities less than 40 cm/sec. Dry et al. [76] observed that bubble velocities in
fluidized beds of Type A powders show an axial dependence in larger-diameter beds
(64 cm) which is not seen in narrow beds (5 cm). In narrow-diameter beds, the
dimensions of the bubbles approach the column diameter especially near the top of
the bed. A perusal of Table II (Section 3.1.2) shows that the general nature of bed
behavior observed by different investigators is in line with the findings of this paper.
The formation of cracks and channels alongside the wall in addition to those inside
the bed suggests that gas bypassing through cracks and channels is likely to diminish
as the bed diameter is increased. The bed structure of a cohesive powder in the
defluidized region is likely to be preserved better in a narrow fluidized bed due to the
presence of wall forces. This suggests that bed diameter could be a variable which
influences the transition between different types of behavior for the same powder.
But the extent of the change in bed behavior as one progresses to larger-diameter

beds has not been investigated.

Discussion - Conventional F Iuidization of Cohesive Powders :

True Type C powders are very difficult to fluidize. They tend to form cracks
at lower velocities and cracks/channels at higher velocities thereby precluding any
actual fluidization. Bed pressure drop measurements are irreproducible due to the
randomness involved in crack and channel formation. As powders increase in

particle size, they begin to undergo a gradual transition in bed behavior. Bubbles start

109

forming which lend stability to the fluidized bed and lead to sustained fluidization.
There is no distinct minimum fluidization velocity. This can be characterized as Type
AC behavior. The bed structure of Type AC powders in narrow fluidized beds
consists of a defluidized region near the distributor where cracks/channels form and a
bubbling region where bubbles ensure that the particles remain in a fluidized state.
Reproducibility of bed pressure drop measurements depends on the variations in the
length and the structure of the defluidized region. In general, a large defluidized
zone with a varying density of cracks, of different inclinations and tortuosities
implies that there will be more scatter in the data. Bed expansion for such powders
increases as particle size goes down. Additional work needs to be done to
characterize the influence of bed diameter and width of the particle size distribution

on the bed behavior of cohesive powders.

6.2 Pulsed Gas Flow :

A solenoid valve with a relay timer was installed before the gas distributor to
pulse the gas flow to the column. Figure 43 shows a plot of the bed pressure drop as
a function of elapsed time for different pulsing speeds for a Type C polyamide
powder.

For the open cycle (no pulsing), the bed initially fluidizes but the formation of
cracks/channels across the entire bed with time results in defluidization of the entire
bed. When the gas flow is pulsed, it leads to the breakup of channels between pulses
i.e. when the gas valve is closed in each cycle, the solids start settling and disrupt the
channels. The bed therefore remains fluidized for a longer period of time. The bed
pressure drop is a function of the pulsing cycle. The pulsing cycles investigated (0-
60 sec open/closed) revealed that the bed pressure drop increases with the time that
the valve is kept open. There is a gradual decrease in bed pressure drop with elapsed

time as the disruption of channels in the closed phase does not keep pace with the

110

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111

formation and growth in the open phase unless the former is so large that it causes

defluidization in each cycle.

Gas pulsing does not have an appreciable effect on the quality of fluidization.
The inherent problems of cracks/channels in the fluidized bed and lack of control of
bed parameters still persist for gas pulsed fluidized beds. Pulsing. only delays the
onset of defluidization for a Type C powder. The cylical behavior of the pulsed
fluidized bed is unacceptable for an impregnation chamber in a powder-prepregging
process since this would lead to non-uniform pickup of particles by the fiber tow.
This led to the conclusion that other options which work at higher frequencies such
as acoustics and ultrasonics should be considered in the design of an optimum

fluidization chamber.

6.3 Aerosolization i :

6.3.1 Determination of Natural Frequency :

The design and operation of the aerosolizer are described in Section 4.2. A 3
inch internal diameter aerosolizer chamber with a 6.5 inch diameter speaker was
initially used to explore its performance. The first step is to determine the resonant
frequency of the chamber. The scheme used in these experiments is shown in Figure
44. The entrained particles from the aerosolizer were trapped in a disposable filter
for a constant duration of time (30 minutes) and weighed to determine the
enu'ainment rate of powder during each experiment. The amplitude, height of the
packed bed and the gas velocities were kept constant while the frequency was varied
from run to run. A plot of such an experiment is shown in Figure 45. The natural
frequency of the system was determined to be approximately 34 Hz for the

 

1 All the aerosolizer experiments discussed in this chapter were done with the polyamide
powder (Orgasol 2001, 9.16 i 3.96 microns diameter) unless otherwise noted.

112

 

 

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[“533 and end of each experiment)

Packed bed of particles

 

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Figure 44. Experimental scheme to determine natural frequency of aerosolizer.

113

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114

2002 Fine Orgasol powder, the height of the packed bed approximately 4 cm for all
the experiments and the amplitude at 15 V peak- to-peak. The particle pickup is the
maximum at the resonant frequency of the system if the other variables i.e. gas
velocity, amplitude of the sound wave and the height of the packed bed are kept

00118an

Reproducibility of these experiments was poor because of the following
reasons - (1) Caking on the walls. The walls of the plexiglass chamber get caked
with particles which absorb sound and reduce the weight of the packed bed. This
causes a deviation from resonance with time and thereby reduces particle
entrainment. (2) Pressure drop across the disposable filter increases with particle
buildup which adversely affects the weight of powder trapped in it with time. (3)
Environmental factors such as relative humidity adversely affect interparticle cohesive
forces and may influence the particle pickup by the filter. Hence there is a marginal
gain if any in determining the natural frequency by rigorous experimentation as
opposed to a frequency sweep to pinpoint the value at which the diaphragms oscillate
with the maximum amplitude. Resonance can be visually detected since the
diaphragms vibrate with the maximum amplitude at this frequency. A sound level
meter can also be used during the frequency sweep to aid in pinpointing the resonant
frequency (maximum sound pressure). This method was subsequently used
throughout the investigation to determine natural frequencies at the start of each
experiment. The natural frequency of the scaled up system (8.2 inches internal
diameter, 15 inches length, 15 inch speaker) with 200-300 gms of the 10 micron

polyamide powder (2001 Orgasol) was determined to be approximately 11-13 Hz.

115

6.3.2 Aerosolizer Behavior at the Natural Frequency :

As outlined in Section 4.2, a SPL meter and a RAM unit (Realtime Aerosol
Monitor) were installed online in the scaled up aerosolizer chamber. The RAM unit
monitors particle concentrations (mg/m3) inside the chamber. The sampling takes
place with a copper tube which conveys the particles to an optical detection unit
outside the chamber. But the inherently high particle charge on the fine polyamide
particles was a constant source of contamination in the optical assembly which
drifted from zero with time during each experiment. Zeroing problems at the end of
each experiment were also encountered due to particles sticking to the optical

detection unit.

The sound pressure was monitored inside the chamber at a height of 10 inches
from the lower vibrating diaphragm. For a system at its resonant frequency, the
sound pressure is proportional to the amplitude of the sound wave. Figure 46 shows
a typical plot of sound pressure vs time for a two hour run at the resonant frequency
of the system. The sound pressure decreased by around 1 db for a typical one hour
run. The decrease in sound pressure for various runs is listed in Table VIII. The
probable reasons for this decrease are caking on the walls and the decrease in weight
of the powder on the diaphragm with a consequent deviation in resonant frequency.
Two runs were conducted with the RAM-S unit online before it malfunctioned due to
zeroing and contamination problems. Figure 47 shows a plot of sound pressure and
particle concentration during an experiment. It shows that particle concentration
follows the same trends as the sound pressure which is to be expected because sound
pressure is the buoyant force which causes the upward motion of the particles.
Nitrogen gas was piped to the chamber at a height above the packed bed. The gas

flow helped in providing an additional buoyant force to the entrained particles and

116

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Particle Concentration (mg/m3)

maintaining a steady concentration of particles in the chamber. The experimental

118

evidence for this principle is presented in Section 5.2.5.

TABLE VIII. SOUND PRESSURE

 

 

 

No Duration of Sound Pressure Level, db
Experiment, mins Maximum Minimum Difference ’

1 60 126.3 124.8 1.5
2 60 124.8 123.8 1.0
3 60 124.3 123.5 0.8
4 60 123.9 123.2 0.7
5 61 126 125.3 0.7
6 80 125.1 122.6 2.5
7 86 123.1 122.2 0.8
8 83 122.4 121.6 0.8
9 57 125.7 124.4 1.3
10 62 125.7 124.2 1.5

 

 

 

 

 

 

 

The aerosolization of 5 micron polyamide particles in the small aerosolizer (3
inch i.d.) was investigated. Agglomeration of the particles was observed at high
amplitudes, the agglomerated clusters reaching sizes of 2-3 cms for the higher
amplitudes (greater than 15 V peak-to-peak). This decreased the particle
concentrations in the chamber to zero since the agglomerates fell down to the lower
diaphragm due to gravity and. grew larger in the packed bed. A gglomeration to form
such large clusters was not observed during the aerosolization of the 9.2 micron
polyamide particles though small agglomerates (1-3 mm in diameter) were noticed
occasionally at high sound pressures near 130 db. This implies that sonic
agglomeration, in addition to increasing with sound intensity (equation 29, Section
4.2) also increases with decreasing particle size, all other conditions in the aerosolizer

being constant. A possible reason for this is that particles oscillate with larger

amplitudes at the smaller particle sizes and therefore have a larger probability of

119

interparticle collisions. Interparticle cohesive forces are also larger for the fine
particles thereby increasing the probability of agglomeration on contact. Due to this
phenomenon of sonic agglomeration, there is an upper limit for achievable particle
concentrations in the aerosolizer chamber. This limit decreases with increasing

particle size.

The system discussed in Section 4.2 to eliminate entrainment to the
surroundings was very effective in performing this function. Practically no leakage
of particles to the surroundings was seen after the casing with the air filter and
exhaust was installed. Leakage was gaged by checking for particle deposits on
adjacent pieces of equipment. The air filter was vacuumed once in 2-3 runs to

ensure that the filter stayed unclogged.

6.3.3 Future Improvements :

The following modifications can be made to improve the performance of the
aerosolizer -

(1) A deionizer should be installed in the sampling tube between the intake in the
aerosolizer and the RAM-S unit to neutralize the charge on the particles before they
enter the optical detection assembly in the RAM-S.

(2) An AccuRate Screw Feed should be installed to feed the aerosolizer with
particles to replenish the loss of powder during the course of the experiments. A
material balance around the chamber to calculate the rate of powder loss can be used
to set the required feed rate for each experiment. An alternative scheme is to
monitor the height of the packed bed within the aerosolizer and control the feed rate
to maintain this height constant.

(3) At present, there is no facility for powder recovery of the particles entrained out
of the chamber. This should be incorporated in order to reduce operating costs. A

possible design scheme is one in which the powder is recovered and recycled at the

120

end of each experiment while the powder sump in the chamber is being replenished
with a feeder. The system consists of an annular chamber with two or more baffles
surrounding the fiber entry and exit slots to the aerosolizer. A slight vacuum is
applied to keep the outer chamber at a lower pressure than the surrounding
environment. The powder collected in this chamber is emptied back into the
aerosolizer at the end of each experiment. This scheme keeps all the operating
parameters of the aerosolizer unchanged during each prepregging run.

(4) The chamber walls were covered with stiff aluminum foil to alleviate the
problem of caking. A long term solution will involve the application of a conductive
coating to rid the surface of static charge. A process that will enable both visual
observation of the aerosolizer and the use of photosensors to determine the height of
the packed bed as a direct.means to control the feed rate of powder into the bed by

maintaining the height at a constant level is desirable.

6.3.4 Discussion - Aerosolizer Performance :

The aerosolizer works on the simple concept of acoustics providing the
buoyant force to lift particles up individually and thereby prevent agglomeration.
The two key variables are frequency and amplitude of the sound wave. At
resonance, the amplitude should be kept below the range where sonic agglomeration
becomes a problem. As shown in the above experiments, the aerosolizer can run for
long periods of time at constant particle concentrations if the weight of the powder
packed at the bonom of the bed remains constant to the extent that resonance is not
affected. Powder recovery can be easily added to the system as suggested in the
previous section on future improvements. The system does not need careful
supervision because of its inherent stability at the resonant frequency. Even in the
case of a fluctuation, response time to changes such as an increase in amplitude of

the sound wave is quicker than for the powder deposition chamber [19,20] since

121

there is no recycling of powder during the experiment. It should also be noted that
particle concentrations in an aerosolizer are around 0200 mg/m3 while that in a
fluidized bed or the powder deposition chamber described in Section 2.6 are orders of
magnitude larger i.e. 10000 mg/m3 or more. This affords better control over the
impregnation of particles into the fiber tow. Overall, the aerosolizer is a stable
system which can provide a constant concentration of particles for long periods of
time if operated at its optimum conditions and with replenishment of the powder in
the packed bed %

6.4 Spreading :

A set of 10 spreading runs was performed with the spreading system. The
spreading operation is described in Section 4.3 (Figure 19). The fiber tow [2] (width
less than 5 mm) was unwound from a spool [1]. It passed through a guide ring [3]
and in between nip rollers [4] before entering the spreader [6]. The spreader
consisted of a 10 inch speaker [6a] (8 ohm, 100 Watts) mounted in a plywood
housing [6g]. The speaker [6a] was operated at different frequencies and amplitudes
with the help of a frequency generator [6c] and a power amplifier [6b]. The fiber
tow zigzagged over and under highly polished shafts [6e] while being spread by the
spreader [6] into its individual filaments [7]. The spread tow was then pulled in
between nip rollers [8] and wound on a takeup drum. The speeds of the two nip
rollers [4] and [8] were controlled by a computer and monitored 9.1 times every
second. This maintained a constant level of fiber tension in the tow as it passed over
the spreader. The speed of the takeup drum [9] was controlled manually to take up
any slack in the tow between the nip rollers [8] and the takeup drum. The amplitude
and frequency of the sound wave entering the speaker were monitored by means of a
multimeter (the voltages reported in Tables IX and X are root-mean-square

amplitudes i.e. Vm, = 0.707 (Amplitude)) and a frequency counter respectively. The

122

width of the spread tow was measured after the tow passed over the last of the shafts
[6d]. The distance travelled by the fiber tow from the fiber spool [11 to the takeup
drum [9] was 65 inches. The duration of each of the runs shown in Table IX was 10
minutes. In Tables IX and X, NR (4) and NR (8) refer to nip rollers [4] and [8]
respectively. The values shown in parenthesis for motor speeds are the standard

deviations of the instantaneous speeds of the nip rollers measured during each run.

Table IX shows the effect of frequency of the sound wave on spreading width
provided the amplitude is kept constant. The carbon fibers used in this example have
an average diameter of 8 microns, hence a width of 4.8 cm implies that the tow has
been spread to expose individual filaments with an average spacing of one fiber
diameter in between adjacent fibers. As can be seen, there is a narrow range of
frequencies between 32-39 Hz at which the efficiency of spreading is the maximum
i.e. the fibers absorb the most acoustic energy causing them to vibrate and the tow to

spread to its individual filaments.

A second set of 6 runs were performed with the same version of the process
as in the first set. Here the frequency of the sound wave was kept approximately
constant at 36.0-36.4 Hz while the amplitude was varied from 4.7 to 11.8 V (Table
X). The measured widths show that spreading improves with increasing amplitude to
a maximum beyond which there is no further improvement with increase in
amplitude. It can be seen above an amplitude of 9.8 V, there is no tangible
improvement in the quality of spreading.

In both sets of experiments, the variations in spreading width are caused
primarily by instantaneous fluctuations in the level of fiber tension in the tow as it
passes over the spreader. At the optimum range of frequencies and amplitudes, the
fibers absorb a significant amount of acoustic energy and are able to retain their
spread shape in response to these fluctuations. Outside this range, the fibers tend to

collapse to a narrow width. Once this happens, they take longer times to spread in

123

proportion to the deviation of the operating variables of the spreader from their

optimum values.

TABLE IX. SPREADING EXPERIMENTS - CONSTANT AMPLITUDE,
VARYING FREQUENCY

 

 

 

 

No Frequency Amplitude (rms) Speed of nip rollers (cm/sec) Width
(HZ) (V) NR (4) NR (8) (CHI)

1 21.1 10.5 3.00 (0.16) 3.00(0.10) 0.5-4
2 25.3 10.7 3.00 (0.16) 3.00 (0.08) 3-7
3 30.0 10.5 3.00 (0.15) 3.00 (0.11) 4—9
4 32.1-32.4 10.5 3.00 (0.13) 3.00 (0.09) 5-9
5 34.3 10.5 3.00 (0.14) 3.00 (0.09) 5-9
6 36.1 10.6 3.00 (0.14) 3.00 (0.09) 6-9
7 38.3-38.4 10.5 3.00 (0.14) 3.00 (0.09) 5-9
8 40.0 10.5 3.00 (0.15) 3.00 (0.10) 4—7
9 42.2 10.5 3.00 (0.14) 3.00 (0.09) 2-6

10 44.1 10.5 3.00 (0.14) 3.00 (0.09) 0.5-5

 

 

 

 

 

 

TABLE X. SPREADING EXPERIMENTS - CONSTANT FREQUENCY,

VARYING AMPLITUDE

 

 

 

 

No Frequency Amplitude (rms) Speed of nip rollers (cm/sec) Width
(HZ) (V) NR (4) NR 13) (ca!)

1 36.3-36.4 4.7 3.00 (0.15) 3.00 (0.09) 0.5-4
2 36.3 7.6 3.00 (0.14) 3.00 (0.09) 4-7
3 36.3 9.8 3.00 (0.14) 3.00 (0.09) 6-9
4 36.3-36.4 10.1 3.00 (0.13) 3.00 (0.08) 7-9
5 36.1 10.6 3.00 (0.14) 3.00 (0.09) 6-9
6 36.0 11.8 3.00 (0.16) 3.00 (0.09) 7-9

 

 

 

 

 

 

 

 

124

6.4.1 Discussion - Spreader Performance :

The spreader designed for this process works very well as compared with
existing directed air methods for spreading fiber tows. The fundamental concept on
which the spreader is based requires only two variables to be controlled - frequency
and amplitude of the sound wave fed to the speaker. The spreading width is limited
only by the length of the spreader over which the fiber tow passes and the spreader
width under a set of optimum conditions (resonant frequency, amplitude of sound
wave greater than a threshold value). System instabilities downstream or sudden
system shutdown do not affect the performance of the spreader or cause fiber damage
unlike existing systems such as the one described by Baucom et al. [20]. When
operating at its optimum settings, the spreader is fairly insensitive to variations in

speed.

6.5 Coalescence :

The sintering and coalescence of the polyamide particles on carbon fibers was
studied with the help of a specially designed hot stage (Section 4.7, Figure 23) which
mounts under an optical microscope. Experiments were performed in the following
manner : Fiber frames were made by punching holes through a stiff aluminum sheet.
Single fibers were mounted across these holes and glued at the two ends. The fibers
were coated with polyamide particles. Each of these frames was placed inside the
hot stage which is maintained at the heater temperature for a specified length of time.
The coalescence events were observed visually under the microscope. These frames
were then mounted on metal stubs with the help of conductive carbon paint and
sputter coated with a thin layer of gold for observation under the scanning electron
microscope (JEOL 35-CF). Table XI lists a series of experiments on single fibers in
which the residence time in the hot stage was varied from less than 5 seconds to 30

minutes. There was a temperature variation of 1-6°C during each experiment due to

125

thermal instabilities whenever a frame was introduced into the chamber.

TABLE XI. COALESCENCE EXPERIMENTS 'l'

 

 

No Temperature, °C t, secs Comments

1 154-160 20 P

2 153-158 20 P, IPS

3 165-173 30 P, IPS

4 =166 20 P, IPS, FF

5 174-177 4-7 P, IPS, FF, PDF
6 173-177 < 5 P, IPS, PDF, DF
7 173-177 < 5 P, IPS, PDF, DF
8 197-204 5-9 FF, PDF, DF

9 187-193 5-9 F, PDF, DF

10 188-193 5-9 F, PDF, DF

11 190-192 < 5 FF, PDF, DF

12 ZOO-208 10 FF, PDF, DF

13 210-215 < 5 IPS, FF, PDF, DF
14 201-205 < 20 FF, PDF, DF

15 201-205 900 DF

16 201-205 900 DF

17 #00 1500 DF

 

 

 

 

 

 

T P = Particles adhering to fibers
IPS = Interparticle sintering
FF = Film formation
PDF = Preliminary droplet formation from the film
DF = Axisymmetric droplets
Figures 48(a) - 48(e) show the sequence of events that occur in the heater as
discussed in Section 3.1.3 and hypothesized in Figure 7. The polyamide particles
initially adhere to the fibers (P, in the above table) because the fibers have a higher
thermal conductivity than the polyamide. Adjacent particles then start sintering with
each other (IPS) as shown in Figure 48(a). Figure 48(b) clearly shows the adhering
of particles to the fiber at the base of each particle. The distinction between particles

adhering to fibers (P) and interparticle sintering (IPS) was established by rapping

l .5 H U 32:: S 4131

 

Figure 48. SEM photographs of coalescence in the heater : (a) and (b) show heat transfer to the
impregnated tow.

127

 

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128

the fiber mounts after each experiment. Without interparticle sintering between
adjacent particles (IPS), only a monolayer of particles is left on the fibers after
vibrating the fiber mounts. Interparticle sintering leads to their coalescence to form a
film on the fiber surface (FF). The film retracts to form droplets (PDF) which adopt
an axisymmetric conformation at long times (DF). Figure 48(e) shows interparticle
sintering, film formation and preliminary droplet formation. The initial formation of
droplets can be seen in Figure 48(d) while 48(e) shows two axisymmetric droplets on
the fiber at long times.

6.5.1 Heat Transfer :

The impregnated tows are initially heated to a temperature above the melting
point of the polyamide. The heat transfer coefficients in the heater were estimated
assuming free-convection heat transfer from horizontal cylinders in gases and liquids

[77] -

Nu = 3‘2 = 0.45 [41]
kg

From this equation, h can be calculated for different cluster diameters. The
contribution of radiative heat transfer to h is calculated to be negligible compared

with that by convective heat transfer.

In Section 3.1.3, the basic assumption of the lumped model is that external
resistances are rate-controlling i.e. the Biot number is less than 0.1. The prepreg
tapes made by the process were mounted in acrylic mounts and polished for
observation under an optical microsc0pe. It can be seen from Figure 49 that the
impregnated fibers show a tendency to cluster in bundles in the heater. Hence it is
obvious that the preferred configuration of the prepreg tapes is an array of fiber-

matrix clusters, each cluster diameter ranging from that of a single fiber to multiple

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130

fibers. Assuming a large cluster diameter of 100 microns (most cluster diameters are
between 10-50 microns), we can calculate Bi to be approximately 0.0002. Here a
value of k, is calculated by a simple rule of mixtures for a 50 volume % fiber and
matrix. This argument clearly proves that convective resistances dominate the heat
transfer step. In such a case, heating times can be calculated for the prepreg tapes to
increase the temperature from ambient to 180 C when Th is 200°C by using equation
3 (Section 3.1.3). Table XII surmnarizes the calculated times for clusters of different
sizes to raise their temperature from ambient (21°C) to 180°C. The time taken for

heat transfer increases with increasing cluster diameter.

TABLE XII. ESTIMATED HEATING TIMES FOR
POLYAMIDE-A84 PREPREG TAPES

 

D, microns 1250 500 300 100 50 20 10

 

t, seconds 166 30.4 10.9 1.22 .304 .05 .012

 

 

 

 

 

 

 

 

 

 

A lower bound for the time taken for heat transfer can be estimated by
considering an isolated particle in a convective medium. For very small spheres,
convection tends to approach pure conduction through a stagnant layer adjacent to the
surface [77] and Nusselt number approaches a value of 1. If the heater temperature
Th is 200°C, the time required for a 10 micron particle to heat up to 180°C is
calculated (equation 1) to be 1 millisecond.

From Table XI, it can be seen that the heat transfer step occurs in much less
than 5 seconds whenever the heater temperature is greater than 171°C (onset of
melting). The exact heating time is difficult to ascertain experimentally since the
particle temperature cannot be measured directly but must be assessed by observing

the progress in physical phenomena resulting from changes in particle shapes.

131

Convection currents occur when the frame is introduced into the chamber and
temperature gradients within the hot stage increase the heating time to a value larger
than the predicted times. This analysis however leads to the conclusion that for the
polyamide, heat transfer to the impregnated tow for this process occurs in less than 5

seconds.

132

6.5.2 Interparticle Sintering and Film Formation :

The sintering of adjacent particles on the fiber surface leads to the formation
of a polymer film. Frenkel’s theory which leads to equation (4) (Section 3.1.3)
predicts that interparticle sinterin g rates are influenced by viscosity, polymer surface
tension and particle size. Surface tension of most polymers lies between 20-50
dynes/cm whereas viscosity can vary by orders of magnitude. Hence interparticle
sintering times (defined to be the time when the interparticle bridge is equal to the
particle diameter) are primarily influenced by viscosity and particle size. Table XIII
lists predictions of sintering times for some engineering thermoplastics of interest in
structural applications. The surface tension in all the cases is assumed to be 30
dynes/cm. As can be seen, an increase in particle diameter and/or viscosity would

serve to increase sintering times.

TABLE XIII. PREDICT IONS OF SINTERING TIMES FOR SELECTED
THERMOPLASTICS BY FRENKEL’S THEORY ‘

 

 

 

 

Polymer PA PEEK PPS PEI PS
Processing

Temp, °C 215 390 315 350 350
Viscosity of

Melt, he 33 3500 2500 2000 2000
t,, sec

10 microns < 0.004 < 0.39 < 0.30 0.22 0.22
100 microns < 0.04 < 3.90 < 3.0 2.22 2.22
250 microns <0.18 < 9.72 < 6.94 5.56 5.56

 

 

 

 

 

 

 

 

(a) PA = Polyamide
PEEK = Polyetherether ketone
PPS = Polyphenylene sulfide
PEI = Polyetherimide
PS = Polysulfone

133

In the coalescence experiments with polyamide, interparticle sintering is an
instantaneous step which cannot be visually detected at temperatures above the
melting point. A perusal of runs 5-17 in Table XI shows that it was not possible to
halt the coalescence process at the sintering step even for times much less than 5
seconds. This is in line with predictions by Frenkel’s theory of sintering times of
less than a millisecond. However, at temperatures lower than 171°C, it was possible
to "freeze" the sintering step as seen in runs 2 and 3. This is because the viscosity
of the material is extremely high below the melting point. Adherence of adjacent
particles to each other is probably caused by the interdiffusion of polymer chains
across the interparticle interfaces because of limited segmental motion available for
the polymer chains at temperatures above the glass transition temperature. At the
higher temperatures, sintering is predominantly a viscous flow phenomenon, surface

tension being the primary driving force for flow across the interparticle neck.

Figure 50 shows an SEM photograph of a polyamide particle at high
magnifications. The semicrystalline nature of polyamide as evidenced by the
presence of nodules as well as the sharp melting transition observed in the DSC runs
suggests that the sintering may be occuring at a rate faster than that predicted by

Frenkel’s theory.

6.5.3 Droplet Formation :

The film which forms after sintering of the polyamide particles retracts back
to form droplets almost all of which are axisymmetric around the fiber axis. It can
be seen from Table XI (runs 5-17) that at a temperature above the onset of melting,
it is difficult to distinguish between the steps leading up to. draplet formation. The
formation of thermodynamically stable droplets over long times is demonstrated in

runs 15-17 and is illustrated in Figure 48(e).

 

Figure 50. SEM photograph of a polyamide particle showing the presence of
nodules.

135

The dimensions of 87 polyamide droplets on fibers were measured by image analysis
(Joyce-Loebl Magiscan 2A). The droplet-on-fiber system was prepared by coating
fibers with polyamide particles and inserting them into a heater at 200 C for 30
minutes. The drop length 1 and drop median diameter 2k were measured for each
droplet. The average fiber diameter was calculated by measuring the diameters of a

number of single fibers.

The fiber diameter was found to be 7.42 i 0.20 microns from 19
measurements. The droplet dimensions of one droplet were measured repeatedly to
determine the error involved in the measurements. The drop median diameter was
found to be 32.7 :1: 0.12 microns while the drop length was found to be 53.5 :l: 1.1
microns. The length dimension has a larger standard deviation because there is some
subjectivity associated with deciding where the droplet meets the fiber. A plot of K
(2k/d) vs L (21/d) is shown in Figure 51.

Section 3.1.3 (c) reviewed the dreary by Yamaki et al. [45] to calculate the
contact angle of a liquid in equilibrium with a cylindrical fiber. The equations (15,
16) were solved for droplet profiles by using a finite difference algorithm (backward
difference) with a Regula-Falsi root-finding subroutine. The finite difference form of
equation (15) (page 35) is -

 

Yr

.—2.- .- _. 23/2 _. 2
(Yr le'i'YrZ) = AP[1+£)1_Z“_1)_] 1[1+_£Xri_r-l)_] [43]

AP - T 408 M
The program (listed in Appendix C) predicts droplet dimensions (K as a function of
L) for each contact angle. These predictions were compared with the measured
dimensions, and the residual sum of squares, 2(Kexp, - Kmmf calculated for each
contact angle. Figure 52 shows a plot of the residual error as a function of the
predicted contact angle. From this analysis, the equilibrium contact angle for the

polyamide-A84 system was determined to be 23°. The solid line in Figure 51 is the

136

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138

prediction by Yamaki’s model for an assumed angle of 23°. The predictions are
excellent for values of K greater than 4 but deviate for lower values. The program
also predicts excess pressures for different-sized droplets. The pressures
approximately range from 12,000 to 60,000 dynes/cm2 for droplets ranging in size
from 46 to 8 microns in median radius respectively.

Yamaki’s analysis ignores the influence of gravity. The validity of this

assumption can be examined by considering a large droplet -

3‘3- = 400 cm-1

7
AP = 12000 dynes/cmz, assuming a value of 30 dynes/cm for y.

l = 121 microns, k = 46 microns for a large droplet with an excess pressure of
12000 dynes/cmz.

From equation (22),

APS = pgh

Here h = 2k

APg = 9.2 dynes/cm2 for the above system.

A corrrparison of the two pressure values AP and APg proves that gravity is indeed
negligible for the polyamide-carbon fiber system.

Figure 53 is a histogram showing the size distribution of polyamide droplets
on carbon fibers. Carroll [38] investigated the transition between axisymmetry and
non-symmetry and anived at equation (21) which is plotted in Figure 11. Equation
(21) can be solved for a contact angle of 23° to give a value of 1.32 for n at which
the droplets make a transition to non-symmetry. This implies that the droplets
become non-symmetric when k < 9.8 microns. The smallest measured axisymmetric
droplet was 10.8 microns in diameter, larger than the dimension calculated by

Carroll’s theory.

139

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140

6.5.4 Spreading of Polymer Droplets on Fibers :

Brochard et al. [42,43] state that if the spreading coefficient of the liquid film
is greater than the critical spreading coefficient, then a polymer sheath of the order of
100-500°A wets the entire fiber surface at equilibrium. Since coalescence phenomena
involve the retraction of a polymer film to form equilibrium droplets, this implies that
a sheath would exist right from the beginning, the equilibrium configuration being the
formation of equal-sized droplets bridged by a thin polymer film. Small droplets
would drain into larger droplets due to Laplace pressure differences and the droplets
would meet the film with a contact angle of zero. The critical spreading coefficient

for carbon fibers can be calculated from equations 10(a) and 10(b) -

3 2/3
a
Here, 7 = 30 dynes/cm, a 2 0.004 p, b = 8 u; Sc = 0.3.

The equilibrium thickness of a wetting film on carbon fibers can be calculated by
equation (7) -

2L1/2
e=a[28] [7]

For carbon fibers, a = 0.004 u, y = 30 dynes/cm and S = Sc = 0.3, the equilibrium
thickness is around 490°A.
But the polyamide droplets make an equilibrium contact angle of 23°. From Young’s

equation, we have -

Yso " Ysr. = 7 C059 [6]

We can calculate 750 — 73L to be 27.6 dynes/cm. Hence the spreading coefficient can

141

be calculated from equation (5b) to be -2.4. A comparison of the spreading
coefficient for the polyamide-A84 system with the critical value indicates that
thermodynamics favors the retraction of the film into droplets leaving areas of
exposed bare fiber in between them. This prediction is confirmed by experiment as
shown in Figure 54. There are many unequal sized droplets sitting adjacent to each
other having the same equilibrium contact angle as evidenced by Figure 51. Figure
48(e) also shows the presence of bare fiber surface between two equilibrium droplets.

6.5.5 Discussion of Coalescence Phenomena :

From the standpoint of high quality prepreg tapes, uniform impregnation of
fibers in the spread tow leads to interparticle sintering and coalescence into an
uniform film. The heat transfer rate for a given fiber matrix system depends on the
average cluster diameter and the heater temperature. It is advantageous to have good
spreading so that individual fibers are exposed thereby reducing the average cluster
diameter. Sintering time between adjacent particles is a function of the matrix
viscosity and the average particle size of the powder. The time taken for sintering
increases with increasing viscosity and particle diameter. Thermodynamic instability
forces the film formed by interparticle sintering to break up into droplets depending
on the value of the spreading coefficient. A spreading coefficient smaller than the
critical value will lead to the exposure of bare fibers while the converse will ensure a
polymer sheath 100-500°A thick all along the fiber surface. In the former case, the
polymer forms a distinct non-zero contact angle at the three phase contact line. The
droplets are either axisymmetric or nonsymmetric depending on the contact angle and
their size. As the equilibrium contact angle increases, the droplet-on-fiber system is
unsymmetric for larger and larger droplets. This has an adverse effect on the
flexibility of the prepreg tapes manufactured by the powder prepreggin g process.
lnterfiber distances have to be larger to avoid the bonding of adjacent fibers by the

142

 

 

 

Figure 54. Axisyrnmetric droplets on a fiber at equilibrium, S < Sc.

143

droplets. The bond strength between droplet and fiber for an unsymmetric droplet is
lower than an equivalent symmetric one because of its reduced fiber-droplet
interfacial area. Hence the probability of losing a part of the impregnated matrix by
attrition during handling is greater for materials which make a large equilibrium
contact angle with the fiber. Large contact angles are also detrimental to the quality
of prepreg tapes even when there are symmetric droplets because of the following
reasons - (l) The fiber-droplet interfacial area decreases with increasing contact
angle for the same droplet volume, and (2) the drop median radius increases with
increasing contact angle thereby requiring that interfiber distances be greater for the

same draplet volumes to avoid contact with adjacent fibers.

6.6 Process :

A set of 6 prepregging runs were performed with the powder prepregging
process. The carbon fiber tow was unwound from a fiber spool with the help of nip
rollers (Figure 20, page 59). The tow was then spread by the spreader which
consisted of a 10 inch speaker (8 Ohms, 100 Watts) mounted in a plywood housing.
The fiber tow passed over the speaker on top of which were mounted 10 polished
steel shafts (3/8 inch diameter) spaced 1 inch apart. The shafts serve to hold the
spread tow in position once they are spread by the speaker. The spread tow passed
through nip rollers and entered the aerosolizer. The aerosolizer consisted of a
plywood speaker box (15 inch speaker, 8 Ohms, 100 Watts) over which a cylindrical
plexiglass column (8.2 inch internal diameter, 15 inches in length) was mounted.
Vibrating rubber diaphragrrrs were placed on a lip between the column and the
speaker box and at the top of the column. The aerosolizer was cleaned and packed
with 225 grams of powder at the beginning of the first run. Both the aerosolizer and
the spreader were operated at the natural frequency of the respective systems. The

natural frequencies were determined as delineated in Section 6.2. The tow was

144

impregnated with particles in the aerosolizer and then entered a heater (12 inch
length) where the particles sintered and coalesced on the fibers. The resulting
prepreg tape was wound on a takeup drum. The distance travelled by the fiber tow
from the fiber spool to the takeup drum was 65 inches.

Table XIV shows the values of the different variables monitored in the
process. The volume fractions were calculated by weighing 28 inch lengths of the
prepreg tapes and comparing the weight of an equivalent length of unimpregnated
fiber tow. The runs have identical oven temperature, aerosolizer and spreader
conditions. Run 1 starts with a clean chamber and the walls get progressively caked
with powder to a saturation level beyond which there is no further caking.
Consequently, particle pickup was higher in run 1 as compared with the other 5 runs.
The gas velocity of run 2 was zero and the volume fraction matrix showed a higher
standard deviation than the other 5 runs. This indicates that a gas flow is
recommended for optimum particle entrainment. The tow velocities of all the runs
were slightly different due to manual speed control of the motors used in the process.
Run 6 indicates that the chamber needs to be replenished with powder. Despite these
discrepancies, the average volume fraction matrix was 22.5 with a standard deviation
of 3.5. The corresponding Figures are 22.4 and 1.5 if the first and last runs are
excluded.

Table XV shows a set of 4 prepregging runs all performed at different
conditions. The volume fractions attained prove that a judicious combination of
aerosolizer conditions and tow velocity can be employed to make a prepreg tape with

any desired volume fraction of matrix.

A set of 21 prepregging runs of 15 minutes duration each were done with a
preliminary alternative version of the process in which the fiber tow after spreading
passed through a separate impregnation chamber which was supplied with entrained

particles from the aerosolizer. The aerosolizer (3.15 inch internal diameter, 6.50 inch

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Figure 55. SEM photographs of prepreg tapes : (a) 90.9% Vf, and (b) 77.5% Vf.

147

 

CEU'SHB

Figure 55. SEM photographs of prepreg tapes : (c) 70.2% Vf, and (d) 33.2% Vf.

 

 

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Bar at bottom right represents 1 cm.

Figure-56. Prepreg tapes of different widths.

149

speaker, 8 Ohms, 50 Watts) and the spreader (6.50 inch speaker, 8 Ohms, 50 Watts)
were powered by the same frequency generator and amplifier (39 Hz, peak-to-peak
amplitude greater than 24 V). The prepregging was done in a semi-continuous mode
i.e. the tow was stationary from time to time to give an effective residence tirrre of 2
minutes in the impregnation chamber. The heater was held at 200°C. In this
version, nip rollers were not used. The volume fraction of the matrix was computed
to be 51.8 with a standard deviation of 3.9. This excludes 4 runs during which there

were problems with fiber motion.

Figure 55(a)-(d) shows a series of scanning electron rrricrographs of prepreg
tapes made by the process. The fiber volume fi'actions of the prepreg tapes are 90.9,
77.5, 70.2 and 33.2 respectively. A perusal of the photographs shows that the
distances between adjacent droplets decreases with decreasing fiber volume fraction.
It can also be seen that intimate wetting of each fiber by the polymer matrix is
successfully realized by the powder prepregging process. The fiber clusters range in
size from a single fiber diameter to multiple fiber diameters as pointed out earlier
(Frgure 49). The efficiency of the spreading step decides the diameter of the fiber
clusters in the prepreg tape. Figure 56 shows a photograph of prepreg tapes of
different widths. The widest tape made by the process was 6 cm. The wide tapes
(greater than 2.5 cm) consisted predominantly of individually coated fibers. Figure
55(b) shows the SEM photograph of such a tape. It should be pointed out that the
tape width in the process was the widest immediately following the spreader and
decreased gradually all the way to the takeup drum. The width of the fiber tow
before it entered the aerosolizer was always maintained at a value greater than 5 cm
(a width of 4.8 cm implies that there is one fiber diameter between adjacent fibers).
Table XVI shows an average variation in prepreg tape width within selected
experiments of 25 %. The primary cause for this variation is the fluctuation in

spreading width which is caused by instantaneous fluctuations in speed of the nip

150

rollers and tow tension.

TABLE XVI. PREPREG TAPE WIDTHS

 

 

No Duration, mins Tape Width, cm
1 121 13.4 :1: 4.2
2 60 21.4 :1: 4.3
3 60 19.7 :1: 4.1
4 60 16.2 :1: 3.3
5 60 11.5 i 3.6
6 60 12.8 :t 2.9
7 60 14.1 i 5.2
8 61 13.6 i 2.6
9 80 20.8 :1: 5.1
10 86 18.3 i 3.0

 

 

 

 

 

The process in its present configuration is capable of manufacturing prepreg
tapes with any desired volume fraction of fiber and matrix with a standard deviation
of 3-4% within each prepregging run. The reasons for the deviation in volume
fraction are - (1) aerosolizer performance : caking on the walls and deviations from
resonance, (2) spreading : variations in spreading width caused primarily by
improper fiber motion, and (3) fiber motion : variations in speed control of the nip
rollers and the takeup drum.

The prepreg tapes manufactured by the process possess the qualities of tack
and drape as defined in Chapter 1. The surface roughness of the tapes is induced by
the undulating contours of loosely bound individually coated fibers. This facilitates
the layup procedure during consolidation since the tapes remain in position when
stacked one on top of each other due to mechanical interlocking. Tape flexibility is
achieved primarily by the excellent spreading of the fiber tow. Post-processing

operations such as weaving can be easily accomplished with such a configuration.

151

6.6.1 Discussion - Process Performance :

The fiber motion system is capable of tow speeds from 2-10 cm/s. The
speeds of the nip rollers can be controlled at the set point with a minimum standard
deviation in instantaneous speeds of 0.1 cm/s. The instantaneous speed is monitored
and controlled 9.1 times a second by the computer. Fluctuations are due to the
inherent friction in the system i.e. in one rotation of the nip roller, the friction
between the bearings and the shafts is different at different locations on the shaft.
This fluctuation is periodic in nature and the computer controls the average speed at

the set point for each rotation.

The spreader, when operated at its optimum settings performs extremely well
in separating collimated fiber tows into their individual filaments. It responds well to
fluctuations in speed and tow tension as evidenced by the experiments described in
Section 5.2.3. The smooth shafts which are mounted in precision bearings turn along
with the fiber tow whenever there is friction. Fiber damage is minimized by this
mechanism and by the fact that the turning angles of the fibers are kept as low as
possible (Figure 57). Motor stalls and malfunctions in other parts of the system do
not cause damage to the fiber tow in the region over the spreader as with directed air
methods. Scaleup of the spreader can be accomplished easily to handle any number
of tows. The extra surface area needed for spreading is created by powering a series
of speakers with an high wattage amplifier.

The aerosolizer is operated in the low particle concentration regime of around
0-200 mg/m3 for the polyarrride powder. Constant particle concentrations in the
chamber can be maintained over long periods of time if the particle sump is
replenished on a periodic basis. Maximum attainable particle concentrations in the
chamber can be increased by increasing the particle size of the powder. Particle
pickup by the fiber tow can be increased either by decreasing the tow velocity or

increasing the dimensions of the chamber for a particular powder. The increased

152

1 inch Fiber tow

 

 

: 3/8 inch

 

 

Polished shafts

0 = 20.60

Figure 57. Turning angles, fiber tow over spreader.

153

charge-to—mass ratio of fine powders results in a natural electrostatic force between
the electrically ground carbon fibers and the polymer particles. This obviates the
need for additional equipment such as charging electrodes to increase the surface
charge on the powder. The oscillatory motion of the particles induces multiple
collisions with the fibers and increases the particle collection efficiency. The
aerosolizer can be scaled up in a similar manner as the spreader - by installing
multiple speakers. An alternative is to design an acoustic horn to cover a larger
surface area. The above discussion also considered a different configuration whereby
the particle impregnation chamber was maintained separate from the aerosolizer.
This is a viable alternative in which case a large impregnation chamber can be
maintained at a constant particle concentration with multiple aerosolizers feeding into

the chamber all powered by the same amplifier.

Coalescence in the heater is described in detail in Section 6.5. The formation
of a film and/or droplets on individual fibers results in the manufacture of flexible
tapes which are suitable for post-processing operations such as weaving and filament
winding. Intimate wetting between the fiber and the matrix also results in reduced
consolidation times since the matrix has to flow over very short distances of the order
of microns to seal up local voids rather than millimeter distances in processes such as
melt impregnation. Hence the role of viscosity is reduced as a factor in the
manufacturing process. Scaleup of the heater is easily accomplished by the
construction of a muffle furnace open at both ends to facilitate the entry and exit of

the powder- impregnated tow.

Chapter 7
CONSOLIDATION

 

The objective of this phase of the investigation was to deternrine optimum
consolidation cycles for the manufacture of void-free parts of different fiber- matrix
volume fractions. The prepreg tapes made by the process were consolidated into
specimens using processing cycles in which the temperature, pressure and time were
controlled and monitored. The specimens were then characterized for their fiber-

matrix volume fractions, void content and their fracture toughness.

7.1 Experimental :

The prepreg tapes were laid up in a two-part mold described in Section 4.7
(Figure 24) and consolidated under heat and pressure in a plate and frame press
(Carver Press) to form composite specimens. A typical temperature-pressure profile
for a consolidation run is shown in Figure 58. The consolidation procedure was as

follows :-

The prepreg tape wound on the takeup drum was cut into 28 or 32 inch
lengths and weighed on a Sartorius balance. An approximate fiber-matrix volume
fraction was calculated by comparing these weights to the measured weight of an
uneoated AS-4 fiber tow. The prepreg tapes were then cut up into 7 or 8 inch
lengths. A non- porous Teflon® film was placed in between the two mold faces and
the laid up tapes. The mold faces were also sprayed with a mold release agent as a

precautionary measure. Platens of a Carver press were heated to the desired

154

155

800 200

 

 

     
   

 

 

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Figure 58. Consolidation cycle, specimen 2.

 

 

 

 

 

 

 

 

 

 

 

Figure 59. EN F test, loading pins and specimen geometry.

156

consolidation temperature. The mold with the prepreg tapes was placed between the
platens with a K-type thermocouple inserted 1 m away from the mold face. The
millivoltage output of the thermocouple (1 mV/°C) was fed to a chart recorder to
monitor the temperature of the part. Ceramic fiber insulation was placed flush on all
the four sides of the mold. The platens were then lowered to contact the mold at a
consolidation pressure based on the fiber-matrix volume fraction calculated earlier.
The temperature of the platens was maintained at the set point for 30 minutes. This
includes the initial period of approximately 10 minutes during which the faces of the
mold get heated to the set point temperature. After 30 minutes, the heater was shut
off and the mold cooled at an approximate rate of 10-15 °Clmin with the help of
cooling water for 15 minutes to ambient temperature. The consolidation pressure
was maintained throughout the duration of the experiment to prevent void formation
due to shrinkage. Two of these consolidated parts were placed in the mold with a 75
micron Teflon® film 1 inch from either end as crack initiators for the end-notched

flexure test and the consolidation procedure repeated.

The resulting part was cut using a water-cooled diamond saw into specimens
for the Mode H fracture toughness (end-notched flexure or ENF) test. Approximately
1/8" was cut flom around the part to eliminate edge effects. Figure 59 shows the
specimen geometry and the location of the loading pins for the test. The specimens
were tested to failure in an Universal Testing Machine (screw-driven, 4480 N load
cell, crosshead displacement rate 0.3 mar/min). Load and displacement below the
center loading pin were monitored for each specimen. The critical strain energy

release rate for mode 11 failure was calculated from the equation [79] -

9gc§
— 2W(21.3 + 3:13)

 

Gm, [44]

157

where
PC = Critical load, N
C = Compliance, calculated from the load-displacement curve by linear

regression. mm/N
a = Crack length, mm
= Specimen width, mm

L
Gn.

Span, the length between the center loading pin and the outer pins, mm
Mode II fracture energy, kJ/m2

These specimens were analyzed both for volume fractions of fiber and matrix and for
void content with the help of an optical image analysis technique called Optical
Numeric Volume Fraction Analysis or ONVFA [80]. Small pieces of the specimens
(1 inch x 0.5 inch) were cut and mounted in acrylic holders and polished
successively to a final grit of 0.05 microns. A 80 grit belt sander, a Struers Abramin
Automated Polisher (240, 320, 1000, 2400 and 4000 grit, 3 minutes each), a LECO
GP20 Grinder/Polisher (5 micron, 1 micron A1203 powder, 5 Minutes each) and a
Buehler Vibromet (0.05 micron A1203 powder, 10-12 hours) were used in the
polishing sequence. The specimens were cleaned in an ultrasonic cleaner for a few
minutes and then cleaned with ethanol for microscopic observation. 15 images were
randomly chosen under the optical microscope and digitized. An Olympus
microcope with a video monitor and an Amiga computer was used for the
digitization. The digitized images were then analyzed using the ONVFA program.
The program performs a fiber count and calculates a fiber volume fraction assuming
an average fiber diameter. The program was also used to generate a histogram of
grey scales to estimate the void fraction in the composite specimen. Void fractions
were reported as a range e.g. 1.2-1.5 to underscore the fact that there was some
subjectivity in deciding the number of gey scales which corresponded to voids. For
most specimens, the void content was estimated by digitizing all the voids present on

158

the polished face. This was possible because at low void fractions, the number of
frames that need to be digitized is usually quite low (less than 20). The
measurement of void fractions greater than 5% was prone to statistical error because
it was not possible to digitize all the frames where voids occured due to the random
and frequent incidence of voids all across the composite specimen.

Section 5.2 discussed the measurement of relative crystallinity for the neat
resin. The same procedure was used to determine the relative crystallinity of the
composite specimens. A small piece approximately 10 mg in weight was cut from
each composite specimen and placed in the DSC sample pan. The DSC run was then
conducted at a ramping rate of 5°C/min from ambient temperature to 200°C. The
area under the melting endotherm was corrected for fiber volume fraction and an
endothermic heat determined for each sample. The fiber volume fraction used in this
calculation was the average value determined by ONVFA.

7 .2 Optimum Cycles for Void-Free Consolidation :

A series of consolidation experiments were performed at different
consolidation pressures for different fiber-matrix volume fractions. The temperature
was maintained at 197-202°C for all but one of the experiments while the time was
maintained constant at the consolidation temperature for 20 minutes for all the
experiments. The fiber-matrix volume fiaction, void fraction and Mode II fracture
toughness were measured for each part. The results of the entire investigation are

presented in Table XVII.

TABLE XVII. CONSOLIDATION AND ONVFA EXPERIMENTS

159

 

 

 

No Pressure Temperature Vfi' Vv‘l' Gm, Vfc‘i
(Psi) (°C) (96) (96) (kl/m2) (‘5)
1 440 197-202 69.8 :t 1.7 Voids 0.297 > 70
2 440 197-202 70.7 :1: 4.7 4.7-6.1 0.133 75.3
3 440 197-202 68.7 i 5.5 2.2-3.6 - 71.2
4 440 197-202 62.5 :1: 7.4 10.4-13.5 0.007 72.3
5 200 197-202 70.8 i: 4.0 344.0 0.223 73.8
6 560 197-202 69.9 :I: 3.6 5.3-5.6 0.011 :1: 0.001 74.1
7 1100 197-202 74.2 :t 1.2 Void-free - 74.2
8 1100 197-202 73.5 :1: 1.1 Void-free 0.128 73.5
9 1060 197-202 74.1 :1: 2.7 1.2-1.6 0.171 1: 0.028 75.3
10 1150 197-202 71.2 i 3.0 5.8-7.1 0.009 76.6
11 440 197-202 58.3 :1: 5.7 7.7-9.8 0.008 64.5
12 200 197-202 69.8 :I: 3.3 Void-free 0.548 69.8
13 440 197-202 63.5 :1: 3.4 0.1 0.657 63.6
14 200 197-202 66.5 i 2.9 Void-free 0.516 66.5
15 225 197-202 62.4 :1: 3.0 0.02 0.505 :1: 0.039 62.4
16 440 197-202 70.6 :1: 3.0 0.36 0.336 :1: 0.036 70.9
17 440 197-202 65.8 :l: 3.9 1.7-2.9 - 67.8
18 80 = 185 40.0 :1: 6.1 Void-free 0.672 :1: 0.100 40.0

 

 

 

 

 

 

1' Vf =Fibervolumefraction

Vfc :- Frber volume fraction if specimen were void-free
V, = Void fraction

 

 

160

Specimens l - 6 showed the presence of voids, indicating that a higher
pressure is required for consolidation while specimens 7 and 8 were both void-free
and specimen 9 had few voids. A limited amount of bleeding was observed for
specimens 7 and 8. All the above-mentioned specimens were in the range of 71-75
% Vfc if they are corrected for voids. From these experiments, one can surmise that
a pressure of around 1100 psi is needed for optimum consolidation of prepreg tapes
with a fiber volume fraction of 71-75 %. This assumes that good intimate
impregnation is achieved in the powder prepregging process. If the impregnation is
not uniform, then even an optimum pressure results in specimens with voids,
especially at fiber volume fractions greater than 75 %. This can be seen in specimens
9 and 10, the latter showing very poor impregnation while the former specimen had a
void fraction of 1.6%. At such high fiber volume fractions, it is imperative that the
polymer matrix be placed in the final position during prepregging. As the fiber
volume fraction increases beyond 75 %, intimate impregnation becomes a key factor
in the consolidation process. From this investigation into the powder prepregging of
8 micron carbon fibers with 9 micron average particle size polyamide particles, it is
believed that a fiber volume fraction of 75 % in the prepreg tape is the maximum
that can be used to make void-free parts reproducibly. It is a matter of conjecture
whether the use of smaller particles e. g. 5 micron polyamide particles will enable the
manufacture of void-free parts with a volume fraction greater than 75 %. This would
depend largely on the uniformity of particle impregnation in the prepregging process.

Bleeding of resin from the part increased with increasing consolidation
pressure for constant fiber volume fractions in the prepreg tapes. A significant
amount of resin bleeding was observed for specimens 12 and 14 while a limited
amount of bleeding was observed for specimens 13, 15, 16 and 17. These
experiments indicated that an optimum pressure of around 440 and 225 psi are
required for fiber volume fractions of 64-68 % and 60-63 % respectively. Specimen

161

18 was consolidated at a lower temperature of 185 C and 80 psi to form a void-free
part with 40 % V; which implies that a lower pressure is required at l97-202°C at
which all the other experiments were performed.

The above analysis suggests a behavior whereby for a particular Vf, as
pressure increases, consolidation improves to an optimum above which bleeding
occurs until at very high pressures, the fiber squeezes out along with the resin leaving
a damaged specimen. The amount of bleeding is proportional to the difference
between the optimum pressure and the applied pressure, the latter being greater than
the optimum pressure. If the desired fiber volume fraction in the final part is much
lower than that in the prepreg tape, a lower consolidation pressure is required than
suggested in the above argument. For instance, a pressure of only 200 psi was
required to make a void-free part of 69.8% Vf (specimen 12). It is also apparent that
the optimum pressure needed for consolidation increases with increasing fiber volume

fraction.

An operating curve for optimum consolidation of powder-impregnated tapes
(polyamide-A84) is shown in Figure 60. The underlying assumptions are that
temperature is kept constant at 197-202°C and the duration of the consolidation cycle
is 20 minutes. The solid line indicates optimum pressures required to make void-free
parts for different fiber-matrix volume fractions in the prepreg tapes. Pressures above
this line result in bleeding the degree of which is proportional to the deviation of the
actual pressure from the recommended value. Pressures below the solid line will
result in the presence of voids in the final part. Bleeding of the resin during
consolidation is encouraged to a limited extent for the formation of void-free parts.
This is to ensure that voids in resin-deficient regions are filled up by the transverse
flow of polymer melt. Figure 61 shows the optical micrographs of two void-free
specimens 9 and 15. Regions of hexagonal close packing can be observed in both

the specimens.

162

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(a) specimen 3, and (b)

Optical micrographs of polyamide-AS4 composites.

Figure 61.

specimen 7.

164

7.3 Intimate Contact and Autobahn :

In Section 3.2, the theory of consolidation is discussed. The two steps of
consolidation, intimate contact and autohesion react differently to increasing
consolidation pressure. The time required for intimate contact is inversely
proportional to the applied pressure while the diffusion coefficient for autohesion
decreases with increasing pressure due to the reduced volume available for segmental
motion of the polymer chains. One measure of the diffusion time required for
autohesion is the relaxation time of the polymer. A Maxwell relaxation time, I. can

be calculated from the rheological measurements by the formula -

N1
2 I12‘!

3. = [45]

 

where
N1 = Normal stress, dyne/cm2
112 = Shear stress, dyne/cm2

y = Shear rate, sec‘1

At a temperature of 187.8°C, N1 = 58.2 dyne/cmz,
1,2 = in = 3.981 x 691 = 2570.9 dyne/cmz
7s = 0.0027 sec.

The relaxation time for the polyamide is calculated to be less than a
millisecond for the entire range of temperatures used for processing in this
investigation. In contrast, a processing time of 20 minutes at temperatures above
180°C is used for consolidation of the prepreg tapes into composite parts. In addition,
the consolidation experiments follow the trends that would prevail if intimate contact
were the only mechanism of adherence i.e. efficiency of consolidation increases with

increasing pressure. Hence it can be concluded that intimate contact is the rate-

165

controlling step in the consolidation process. If autohesion was of greater importance,
then it may be advisable to use a two- stage consolidation cycle - a period of high
pressure to achieve intimate contact followed by one of lower pressure to facilitate

autohesion.

7.4 Crystallinity :

The degree of crystallinity of the matrix affects the mechanical properties of
the composite. Lee et al.[54] and Manson et al.[55] noted a decrease in fracture
toughness with increasing crystallinity for AFC-2 composites. DSC was used to gage
the level of crystallinity in this investigation and thereby ensure that it stayed the
same for each specimen. DSC runs performed on three composite specimens gave an
endothermic heat of 50 :l: 8.4 J/gm over a series of 12 runs. The experiments on the
neat resin for different cooling cycles showed that the endothermic heat was around
50.8 :I: 2.9 J/grn (Section 5.1.2). A comparison of the two indicates that the average
level of crystallinity is the same for both the neat resin and the composite specimens.
The latter however showed a large standard deviation which is due in part to local
variations in volume fraction of matrix (including the presence of voids) in the
composite specimens. Average volume fractions measured by image analysis for

each specimen were used to compute the endothermic heat absorbed by the matrix.

Within the limits of this experiment, it can be stated that the levels of
crystallinity are approximately equal for all the tested specimens. This is not
surprising since a cooling rate of around 10-20 °Clrnin was used for all the
consolidation experiments. However, a rigorous technique to measure the exact
fiber-matrix volume fraction in the DSC sample is required in order to calculate the
relative crystallinity in each specimen with more accuracy than afforded by the above
set of experiments.

166

7.5 Fracture Toughneu and Failure Mode :

The fracture toughnesses were measured by the end-notched fiexure test.
Figure 62 is a plot of Gllc as a function of fiber volume fraction for specimens 9, 15,
16 and 18 each of which were averaged over 34 tests. The fracture toughness
decreases with increasing fiber volume fraction for void-free or near void-free

specimens from a value of 0.672 kJ/m2 for 40% vf to 0.171 1mm2 for 74.1% v,.

A SEM study was undertaken to understand the failure mechanisms for
fracture. Specimens 15 and 16 undergo extensive plastic deformation i.e. matrix
deformation in the direction of crack propagation. Triangular ribbons of the matrix
are pulled at an angle of approximately 45°. This phenomenon occurs because even
though the specimen is loaded in shear, there is a tensile stress component at an
angle of 45° to the fracture surface [81]. This is shown in Figure 63(a) and (b)
which are micrographs of specimen 15. Specimen 9 which is shown in micrographs
63(c) and (d) shows both plastic deformation and the presence of bare fibers. This is
understandable since the higher volume fractions confine the matrix to smaller
amounts and thinner dimensions. Many regions of hexagonal close packing were
noticed under the optical microscope. Hence the toughness of the matrix cannot be
achieved to the same extent in the composite. The SEM study indicated that the
composite specimens with fiber volume fractions of 60- 65 % which are of interest in
the composites industry showed excellent wetting between fiber and matrix. The
predominant mode of propagation for fracture is plastic deformation of the matrix at

these volume fractions.

Figure 64 shows a plot of Mode 11 fracture energy as a function of void
fraction in the composite for a fiber volume fraction of around 70 %. As can be
seen, the fracture energy is maximum for the void-free part and falls with increasing
void content. There is a precipitous drop in fracture toughnesses for void fractions

greater than 5% as evidenced by Figtne 64 and the Gm, values of specimens 4, 6, 10

167

 

 

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Figure 63. SEM photographs of fractured specimens: (c) and (d) specimen 9.

170

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171

and 11 listed in Table XVII. It should be noted that there is a statistical error
involved in the exact measurement of large void fractions in the composite specimen
as pointed out earlier in the experimental section. The correlation between fracture
toughness and the void content of the composite as characterized by ONVFA proves
that fracture toughness is an effective mechanical test in gaging the quality of the
consolidated composite specimen.

7.6 Discussion of Consolidation Experiments :

The consolidation experiments led to the development of an operating curve
for the manufacture of void-free composite parts. For a given fiber volume fraction
in the prepreg tape, as consolidation pressure increases, void content decreases until
an optimum pressure is reached which results in a void-free part. Above this value,
resin bleeds out of the part with increasing pressure finally resulting in a damaged
specimen as the fibers flow out of the part along with the matrix. The optimum
pressure required for consolidation increases with decreasing fiber volume fraction in
the composite if temperature and consolidation time are kept constant. The relative
crystallinity of each specimen stays approximately constant if the cooling rate during
the consolidation cycle is controlled between 10-20°C/min. Consolidation cycles are
shown to be simple and require the use of temperatures above the softening or
melting point of the polymer, an optimum pressure which depends on volume
fraction of fibers in the composite (for a given matrix at constant temperature and
contact time) and a contact time which allows for intimate wetting between interfaces
and interdiffusion of polymer chains across the interface. Intimate contact is the
rate-determining step in the consolidation of polyamide-carbon fiber composites.
Image analysis and fracture toughness testing of the specimens were effectively used
to gage the efficiency of the consolidation cycle. There is good correlation between

the quality of consolidation as characterized by ONVFA (fiber-matrix volume

172

fraction, void content) and the fracture toughness of the specimen, the latter

decreasing with increasing void fraction in the composite part.

Chapter 8
UNIFIED APPROACH

 

The entire experimental investigation was conducted using polyamide particles
and carbon fibers. However, the principles involved in the manufacture of
polyamide-carbon fiber composites can be applied to any other fiber-matrix
combination. This section lays down general guidelines for the selection of process
parameters in order to be able to pre-impregnate any reinforcing fiber with any
thermoplastic matrix.

8.1 Fiber Motion :

The fiber motion system may need to be optimized in terms of its PII) control
parameters to ensure synchronous speeds of the nip rollers. If an alternative system
which senses tow tension to control speed of the takeup drum is used, then it has to

be calibrated for tow tension as a function of pulling force.

8.2 Spreader :

The frequency at which the reinforcing fibers absorb the most energy and the
minimum amplitude at which they respond quickly to instabilities in the system are
measured for each type of reinforcing fiber. These parameters can be used for the
spreader regardless of the number of fibers/tow if sufficient surface area is available

for spreading.

173

174

8.3 Aerosolizer :

The natural frequency of the system which includes the chamber and the
weight of the powder on the lower diaphragm is determined prior to each run. The
maximum sound intensity inside the chamber that does not permit sonic
agglomeration is determined by a initial series of test runs on the powder being used
for prepregging. An Operating curve which gives the particle pickup as a function of
sound amplitude at the resonant frequency and tow velocity is empirically generated

as an aid in setting aerosolizer conditions for each prepregging run.

8.4 Heater :

A fundamental study of coalescence times in the heater is the first step in
deciding residence times of the impregnated fiber tow in the heater. An operating
envelope for the heater should define the maximum possible tow speed for each
temperature at which the heater is maintained, up to the matrix degradation
temperature. This residence time would ensure that the particles sinter, coalesce and
begin to form droplets on the fibers before the prepre g tapes exit the heater. The
quality of prepreg tapes during test runs with the predicted residence times would
further help in defining the control process. The findings of the coalescence study
will also be of value in deciding whether the fiber-matrix interface has to be modified
to promote better wetting which is essential in order to make high quality prepreg
tapes.

Table XVIII is a summary of the key properties and process parameters for
each unit operation in the powder prepregging process. In general, the process in its
present configmation can be easily adapted to make prepreg tapes with any fiber-
matrix combination. Most of the experiments described above were demonstrated in

this investigation and can be performed on other materials without expending a

175

TABLE XVIII. UNIFIED APPROACH - POWDER-PREPREGGING PROCESS

 

Unit Operation Key Properties Process Parameters

 

 

Fiber motion * Tow weight/length * Proportional, derivative and integral
constants for speed control

Spreader * Type of fiber * Natural frequency,
* Minimum amplitude
Aerosolizer * Particle size * System natural frequency
* Charge-to-mass ratio * Maximum amplitude
* Hausner ratio * Operating curve for particle

pickup vs tow velocity, amplitude

Heater * Convective heat * Operating envelope - coalescence times
transfer coefficient vs heater temperature

* Particle size

* Matrix viscosity

* Spreading coefficient

 

 

 

 

significant amount of effort. Key material properties that need to be measured or
calculated are particle size, fiber diameter, fiber- particle interactions in terms of
electrostatic attraction, matrix viscosity, spreading coefficient of the matrix on the
fiber and the convective heat transfer coefficient to the impregnated tow inside the
heater. Consolidation of these prepreg tapes to make void-free parts requires the use
of heat and pressure in simple processing cycles that can be determined by a set of
consolidation experiments to result in an operating curve such as the one developed

in this investigation (Figure 60, page 162).

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Chapter 9

 

CONCLUSIONS AND FUTURE WORK

The conclusions that can be drawn as a result of this investigation are :

(1) The dry powder prepregging process developed in this investigation is ca-
pable of impregnating reinforcing fibers with any desired volume fraction of
matrix. It is independent of matrix viscosity, does not use any solvents, relies
on the naturally high charge-to-mass ratio for adherence of fine polymer parti-
cles to fibers and results in the manufacture of prepreg tapes in which each
fiber is intimately wetted by the polymer matrix. The prepreg tapes are almost
as flexible as the reinforcing fiber tow with better handling properties. The
tapes are also tacky (sticky) because of the roughness induced by the presence
of droplets on individual fibers or clusters of fibers and hence do not move re-

lative to one another during the layup procedure prior to consolidation.

(2) The key elements of the process are : (l) The use of fine particles rough-
ly of the order of dimensions of the reinforcing fiber, (2) the aerosolizer which
delivers a controlled concenu'ation of fine particles to the fiber tow, (3) the
spreader which spreads fiber tows to a width so that individual fibers are ex-
posed, and (4) the heater where the particles coalesce to form droplets on the
fibers.

(2a) It is extremely difficult to fluidize cohesive polymer powders less than 30

176

177

microns in size. The bed profile for such powders includes a defluidized region
near the distributor where cracks/channels form and a bubbling region above
where bubbles disrupt crack formation and ensure that the particles remain in a
fluidized state. The height of the defluidized region increases as particle size
goes down. Good control over fluidiution parameters like entrainment rate and
bed height is not possible in this particle size regime.

(2b) The aerosolizer which utilizes acoustics to provide a buoyant force to the
particles is a stable entrainment system which can provide an aerosol of con-
stant particle concentration for extended periods of time. It operates best at its
natural frequency below sound pressure levels at which acoustic agglomeration
becomes a problem. Sonic agglomeration increases with decreasing particle

size for the same sound intensity levels inside the chamber.

(2c) The spreader which works on the principle of acoustic energy is shown
to be a reliable system to spread collimated fiber tows into their individual fila-
ments. It works best at the natural frequency of the reinforcing fibers above a
threshold value of sound pressure in the region over the speaker. This thres-

hold value is set by the amplitude of the sound wave metered to the speaker.

(2d) Coalescence of particles on fibers is a sequential process which
comprises of .heat transfer to the impregnated fiber tow, interparticle sintering,
film formation and retraction of the film to form stable droplets on fiber sur-
faces. Each step has a resistance associated with it and coalescence time is the
sum of all the individual times. The material parameters which control each
step are the convective heat transfer coefficient (heat transfer), matrix viscosity
and particle size (sintering), and the spreading coefficient of the polymer melt
on the fiber surface (film and droplet formation).

178

(3) Simple consolidation cycles can be used to make void-free composite
parts from the flexible prepreg tapes manufactured by the process. The require-
ments for an optimum consolidation cycle are the use of temperatures above the
melting or softening point of the polymer, and consolidation pressures at which
intimate contact of the polymer interfaces and interdiffusion of polymer chains
across these interfaces are both given sufficient time to occur. The first step of
intimate contact is the rate-controlling step in the consolidation of polyamide-

carbon fiber composites.

The following recommendations for future work are made as a result of this

investigation -

- The behavior of the aerosolizer can be enhanced with a range of improve-
ments which include an anti-static coating on the chamber walls, a constant
feed of particles to the packed bed at the base of the chamber, powder recovery
and a deionizer unit online to the Realtime Aerosol Monitor to neutralize

charge on the particles.

- Performance can be enhanced by a modification whereby the aerosolizer
feeds into an impregnation chamber where the spread fiber tow is impregnated
with the entrained particles. Advantages include selective entrainment out of
the aerosolizer which would exclude agglomerates and the possibility of ease of
operation at constant concentrations by controlling the flow rate of entrained

particles into the impregnation chamber.

- A fundamental study should be conducted into the behavior of the aero-
solizer. It should take into consideration various factors such as sound attenua-
tion inside the chamber, shear stresses imposed by flow of the entrained parti-

cles, particle size, interparticle collisions, acoustic and hydrodynamic forces in

179

order to predict particle concentration profiles in the chamber. An experimental
part i.e. measurement of sound pressures and particle concentrations at various

locations inside the chamber should be conducted to verify and iterate on the
model proposed by theory.

- The charge-to-mass ratio of the polyamide particles is inherently high so
that the particles adhere to the electrically ground carbon fibers without the use
of an external charging device. This behavior needs to be understood with the
help of a method to measure the triboelectric charge of the powder. Such
measurements will aid in the understanding of charge-to-mass ratios essential
for the natural adherence of particles to fibers in the process and hence lay
down guidelines for prepre ggin g with other fiber-matrix combinations.

- Interparticle forces in fine polymer powders lead to agglomeration of the
particles to form clusters. A method to gage the magnitude of interparticle
forces will help in understanding the behavior of different polymer powders in
the aerosolizer. A powder tester can be used to measure the ratio of the tapped

to loosely packed density (Hausner ratio) of a powder.

- The spreader was used to spread unsized carbon fibers. The dynamics of
spreading other reinforcements such as glass and kevlar fibers may be different
and may require pretreatment to remove sizings and surface finishes. The unit
operation of spreading and the absorption of acoustic energy by different
fibrous reinforcements at their natural frequencies needs to be explored in a

systematic manner.

- The fiber motion system in its present configuration can be improved by
insralling the second set of nip rollers away from the heater to prevent matrix

loss by attrition. An alternative system for fiber motion which may perform

180

better than the existing system includes the fiber spool to be mounted on air
bearings and the tension controlled between the spool and the takeup drum.
This system would circumvent the use of nip rollers with synchronous control
of motor speeds which is a difficult operation and require only one motor driv-
ing the takeup drum.

- The replacement of the heater with a through feed muffle furnace to en-
able prepregging with high temperature polymers.

- Further work in the coalescence process to study the effect of capillarity
between adjacent fibers on flexibility of the prepreg tapes. The relationship
between tape width and flexibility also needs to be explored.

- Investigate the effect of consolidation time and temperature on the conso-
lidation process. A complete study into consolidation would attempt to reduce

consolidation times for void-free consolidation and thereby reduce labor costs.

- The final issue which needs to be addressed is the question of scale-up of
the process to manufacture prepreg tapes at feed rates which would make it

competitive with existing processes.

 

APPENDICES

181

 

Appendix A
ENGINEERING DRAWINGS

This appendix contains the engineering drawings of the different equipment
designed for the process. They include the following : aerosolizer (figures la-d),
spreader (figures 2a-b), nip rollers (figures 3a-g), bearing mounts for fiber spool and
takeup drum (figures 4a-d), linear motion of takeup drum (figures 5a-k) and
consolidation mold (figures 6a-b).

182

 

183

 

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Figure 1a. Aerosolizer (all dimensions in inches).

 

184

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185

 

 

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Figure 1d. Plexiglass casing for aerosolizer (encases the plexiglass
tubeoftheaerosolizerandhasanexhaustfanwithan
air filter attached to the backface).

3 231'

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187

 

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into sides

 

 

 

 

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188

 

 

 

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190

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Figure 6a. Consolidation mold (All dimensions in inches).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Smooth finish (the lies in
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Figure 6b. Consolidation mold (See figure 24 ).

Appendix B
AUTOMATION

 

This appendix discusses the automation scheme implemented for the process
both in terms of hardware and software. The different inserts include a description
of the hardware, the electrical diagrams, the component locations in the Composite
Line Controller or CLC, cable descriptions and the two main software programs clc.c

and routinesc which control the process.

203

204

1. Hardware Description for Composite Line Controller :

The hardware of the Composite Line Controller is composed of several subcircuits: two motor
power controllers, two pulse counters, an oven and track controller, two audio volume
cmuoflasatapeheightsensmmdmkamspoolwnnoua,arflavarietyofmwrfacem
Mamiycunponem

InterfacingtotheA/Dboardislargely oonnolledbya4-bitdatabusand4-bitaddressbus.
'Iheaddressbuscontmlswhichregister(readorwriteonly)isacfiveandthedatabustransfers
data.ThetwobusesareimplememedusingtheSbitinputandsbitoutpmpomontheA/D
boudA74lSlS4danuldplexerisusedmdecodedwaddressbusEachaddreuwiflbe
referred to as a register throughout the documentation.

The motorpower controllers operate onapulse-width modulation scheme. The4 MHchock
comprisedofU30andXTALlisdividedbyaleitcountertoyieldareferenceclockfor-the
motor power controllers. Each time the 12 bit counter overflows. it pulses the LOAD line on
thetwomotoreountersloadingthenumberstoredinthepreloadregism(4-6,7-9).'Ihemotor
countersthencountupuntiltheycarry(at4096).Dmingdusfiacdmofeachcyclethemotm
power transistors are“ enabled. Thus pulse-width modulation control of each motor is obtainable
with l2-bit resolution. The twomainroller motorsareeontrolled bythisscheme; thetakeup
mooliscontrolledbyasimplerschememescribedlater).

InorderfortherollermomtorunnhreeotherconditiommustbemetFirst.ageoeralmotor
emble bit (register 10, bit 0) must besetby software. In addition, theMOTORS switchon the
frontpanelmustbeon.F'mally,thesoftwaremustbeperiodicallypollingregister3(pulse
counterlTRANSFERseebdow).1hislasteondidonatsmesthadwmomstopmdieevent
of software or computer failure.

nepulsecountercirautsrespondwmeopdcaldiscsmomwdmmetwomomUnda
namaloperation,eachcounterirmmentsuponreceivingapulsefiunitssensu'.Whenthe
clcsoftwarewishestoreadthevalueinthecounters,itpulsestheTRANSFERlineaegistu3
or13),enablingatransferoftheoounttotheholdingregisters.Whenthenextpulsearrives,
theoumisu'ansfenedandthenumberlisloadedintothecounter.Thesoftwareisthenfreeto
readthecountfmmtheholdingregisters(land2,lland12).

RegisterOistheonlyotha'readableregisterondteboardltholdstwostatusbitsfromeach
pulsecotmtercireuit:anoverflowbigwhichsignifiesthatmorethanZSSpulseswerereceived
wuhomdwmgistabdngreadbysoftwamandauansfamquenimanpletebitsetfiomthe
timeatransferisrequesteduntilitiscompletedbythereceptionofanewpulsefromthe

'Ihetrackcontroller cireuitisrelatively simple. Two switches,oneateachendofthetrack’s
travel. cause a track direction flip-flop to toggle. This drives a direction-reversing relay
mmmtedinsidetheuack speedcontroller box.‘Ihetrackdrive motoriscycled on and off(as
per motor speifiations) by a relay driven by bit 2 of register 10. Mounwd on the linear rack is
aslacktakeupspoolwhosemomrisdnvenbytwOpowa’uansistomandarheostaLthnbit
3ofregister lOis set, the motorrunsataratedeterminedby its positive supply voltageand
the position of the rheostat (mounted on the omposite processing line’s frame). When tape
slxkissemedbuweendwopfimlsam.modwrmismrismabled,bymssingdwmemm
andoperatingthetakeupmotoratahigherrateuntiltheslackisnolongerpresent.

205

'lheovencontrolcircuitryisamixofdigitalandanalog.’lhedifferentialtemperattneoutput
fromtheOmegacontrolboxisconvertedtosingle-endedbyasimpleop—ampcircrfiuandbd
intoanalog inputOJhesofiwammmdetermineswhentheovwshouldbecycledonmdofl',
andsetsorresetsbitlofregister lOaccordingly.’l‘hisintumoveridestherelaydriverinthe
Omegacontrollertotmnmeovenonandoff.

Otheranalogcircuitry inchrdesmeaudioconuolcircuitsandSPLandparticlemnuation
circuits.ThelanertwomemlyauenmtemeSPLandparddeconeenuadoninptmfiommetwo
meterssothattheyfaflwimindieo-SvoltmngeoftheA/Dboard'lhetwoaudiocontrol
circuitsareidenticalindesign.'lhetwoanalogoumutsoftheA/Dboardaresuppliedtothe
Volumepins(l)oftheDM205audiocontrollerchips.'Iheremainderofthesupportciratitry
ensmesthatthesignalspassundistortedfiewidtombassm'uebleboost)throughtheDMms.
Anopmnpmmeoutpmrenaudwmiginalvolmgelevelofmeaudiompmwcanpmsac
fortheattenuation oftheDMZOS’s.

FomgreenstamslampsamnwuntedoamefiontofthecmndlaboxlheCABlBlampis
illuminatedwheneverregister lSismtbeingread.Ifthecableisdisconnected,theoontroller
defaultstoreadingregiswr lSandthustheCABLElampwouldbeoff.NotethattheCABIE
lampbeingoffmaybeduetootherproblems(smhassofiware).'I‘hePROGRAMlampison
whenevertheclcprogramisreadingregistero.‘lheclcprograrnalwaysremrnstoreading
mgistaOahaithasaccessedanyodwmgistuzhenceiftheCABmhmpismmdthe
PROGRAMlampisoff,thesoftwarehascrashed.’I‘heLOOPlightisilluminatedforZOO
miflisecmdsaftaexhdmedwmgramreadsmgista3.“fismgistaismofdwptdse
comterregistersformotor1.1'heLOOPlightthusindicatesthatthemaincontrolloopinthe
programiscbeckingdwpulsemmtaspaiodicdlyfihelDOPthdmmabludnmom.
WheneverdeLOOPlightisoff,motmsland2amdisabbdwprevemmem&omnmning
whentheyarenotbeingmonitoredbysofiware.

206

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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.1}. ___——————_———_—————__——————————————————————————— J

CO

212

C

Integrated Circuit Component Locations

 

 

 

 

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LINEAR RACK |Ul=74Ls74| . |UZ:74L8123| |U3:74L5154| [04:74L5367l
CONTROL ¢ + . + e + 4 + +
. |U5:74LS74| |UG:74L5161| |U7:74L5374|
PULSE INPUT BUFFERS . + —¢ ¢ e i 4
. [038:74L514l [08:74L5161I |U9:74Ls374|
. |UlO=74LS74| [011:74L8161| |012:74L5374|

AUDIO CONTROL .
+ ¢ ¢ . PULSE # i # %
U36:DH205|'|U37:DM205| . COUNTERS |013z74L5161| |014:74LS374|
# + TAPE . + 4 + ¢ ¢ ;
[039:CD404SI SLACK . |015:74L8193| |U16z74L8193| |U17:74L5174|
[018:74L8193l |019z74L5193| |020:74L5174|
[021:74L8193l |022:74L8193| |023:74L5174|
MOTOR CONTROLLERS + + ¢ ¢ ¢ #
AND DRIVERS |U24z74HC08| [025:74L8193l [026:74LSI7SI
|U27:74L510| |028:74L5193| [029:74L817SI
|U30:74LSO4| |U31=74LSI93| |U32:74LSl75|

:OVBN CONTROL:

 

U35:74L8174

 

+— 4+-
+*-+

+——————-——————-———————--—-——————-——————-——————-———-——— +

 

213

COMPOSITE LINE CONTROLLER

Internal Cables Description

Digital Cable (D825 Female on Main Board, toward rear)

 

 

 

 

 

 

 

 

l Pin Function Pin Function
1 I07 14 Digital Gnd
2 I06 15 Digital pm: (10V)
3 IDS 16 Cable Status
4 ID4 17 Program status
5 Ina—Read 18 Loop Status
6 Inz-Read 19 Slack Status
7 ID1-Read 20 Motor 4 dir
8 IDO-Read 21 Motor 4 on
9 Motor En SH 22 Motor 1
10 Oven Relay 23 Motor 2
11 Limit Sw1 24 Motor 3 High Speed
12 Limit Sw2 25 Power Gnd
13 Motor 3 Constant
Analog Cable (0325 Female on Main Board, center)
| Pin Function Pin Function
1 Part. Conc 14 A02 (Part. Conc.)
2 SPL 15 AD3 (SPL)
3 Oven Temp. 16 AD4 (Oven Temp.)
4 Audio Src. 1 17 ADO (Audio 1)
5 Audio Amp 1 18 A01 (Audio 2)
6 Audio Src. 2 19 DAD (Spkr. 1 Vol.)
7 Audio Amp 2 20 DAl (Sp . 2 Vol.)
8 Dist Sns 1 Pwr 21 ID3-Write
9 Dist Sns 1 Pulse 22 ID2-Write
10 Diet Sns 2 Pwr 23 IDl-Write
11 Dist Sns 2 Pulse 24 Ibo-Write
12 Height Array Pwr 25 Height Array Pulse
13 Analog Gnd

 

 

214

COMPOSITE LINE CONTROLLER

External Cables Description

 

Cable Conductors Connectors (Unit:Box) Length (in) Cable 1

Motor 1 2 - : -- 139
Motor 2 '2 - : -:- 8-pin DIN 101 1
Motor 3 2 - : -l 125
Part. Conc. 2+shield ? : 1/8" 3C 105 2
Sound Level 2+shie1d 1/a~ 2c : 1/8” 3c 129 3
Temperature 2+shie1d ? : l/B" 3C 114 4
Oven relay 2 1/8" 2C : 1/8" 3C 114 5
Power- low 2 Banana : Banana 89 6
Power- high 2 Banana : Banana 81 7
Audio Src. 1 1+shield Banana : Phono 7o - 8
Audio Amp 1 1+shie1d 1/4” : Phono 80 9
Audio Src. 2 1+shie1d Banana : Phono 70 10
Audio Amp 2 1+shie1d Phono : Phono 80 11
Dist Sns 1 2+shie1d - : 1/8" 3C <170 12
Dist Sns 2 2+shie1d - : 1/8" 3C <130 13
Eeight Array 2+shie1d - : S-pin DIN <105 14
limit SW 1 2 - : 1/8" 2C <100 15
Limit Sw 2 2 - : 1/8” 2c <120 16
Motor 4 dir 2 ? : -- 91

l- 5-pin DIN 17
Motor 4 on 2 ? : -- 91

Motor 4
2 Speaker 1

Speaker 2

(pre-existing wiring)
(pre-existing wiring)
(pre-existing wiring)

215

2. Software Description for Composite Line Controller:

Thebmdwmfordwprooessiswnuolledbymeansoftwoprogrmsdccmdmudnac
writteninClanguage. msecmdprogramroutinesccontainsalistofsubtoutineswhieh
commuMcawmmmeconuolhmdwamwhilemefirstprogmmdccisthemainptogmn
whichacquiresdataandoonuolsthepocess.

2.1 clc.c:

Thisprogramisthemainmodule. Itacoessestheoontrollerboxthroughroutinesdefinedin
routinesc. A sectional description follows:

main() initialization. main program loop.

ntn( ) do one run bamd on current settings.
(includes PID speed/slack control)

set_oven( ) cycle the oven based on current and desired temperature.

set_track() turnthetrackon and offat intervals.

batch() doseveralrunsbasedonaninpmfile.

read_input_data( ) read the input file data.

all__done( ) exit the program gracefully.

change( ) change the current settings.

menu( ) display menu and return choice.

tick() executed every timer tick (1/182)sec.

power( ) raise a number to a power.

keywait() waitforakeytobeprecsed.

2.2 Routinesr:

Thismodrfleoontainsmufineswhichpmvideaocesstotheflneandwhichwillnothavetobe
changed unless the hardware scheme of the controller changes. Understanding the logic behind
theeerequiresanunderstanding ofthecontrol hardware.

(Xalor2formotornumberorspeakernumber.)

get_counterX( ) get # of counts from slotted disk X. (0-255)
set_motorX( ) set motor speed X. (04095)

get_register( ) get data from a control register. (reg 0-15, data 0-15)
set_register( ) send data to a control register. (reg. 0-15, data 0-15)
set_volumeX( ) set volume of speaker X. (0-4095)

get_conc( ) get particle concentration in chamber. (0-4095)
get_spl() get sound pessure level in chamber. (0-4095)
get_temp( ) get temperature in oven. (0-4095)

oven_on() turn oven on.

oven_off( ) turn oven off.

motors_on() enable all motors.

motors_off( ) disable all motors.

track_on( ) tum track controller on.

track_off( ) tum track controller off.

a2d_init( ) initialize AID system.

ctrlc( ) handle control-c interrupt.

216

Program 1 : clc.c

217

lt Electronic & Computer Services */

It Composite Line Controller Software x/

/t Frank Palazzolo 6/7/90 */

tinclude <stdio.h> It Standard Library Modules x/

tinclude (signal.h) It (Described in Microsoft C manual) 1/
ninclude <stdlib.h) /* Provides support for all string, */
tinclude <process.h> It dos, bios, and graphics functions x/

linclude (dos.h)

{include (graph.h)
{include <ctype.h>
{include <bios.h>
tinclude (nath.h)

int get_counter1( )3 It Function Prototypes for routines.c r/
int get_counter2( )3 /t (See routines.c for full descriptions t/

int set_notor1(int)3
int set_notor2( int);
int get_register( int):
void set_register( int, int )3
void set_volune1(int)3
void set_volune2(int)3
int get_conc( )3

int get_spl()3

int 90t_teIP( )3
a2d_init( )3

int ctrlc( )3

void oven_on( )3

void oven_off( )3

void notors_on( )3
void notors_off( )3
void track_on( )3

void track_off( )3

/t Function Prototypes for this nodule t/
l: (Descibed in detail at beginning of each routine) I/

void interrupt far tick()3
void diag( )3

void run( )3

void change( )3

void batch(.)3

void alldone( )3

char new( )3

void read_input_fields( )3
int read_input_data( )3
float set_oven( )3

void set_track( )3
unsigned long power(int, int):
void keywait()3

ls Global Variable Definitions t/

unsigned long counts; /3 lhis is increeented every timer tick (1/18.2 s) t/

unsigned long ovencounts; It Sale as counts. but set to zero by set_oven #/
. /* twenty_seestl/mj sees. (”20 s) */
unsigned long bigcounts; It Increnented every 20 secs by set__oven t/

unsigned long twenty_secs; /* Twenty secs of timer ticks x/
unsigned long oven_on_width3 /x Oven on pulse width (0 to twenty_secs) */

void (interrupt far xoldvector)()3
int int_flag3
struct paran (

float length;
float linespeed;
float pconc;
float vspr3
float veer;
float temp;

}

struct parse *settings3

FILE *fpin, *fpout:

char tinfile = 'NONAHE.IN'3
char toutfile = 'NONAME.0UT'3
int lineno;

struct dosdate_t currdate:
struct dostine_t currtine:
It Hain Program Loop x/
nain(int argc, char xargvfl)
{

int i3

char choice;

oven_off( )3
notors;off()3
track_off( )3
twenty_secs = 3643
oven_pn_width = 03
counts = 03
bigcounts = 03
ovencounts = 03

218

It Space to save old jump vector s/

/t Set to one every other tick (1/9.1 s) r/
/* Current settings structure */

/¥ Run Length - Not Used t/

/* Line Speed *I

I: Particle Concentration - Not Used t/

It Voltage Level for spreading speaker x/
ls Voltage Level for Aerosolizer x/

/* Oven Temperature :1

It Current settings t/
It File Pointers */
/x Default file nanes t/

It Input file line number x/
It Date and Tine x/

/# general integer variable x/
/* selected nenu choice t/

/* Shut off everything */

It twenty seconds (in timer ticks) x/
/* oven off (cooling) */

/* initialize counters */

It Set up I/O file routine according to conaand line argueeents t/

switch (argc) {

case 3: outfile = argv[2]3
/* Custom outfile & infile x/
case 2: infile = argv[l]3
It Only custom infile */
break;

case 1:
case 0: break;

default: printf('Usage: clc (inputfile) (outputfile)\n')3
printf(' defaults: NONAHE.IN & NONAHE.OUT\n')3
/* Improper nunber of arg’s - exit t/
exit(0)3

/x
/*

Install interrupt handler for Ctrl-C
Program will jump to ctrlc() when ctrl-c is hit 1/

*/

if (signal($IGINT,ctrlc) == (int(*)())-1) {
fprintf(stderr,'Couldn’t set SIGINT\n')3

abort()3

219

float f.dummy3 /3 general purpose float’s */

int loopdone = 0; /1 flag x/

unsigned c3 It keyboard char */

float conc, spl; /* Current particle conc., spl */

float speedl, speed23 It instantaneous motor speeds (cm/sec) x/
int n3 /* printf every 1/18.2 x 2“n x/
int nfpr; It fprintf every 1/18.2 * 2“nfpr */
int num3 It number of speeds taken t/

float suml, sum23 /* sum of motor speeds */

float sumsql, sumsq23 It sum of motor speeds squared x/

float avgl, avg23 It average speeds x/

float stdl, std23 It standard deviations t/

unsigned long pmask, pmatch3 It mask and counts to match for print loop r/
unsigned long fmask, fmatch; It mask and counts to match for fprint loop */

ls Controller variables */

float
float
float
float
float
float
float
float
float
float
float
float
float
float

double

float

It

01,011,012; lt u(k). u(k-1), u(k-2) for motor 1 x/

02,021,022; /* u(k), u(k-1). u(k-2) for motor 2 t/

Uset; I: Set point for current linespeed (counts/tick) t/
A1.A2.A33 It Coefficients for PID controller #/

81.82.83; It (Same for motor 2) */

slack; /x cm’s of slack x/

slackedj; It Adjustment to Uset for motor 2 (counts) */
0M1.DM23 It Functions of 0 to eliminate derivative kick */
DELI: It Delta T = 1/9.1 secs */

P1.P23 It y(k) for motor 1 a 2 t/

El.E2,633 /* e(k), e(k-1), e(k-2) for motor 1 */

F1,F2,F33 It same for motor 2 */

K1.TIl,TDl3 /* Gain. Taus for Int. 1 Diff. - motor 1 */
K2.IIZ.TDZ3 /* Same for Motor 2 */

sqrt(double)3

x3

Speaker coefficients r/

I: After calibration: t/
It ln(Voltage) = spr21f‘2 + sprltf + spro 1/
l: where f is the setting value r/

float

float

spr2 = 0, spr1 = 810, sprO = 20903
aer2 = 0, aer1 = 810, aerO = 20903

/* Printf run stats every ~3.5 seconds x/
l: Fprintf run stats every ~28 seconds */

n = 73

nfpr = 103

pmask = (unsigned longXpower(2.0,(double)n) - 1.0)3
pmatch = pmask - 23

fmask = (unsigned long)(power(2.0,(double)nfpr) - 1.0)3
fmatch = fmask - 43

It Print heading */

_clearscreen( _GUINDOV )3
printf('Composite Line Controller

printf('

/* Print current date & time to output file */

Electronic & Computer Services - M.S.U.\n')3

220

/* Install interrupt handler for timer ticks :/
/* Program will jump to tick() every 1/18.2 secs. t/

oldvector = _dos_getvect(8)3
_disable;
_dos_setvect(8.xtick)3
_enable;

/r Set default settings x/

settings = malloc(sizeof(struct param))3

settings-liength = 3003 It cm to run (Not Used) */
settings-)linespeed = 2; /* cm/sec */
settings-)pconc = 503 /* mg/m‘3 (Not Used) x/
settings-)vspr = 5; /* Volts */

settings-)vaer = 5; /t Volts x/
settings-)temp = 2103 /* degrees C */

/* Open files t/

if((fpin = fopen(infile,‘r')) == ML) (
printf('zs could not be opened for reading.\n',infile)3
alldone( )3

} .

if((fpout = fopen(outfile,'w')) == ML) {
printf('zs could not be opened for writing.\n',outfile);
alldone();

}

/* Menu Loop x/ y
/* Based on menu choice - jump to appropriate routine 3/

while (1 == 1) (
choice = menu()3
switch( choice) (

case ’1’: rut-()3
break;
case '2': batch( )3
break;
case '3’: chatted);
break;
case ’4': alldone();
break;
}
l
l
I! run() - Do one run with current settings */
/* saving pertinent info to a file. t/
/* This routine uses a PID controller for x/
/* Motor speed control, takes care of slack *1
l: control. and calls set_pven & set_track x/
void run( )
{
fdefine MCONST 14.652 /* conversion from ticks/(1/9.1) sec to cm/sec x/
int i, v; I! general purpose int’s */
int tempset; /x set point temp (0-4095) x/

int tempnow; /* current temp (0-4095) t/

It

/*

/*

221

_dos_getdate(&currdate);

_dos_gettimm(&currtime)3

fprintf(fpout,'\'zs:td\' \‘22d/12d/t4d\' \'22d:22d:22d\'\n',infile,lineno,
currdate.month,currdate.day,currdate.year.currtime.hour.
currtime.minute,currtime.second)3

/* Set oven to initial temp - runs until key is pressed t/

printf('Regulating oven temperature - Please wait...\n');
counts = 0; /t Reset Counters x/
ovencounts = 0;
loopdone = 0;
while (loopdone == 0) {
int_flag = 0;
while (int_f1ag == 0);
int_flag = 03
if ((counts & 7) == 7) (
I: try about once every half second to update us on temp. stats. x/
f = set_oven( )3
_clearscreen( _GUINDOU )3
printf('Set Oven Temp = z.1fc Current Temp = z.1fC\n',
settings->temp,f)3
if (_bios_keybrd(_KEY8RD_READY) != 0) {
. c = gate“ )3
loopdone = 13

/* If key pressed - oven ready 3/

}

Initialize variables for motor control r/

K1 T11 T01 13 /* Default Controller Coefficients x/
K2 TIZ T02 13

P1 = P2 = 300; l: Initial output pulse-width x/

DELT = 1/9.13 . /* Delta T, (tau) = 1/9.1 */
printf('K1?\n'); l: Read in controller coefficients x/
scanf('zf',&K1)3

printf('TIl?\n')3

scanf('zf'.&TI1);

printf('TD1?\n')3

scanf('zf',&T01)3

printf('K2?\n')3
scanf('zf',&K2)3
printf('T12?\n')3
scanf('2f',&I12)3
printf('T02?\n');
scanf('zf',&T02);

Turn on the speakers to their proper volume *I

f = log(settings->vspr);

v = (inthperfxflsprlxflsprO);
set_volume1(v)3

f = log(settings->vaer);

v = (intXaer2:frf+aer1*f+aer0)3
set_volumez( v )3

set_yolume1((int)settings-)vspr)3

222
set_volume2((int)settings-)vaer)3 */

/t Initialize error terms to zero t/

62
F2

El
F1

II II
'71
(A)
I
5D

I! Reset statistics variables */
num = 03

suml = sum2 = 03

sumsql = sumqu = 0;

/x Set up PID coefficients r/

A1 = K1x(1 + DELTI(TII*2));
42 = K1*(-1 + DELT/(TIl*2));
A3 = K1x101/DELT;

81 = K2*(1 + DELT/(TIZ*Z))3
B2 = K2*(-1 + DELI/(11212));
33 = KZxTDZ/DELT3

I: Set slack to zero x/

slack = 03

slackadj = 03
011 = 012 = 03
021 = 022 = 03

It clear counters */

01 = (float)get_counter1()3

02 = (float)get_counter2();

_disable;

ovencounts = 03 /* Reset counters */
int_flag = 0;

_enable:

/* Clear screen x/
_clearscreen( _GUINDON )3
/r Set the linespeed set point x/

Uset = settings-)linespeedrMCONST3
motors_on( )3
loopdone = 03
while (lloopdone) (
if (int_fla == 1)
printf('xxttt Latency xtxxx\n')3
while (int_flag == 0); /t Hait for end of time period t/

It Get current speeds t/

01 = (float)get;counter1()3
02 = (float)9et;counter2()3
int_flag = 0; It Reset flag for next cycle t/

/* Check for errors x/

It

223

if (01 == -1) {
01 = 255; /x overflow t/
printf('Error - 80x Disconnected or not turned on.\n')3
keywait()3
100pdone = 13

)

else if (02 == -1) {
02 = 255; /* overflow t/
printf('Error - Box Disconnected or not turned on.\n');
keywait()3

loopdone = 13

}

if (UI == ~2) {
printf('Motor 1 Stalled\n');
01 = 0;

}

if (02 == -2) {
printf('Motor 2 Stalled\n');
02 = 03

}

l: Calculate Output x/
I: PID with derivative kick control (0M1, DMZ) */
l: and bounded by slack control */

E3 = E23

£2 = E13

El = Uset - 01;

F3 = F23

F2 = F1;

F1 = Uset - 023

0M1 = 01 - 2*011 + 0123

0M2 = 02 - 2*021 + 0223

P1 = P1 + A1xfil + A2362 - A3XDM1;
P2 = P2 + 81*F1 + 82tF2 - 83*DM23

/* Slack adjustment t/

slack = slack + (01 - 02)/MCONST3
if (slack ( .5)
slackadj = -53
else if (slack ) 2)
slackadj = +53
else
slackadj = 03

It If slack is too small or too great - exit x/

if ((slack ( .3) :: (slack ) 5)) (
set_motor1(0)3
set_motor2(0)3
oven_off( )3
printf('Slack is zfcm, shutting line off\n',slack);
keywait()3
loopdone = 13
l */

/3 Bound output x/

224

if (P1 > 4095) 91 = 4095;
if (P2 > 4095) P2 = 4095;
if (91 < 0) P1 0;
if (P2 < o) 92 o;

l: Time passes... */

012 = 011;
011 = 013
022 = 021;
021 = 02;

/x Convert speeds to cm/sec x/

speedl = Ul/MCONST:
speed2 = UZIMCONST:

It Keep Statistics t/
/t (Sums and sums of squares) x/

num = nun + 1;

sum1 = sum1 + speed1;

sum2 = sum2 + speedZ;

sumsql = sumsql + speedlxspeedl;
sumsqz = sumqu + speed2*speed2;

I: Every second or so, update oven 1 track settings */

if ((counts & 15) == 15) {
f = set_oven( )3
set_track( )3

}

/* Printf every 1/18.2 * Z‘n seconds x/

if ((counts & pmask) == pmatch) {
conc = ((float)get_conc())l20.48;
conc = ((float )get_conc( ))/20.483
spl = ((float)get_spl())/40.96+60.03
spl = ((float)get_spl())/40.96+60.03
printf('z.2f\tz.2f\tz.2f\tz.2f\tz.2f\n',speedl,speed2,f,spl,conc);

}

/x Fprintf every 1/18.2 * 2“nfpr here r/

if ((counts 1 fmask) == fmatch) {

conc = ((float)get_conc())/20.483

conc = ((float)get_conc())/20.483

spl = ((float)get_spl())/40.96+60.03

spl = ((float)get_spl())/40.96+60.03

if ((num != 0) && (num != 1)) (
avg1 = sum1/nun;
avg2 = sum2/num;
x = (float)((numxsumsql-sumlxsum1)/(num*(num-1.0)))3
std1 = sqrt((double)x);
x = (float)((numxsumqu-sumszum2)/(numx(num-1.0)));
std2 = sqrt((double)x)3

else
avg1 = avg2 = stdl = std2 = 0;

225
4d08 ettime(&currtime);
fprintf(fg
, currtime.hour,currtime.minute,currtime.second,
avg1,std1,avg2,std2,f,spl,conc);
printf('\'22d322d=22d\' 2.2f 3.3f %.2f 2.3f t.2f 2.2f t.2f\n',
currtime.hour.currtime.minute,currtime.second
,avg1,std1,avg2,std2,f,spl,conc);
num = 0;
sum1 = sum2 = 0;
sumsql = sumsqz = 03
}

/* Send new motor speeds */

set_motor1( ( int )P1 )3
set _motor2( ( int )900 )3

It Exit if key pressed :/

if (_bios_keybrd(_KEYBRD_READY) 1: 0) (
c=mme
loopdone = 13

l

I: Everything off t/

motors;off();
oven_off( )3
track_pff();
set_yolume1(0);
set_volumeZ( 0 )3

l

/t setgoven resets oven_pn_width to a number */
I: based on the oven temperature a the desired 1/
/x oven temperature. In addition. set_pven turns */
l: the oven on or off based on the current time */

It in the cycle */

float set_oven()

{
int tempset; Ix Temp. set point (0-4095) r/
int tempnow; /* Current temp (0'4095) ¥/
int temptemp; I: Temporary temperature *7
int temperr; It Flag for temperature error x/
int i; It general purpose */
float ovencutoff = 53 /* regulating window is +-5 degrees */
float reset = 0; It for fine tuning */
float conv = 3.482; /* conversion from degrees to read value t/
float factor - 1.00888; It correction factor and offset */

float offset = 0.71447;

/x Assuming sensor reads SmV/degree C */

tempset = (int)(convxfactorxsettings-)temp+offset)3
tempnow = 0;

temperr = 0;

l: Calculate new temperature by sampling */

out.'\'22d322d322d\' 2.2f 2.3f 2.2f 2.3f 2.2f 2.2f 2.2f\n'

226

temptemp = get_temp()3
for (i=03i(5;i++) {
temptemp = set_temp( )3
if (temptemp/conv ( 10)
temperr = 13
tempnow = tempnow + temptemp;
}
tempnow = tempnow/53
if (temperr) '
printf('Invalid Temperature Reading - Shutting oven off\n');

/x Set new oven_on_width x/

tempset = tempset + (int)convtreset3
if ((tempnow - tempset) ) (int)convxovencutoff)
oven_on_width = 03
else if ((tempset - tempnow) ) (int)conv*ovencutoff)
oven_on_width = twenty_secs - 1;
else
oven_pn_width = (tempset-tempnow)/(convxovencutoff)ttwenty_secs/2+twenty_secs/23

/* Increment bigcounts every 20 secs x/

if (ovencounts > twenty_secs) {
ovencounts = 0;
bigcounts++3

)

l: Turn oven on or off accordingly *I

if (temperr)
oven;off();

else if (ovencounts )= oven_on_width)
oven_off();

else
oven_on( )3

It Return converted temp 1!

return( tempnow/conv )3

}
I: set_track() turns the track on for 60 secs, then off for 20 x/

void set_track()

{
if (bigcounts ) 3)
bigcounts = 03
if (bigcounts > 0)
track_pff()3
else
track_on( )3

l

l: batch() reads in the data from the current input file. *I
/x The first line of the file is assumed to contain the field names. x/

227
/x All other lines are data, one run’s worth per line :/

void batch()
{
char c3
It Print header r/

_clearscreen( _Gwmoow )3
printf('Composite Line Controller Electronic & Computer Services - M.S.U.\n')3

printf(' \n\n')3
lineno = 13

/x Get the fields from line 1 */

while (read_input_data() != -1) (
run( )3

lineno++3

)

Ix read_input_data() reads directly into the x/
I: settings structure x/

int read_input_data( )

{
/* Read in the data *I
/* (aborting at EOF) */
printf('Reading from line 31d of file: zs\n',lineno.infile)3
if (fscanf(fpin.'zf',&(settings-)linespeed)) == EOF)
return( -1 )3
if (fscanf(fpin,'zf',&(settings-)vspr)) == EOF)
return(-1);
if (fscanf(fpin,'tf',&(settings-)vaer)) == EOF)
return( -1 )3
if (fscanf(fpin,'zf',&(settings-)temp)) == EOF)
return( -1 )3
}

It If you really want to, alldone() allows you to exit the program t/
It gracefully. 3/

void alldone()
{
char c3
printf('Are you sure?\n')3
c = (char)getche();
if ((c == ’Y’) H 6 == ’Y’)){
I: Ignore ctrl-c x/
signal(SIGINT,SIG_IGN)3
/t shut everything off x/

motors_off()3

228

oven_off();
track_off()3
set_volumel(0);
set_volume2(0);

/* reset timer tick vector */
_disable3

_dos_setvect( 8 .oldvector )3
_enable;

/* close files and exit 1/

fclose(fpin)3
fclose( fpout )3
exit(0)3
}
1
It Change() queries the user for new settings information and sets t/
It up the settings structure accordingly.
void change( )
{
char c;

I!

/x

float response;

_clearscreen( _GUINDON )3
printf('Composite Line Controller
printf('
printf('Line Speed is 2.1f cm\n',settings-llinespeed)3
printf(' New Line Speed (1-10)? \n');
scanf(‘tf',&response)3
fflush(stdin)3
if ((response < 1) :: (response ) 10))
printf('- Unchanged -\n')3
else
settings->linespeed = response;
printf('Voltage Level for spreading speaker is 2.1f V\n',settings-)vspr)3
printf(' New Level for speaker? \n');
scanf( 'zf ' ,aresponse)3
fflush(stdin)3
if ((response < 1) :: (response) 100))
printf('- Unchanged -\n')3
else t/
settings-)vspr = response;
printf('Voltage Level for aerosolizer is z.1f V\n',settings-)vaer)3
printf(' New Level for speaker 2? \n');
scanf(‘tf',&response)3
fflush(stdin)3
if ((response ( 1) :: (response > 100))
printf('- Unchanged -\n');
else #/
settings-)vaer = response;
printf('Oven Temperature is z.1f C\n',settings-)temp);
printf(' New Oven Temp? \n');
scanf(“tf',&response)3
fflush(stdin)3
if ((response ( 1):: (response ) 500))

*/

Electronic & Computer Services - M.S.U.\n')3

\n\n')

229

printf('- Unchanged -\n');

 

' \n\n')

else
settings->temp = response;
}
/t menu() - Display Menu & return response */
char menu()
{
_clearscreen(_GUINDON)3
printf('Composite Line Controller Electronic & Computer Services - M.S.U.\n');
printf('
printf(' 1 - Run line from with current settings\n\n');
printf(' 2 - Run line from batch file\n\n')3
printf(' 3 - Change current settings\n\n');
printf(' 4 - Exit to DOS\n\n')3
fflush( stdin);
return( (char )getch( ))3
l
l: Interrupt Handler for Timer t/

/x (executed every 1/18.2 secs) x/

void interrupt far tick()

{

/* Increment the two counters */

counts++3
ovencounts++3

lt Every other time set int_flag r/

if ((counts 3 0x01) == 1)
int_flag = 13

/* 60 about normal business x/

_chain_i ntr( oldvector )3

l
l: power() returns x“y x/
unsigned long power(int x, int y) {

unsigned long 2;
int i;
z = (unsigned long)x3
for(i=13i(y3i++)
z = 2*(unsigned long)x3
return(z);
)

lx keywait() - Prompt and wait for a key to be pressed */

void keywait() {

char c3

230
fflush(stdin);
printf('- Hit any key to continue -\n');
scanf(‘kc',&c);

231

Program 2 : Routinesc

232

/* Electronic & Computer Services x/
/* Composite Line Controller Software x/
/* Frank Palazzolo 6/7/90 x/

/* DT2811 Board Register Definitions t/

Qdefine BASEADDR 0x0218 lt Base Address for DT2811 t/
ldefine ADCSR BASEADDR+O l: AID Control/Status (R/H) x/
Idefine ADGCR BASEADDR+1 It AID Gain/Channel (R/H) x/
tdefine AD_pA0 BASEADDR+2 lx AID and DACO Data Word (R/H) x/
Idefine 0A1 BASEADDR+4 It DACI Data Hard -(H) */
ldeflne DIO BASEADDRf6 l: 010 Port 0 / 010 Port 1 (RIM) 3/
{define TMRCTR BASEADDR+7 Ix Timer / Counter (R/H) t/
{include <stdio.h> It Necessary libraries */

[include (signal.h)

#include <stdlib.h)

linclude (process.h)

flinclude (dos.h)

unsigned long counts:

void (interrupt far toldvector)()3

void interrupt far tick()3

int reglOstat = 23 It Global variable - status of register 10 */

It For more information about these routines - see the A/D board guide, */
l: and the specifications for the composite line controller box. 1/

int getgcounter1()

/¥ Routine to get number of counts from motor 1 *l

(

int tenpl. notineout;
unsigned long temp;

tenpl = get_register(O):
if ((templ & 1) == 1) {
get_register(3):
return( -1 )3
}
get_register(3)3
temp = counts:
notineout = 13
while ((((temp1 = get_register(o)) a 2) == 2) && notimeout)
if (counts ) (teap+1)) notineout = 03
if (notimeout == 0)
return( -2 )3
else
return( get_register( 2)*16+get_register( 1 ) )3

}
int get_counter2( )

/x Routine to get number of counts from motor 2 x/

{

. . 233
wt templ , notueout:

unsigned long temp:

tenpl = get_register(O):

if ((templ a 4) == 4) {
get_register(13):
return( -1 )3

get_register(13):

temp = counts:

notineout = 13

while ((((temp1 = get_register(0)) 8: 8 == 8) && notimeout)
if (counts ) (teap+1)) notineout = 03

if (notineout == 0)
return(-2):

else
return( get_r egister( 12 )316+get_register( 11 ) )3

}

int set_potor1(int value)

It Routine to set speed for motor 1 x/

{
value = 4095 * value:
set_register(£,value & 0x0F):
set_register(5,(value a 0x0F0) )) 4):
set_register(4,(value a OxOFOO) )) 8):
}

int set_lotor2( int value)

It Routine to set speed for motor 2 x/

{
value = 4095 - value:
set_register(9 ,value a OxOF )3
set_register(8,(value a 0on0) )> 4):
set_register(7,(value a OXOFOO) n 8):
}

int get_register(int reg_nunber)

/* Routine to read from register on controller board */

{
int temp:

outp(DIO,reg_mnbert16):
ten: 3 (OxOf & iMDIOD:
outp(DI0,0):
return(teep):

}

set_register(int reg__nunber, int value)

It Routine to write to register on controller board 3/

234

outp( DIO ,reg_number*16+value ):
outp(DIO ,value )3
}

set_volunel(int value)

/x Routine to set the volume level of speaker 1 x/

{
}

set_volune2( int value)

outpw( AD_DAO.value )3

/* Routine to set the volume level of speaker 2 t/

{

outpw( 0A1 ,value )3
}
int get_conc( )

/x Routine to get particle concentration level *I

{
a2d_init( )3
outp(ADCSR,O)3
outp(AOGCR.0):
while( inp(ADC$R)&128 == 0):
return( inpw(AD_DAO)):

}

int get_spl( )

lt Routine to get sound pressure level (speaker 2) t/

{
a2d_init( )3
outp(AOCSR,0)3
outp(AOGCR,1)3
while( il'IP(ADC$R)&128 == 0):
return(inpw(AD_DAO)):

}

int get_tenp( )

It Routine to get oven temperature level at/

{
a2d_init( )3
outp(ADCSR,0):
outp(AOGCR,2):
while( inp(ADC$R)&128 == 0):
return( inpw(AD_DAO)):

}

void oven_on( )

l

235

reglOstat = reglOstat & OxFD:
set_register(10,reglOstat):

void oven_off()

{

}

reglOstat = reglOstat : 0x02:
set_register( 10 ,reg103tat )3

void motors_on( )

{

}

reglOstat = reglOstat : 0x01:

set_register( 10 ,regIOstat )3

void motors_pff()

{

}

reglOstat = reglOstat & OxFE:

. set_register( 10 ,reglOstat )3

void track_on( )

{

}

reglOstat = reg103tat : 0x04:

set_register( 10 ,reglOstat )3

void track;off()

{

}

reglOstat = reglOstat a OxFB:

set_register(10,reglOstat):

a2d_jnit()

l: Routine to initialize A to 0 system x/

(

}

int i.dumny:

outp( AOCSR,0):
for(i=o:i(1000:i++)3
dummy = inpw(A0_pA0);

int ctrlc()

l: Routine to Handle Ctrl-C Interrupt x/

(

char c:

236

/* disable Ctrl-C */
signal($IGINT,$IG_IGN)3

motors;off()3
ovengoff()3
track_pff():
set_volume1(0):
set_yolume2(0):

printf('Are you sure you want to quit?\n'):
c = (char)getche( )3
if ((c == ’y’) :3 (c == ’Y’)){

/t reset timer vector t/

_disable:
_dos_setvect(8,oldvector)3
_enable:
exit(0)3

}

else {

aotors__on( )3

/: set ctrl-c vector back to this routine x/

signal(SIGINT, ctrlc):

Appendix C
CONTACT ANGLE PROGRAM

 

This appendix lists the finite difference program written to solve for the
contact angle that a polymer matrix makes with a cylindrical fiber. A sample output
from a simulation is also enclosed.

237

238

Program Algorithm

Thealgaidtmofmefinitedifi'erenceprogramconsistsofthefouowingsteps:

(1) Read data fiom a user file in the following sequence - fiber diameter (DIAMETER),
predicted contact angle (THE'I‘A), maximum number of iterations (NMAX) and tolerance
(POL) used in subroutine FALSI, ratio of excess pressure to polymer surface tension
(DPYLV), the minimum (DPYLVI) and maximum (DPYLVM) values of this ratio (which are
related to droplet size) and the step size (DPS'I'EP) and the regression coefficients (BO, BI, 32
andBB)thatareusedtofittheexperimentaldataforthefiber—matrix system.

(2) Foreachdropletsizedictatedbythevalue ofDPYLV,startwithan initialguessforYa),
solve the finite difference equation given in the subroutine FDROP by means of a root-finding
algorithm FALSI for the actual value of ‘10).

(3) Continue this procedure for each Y(I) till the droplet profile is complete it! the contact
angle 'I'HE’I‘A and the drop size dictated by DPYLV. '

(4) Compare the predicted values of drop median radius fa a given drop lengthwith that
memmedbyexperiment. Calculatearesidualsumofsqrmesforthatparticularvalueof
THETAforarangeofdropletsizeswithuniformstepsfromtheminimumtothemaximum

droplet size.

Theresidualsmnsofsqumesumtreafitsfiuneachconmanglesimulafionmethen
compm'edwarfivemfiieconmctanglewhichbestdescribesdwexpaimmtaldam.

00000000000000000000000000000000000000000

000000

0000

239
CONTACT ANGLE PROGRAM

This program.calculates the contact angle that a liquid makes with a
cylindrical fiber. It uses finite differences (backward difference)
and a root-finding algorithm (Regula-Falsi) to solve the ordinary
non-linear differential equation. The drop profile is solved for
the wide range of droplet sizes by varying the excess pressure
inside the drop.

Variables used:

A, B - INITIAL GUESSES'FOR Y THAT ARE FED AS ARGUMENTS IN THE
FALSI SUBROUTINE
BO,Bl,BZ,BS - REGRESSION COEFFICIENTS FOR THE LINE THAT FITS THE
DROPLET EXPERIMENTAL DATA IN THE FORM :
K - BO + Bl*L + BZ*L**2 + B3*L**3

DIAMETER - DIAMETER OF THE FIBER

DPYLV - EXCESS PRESSURE / LIQUID SURFACE TENSION

DPYLVI - INITIAL VALUE OF DPYLV

DPYLVM - FINAL VALUE OF DPYLV

DPSTEP - STEP SIZE FOR DPYLV

DX - STEP SIzE USED IN THE FINITE DIFFERENCE ALGORITHM

F - DUMMY EXTERNAL FUNCTION USED IN THE SUBROUTINE FALSI

I - COUNTER USED IN MAIN PROGRAM

N - ITERATION COUNTER USED IN SUBROUTINE FALSI

NMAX - MAXIMUM NUMBER OF ITERATIONS USED IN SUBROUTINE FALSI

RL - L, GIVEN BY 2*DROPLET LENGTH/DIAMETER

RK - K, GIVEN BI 2*DROP MEDIAN RADIUS/DIAMETER

RKEXPT - x, MEASURED BY EXPERIMENT

SUMSQ - SUM OF SQUARES OF TEE ERROR I.E. DIFFERENCE BETWEEN
RX AND RXEXPT

TOL - TOLERANCE USED IN SUBROUTINE FALSI

Xo - FINAL VALUE FOR Y CALCULATED BY SUBROUTINE FALSI

x - AXIAL DISTANCE ALONG THE FIBER, X - 0.0 AT THE
BEGINNING OF THE DROP

Y - RADIAL DISTANCE OF THE DROP FROM THE FIBER AXIS

Characterization of variables :

IMPLICIT REAL*8 (A-H,O-Z)
DIMENSION Y(1000)
CHARACTER*20 DIN

INTEGER I,NMAX,IC

COMMON DX,DPYLV,Y,IC
EXTERNAL FDROP

Enter input and output file names :
(The program is set up so that it interactively prompts the user
for input and output filenames each time it is run).

PRINT *, 'ENTER THE OUTPUT FILE NAME'
READ (*,100).DIN

OPEN (UNIT-10, NAME'DIN,STATUS-'NEW')
PRINT *,'ENTER THE INPUT FILE NAME'
READ (*,100), DIN

OPEN (UNIT=14,NAME=DIN,STATUS='OLD')

Read the data file entered by the user -

READ (14,*) DIAMETER,THETA,NMAX,TOL,DPYLVI,DPYLVM,DPSTEP,

0000

00000 0000

000000 0000

000000

0000000

20

10

240
$ BO,BI,BZ,B3

Write the data filename and all the data read from the file into

Initialize the error sum of squares

an output file :
WRITE (10,*) ’ DATA FILENAME = ', DIN
WRITE (10,*) ’
WRITE (10,*) ' DIAMETER - ',DIAMETER
WRITE (10,*) ' THETA - ’,THETA
WRITE (10,*) ’ NMAX - ',NMAX
WRITE (10,*) ' TOLERANCE - ',TOL
WRITE (10,*).' DPYLVI - ’,DPYLVI
WRITE (10,*) ' DPYLVM - ',DPYLVM
WRITE (10,*) ’ DPSTEP - ',DPSTEP
WRITE (10,*) ' BO - ’,BO
WRITE (10,*) ’ Bl - ',Bl
WRITE (10,*) ’ 82 - ',BZ
WRITE (10,*) ' 83 - ’,33
WRITE (10,*) ’ ’

SUMSQ - O

The finite difference step used by the program is 1/20 Of the
fiber diameter :

DX - DIAMETER/20.0

Write headings for the columns in the output file :

WRITE (10,20)
FORMAT (6X,'DPYLV' ,7X, 'l',7X, 'k' ,7X, 'L',7X,’K',7X,’K(expt) ')

Initiate a do-loop to iterate for each value of DPYDV frmm the
minimum.to the maximum.value in steps. This covers the entire
range of droplet sizes.

Do 200, DPYLV - DPYLVI,DPYLVM, DPSTEP

For each droplet size (which is dictated by the value of the excess
pressure or DPYLV, initialize Ytl) and Y(2), the starting points
for the drop profile.

2(1) - DIAMETER/2.0
2(2) - Y(l) + DX*TAN(THETA*3.1415927/180)
I - 2

If the value of y"is greater than or equal to the previous value,
then calculate an initial guess for y and feed the initial guesses to
the Regula-Falsi subroutine. If the converse is true, then the
droplet profile is complete.

IF (Y(I) .GE. Y(I-1))THEN
I a I+1
Y(I) = 2*!(1-1)
A = Y(I)
B = Y(I-1)

- Y (I-Z)

241
IC - I
CALL FALSI (A,B,FDROP,X0,TOL,NMAX)
Y(I) = X0
GOTO 10
ELSE
IMAX = I
ENDIF

Convert the maximum.calculated values of x and y for the completed
drop profile to dimensionless values.

00000

x - DX*(IMAX - 1)
RL - 4*X/DIAMETER
RK - 2*!(IMAX)/DIAMETER

Compare the predicted drop dimensions with the experimentally
measured values by means of residual sum of squares for the
entire range of droplet sizes. Write the calculated values of
different parameters in column format.

0000000

RKEXPT - - BO + 81*RL + BZ*RL**2 - B3*RL**3
SUMSQ - SUMSQ + (RK - RKEXPT)**2

WRITE (10,30) DPYLV,2*X,Y(I),RL,RK,RKEXPT
TYPE *,RK,RKEXPT,DPYLV

Go back to the beginning of the DO loop to calculate drop dimensions
for the next value of excess pressure.

00000

200 CONTINUE

Write the residual sum of squares for the contact angle THETA.

0000

WRITE (10,*) 'ERROR SUM OF SQUARES = ',SUMSQ
30 FORMAT (2X,F10.4,2X,F10.4,2X,F10.4,2X,F10.4,2X,F10.4,2X,F10.4)
100 FORMAT (A)

END
C
**************************************'k******************************
C
C
C Subroutine FALSI is a general subroutine to determine the zero of
C of a function F(X), the arguments used are as follows :
C
C A, B = The 2 starting values of X
C F - External function of X
C X0 - Root of X
C TOL - Tolerance on F
C NMAX - Maximum.number of iterations
C
C The subroutine has a nested loop structure which ultimately yields
C the root after Checking for convergence and tolerance.
C
SUBROUTINE FALSI (A,B,F,X0,TOL,NMAX)
IMPLICIT REAL*8 (A-H,O-Z)
DIMENSION Y(1000)
INTEGER NMAX,N
EXTERNAL F
C
N = 1

00000000 *0

C

20

242
X0 = (A*F(B) - B*P(A))/(F(B) - FtA))
IF (ABS(F(X0)) .GT. TOL) THEN

IF (N .LT. NMAX) THEN
IF (ABS(F(A)) .LE. ABS(F(B))) THEN

B - X0
ELSE
A - X0
ENDIF
N I N+1
GOTO 20
ELSE
TYPE *, ’ THE FUNCTION HAS NO ROOT'
ENDIF
ENDIF
RETURN
END

******************************************************************

Function FDROP is a real function which calculates the value

of the finite difference equation for a specific value of y
referred to as A by the FALSI subroutine. DX, DPYLV, the array
of y values before 2(1) i.e. Y(I-1), 2(1-2) etc are all passed
on from.the main program.through the COMMON statement..

REAL FUNCTION FDROP (A)
IMPLICIT REAL*8 (A-H,O-Z)
DIMENSION Y(1000)

INTEGER I,Ic

COMMON DX,DPYLV,Y,IC

I - Ic
TERMl - (A - 2*I(I-1) + Y(I-2))/(DX**2)

TERM2 - DPYLV*(1 + (A - Y(I-1))**2/DX**2)**1.S
TERM3 - (1 + (A-Y(I-1))**2/DX**2)/A

FDROP - TERMI + TERM2 - TERM3

RETURN
END

C*tt************************************************************

243

DATA FILENAME = theta24.dat

DIAMETER
THETA
NMAX
TOLERANCE
DPYLVI
DPYLVM
DPSTEP
80

B].

82

B3

DPYLV
400.0000
500.0000
600.0000
700.0000
800.0000
900.0000

1000.0000
1100.0000
1200.0000
1300.0000
1400.0000
1500.0000
1600.0000
1700.0000
1800.0000

1

0.0120
0.0099
0.0084
0.0073
0.0065
0.0058
0.0052
0.0047
0.0044
0.0040
0.0037
0.0034
0.0032
0.0030
0.0027

ERROR SUM OF SQUARES -

7.4189999999999999E-04
24.00000000000000
200

1.0000000000000000E-05

= 400.0000000000000

- 1800.000000000000

- 100.0000000000000
0.5324824000000000
0.2425831000000000
8.9802280000000000E-03
1.30426500000000008-04

L K K(expt)
0.0046 32.4000 12.4361
0.0036 26.6000 9.7474
0.0030 22.6000 7.9589
0.0025 19.6000 6.6854
0.0021 17.4000 5.7329
0.0019 15.6000 4.9954
0.0016 14.0000 4.4092
0.0015 12.8000 3.9317
0.0013 11.8000 3.5363‘
0.0012 10.8000 3.2057
0.0011 10.0000 2.9246
0.0010 9.2000 2.6849
0.0009 8.6000 ' 2.4772
0.0009 8.0000 2.2976
0.0008 7.4000 2.1422

0.7914268496853361

12.3182

9.8195
8.0311
6.6899
5.7202
4.9421
4.2659
3.7704
3.3661
2.9706
2.6609
2.3578
2.1350
1.9161
1.7015

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