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thesis entitled

EXPERIMENTAL AND NUMERICAL STUDY OF STAMP HYDROFORMING
FOR PROCESSING GLASS MAT FIBER REINFORCED THERMOPLASTIC
SHEETS

presented by

Michael A. Zampaloni

has been accepted towards fulfillment
of the requirements for

M.S. . Mechanical Engineering
degree in

 

 

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December 15, 2000
Date

 

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EXPERIMENTAL AND NUMERICAL STUDY OF STAMP HYDROFORMING
FOR PROCESSING GLASS MAT FIBER REINFORCED THERMOPLASTIC
SHEETS

By

Michael A. Zampaloni

A THESIS

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

MASTER OF SCIENCE

Department of Mechanical Engineering

2000

ABSTRACT

EXPERIMENTAL AND NUMERICAL STUDY OF STAMP HYDROFORMING
FOR PROCESSING GLASS MAT REINFORCED THERMOPLASTIC SHEETS

By

Michael A. Zampaloni

The goal of this study was to verify, through experimentation and numerical
modeling, that the stamp hydroforming process provided a suitable alternative to
conventional methods such as thermoforming and stamp forming as a means for
processing thermoplastic materials. Hydroforming involved supporting the
thermoplastic sheet with a bed of viscous ﬂuid that applied a hydrostatic pressure
across the part during forming. The external support provided a through-
thickness compressive stress that delayed the onset of tensile instabilities as well
as reduced the formation of wrinkles due to tensile frictional forces. Preliminary
experiments were conducted using a procedure that was designed and built in-
house. Initial complications arose during the experimentation but the beneﬁt of
the hydrostatic pressure was qualitatively proven. The numerical analysis,
conducted using MARC, showed results that correlated with the experimental
trends. Overall the experimental results, coupled with the numerical modeling,
showed that the hydroforming process was a viable processing method for
thermoplastic materials that warrants attention based on the signiﬁcant

advantages in cost savings and part production accuracy.

Copyright by
MICHAEL ANDREW ZAMPALONI
2000

To Suzanne and Andrew, thank you for all your love, support and patience

ACKNOWLEDGMENTS

I would like to thank Dr. Farhang Pourboghrat and Dr. Andre Benard for all
the patience, support and guidance they have provided during the course of my
study in pursuit of my Masters of Science degree, without their encouragement

and leadership the research could not have progressed.

The research was made possible through funding received from the
Composite Material and Structures Center (CMSC) at Michigan State University.

Their support is greatly appreciated.

I would also like to acknowledge Dr. Enamul Haque, Mr. Dennis Spencer and
Mr. Tom Wood of Azdel Inc. for the generous resources provided in support of
the stamp hydroforming research effort. In addition, I would like to thank Mr.
Tom Driggers and Mr. Dave IGearing of lnterlaken Technology for all their

assistance during the course of this work.

Most importantly, I would like to thank my wife Suzanne for all her patience,
encouragement and support over the past couple of years. , I could not have

done it without her, thank you.

TABLE OF CONTENTS

LIST OF FIGURES.........

LIST OF ABBREVIATIONS

CHAPTER 1

INTRODUCTION TO HYDROFORMING................................................ ..
Hydroforming Applications

CHAPTER 2

CHAPTER 3

LITERATURE REVIEW
Sheet Metal Literature ReVIew
Thermoplastic Literature ReVIew

CHAPTER 4

EXPERIMENTAL WORK
....28

Experimental Apparatus...
Hydroforming Challenges

Current Experiment, Hydroforming with.” HemIspherIcal Punch

CHAPTER 5

NUMERICAL ANALYSIS
Numerical Analysis Theory

Numerical Analysis Results...

CHAPTER 6

FUTURE WORK...
Future Experimental Work
Future Numerical Work...

CHAPTER 7

vi

...vi

..11

..15

......'.15
..21

..28

.38

43

...62

".'.'...'.'62
...66

.71

...74

LIST OF FIGURES

Figure 1. Schematics of a hydroforming press with a blank holding support during
the forming of a cup.

Figure 2. Illustration of the plug-assisted thermoforming processing method for
thermoplastic composite materials.

Figure 3. Double action servo press 75 manufactured by lnterlaken Technology
Corporation, Eden Prairie, MN.

Figure 4. Schematics of the double action servo press with a simple limiting
dome height test die in place.

Figure 5. Schematic of a simple limiting dome height (LDH) test die set.

Figure 6. The modiﬁed lnterlaken servo press 75 used for the hydroforming of
composite sheets.

Figure 7. Schematic \erw of the Experimental Apparatus used for Hydroforming
Hemispherical Cups [31].

Figure 8. The in-house designed die set for hydroforming composite sheets.

Figure 9. Regulator and Controller used for the control of the ﬂuid pressure
within the forming chamber.

Figure 10. Pressure intensiﬁer and pressure reservoir used in the hydroforming
experimental set-up.

Figure 11. Generic curve illustrating the optimum ﬂuid pressure-punch stroke
path for the stamp hydroforming process.

vii

Figure 12. Sheet of the Azdel glass mat ﬁber reinforced polypropylene
thermoplastic material prior to and at the completion of the stamping process.

Figure 13. Example of material sag in unsupported regions of the initial
hydroforming die design.

Figure 14. Comparison of the hemispherical part formed with an applied
hydrostatic force and with no applied pressure, respectively.

Figure 15. Stress-Strain plot for 40 % continuous strand mat, polypropylene
matrix material.

Figure 16. Stress-Strain plot for 32% oriented, long chopped ﬁber polypropylene
matrix material.

Figure 17. Stress-Strain plot for 32% random, long chopped ﬁber polypropylene
matrix material.

Figure 18. Three-Dimensional model of the hydroforming process created using
MARC.

Figure 19. Two-Dimensional MARC model.
Figure 20. von Mises yield surface in tvvo-dimensional stress space.

Figure 21. Zoned regions of the shaped hemispherical cups to be used in the
discussion.

Figure 22. MARC model displacement results, depth of 3 inches.
Figure 23. von Mises stress MARC model results, ﬂuid pressure of 0 psi.

Figure 24. von Mises stress MARC model results, ﬂuid pressure of 1000 psi.

viii

Figure 25. von Mises stress MARC model results, ﬂuid pressure of 2000 psi.
Figure 26. von Mises stress MARC model results, ﬂuid pressure of 3000 psi.
Figure 27. Total equivalent strain MARC model results, 0 psi ﬂuid pressure.
Figure 28. Total equivalent strain MARC model results, 1000 psi ﬂuid pressure.
Figure 29. Total equivalent strain MARC model results, 2000 psi ﬂuid pressure.
Figure 30. Total equivalent strain MARC model results, 3000 psi ﬂuid pressure.

Figure 31. Plot of von Mises stress versus displacement for ﬂuid pressures of 0,
1000, 2000, and 3000 psi.

Figure 32. Enhanced plot of von Mises stress versus displacement for ﬂuid
pressures of 0, 1000, 2000, and 3000 psi.

Figure 33. Plot of total equivalent plastic strain versus displacement for ﬂuid
pressures of 0, 1000, 2000, and 3000 psi.

Figure 34. Enhanced plot of total equivalent strain versus displacement for ﬂuid
pressures of 0, 1000, 2000, and 3000 psi.

Figure 35. Plot of von Mises stress versus displacement for ﬂuid pressures of 0,
100, 200, and 300 psi using the modiﬁed work hardening model.

Figure 36. Enhanced plot of von Mises stress versus displacement for ﬂuid
pressures of 0, 100, 200, and 300 psi using the modiﬁed work hardening model.

Figure 37. Plot of strain versus displacement for ﬂuid pressures of 0, 100, 200,
and 300 psi using the modiﬁed work hardening model.

Figure 38. Enhanced plot of strain versus displacement for ﬂuid pressures of 0,
100, 200, and 300 psi using the modiﬁed work hardening model.

Figure 39. Schematic of the newly designed die that will alleviate the material
sag complication associated with the current experimental set-up [31].

LIST OF ABBREVIATIONS

01.2.3 - Principal Cauchy Stresses
3 - von Mises Stress

a}; - Deviatoric Cauchy Stress

c; - Stress Increment

2: - Strain Increment.

xi

INTRODUCTION

There exists an abundance of ﬁber-reinforced composite materials that exhibit
material properties such as strength and modulus that are either comparable to
or better than traditional metallic materials. Typically, the composite materials
have better strength to weight ratios and modulus to weight ratios than metals
and can also possess excellent fatigue strength to weight ratios. Therefore,
ﬁber-reinforced composite materials have been gaining popularity as
substitutions for many of the weight critical components in the aerospace and

automotive industries [1].

The ﬁbers are the principal constituent of the ﬁber-reinforced material,
occupying the largest volume fraction and sharing the majority of the load acting
on the material. There are multitudes of commercially available reinforcing ﬁbers
ranging from glass to kevlar ﬁbers. The choice of the type of reinforcing ﬁber
depends greatly on the material properties desired from the ﬁnished product.
The second constituent that makes up the composite material is the polymeric
matrix. The matrix serves three distinct functions; it is responsible for distributing
the stresses between the reinforcing ﬁbers, it protects the surface of the ﬁbers

from abrasion, and it protects the ﬁbers from the adverse environmental effects.

The polymeric matrix can be split into two general categories, thermosets and
thermoplastics. The thermoset polymers consist of molecules that are chemically

bonded by cross-links forming a three-dimensional network structure.

Thermoplastic polymers consist of individual molecules that form a linear
structure with no chemical linking, these molecules are held together by weak
secondary bonds such as van der Waals bonds and hydrogen bonds. Once
formed, thermoset materials cannot be melted and reshaped whereas a

thermoplastic polymer can be melted and reshaped as often as desired [1].

The use of a thermoplastic matrix lends itself very easily to the various high-
volume and accuracy production rates that are required in the automotive
industry. Some of the advantages of a thermoplastic matrix over a thermoset
matrix includes: a controllable, constant molding behavior, even after being
stored for long periods of time, parts can be reformed as needed, can be joined
by hot-welding methods, can be bent, twisted, or otherwise hot-formed, better
impact resistance and there is typically no cure time associated with these

materials, thereby allowing for a much quicker forming time.

Even though these materials may present distinct advantages over the
traditional metal materials, there is still the issue of manufacturing the parts'while
still achieving the same level of volume and accuracy. Over the years numerous
manufacturing processes have been proposed to shape thermoplastic composite
materials, ranging from injection molding to sheet stamping and ﬁlament winding.
Shaping operations such as sheet forming, thermoforming, match die molding,

contact molding, and resin transfer molding have been studied fairly extensively

and are currently used by industry to manufacture polymer reinforced products of

varying quality.

Due to its high success with metals, various attempts have been made to
apply sheet-stamping techniques to composites. A difﬁculty in using
therrnoplastics in stamping, however, is the inﬂexibility of the thermoplastic
material prior to heating and the heating requirements necessary to bring the
matrix material to its glass transition temperature, enabling the part to be formed.
The forming of straight, continuous ﬁber or Woven ﬁber composite sheets
typically results in wrinkling of the ﬁbers and distortions. Randomly oriented
ﬁbers have provided good formability, but without the advantages of the highly
directional properties often desired in composite parts. The more formable sheets
that consist of aligned, discontinuous ﬁbers appear to have been used with more

success than continuous ﬁbers [2].

Therefore, there exists a current need for forming and shaping methods that
can produce complex structures utilizing continuous-ﬁber or woven-ﬁber
composites with limited wrinkling and distortion. One manufacturing process that

can achieve this desired result is hydroforming.

In hydroforming, a controllable pressurized ﬂuid is employed against the
workpiece to aid in the forming of the ﬁnal part. The ﬂuid is pressurized in an

attempt to force the material to conform to shape of the punch. In addition, the

ﬂuidized pressure may also be used as a self-adjusted holding force for the
material draw blank. Hydroforming differs from the conventional drawing process
due to the presence of this pressurized ﬂuid that replaces the female die typically

associated with the process.

The advantages of such a process are numerous and it is receiving signiﬁcant
attention from the automotive and aerospace industries. Some of the
advantages include highly improved drawability of the blank due to the applied
pressure by the ﬂuid, low wear rate of dies and punch, reduced thinning in the
ﬁnal product when compared to conventional drawing, signiﬁcant economic
savings associated with the decreased tooling, and the potential for reducing the

amount of ﬁnishing work required [3].

In the following, a brief review of hydroforming and its potential application to
forming and shaping composite structures will be presented followed by a
presentation of the current state of research regarding this area of exploration.
This will be followed by a discussion of the preliminary results obtained from
thermo-hydroforming experiments and will then segue into the formulation

method and results of the ﬁnite element analysis model created for this project.

 

Chapter 1

INTRODUCTION TO HYDROFORMING

The hydroforming process, as shown in Figure 1, represents a part that is
being formed by a simple hemispherical punch. Prior to the start of the process
the thermoplastic composite material is heated in an oven to bring the material to
its forming temperature. Once the pan has been heated to the appropriate
temperature the workpiece is transferred to the stamping press and. is placed on
the clamping mechanism, as shown in Figure 1.1. Figure 1.2 shows the upper
ﬂuid chamber being lowered and the workpiece being clamped securely between
the two die halves, creating a seal for the upper ﬂuid chamber. The ﬂuid is then

injected into the chamber and is given an initial pressurization.

As the punch travels the workpiece begins to deform into a hemispherical
shape initially, and ﬁnally deforms into a fully formed part after the punch
penetrates deeper into the blank, Figure 1.3. While the punch is deforming the
workpiece the ﬂuid volume within the upper chamber is decreasing, thereby
causing the pressure within the upper chamber to increase. This increased
pressure is used as a means of forcing the material to conform to the shape of

the punch.

Once the punch has reached the prescribed draw depth, the ﬂuid can be

drained and the chamber can be raised, Figure 1.4. If the part has solidiﬁed

 

 

adequately the punch can be retracted and the part can be removed, if more
solidiﬁcation time is required, the punch can be left in place until the part has
achieved solidiﬁcation. If the environmental surroundings are not adequate for
the part solidiﬁcation then the upper ﬂuid chamber can be drained and either cool
ﬂuid or air can be injected to help decrease the ﬁnished parts total solidiﬁcation

time.

 

 

 

 

 

 

  

 

 

 

Fluid
Chamber
I! Draw Bead
—"'*- ’
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""F - , , Material
1' . and
1 I‘ Flexible 2 ‘
é Diaphragm . .
1. Material is placed on the draw head with 2' Fluid “Mb" i' lowed "'6 filled with

heated fluid. Material held in place by
damping mechanism.

the fluid chamber in the raised position.

 

 

 

 

 

 

 

 

3. Punch begins to move «pm, Fluid 4. Fluid is drained. the fluid chamber is
pressure in chamber is controlled to mind and the punch lowered from
force the material to conform to the the completed part
shape of the punch.

Figure 1. Schematics of a hydroforming press with a blank holding support during
the forming of a cup.

 

 

The process of hydroforming, unlike conventional stamping, involves
supporting the bottom of the sheet with a bed of viscous ﬂuid during the stamping
process. This external support provides a through-thickness compressive stress
that will improve the forrnability of the sheet by delaying the tensile instability (i.e.
necking). Also, this external support reduces the formation of wrinkles due to

tensile frictional forces.

In the hydroforming of sheet metals, and the same issue will arise for
composite materials, the difﬁculty lies in ﬁnding an appropriate ﬂuid pressure-
punch stroke path which will avoid rupture of the material yet control the onset of
wrinkling instabilities. For the sheet metal case there have been studies
conducted in an attempt to identify this optimum path. These studies, along with

lessons learned, will be discussed in detail in the literature review section.

The hydroforming process, when applied to composites, must be modiﬁed
slightly due to the inherent differences between polymers and metals. Heat must
be applied in order to reduce the stiffness of the thermoplastic matrix by
increasing its temperature between the glass transition point and the melting
point. Increasing the temperature of the pressurized ﬂuid will allow the
application of heat to the composite workpiece. Since a heated ﬂuid is used to
shape the piece, good productivity can be expected from hydroforming due to the

high heat transfer coefﬁcient of the ﬂuid.

Finally, a signiﬁcant problem with stamping of composite sheets is to maintain
the blank in place by using clamps. If the load needed to draw the sheet is higher
than the shear yield stress of the composite, the sheet will slide from under the
clamps [4]. Hydroforming requires signiﬁcantly less force, if the workpiece is to
be clamped at all, as the hydrostatic pressure is often sufﬁcient to hold the
workpiece in place. This last problem is often signiﬁcant with composites as the

polymer'matrix can yield easily in the clamped region.
1.1. Hydroforming Applications

Fiber reinforced thermoplastic matrix composites are attracting the interest of
the automotive, aerospace and other industries as the beneﬁts of these materials
become more readily apparent. Parts manufactured from ﬁber reinforced
polymers are typically more expensive than their metal counterparts but their
advantages, including strength to weight ratio and material shelf-life, are

beginning to overweigh the short-term economic concerns.

As the cost of fuel continues to increase, the use of ﬁber reinforced
composites in the automotive industry is starting to become very common due to
the high strength to low weight ratio of these materials. Glass-mat
thermoplastics (GMTs) are ﬁnding current favor in the automotive industry due to
their low weight, ease of processing, recyclability, noise suppression and price .

These reinforced materials can exhibit the same strength properties as sheet

steel, but at a fraction of the weight [5]. Currently in production there are already
several composite automobile parts such as suspension springs, space frames,
body panels, and entire assemblies. There are also a multitude of others that are
being planned in the near future; including the introduction of an automobile body

frame created entirely from ﬁber reinforced composite materials [6].

The use of composite materials, especially high performance composites, has
become almost synonymous with the aerospace industry. Stamp hydroforming
could be used as an alternative processing method for a variety of applications

such as cabin wall panels and in a variety of internal structural components.

Since the use of stamping operations is already a common occurrence
throughout industry the applications for the stamp hydroforming process are too
numerous to mention. The hydroforming process is currently utilized as a viable
alternative to the sheet metal forming operations and the same concept can be
applied to industry when trying to evaluate the potential for the use of the
hydroforming process for the sheet stamping of ﬁber reinforced composite
materials. As the increased interest in the use of composite materials increases
there is also the need to determine processing methods that can create ﬁnished
parts in a manner that is conducive to the economic and time constraints faced
by industry. One method that may be able to provide a suitable alternative to the

thermoforming and sheet stamping operations is stamp thermo-hydroforming.

 

 

Chapter 2

BACKGROUND

The idea behind this research effort started with a simple analysis of
composite shaping techniques such as thermoforming and vacuum bag molding.
The thought was that there are a variety of methods that can be used to shape
and process ﬁber reinforced thermoplastic and thermoset composite materials
but that each method had its distinct drawbacks such as economic cycle time
concerns. The initial goal was to review these different processing methods and

to identify areas that could be improved upon.

One of the processes that were evaluated was the thermoplastic sheet
forming method commonly referred to as thermoforming or vacuum forming. In
thermoforming, illustrated in Figure 2, the thermoplastic sheet is clamped above
a negative, or female, mold and the sheet is heated. After the material is
softened to its forming temperature the air beneath the sheet is evacuated
I through small holes that are machined into the mold. By evacuating the air from
the chamber the thermoplastic material is sucked down into the mold thereby
taking the required shape. Typically this process can be just a straight vacuum
operation or may use a ram or plug to assist the processing (plug assisted

method is illustrated in Figure 2).

10

 

 

 

l l
L_X m /_T
1. Composite sheet fs placed across
the ferrule mold and clamped tightly.

Composite Material Meclnnically controlled plug kept In

\ elevated position until the sheet has
Afr Vents Female
/ \ Die

 

been heated to its filming temperature

 

 

 

 

 

2. Plug moves Into the composite sheet

- - material as the aft is evacuated tom the
ferrule die cafvlty. Material confbms to
the shape of' the ferrule dle.

\ I 3. Finished pert.

Figure 2. Illustration of the plug-assisted thermoforming processing method for
thermoplastic composite materials.

 

 

 

While the thermoforming method is quite simple and relatively inexpensive,
there are some disadvantages associated with the process. First off is that the
material is very difﬁcult to control as it moves through the lower chamber. This
has the tendency to create parts that may have varying wall thickness and poor
material distribution. The process has a considerable amount of waste
associated with it and a fair amount of ﬁnishing is required at the completion of
the process. In addition the range of shapes is limited and the ability to create

parts with great detail is not attainable [7].

11

 

 

In general, the most important complication associated with the
thermoforming process is the ability to control the onset of both rupturing and
wrinkling instabilities. These instabilities typically occur due to the nature of the
process. As the air is evacuated from the female die chamber the material is
drawn into the chamber and conforms to the shape of the female die. One of the
obstacles is the uncontrolled nature of the material movement through the
chamber. The thermoforming method requires very accurate control of both the
draw rate and the clamping force used to hold the material in place. In addition,
the thermoforming process as shown in Figure 2 allows for the formation of parts

due to pure stretch only, no material draw-in is allowed.

An evaluation of the rupturing instabilities began with an investigation into the
general manner in which thermoplastic material may fracture. In the most
generic sense, the ﬁrst step of the fracturing process is void formation. As the
material undergoes deformation the matrix and ﬁber material will begin to move,
sometimes independent of one another. As the stress in the part increases the
voids that were created during the manufacturing process will begin to grow in
size. As they grow they start to come in contact with other voids, eventually, as
the deformation of the part continues, enough voids will form to propagate across
the part and will lead to material fracture.

The next step was to try to evaluate methods that could be used to alleviate

the onset of rupturing within the framework of the thermoforming process. The

12

attention turned to the control of fracture within the sheet metal industry.
McClintock (1968) [8] and Rice and Tracey (1969) [9] conducted studies on sheet
metal blanks that demonstrated rapidly decreasing fracture ductility as a
hydrostatic pressure, applied across the material, was increased. Clift, Hartley,
Sturgess and Rowe (1990) [10] and Hartley, Pillinger, and Sturgess (1992) [11]
demonstrated that for sheet metal draw blanks, the use of a hydrostatic pressure

prevented the initiation and spreading of microcracks within the metallic material.

This ﬁnding led to the idea of using a hydrostatic pressure as a means of
controlling material fracture during the processing of thermoplastic materials.
One method of hydrostatic pressure application that was investigated was the
use of stamp hydroforming as a means for processing composite parts. In
addition to the fracture control the use of the hydrostatic pressure has the beneﬁt

of aiding in the reduction of wrinkling during the forming process.

The stamp hydroforming process is used for the shaping of sheet metal parts
but no information could be located about the application of the hydroforming
method to the shaping and processing of thermoplastic composite materials.
Therefore, it was concluded that the study of the stamp hydroforming process, as
a viable alternative to the conventional processing methods such as
thermoforming and stamp forming, as a means for processing thermoplastic

composite materials was warranted.

13

Chapter 3

LITERATURE REVIEW

Through a thorough literature review there were no investigations found
concerning the use of the hydroforming as a means for processing either
thermoplastic or thermoset composite materials. Therefore, the main emphasis
of the remaining literature review focused on the most recent experimental and
numerical developments in the sheet metal hydroforming processes as well as
the current state of experimental and numerical methods used for the processing

of thermoplastic composites, speciﬁcally stamp forming and thermoforming.
3.1. Sheet Metal Literature Review

Based on the success found with using a hydrostatic pressure to delay‘the
onset of fracture within metallic materials the same idea was extrapolated to the
possible use of a hydrostatic force during the processing of thermoplastic
materials. This led to the idea of adopting the use of sheet hydroforming
currently used by sheet metal industries as a means of processing ﬁber
reinforced thermoplastic composite sheets. In order to better understand the
hydroforming process the literature review began by evaluating the current state

of both the experimental and numerical sheet metal stamp hydroforming

operations.

14

 

 

Yossifon and Tirosh (1977 - 1988) [12—16] published a series of articles
dealing with the analysis of the hydroforming deep drawing process as applied to
the formation of cups from metallic materials such as copper, aluminum, steel
and stainless steel. The goal of the studies was to establish a hydroforming ﬂuid
pressure path, relative to the punch stroke, that would prevent part failure due to
rupture or to wrinkling. Their earlier studies demonstrated the effect that
excessive and insufﬁcient ﬂuid pressures have on the premature failure of
hydroformed parts (rupture and wrinkling respectively). The purpose of the later
investigations was to determine a predetermined path that can be followed to

produce parts that are free from these types of defects.

In order to minimize wrinkling instabilities the ﬂuid pressure was held to the
minimum possible. The pressure relationship, based on equating the bending
energy of the buckled plate and the work against lateral load (spring-type
blankholder or ﬂuid pressure) to the work done by the in-plane compressive
membrane forces, included the governing parameters of friction coefﬁcient and
anisotropy. Through their work they were able to show that rupture instabilities
occur when the ﬂuid pressure being used for the hydroforming process was too
high. The ﬂuid pressure constrained the motion of the part and forced the punch
through the material. The ﬂuid pressure to prevent rupture was evaluated in
terms of average friction coefﬁcient, material properties, and geometrical
considerations. Using these two ﬂuid pressure values a range was determined

that allowed for the manufacture of parts without the occurrence of wrinkling or

15

rupturing. This theory was tested experimentally and the results were very

favorable with the predicted outcomes.

Lo, Hsu and Wilson (1993) [17] expanded upon the earlier work of Yossifon
and Tirosh by applying the deep drawing hydroforming theory to the analysis of
the hemispherical punch hydroforming process. The purpose of this work was to
determine a theoretical method of predicting failure due to wrinkling (buckling) or
rupture (tensile instability) during the punch hydroforming of hemispherical cups.
This work was basically an extension of the work done by Yossifon and Tirosh by
incorporating a general friction-force expression into the analysis and expanding

to more complicated geometries.

In order to predict failure the part was split into three regions based on the
geometric characteristics of this operation. First there was a region where the
part was free from contact with the die, a second region that consisted of the
unsupported area termed the “lip area”, and the third region that was the area of
the part that had already come into contact with the surface of the punch. Along
with the determination of the failure areas, the study also attempted to identify an
upper and lower bound for manufacturing, a region termed the “work zone”. It
was proposed that if processes were run within these limits then there should be
limited potential for failure. They were able to conclude that the working zone
could be expanded by low friction forces, high strain hardening exponents, small

drawing ratios, thick workpieces, and through the use of orthotropic materials.

16

Hsu and Hsieh (1996) [18] attempted to verify the theory developed by Lo,
Hsu and Wilson through a series of experimental procedures. The purpose was
the validation and veriﬁcation of the failure prediction method for wrinkling and
rupture instabilities during the punch hydroforming of sheet metal hemispherical
cups. Various hydroforming pressure paths were tested during the process to
validate the theory. They determined conclusively that a path that intersected the
lower boundary of the working zone would lead to premature material failure due
to wrinkling in every case. The same result was found for the pressure paths that
intersected the upper boundary of the working zone. Through a series of varying
parameter experiments the results achieved experimentally were very

comparable to the theoretical predicted results.

Gelin, Delassus and Fontaine (1994) [19] experimentally and numerically
studied the effects of process parameters during the aquadraw deep drawing
process. The purpose of the study was to determine the main parameters that
inﬂuence the aquadraw deep drawing process, speciﬁcally, the determination of
the pressure in the cavity and under the blankholder as functions of process
geometry, material parameters, and ﬂuid parameters. Aquadraw deep drawing
compared to hydroforming differs due to the use of a thin layer of water,
subjected to ﬂuid ﬂow, that replaces the thin rubber diaphragm between the
material and the die cavity. The investigation, limited to axisymmetric sheet

metal materials, proposed a cavity pressure modeling technique based on the

17

 

optimal parameters of the process instead of being modeled by the Reynolds

equaﬂon.

A relationship to determine the cavity pressure was based on the material
behavior, the material thickness, the die entrance radius, and the drawing ratio.
The value determined was always the maximum value. The paper evaluated the
inﬂuence of each of these parameters on the overall cavity pressure
determination. The study referenced other experiments performed that
demonstrate the effectiveness of these parameters on the determination of this
cavity pressure, but no experiments were performed that physically validated the

new relationships proposed through this investigation.

For the numerical analysis portion of the investigation the ﬁnite element
modeling code POLYFORM was utilized to simulate the deep drawing process in
order to validate these relationships. Overall, the predicted behavior was

comparable to the experimental behavior for the parts analyzed.

Gelin, Ghouati and Paquier (1998) [20] and Baida, Gelin and Ghouati (1999)
[21] both expanded upon the numerical work conducted in the Gelin, Delassus
and Fontaine work dealing with the aquadraw deep drawing process. These two
investigations expanded upon the numerical work by adding the process
parameters monitoring, identiﬁcation tools and general sensitivity analyses to the

numerical method used as a predictor of the die cavity pressure during the deep

18

 

h

drawing process. Overall their respective results showed very good correlation

between the numerical and experimental behavior of the material.

Shang, Gin and Tay (1997) [22] spent time on the evaluation of the copper
spherical shell hydroforming process by studying the effects of intermittent draw-
in during the operation. The purpose of this investigation was to examine,
experimentally and numerically, the effects these intermittent changes would
have on the formability of the blank material. During the processing of the cups
there were two main formability factors that were investigated; the radius of the
die shoulder and the blank holding force. Reducing the die shoulder radius
increased formability but the use of a small radius had the potential of causing
premature tearing of the blank along the die shoulder. Reducing the blank
holding load encouraged draw-in, inward ﬂow of the ﬂange material, thereby
increasing .the average thickness of the product and delayed the onset of

material failure.

Since the radius of the die shoulder is normally ﬁxed or limited by the product
speciﬁcations then the logical approach to increasing formability would be to vary
the blank holding load. During this study the copper material was formed into a
nearly spherical shell using four different approaches. The ﬁrst approach was a
single-stage hydroforming process using two different deformation paths, one
that allowed for the draw-in of the ﬂange, and one that did not allow the draw-in

to occur. The second approach evaluated the effect of a double-stage

19

hydroforming process also using two different ﬂow paths. The ﬁrst path allowed
for the draw-in during the ﬁrst stage, and restricted it in the second. The second
path was just the opposite, draw-in was not allowed during the ﬁrst stage yet was
permitted during the second stage. The results showed that during the single-
stage hydroforming process, the formability of the material was greatly improved.
For the double-stage hydroforming operation, the best results were achieved
during the path that did not allow for the draw-in of the ﬂange during the ﬁrst

stage, but did during the second stage.

3.2. Thermoplastic Forming Literature Review

Hou and Friedrich (1991) [23] investigated the development of a
thermoplastic composite stamp forming process for carbon ﬁber reinforced
polypropylene. The main goals of the research were the establishment of a
useful processing technique and the control of the parameters that led to the
production of a quality composite part. The useful processing conditions
included process temperature, cycle time, stamping velocity and stamping
pressure. The experiments were conducted using a right angle matched tool
forming parts from a continuous carbon ﬁber reinforced polypropylene composite
material. Important conclusions drawn were that the stamping pressure is
related to the stacking sequence of the laminates, it decreases with an increase
in the number of 90° lay-ups due to transverse ﬂow. The stamping temperature

was determined to be at a range that is slightly higher than the melting

20

temperature of polypropylene and that the stamping pressure had more inﬂuence

on the ﬁnal part properties than the stamping velocities.

Hou (1997) [24] continued the earlier work of Hou and Friedrich by applying
the same concepts and principles to the stamp taming of continuous
unidirectional glass ﬁber reinforced polypropylene composite materials. The goal
was the same as before, to establish a useful processing technique that leads to
the production of a quality part. Experimentally the hold-down pressure became

the limiting factor for the stamp forming process.

Harper (1992) [25] investigated the most recent developments of the
thermoforming processing methods for shaping thermoplastic matrix composites.
Some of the major disadvantages associated with the thermoforming method
were discussed and addressed. The disadvantages included: the difﬁculty of
stretching the material when trying to clamp it to the frame, the possibility for the
material to be incompressible in thickness due to the density of the packed
continuous ﬁbers, buckling concerns, the speed of the forming requirements and

the difﬁculties associated with the control of the ﬁber placement.

Pegoretti, Marchi and Ricco (1997) [26] evaluated the anisotropic fracture
behavior of polypropylene cups created by a vacuum thermoforming process.
The anisotropic behavior was studied through an elasto-plastic fracture

mechanics approach. Experiments were conducted using samples with high

21

length/width ratios drawn to depths of 100 and 58 mm. Results illustrated that
the anisotropic behavior of the polypropylene was pronounced as the
thermoforming draw-ratio increased. In all cases, the yield strength was found to

be higher along the drawing direction

0’ Bradaigh, McGuinness and Pipes (1993) [27] studied a general-purpose
ﬁnite element simulation code that predicted the stresses and deformations in a
composite sheet subject to, predominantly, planar forming forces during a
diaphragm forming operation. The numerical analysis method incorporated the
kinematics and rate dependence of the instabilities encountered during
manufacturing, while still allowing for geometric generality. The two most limiting
modeling assumptions made through this study were the planar restrictions and
the purely viscous response assumptions. The ﬁnite element modeling was
accomplished utilizing FEFORM, based on the ﬁnite element analysis (FEA)
code PCFEAP.

In conjunction with the FEA analysis, experimentation was performed using a
heated circular punch and mold. The objective was to investigate the stress and
deformation states of the composite sheet and to draw conclusions regarding the
sensitivity of the shear-buckling phenomenon to the different process parameters
that could be varied including the uniform radial velocity, the uniform radial

pressure, and pressure loading. The results showed very good agreement

22

between the FEA modeling and the experimental results in the ﬁber direction.

Somewhat poorer results were found in the transverse direction.

McGuinness and O’Bradaigh (1995) [28], through experimental and numerical
work, focused on the occurrence of buckling during sheet forming of ﬁber
reinforced composite materials into a hemispherical mold. The purpose of this
experimental procedure was to study the effect that changes to the preform
shape would have on the buckling patterns observed during the forming of quasi-
isotropic laminates. More speciﬁcally, the goal was to determine if a square
laminate was less prone to buckling at the 45° point than at the 0 and 90°

points.

The physical portion of the experiment was accomplished using a computer-
controlled thermoforming autoclave; the parts were not mechanically stamped
but were formed by utilizing a pressure differential. Four types of preform shapes
were evaluated; square, large rectangular, small rectangular and a truncated
square preform achieved by cutting two comers off the square preform. No
deﬁnitive conclusions were drawn from the experimental study about which
shape outperformed the other. The numerical analysis results showed very good
correlation with the experimental results. Overall conclusions of the study
illustrated that for unidirectional and cross-ply laminates the shear stress at 45 °

to the ﬁber directions controlled the buckling pattern. For the quasi-isotropic

23

laminates, the axial compressive stress of the ﬁbers that ran tangent to the

buckling site determined the occurrence of the instability.

Long, Rudd and Middleton (1996) [29] were concerned with the development
of mathematical modeling techniques that describe the deformation of continuous
random ﬁber reinforced thermoplastic materials during preform manufacture.
The investigation used a numerical ﬁnite differencing scheme developed to
simulate the material’s behavior. The local stresses and strains were derived
from equilibrium of forces, mass continuity, and plasticity theory. The model was
veriﬁed through an experimental axisymmetric stretch forming process using both
a hemispherical and a wheel hub punch. The main goal of the study was to
develop a modeling method that could be extended from the simple

hemispherical and wheel hub punch geometries to more complex forming

operations.

Overall, the results from the modeling process were relatively similar to the
actual experimental results. The conclusions of the paper were that the results
could be used for the material tested, but that the assumptions that went into the
calculations should be re-evaluated before changing the material. This is due to

the changing nature of different composites as they are manufactured.

Koziey, Pocher, Tian and Vlachopoulos (1997) [30] presented the advantages

and disadvantages of various constitutive equations for the description of the

24

extensional behavior of polymers. The study’s purpose was to introduce and
evaluate the following mathematical models for the prediction of wall thickness
distributions for therrnofonned parts: Mooney-Rivlin model, Ogden model,
G’Shell model, Modiﬁed G’Shell model and K-BKZ model. The conclusions
drawn were that the best results were achieved through the Modiﬁed G’Shell
model but that these results were still less than perfect. The reason for this
discrepancy was attributed to the fact that uniaxial data was used in an attempt

to predict biaxial deformations.

Hsiao and Kikuchi (1997) [4] developed a methodology of analyzing the deep
drawing process for thermoplastic composite laminates where the processing
governing equations and the corresponding material properties of the composites
were derived by the homogenization method. The ﬁnite element modeling at the
macroscopic and microscopic levels was then developed for the simulation of the,
deep drawing process. In this study, numerical results from this methodology

were demonstrated and compared with experimental observations.

The study proposed to break the process into two distinct stages;
Thennoforming and Cooling. The governing equations for each stage were
developed and the homogenization method was utilized to make these equations
adaptable to the FEA environment. The homogenization method was able to de-
couple the governing equations into a set of microscopic and macroscopic

equations. The microscopic equations accounted for the characteristic

25

defamation within the microstructures while the macroscopic equations
accounted for the average deformation for the composite structure. The
microscopic equations were solved and used as input information for solving the

macroscopic equations within the FEA analysis.

The process was veriﬁed by running experiments utilizing cylindrical and
square punches. The experimental results for the ﬁber orientation prediction
compared very favorably with the predicted theoretical results for both punches.
Overall the numerical analysis proposed showed good results for predicting the

macroscopic and microscopic stresses and strains, the ﬁber orientation and the

ﬁnal shape.

26

Chapter 4

EXPERIMENTAL WORK

In this section, the experimental apparatus designed and built in-house for
sheet composite hydroforming will be described, followed by the results from the

preliminary experiments that have been performed using a hemispherical punch.

4.1. Experimental Apparatus

The experimental apparatus was built around a double action servo press,
Figure 3, manufactured by lnterlaken Technology Corporation, Eden Prairie,
Minnesota. The double action of the press refers to the fact that the clamping
mechanism can move independent of the punch mechanism. This allows for the
boundaries of the composite draw blank to be clamped while the punch pushes
the composite sheet into the die cavity ﬁlled with supporting ﬂuid. The ability to
independently control both the clamp and the punch affords the opportunity for

various modiﬁcations of the experimental procedure.

The ﬁrst step in the creation of the experimental set-up was to design a
special die set that could be used to accurately study the hydroforming process.
The initial design started with a simple limiting dome height (LDH) test die that is
currently used for the evaluation of lubricants in the sheet metal industry. The

LDH die is essentially a pair of cylinders that are clamped together after placing a

27

draw blank between them. The punch moves through one chamber, meets the
material and stretches it into the second cylinder. The clamping mechanism
typically contains a draw bead thereby allowing for the study of pure stretch only.
Figure 4 schematically represents the press with a simple LDH die set in place
while Figure 5 is a schematic drawing of the simple LDH die set that was used

prior to modiﬁcations for the hydroforming process.

 

Figure 3. Double action servo press 75 manufactured by lnterlaken Technology
Corporation, Eden Prairie, MN.

 

Figure 4. Schematic of the double action servo press with a simple limiting dome
height test die in place.

28

 

inje-
dur

Wit

 

Figure 5. Schematic of a simple limiting dome height (LDH) test die set.

The overall experimental process as illustrated in Figure 6 started with a few
modiﬁcations that were made to the LDH die set. Initially the die was retroﬁtted
with four ports; one for measuring the pressure within the ﬂuid cavity, one for
injecting ﬂuid into the die cavity, one for removing the air from the chamber
during the ﬁll process and one that is used to measure the ﬂuid temperature
within the chamber during the process. Figure 7 is schematic illustrating these
changes while Figure 8 is a picture of the in-house designed die that was used

for studying the hydroforming process as it was applied to composite materials.

29

 

 

Figure 6. The modiﬁed lnterlaken servo press 75 used for the hydroforming of
composite sheets.

Open All“
Reservoir COMM (gimme:-

 

 

 

  
 

Fluid Chamber

 

Thermocouple
Probe

 

 

 

 

 

Figure 7. Schematic View of the Experimental Apparatus used for Hydroforming
Hemispherical Cups [31].

30

 

Figure 8. The in-house designed die set for hydroforming composite sheets.

Attached to the ﬂuid line is a regulator/controller that is used to accurately
control the ﬂuid pressure within the die cavity as the composite material is
stamped, Figure 9. If the pressure is too high, based on a user-deﬁned
algorithm, then the pressure in the system is reduced to the appropriate level. If
the pressure is too low then the regulator pulls additional pressurized ﬂuid from a
pressure vessel that is in line with the rest of the system. A pressure intensiﬁer is
used to supply the necessary volume and pressure to the reservoir prior to the
start of the hydroforming process, Figure 10. The details of the user-deﬁned
pressure algorithm are still being developed through a series of multiple testing

cycles.

31

 

 

Figure 9. Regulator and Controller used for the control of the ﬂuid pressure
within the forming chamber.

 

Figure 10. Pressure intensiﬁer and pressure reservoir used in the hydroforming
experimental set-up.

In addition to the pressure controlling modiﬁcations, the system is also
designed to take advantage of the heating that is required to form thermoplastic
materials. Prior to entering the ﬂuid chamber, the ﬂuid is heated to a temperature
of approximately 300 degrees Fahrenheit using a hot plate. Through the

injection of heated ﬂuid, the natural cooling that typically occurs during this

32

operation is eliminated and leads to a better-formed part. The second type of
heating source that is used involves the use of a convection oven to bring the
thermoplastic test sample to the appropriate forming temperature, which in this

case is around 200 °F.

The third and ﬁnal heating source used for this manufacturing process
involves the heating of the die and tool prior to placing the sample in the
experimental apparatus and during the course of the process. Heating tape is
placed around the upper ﬂuid chamber and the lower punch chamber. While the
material is being heated to its forming temperature the heating tape is used to
preheat the die surfaces. This ensures that the part is not prematurely cooled
prior to the closing of the draw bead and the injection of the heated ﬂuid. Once
the draw blank is in place and the draw bead is clamped in place, the heating
tape is used to ensure that the process maintains a temperature .of around 300

°F during the entire process cycle.

4.2. Hydroforming Challenges

The challenges that are present during the stamp hydroforming of composite
materials process can be classiﬁed into three broad categories: material, ﬂuid
pressure and temperature. The material challenges refer to the choice and
behavior of the draw blank material. One of the major obstacles concerns the

delicate balance between the ﬂuid pressure and the ductility of the material

33

chosen for the hydroforming process. The ﬂuid pressure needs to be high
enough to bend the work piece through its radius of curvature to conform to the

shape of the punch yet the material needs to be ductile enough to take this bend

without rupturing.

The second material challenge concerns the macroscopic and microscopic
behavior of the material. The behavior of the thermoplastic materials during the
processing operation is not easily predicted using just the macroscopic properties
of the material. When dealing with the composite structures, the better predictor
of overall material behavior comes from a very thorough understanding of the
microstructural behavior of the material. It is important to understand how each
ﬁber moves in relation to the other ﬁbers and how their movement affects the
overall matrix in order to predict the overall shape of the ﬁnished part. It is also
important to recognize that these microscopic changes in material behavior are
not only going to be dependent on the punch displacement but also on the

temperature, ﬂuid pressure and strain rate alterations.

Currently the initial experiments were based on the assumption of
macroscopically isotropic material behavior and led to the determination of a
stress and strain failure criteria based on this assumption. While this
macroscopic isotropic behavior is known to be a weak assumption it does
provide an adequate starting point for the determination of the failure criteria,

criteria that will be altered as more experimental results become available. Since

34

there currently is no quantitative experimental data to compare against, the
discussion concerning the stress and strain failure criteria will be left to the

section on numerical analysis results.

The second classiﬁcation of hydroforming challenges to be discussed is the
ﬂuid pressure category. Fluid pressures within the upper ﬂuid chamber that are
too high will cause the material to move through the radius of curvature much
faster than the ductility of the material will allow. This will lead to premature
rupturing of the draw blank material. On the other hand, if the ﬂuid pressure is
too low then there is not enough stretching being forced to occur during the

process and the material will be prone to wrinkling.

Therefore there is the need to establish an upper and lower limit on the ﬂuid
pressure, as it relates to the punch stroke, to determine an optimum ﬂuid
pressure punch stroke path to ensure limited rupturing and wrinkling failures of
the ﬁnished part. A generalized curve is illustrated in Figure 11 to help
demonstrate one of the goals of the experimental research, the determination of
the optimum ﬂuid pressure-punch stroke path for the stamp hydroforming of

glass mat ﬁber reinforced polypropylene thermoplastic material.

35

Fluid Pressure

     

ernldlng Failure Area

 

 

Punch Sink:
Figure 11. Generic curve illustrating the optimum ﬂuid pressure-punch stroke
path for the stamp hydroforming process.

The third classiﬁcation of the hydroforming challenges is the temperature
category. Thermoplastic material at room temperature is very brittle and will
shatter if put through the stamping process. In order to shape thermoplastic
materials they must ﬁrst be heated to, or above, their glass transition temperature
or forming temperature. The forming temperature of the material refers to the
temperature at which the matrix has become malleable and can easily be
shaped. This is currently done by placing the polypropylene thermoplastic

sheets in a simple oven and heating them for sixty minutes at 300 °F.

While the sheets are being heated the ﬂuid that is going to be injected into the

chamber is also heated to 300 °F using a hot plate. Simultaneously, heat tape is

36

placed around the upper ﬂuid chamber and the lower punch chamber in order to
preheat the metallic surfaces prior to the start of the hydroforming process. Once
the material has reached its forming temperature it is placed across the draw
bead and the system is clamped. The ﬂuid is injected into the chamber and the
process begins. In order to try to keep the process as isothermal as possible the
heating tape continues to heat the entire chamber through coordination with a

thermocouple placed within the upper ﬂuid cavity.

The challenge is the timing involved with all these systems. As mentioned
earlier the material is heated for approximately sixty minutes. During that time
the die surfaces and the ﬂuid are also heated to their respective temperatures.
The thermoplastic material does not retain heat for long periods of time and can
typically lose between 25 - 50 °F during the transfer between the oven and the
die. Therefore it is important to keep the transfer time to a minimum while
ensuring that the die and ﬂuid will not remove heat from the material before it has

been shaped by the punch.
4.3. Current Experiment, Hydroforming with Hemispherical Punch
Currently the experimental set-up is designed to fabricate simple four-inch
diameter hemispherical cups using glass mat ﬁber reinforced polypropylene

thermoplastic material that is supplied through a partnership with Azdel Inc. The

choice of this punch geometry was based on its popularity in current metal and

37

composite research [17, 18]. By performing experiments using the hemispherical
punch, the data collected can be readily compared against the data that exists for
operations such as composite sheet stamping, thermoforming, and even sheet
metal hydroforming operations. Figure 12 illustrates a sheet of the Azdel glass
mat ﬁber reinforced polypropylene thermoplastic material prior to and at the

completion of the stamping process.

 

 

Figure 12. Sheet of the Azdel glass mat ﬁber reinforced polypropylene
thermoplastic material prior to and at the completion of the stamping process.
One of the unique opportunities associated with the choice of the
hemispherical punch is that it allows for the study of material tearing without
wrinkling during the hydroforming process. This allows for the optimization of the
ﬂuid pressure and heating schemes that can be maximized to allow for deeper

drawing of the parts before rupturing.

Through a series of preliminary experiments the initial result for the test

material was not exhibiting the trends that were anticipated. The parts that were

38

hydroformed were found to fail at lower draw depths than the parts that were
formed using no resisting ﬂuid. After a careful analysis of the experimental
procedures it was discovered that the results were not turning out as expected
due to the complications associated with the process being built in an attempt to
counteract the effects of gravity. As the ﬂuid was injected into the chamber it
was initially pressurized. This initial pressurization, coupled with the gravitational
effects of the heavier material caused the material to sag at the unsupported
regions, material regions not in direct contact with the punch, illustrated in Figure

13.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 13. Example of material sag in unsupported regions of the initial
hydroforming die design.

39

This ﬂuid-induced sag caused the material to experience an additional tension
equivalent to the ﬂuid pressure times the area of the unsupported region. This
additional tension within the material led to premature rupturing of the part as the
ﬂuid pressure increased within the chamber. In addition to the increased tension
within the part, the material was also subjected to a reverse bending effect. As
the punch came into contact with the sagging material it reversed the direction of

the material ﬂow and added an additional stress to the part.

In an attempt to still validate the method and to explore different design ideas,
the process was conducted using a vinyl diaphragm material in place of the
counteracting ﬂuid. The vinyl material was a stiffer material that was used to
simulate the addition of a hydrostatic ﬂuid pressure only at the material locations
that were in direct contact with the punch. As the punch moved into the draw
blank material the vinyl diaphragm counteracted the motion and added a
pressure at the location of the material that was in contact with the punch. Due
to the stiffness of the vinyl material the unsupported regions of the draw blank
material were unaffected by the use of this diaphragm, therefore the only sag that

could occur in the material was due to the natural gravitational effects.

Figure 14 compares the parts that were formed without a counteracting
hydrostatic pressure and a part that was formed utilizing the diaphragm-induced
hydrostatic pressure. The use of the hydrostatic pressure demonstrated

appreciable qualitative increases in draw depth for the hemispherical part.

40

Based on the nature of the diaphragm material, and the experiments being
conducted, the results of the concept were not quantiﬁed but rather were used
just as a proof of the general concept. Variations to the die and to the
experimental procedure will be adopted in an attempt to accurately quantify these
results, but the preliminary results do illustrate the potential beneﬁts of this
method. The further experimentation and method validation will be discussed in

the Future Work section.

 

 

 

Figure 14. Comparison of the hemispherical part formed with an applied
hydrostatic force and with no applied pressure, respectively.

The current experimental set-up requires the use of the draw bead to ﬁx the
borders of the material during the forming process. This forces the part to be
formed through stretching of the workpiece only. One of the changes that is
presently being adapted into the system is to allow for the material to be drawn in
as it forms. The ﬂuid pressure within the chamber will force the excess material
to form to the surface of the punch, allowing the parts to achieve a deeper draw

while still maintaining a uniform part thickness. This may lead to more wrinkling

41

instabilities but it will allow for the optimization of the process with regard to both
wrinkling and rupturing instabilities. These issues will be addressed in future
experiments in order to try to hone this process in an attempt to correlate the

theory with the experimental results.

42

Chapter 5

NUMERICAL ANALYSIS

One of the most important steps in the development of a new product is
determining a numerical method for the prediction of ﬁnal part geometry and for
the optimization of the process to meet certain product speciﬁcations. When
working with composite materials this becomes even more critical since these
types of materials are prone to wrinkling and buckling during the manufacturing
process. In addition, when altering composite materials, anisotropy may be

introduced in the part by the rearranging of the ﬁbers within the matrix.

One very important tool that can be used to aid in the optimizationprocess is
ﬁnite element analysis (FEA). FEA can be used as a predictor of part geometry
as changes are made to the ﬂuid pressure, ﬂuid temperature, part geometry,
material properties, experimental conditions, or a combination of all or some of
these factors. When dealing with composite materials the interactions between
the ﬁber and the matrix are very difﬁcult to predict accurately so typically speciﬁc

numerical codes need to be developed to account for these effects.

Before taking the rather large step of developing a specialized FEA code for
this project it is imperative to ﬁrst study the process using existing commercial
codes to determine the feasibility of these programs as they apply to the

hydroforming process. Commercially available FEA codes do provide some

43

distinct advantages over specialized codes. They are relatively easy to use and
they provide an efﬁcient method for establishing baseline data for comparison
purposes. For the hydroforming 0f hemispherical cups, preliminary numerical

modeling has been performed using the commercial code MARC.

5.1. Numerical Analysis Theory

The ﬁrst step toward creating a ﬁnite element model for hydroforming was to
determine the material properties that were needed to represent the composite
sheets. Through a series of tensile tests the stress-strain plots, at different
temperatures, for different types of composite sheets were created, Figures 15 -

17. This data was used as input into the model to provide the baseline material

properties for the MARC model.

Stress StrainDatafoMO‘IGContinuousStrandMat

 

 

 

 

20000 1 ° 35 ,
-.-,” 23 c
80 C
15000 I
E
3: 10000 I
a)
5000
0 ,
0 0.005 0.01 0.015 0.02 0.025
strain (Inrm)

Figure 15. Stress-Strain plot for 40 °/o continuous strand mat, polypropylene
matrix material.

44

Stress Strain Data for 32% Long Chopped Fibers

 

18000 - 35 C Mactine
16000 l

“000 I 80 c Machine

12000

10000 <

Stress (psl)

-35 C Transverse
8000 4 23 C Madllne

23 C Transverse

 

 

 

6000 <
BOCTIansverse
4000 .
/
2000 . //
0 r r . . ’
0 0.005 0.01 0.015 0.02 0.025 0.03

Strain (infrn)

Figure 16. Stress-Strain plot for 32% oriented, long chopped ﬁber polypropylene
matrix material.

Stress Strain Date for 32% Random Glass Fibers

 

 

 

 

20000 I
23 C mains
00 C Mun a

15000 4
‘5
8
3 23 C Transverse
£3 10000 ~ _
(D

m C Transverse
5000
o . . .
0 0.005 0.01 0.015 0.02 0.025 0.03

Slra'n (Win)

Figure 17. Stress-Strain plot for 32% random, long chopped ﬁber polypropylene
matrix material.

Using MENTAT, the graphical input program for MARC, a three-dimensional

graphical model of this process was created, see Figure 18. Initially the focus

45

was placed on only modeling random ﬁber reinforced polypropylene matrix
composite material formed into hemispherical cups. This allowed for some

simplifying assumptions that eased the computational time and provided a

general idea of whether the modeling procedure was valid.

 

 

 

Figure 18. Three-Dimensional model of the hydroforming process created using
MARC.

The ﬁrst assumption used to simplify the model was to assume that the work
piece is isotropic. Since the initial modeling focused on a random ﬁber reinforced
thermoplastic, this assumption was considered valid on the macroscopic scale.

The second assumption that went into the modeling process was that the punch

46

and die were treated as rigid and therefore did not deform during the process.
Using these assumptions, and utilizing the material properties from the tensile
tests, a much simpler, two-dimensional, axisymmetric ﬁnite element model of the
hydroforming of composite material hemispherical cup process was created and

is shown in Figure 19.

 

Inc: 0
Tine: 0.000e+00

ms®x

I wet-«es— ».g I

1.000e+00

,_ 9 .000e-01

 

8.000e-01

 

7.0009-01
6.0009-01

“5.000e-01
\2

~\
\

4.000e-01 _
3.000e-01
2.000e-01
1.0009-01

0.0009+00

jobl

 

 

 

Displacement X 1

Figure 19. Two-Dimensional MARC model.

47

The model accounted for the contact analysis involving the clamping
mechanism and the composite material work piece by modeling the opposing
clamping draw bead halves as two rigid bodies, one static and one dynamic.
This allowed the model to analyze the interactions between the composite
material and the draw head of the clamp as the clamping mechanism was

closed.

Once the work piece was clamped, the dynamic rigid punch traveled to the
material and began the deformation of the work piece. As this punch began to
deform the material, a user-deﬁned algorithm was utilized to simulate the
changes in ﬂuid pressure associated with the volume displacement in the
pressure chamber. Utilizing an edge load that was placed on the surface of the
material the ﬂuid pressure within the chamber was numerically simulated. As the
part deformed, this edge load stayed normal to the surface at all points thereby

giving a fair representation of the ﬂuid in the die cavity during the hydroforming

operation.

The material defamation process was modeled using a rigid-plastic,
incremental analysis that uses large displacements and an updated Lagrangian
procedure. The modeling was conducted for a part that was drawn to depths
varying from 1.5 to 3 inches (in) while varying the die cavity ﬂuid pressures
between 0 and 3000 pounds per square inch (psi). The boundary conditions

utilized included the restriction of the y-directian movement of the lower end of

48

the axisymmetric part to account for the axis of symmetry within the material.
This allowed for a further simpliﬁcation by analyzing only half of the workpiece

and assuming symmetric behavior of the overall part.

Two basic failure criteria were considered for this analysis; equivalent von
Mises stress and total equivalent plastic strain. The yield stress of a material is a
measured stress level that separates the elastic and inelastic behavior of the
material. The magnitude of the yield stress is generally obtained from a uniaxial
test. However, the stresses in a structure are usually multiaxial. A measurement
of yielding for the multiaxial state of stress is called the yield condition.
Depending on how the multiaxial state of stress is represented, there can be
many foms of yield conditions. For example, the yield condition can be
dependent on all stress components, on shear components only, or on

hydrostatic stress.

Although many foms of yield conditions are available, the von Mises criterion
is the most widely used, and was the criterion selected for the numerical analysis
of the composite hemispherical cups hydroforming process. The success of the
von Mises criterion is due to the continuous nature of the function that deﬁnes
this criterion and its agreement with observed behavior for the commonly
encountered ductile materials [33]. The von Mises criterion states that yield

occurs when the effective (or equivalent) stress (0) equals the yield stress (Cy) as

49

measured in a uniaxial test. Figure 20 shows the von Mises yield surface in two-

dimensional stress space.

 

 

Figure 20. von Mises yield surface in two-dimensional stress space.

Mathematically, for an isotropic material, the von Mises yield criterion is

deﬁned in equation 1,

5=I(01-02)2+(02-03)2+(03-01)2I/2/\/5 (1)

where 01, <52, and 03 are the principal Cauchy stresses.

Scan also be expressed in terms of non-principal Cauchy stresses as

illustrated in equation 2.
E: [(0', —0'y)2 +(a'y —0',)2 +(0'z —0',,)2 +603; + 7,22 + Tin!” H5 (2)

The yield condition can also be expressed in terms of the deviatoric stresses

as shown in equation 3.

50

Where a} is the deviatoric Cauchy stress expressed as shown in equation 4.

. l
Gaza-,1. —§au60 (4)

Total equivalent plastic strain refers to the ability to relate multiaxial strain
increments to an equivalent increment in a uniaxial tensile test. Setting the one-
dimensional plastic work equal to the plastic work done in a general state allows
for the deﬁnition of an equivalent or effective strain increment, d E, as illustrated

in equation 5 (principle of equivalent plastic work) [32].

Ed? = a'ydsy. = 0,615,. : aldg, +02d82 +0300;3 ‘ (5)

Where 3 is the effective stress, oi is the stress increment and a is the strain

increment.

For the initial evaluations, the strain criterion was based on the results of a
simple power law equation ﬁt to the stress strain curves (Figure 17). This

resulted in the expression in equation 6.
0' = 56479030905" (6)

Equation 6 is in the fom of the basic Hallomon equation, a=ks", where k is

the strength coefﬁcient and n is the work hardening rate. As a baseline

51

n‘

approximation for the strain failure criteria, the Considere criterion was used
resulting in a strain failure criteria of e = n or e = 0.90. Even though this criterion

is typically only applied to metallic materials, it can be equally applied to polymer

materials.

There are two physical factors that must be considered when applying this
criterion to polymeric material. First is that the dissipation of mechanical energy
as heat in the necking region. This can raise the temperature of the material,
which can cause signiﬁcant softening, as the strain-rate increases, so will the
softening effect. The second factor to be considered is the deformation
resistance at the necking region. At this region of the forming material the strain
rate is higher than in the surrounding material. Therefore, depending on the
strain-rate dependence of the yield stress, the defamation resistance in this

region can increase [7].

The importance of these two opposing physical factors will depend upon the
length of the necking region of the draw blank material as well as the thickness of
the material and the strain rate of the hydrofoming process. Based on these
limitations, the use of the Considere criterion, while not an ideal choice for the
polymeric material, will provide a starting point for the evaluation and will be
modiﬁed as the correlation between the experimental and numerical procedure

progresses.

52

5.2. Numerical Analysis Results

Overall the model showed results that were qualitatively consistent with the
experimental ﬁndings. To better illustrate the observations made about the
results it is important to establish a frame of reference. For the purpose of this
discussion the ﬁnal shaped hemispherical part has been split into three distinct
regions as illustrated in Figure 21. Zone I represents the draw bead area of the
hydrofamed part, Zone II is the area of the part that foms against the sidewall of
the pressure cavity entrance, and Zone Ill represents the dome of the

hemispherical part being famed.

    

 

 

Zonell

 

Zonel

Figure 21. Zoned regions of the shaped hemispherical cups to be used in the
discussion.

Figure 22 illustrates the model for a part that has been drawn to a depth of 3
in. Figures 23 through 26 illustrate the changes in von Mises stresses for ﬂuid
pressures of 0, 1000, 2000 and 3000 psi, drawn to a depth of 1.5 inches.
Figures 27 through 30 illustrate the changes in total equivalent strains for the
same ﬂuid pressure changes and draw depth. The 1.5 inch depth was chosen to
correspond with the depth that the material ruptured during the experiments in

the absence of an applied ﬂuid pressure. This depth allowed for a direct

53

comparison between the numerical and experimental stress and strain values to

determine the correlation between the two experimental and numerical analyses.

 

Inc : 121 _ M
Tine : 8.360v00 le‘RC

_ 2.994e+00
_ 2.688e+00_
E 2.383e+00— ".
2.0772400
_1-..7Z.19_+99_ .,_,_. .\_
1.465e+00
1.16OE+00
8.5382-01
5.481e-01
2.4239~01

-6.3418-02

 

 

release

 

Displacement x ’ ‘ 1

 

Figure 22. MARC model displacement results, depth of 3 inches.

54

 

Inc: 65 \\
Tine: 3.2502+oo WA

_ 2.593e+05
.. 2.338e+05

2.083e+05

 

 

Mics-aid" 4]

1.828e+05

 

1.573e+05

 

1.318e+05

1.063er05

8.074e+04

5.523e+04

2.972e+04

4.209e+03

 

 

.\

Equivalent Von Mises Stress

Figure 23. von Mises stress MARC model results, ﬂuid pressure of 0 psi.

55

 

 

Inc: 65
lire: 3.250e+oo Ilse)

_ 2.572905
2.4092I05

2.1469+05

 

 
   
 
   

 

1.8829+05

 

Lﬁkwﬁ

 

l.3559+05

1.0929+05

8.28Ge+04

5.652e+04

3.018e+04

3.837e+03

 

 

\

 

I Equivalent Von Mises Stress .

Figure 24. von Mises stress MARC model results, ﬂuid pressure of 1000 psi.

56

 

Inc: 65 ‘\
Tine: 3.250e+oo M590

;. 2.770e+05

_. 2.497e+05

 

.. 2.224e+05

   
 
   

 

 

1.9519+05

1.678e+05

 

1.4059+05

1.131e+05

8.582e+04

5.850e+04

3.119e+04

3.869e+03

 

 

Equivalent Van Mises Stress

'4

 

Figure 25. von Mises stress MARC model results, ﬂuid pressure of 2000 psi.

57

 

. 2.921e+05
2.634e+05

‘ 2.346e+05

 

 

 

' 2.058e+05

1.77ie+05

 

1.483e+05

1.1969+05

9.08le+04

6.205e+04

3.329e+04

4.52Se+03

 

 

. indent

 

l Equivalent Von Mises Stress 1

Figure 26. von Mises stress MARC model results, ﬂuid pressure of 3000 psi.

58

 

Inc: 65
Time: 3.250e+oo “5C \

_. 4.2369-01

_. 3.8199-01

_‘ 3.401e-01

 

 

‘ 2.983e-01

 

2.566e-01

2.148e-01

1.7308-01

1.313e-01

8.952e-02

4.776e-02

5.997e-03

 

 

 

 

 

 

 

 

 

 

 

indent

 

 

 

 

Total Equivalent Plastic Strain

Figure 27. Total equivalent strain MARC model results, 0 psi ﬂuid pressure.

59

 

Inc: 65 ~\_
line: 3.250e+oo “59/\

LI 4.3799-01
_ 3.947e-01

_ 3.5158-01

H l

 

 

‘ 3.082e-01

0
I I"‘ I

2.6509-01

 

2.217e-01 ‘5 ‘*-.\_
1.785e-01
1.352e-01
9.1969-02
4.872e-02

5.467e-03 ‘s ’ . Y

 

 

 

 

 

 

 

 

 

 

 

indent

 

 

Total Equivalent Plastic Strain 1

Figure 28. Total equivalent strain MARC model results, 1000 psi ﬂuid pressure.

60

 

Inc: 65
Tire: 3.250e+oo W)

.1 4.557e-01

_ 4.107e-01

 

 

I 3.657e-01 :

3.207e-01

 

2.7569-01

 

2.3069-01

1.8569-01

1.406e-01

9.556e-02

5.053e-02

5.512e-03

 

\

Total Equivalent Plastic Strain .

 

 

Figure 29. Total equivalent strain MARC model results, 2000 psi ﬂuid pressure.

61

 

Inc: 130
Time: 3.250900 “5C -\

.. 4.8319-01

_ 4 .3549-01

_ .10 ..

3.877e-01

 

 

 

mew-l

3.401e-01

2.924e-01

 

 

2.448e-01

IW'F. _. a; .-

1.971e-01

1.494e-01

1.018e-01

5.4119-02

6.447e-03

 

indent

In,-

 

 

Total Equivalent Plastic Strain

It; _

 

Figure 30. Total equivalent strain MARC model results, 3000 psi ﬂuid pressure.

Figures 31 and 32 represent a cumulative plot of the von Mises stresses

plotted versus displacement for the varying ﬂuid pressures. Figures 33 and 34

62

illustrate the total equivalent strains plotted versus displacement also or the
varying fluid pressures. The second plot of each series is just an expanded
portion of the ﬁrst plot illustrating in greater detail the trends that have been

exhibited by the model.

Through a comparison of the results from Figures 31 and 32 to the expected
stress failure criteria of 137 megapascals (MPa) a discrepancy between the
model and the experimental results was illustrated. The numerical analysis
showed stress results at the 1.5 inch experimental draw depth failure that was an
order of magnitude higher than the yield stress of the material. The numerical
results illustrated in Figures 33 and 34 showed that predicted strain failure criteria
of 90% strain was not achieved until a draw depth that was well above 2 inches.

Again, this result did not correlate with the results found through the experiments.

These discrepancies could be attributed to the work hardening model that
was used for the numerical analysis. The initial work hardening model was
based on uniaxial stress-strain data and was used as a baseline to start the
numerical analysis. The initial uniaxial data (Figure 17) corresponded to
material that was tested at two different temperatures, both below the forming
temperature of the material. The stress-strain behavior of the material at, or
above, the forming temperature was not a priori available so the work hardening
model used for the numerical analysis had to be modiﬁed based on observations

about the nature of the equation and trial and error methods.

63

 

 

 

 

 

Numerical Stress versus Displacement Results for
Random Glass Mat Fiber Reinforced Polypropylene
6000
5000
. 4000 .
8
E
3000
g Increasing Fluid Pressure
2000 .
1000 «
0 . . , -
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0
Displacement (mm)

 

 

 

Figure 31. Plot of von Mises stress versus displacement for ﬂuid pressures of 0,
1000, 2000, and 3000 psi.

 

 

 

 

 

Numerical Stress versus Displacement Results for Random Glass Mat Fiber
Reinforced Polypropylene, Zoomed In Version

3“!)

3300
E Increasing Fluid Pressu
E
g 3200
00

31C!)

3000

55 56 57 58 59 co
Displacement (mm)

 

 

 

Figure 32. Enhanced plot of von Mises stress versus displacement for ﬂuid
pressures of 0, 1000, 2000, and 3000 psi.

64

 

Numerical Strain versus Displacement Results for
Random Glass Mat Fiber Reinforced Polypropylene

 

r‘
a.

.a
O
N

r"
O

  
 

,o ..
on

Increming Fluid Pressure

Strain (mmlmm)
p
E”

.0
A

.0
M

 

 

 

.O
o

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0
Displacement (mm)

 

 

 

Figure 33. Plot of total equivalent plastic strain versus displacement for ﬂuid
pressures of 0, 1000, 2000, and 3000 psi.

 

Numerical Strain versus Displacement Results for Random Glass Mat
Reinforced Polypropylene, Zoomed in Version i

 

1.0 l

Increasing Fluid P we

0.9 ----.SILairiEailureCn‘tedoo ........ - .......... ---- _____________________

Strain (mmlmm)

 

 

 

 

0.8
l 57 so 59 so 61 62 63 64 65 so ‘

Displacement (mm)

 

Figure 34. Enhanced plot of total equivalent strain versus displacement for ﬂuid
pressures of 0, 1000, 2000, and 3000 psi.

65

The first modiﬁcation that was made to the work hardening model was simply
reducing the strength coefﬁcient, k, by an order of magnitude from 564790 to
56479 while keeping the work hardening rate, n, the same at 0.9, therefore the
new work hardening model became a = 56479209. The numerical analysis was
performed under the same conditions as the previous trials with one change.
Since the k value had been reduced by an order of magnitude, the same order of
magnitude change had to be incorporated into the ﬂuid pressures to ensure an
accurate comparison between the two models. Therefore, the new numerical
analysis was conducted using ﬂuid pressures of 0, 100, 200 and 300 psi.
Figures 35 and 36 graphically illustrate the numerical stress results for that were

achieved through the use of the new material model whereas Figures 37 and 38

represent the strain results.

As shown in Figures 35 and 36 very good correlation between the numerical
and experimental results was achieved through the use of the new work
hardening model. The numerical model showed stress values on the order of
137 MPa at the 34 mm draw depth corresponding to experimental material
failure. The same trend noted earlier was also found in this model, as the ﬂuid

pressure in the chamber was increased the part failed at shallower draw depths.
A new strain failure criterion of approximately 37% was determined by

correlating the experimental failure draw depth to the numerical strain data

illustrated in Figures 37 and 38. This is well below the 90% strain predicted by

66

the Considere criterion but the question still remains as to the accuracy of this
value. Based on a pure bending analysis of the material the strain failure should
be at approximately 8%. From the uniaxial stress-strain data (Figure 17) the
material should fail at a strain of approximately 2.5%. Which value was most

accurate and representative of the material still remained.

Through a careful examination of the 37% strain and what the value
represented it was suggested that the modiﬁed strain value might not be too far
off. For the random ﬁber material the glass reinforcement was not continuous so
as the material was deformed a glass ﬁber may have broken due to either stress
or strain failure but that the failure of one ﬁber did not imply failure of the overall
material. The polypropylene matrix of the material had a strain failure criteria that
ranged anywhere from 25 - 600% strain depending on the temperature of the
material and the method used to manufacture the composite. Therefore it was
suggested that the ﬁber might have broken at lower strain values but that the
matrix material may not have reach strain failure thereby leading to the higher

strain values shown by the model.

When increasing the ﬂuid pressure in the die cavity, the expected result was
the ability to draw the part to a deeper depth before failure. The model was not
able to conﬁrm this expected result but the modeling results were consistent with
the experimental results. As the ﬂuid pressure increased, it caused the material

to sag and added a tension to the material, especially at the interface between

67

Zones ii and III. This increased tension led to the premature failure of the

material.

The second factor associated with this increased pressure was the reverse
bending effect. As mentioned in the experimental section of this report, the
material was unsupported at the locations where the punch was not in contact
with the material. As the punch began to deform the material the decrease in
volume led to an increase in pressure. This increased ﬂuid pressure acted upon
the unsupported regions by forcing the material downward. As the bent material
came into contact with the punch the material was then forced to reverse
direction and began moving upwards. This direction reversal led to an increased
amount of stress being imparted to the material and coincided with the location of
the premature material failures. As expected, as the ﬂuid pressure was
increased from 0 to 3000 psi, the draw depth of the hemispherical part decreased
yet the location of the failure remained consistent, at the interface between

Zones II and Ill.

68

 

 

 

Numerical Results for von Mises Stress versus Displacement using the Modified Material
Model (k reduced by one order of magnitude)

 

1w ,
160 E
140
120

100

von Mises Stress (MPa)

 

 

 

 

0 5 10 15 20 25 30 35 40 45 f
Displacement (mm)

L_..

 

 

 

Figure 35. Plot of von Mises stress versus displacement for ﬂuid pressures of 0,
100, 200, and 300 psi using the modiﬁed work hardening model.

 

Numerical Results for von Mises Stress versus Displacement using the Modiﬁed Material
Model 0: reduced by one order of magnitude)

l
Stress Failure Criteria // / !

Increasing Pressure

 

 

 

 

125

 

 

Dis-m (run)

Figure 36. Enhanced plot of von Mises stress versus displacement for ﬂuid
pressures of 0, 100, 200, and 300 psi using the modiﬁed work hardening model.

69

 

 

 

 

 

 

 

 

Numerical Results of Strain versus Displacement using New Material Model (it reduced
by one order of magnitude)
0
0 4
o .
o
E
3 ° ‘
.5.
g: o
o 4
o . r
o
o . . . .
o 5 10 15 20 25 30 35 40 45
L Displacement (mm)

 

 

Figure 37. Plot of strain versus displacement for ﬂuid pressures of 0, 100, 200,
and 300 psi using the modiﬁed work hardening model.

 

Numerical Strain versus Displacement Results for
Random Glass Mat Fiber Reinforced Polypropylene

g

 

p
8

Increasing Fluid Pressure

9::
‘13

Modiﬁed Stra'n Failure Criteria

9
O)
‘1

 

Strain (mmlmm)
p o
a. s

p
3‘

p
3‘3

 

.0

l6
g) .
A

 

 

32 33 34 35
Displacement (mm)

 

 

 

Figure 38. Enhanced plot of strain versus displacement for ﬂuid pressures of 0,
100, 200, and 300 psi using the modiﬁed work hardening model.

70

When evaluating the part from a strain failure perspective the same trends
were found. As the ﬂuid pressure within the die cavity was increased the
material was found to exhibit premature failure. This trend was consistent with
the experimental data and can be attributed to the same factors associated with

the premature stress failures.

Another advantage that was expected during the hydroforming process was
the ability of the pressure to force the material onto the punch when working with
higher ﬂuid pressures. This would allow for better shaping of the ﬁnal part in
addition to aiding in the decrease of one of the high stress concentration areas
typically found in these types of parts. Traditionally a high stress concentration
was found in Zone ll due to the contact between the material and the leading
edge of the die cavity. By utilizing the ﬂuid pressure the material in this area was
forced to conform to the punch and was prevented from coming into contact with
the die cavity surface. So far the modeling results are inconclusive in regard to
the uniform thinning that was anticipated. Once the model is modiﬁed to account

for an equalizing pressure on the punch side of the material the uniform thinning

should be readily apparent.

71

Chapter 6

FUTURE WORK

The initial experimentation and numerical analysis did not provide the results
that were expected but the correlation between the two was very similar. The
use of the thin diaphragm material illustrated the beneﬁts of an applied
hydrostatic pressure so the process needs to be redesigned to take advantage of
this beneﬁt. There are a series of steps that will be outlined for both the
experimental and numerical portion of this research in an attempt to further along
the research goal of the veriﬁcation of the stamp hydroforming method as a

viable alternative to traditional composite processing methods.

6.1. Future Experimental Work

As mentioned earlier, the main obstacle that has arisen during the
experimental phase of this research is material sag during the initial material
deformation/chamber volume displacement operation (Figure 13). This material
sag is leading to an increase in the tension within the material and is leading to
premature rupture of the material. A new design has been created and is

currently being built that may alleviate this complication.

The new design, illustrated in Figure 39, ﬁlls the bottom chamber with ﬂuid

that is equalized with the ﬂuid in the upper chamber. As the pressure in the

72

upper ﬂuid chamber increases due to the volume change, the displaced ﬂuid will
be forced into the bottom chamber thereby equalizing the pressure between the
chambers. This will allow for the support of the material that is not in contact with
the punch and will prevent the material from sagging in these regions. In
addition, the material that is in contact with the punch will experience a pressure
that is representative of the stiff material induced localized hydrostatic pressure

that was shown to give a deeper draw prior to material failure.

   
 
     
     
 

Pressure
lmenslﬁer

Pressulzed
Reservoir
—>

Open Air

 

 

 

 

 

 

 

 

 

 

Pressure
Equalization Une
<——

 

 

Upper Fluid Chamber

 

Pressure
Transducer

 

 

Thermocouple
Probe

._) Thermocouple

 

 

Loser Fluid Chamber

 

 

 

 

 

Punch

 

 

 

 

 

 

H

Figure 39. Schematic of the newly designed die that will alleviate the material
sag complication associated with the current experimental set-up [31].

l

 

73

A valve is placed on the equalization line that will allow for the interruption of
the ﬂuid flow to the lower chamber. This will be used near the end of the cycle
when additional pressure is required to ensure that the material conforms
adequately to the shape of the punch. Using the new design the process will be

reevaluated and optimized with regard to rupturing instabilities.

Once the process has been optimized for rupturing, it is important to initiate
an evaluation of the wrinkling effects during the hydroforming process. This can
be accomplished by studying hydroforming with an elliptical punch. Due to the
nonsymmetrical nature of the ellipse this geometry provides a great opportunity
to study the wrinkling effects on the thermoplastic material as it is formed. Again,
the elliptical punch is a widely used geometry for studying wrinkling effects and
will allow for the comparison of the hydroforming results to the existing wrinkling
data for other thermoplastic composite shaping methods such as thermoforming

and stamping.

The experimental study of hydroforming with an elliptical punch will allow for
the optimization of the processing methods, this time with regard to wrinkling
effects. Used in conjunction with the rupturing optimization an ideal ﬂuid
pressure-punch stroke path from Figure 11 should be determined and will lead. to

the next step of the experimentation process.

74

This next step will be to study the effects of simultaneous wrinkling and
tearing during the hydroforming process. This type of experimentation could be
accomplished by using a tapered square cup or some other readily accepted
geometry. Using the already determined optimized pressure and temperature
data from the prior experiments the new experiment can be run and the results

can be optimized once again.

This will lead to the ﬁnal optimization and should lead to the experimental
process being readied for implementation in industry by demonstrating the
advantages that hydrofon'ning has over the traditional composite forming
methods. Advantages that include the cost savings associated with the
elimination of the female die and the ability to shape parts that have more

uniformity, deeper drawing and minimal thinning in the draw-in area of the part.

Once the advantages of the hydroforming process have been veriﬁed for the
glass mat ﬁber reinforced polypropylene thermoplastic materials, experimentation
can be performed for other types of materials. Thermoplastics such as
polyethylene, polystyrene, or nylon matrices with various types of reinforcement
such as synthetic, cellulose or carbon ﬁbers could be evaluated. In addition, the
experiments could be extended to study the effects of the hydroforming process

on the forming of thermoset materials.

75

 

6.2. Future Numerical Work

Even though the preliminary results of the modeling already completed
demonstrate that there is correlation between the trends predicted by the model
and the actual experimental results, a more detailed numerical analysis needs to

be accomplished to accurately model the hydroforming operation.

As illustrated in the numerical analysis section, the current work hardening
model being used in the analysis shows the same trends but the accuracy of the
strain values can be questioned. The preliminary work hardening was based on
a power law equation derived from the uniaxial stress-strain data provided by
Azdel. As shown by Koziey et al [30] the use of uniaxial data to predict the
behavior of biaxial deformations is very difﬁcult and leads to discrepancies
between the model and the experimental results. Therefore the model needs to
be reﬁned to more accurately represent the deformation behavior of the

composite material.

One way to reﬁne the model would be to compare the force-displacement
data of the experiment with the force-displacement data from the model. From
this information a theoretical stress-strain curve for the biaxial stretching of the
material could be determined and used as the work hardening curve in the
model. This should allow for the more accurate representation of the

hemispherical shaping process as it is being performed experimentally.

76

' u— . '. '.'_'-_n.b.-Y 3.: ‘E."
t

 

 

Once the work hardening curve has been adjusted to better represent the
actual experimental procedure, adding a supporting ﬂuid pressure on the punch
side of the material will be needed in order to correlate the modeling with the
changes being to the experimental procedure. This would eliminate the material
sag that has been identiﬁed and would allow the numerical model to reﬂect the
changes being made to the experimental set-up. The inherent complication with
this aspect of the modeling is determining whether the commercial code MARC
has this capability. It is desired to create a pressure load on the punch side that
will be removed once the punch comes in contact with the material (i.e. no

additive punch and pressure loads acting at the same material point).

The next change that needs to be made to the commercial code modeling is
an evaluation of the effects that changes in temperaturemay have on the overall
process. Based on the nature of the thermoplastic composite material, an
increase in temperature should have a profound effect on the stress levels within
the material. The current model utilizes an isothermal assumption that may not
be entirely accurate. Therefore, in order to optimize this part of the process the
temperature effects need to be incorporated into the model to create an accurate

prediction method.

Once these changes have been made to the model, and the results validated

through the experimental work, the next modeling step that needs to be

77

accomplished is a FEA modeling analysis that takes into account the anisotropic
properties typically associated with glass ﬁber reinforced polypropylene
thermoplastic material. This will require some additional material tests to
determine its behavior in different directions. Once that data is collected a
phenomenological yield function can be developed and incorporated into the
ﬁnite element model to represent the through-thickness and planar anisotropy of

the composite sheet during the hydroforming process.

If good correlation is found between this FEA analysis and the experimental
results, then there should be no need for the development of a specialized ﬁnite
element code for the hydroforming manufacturing process. The natural
progression, once this point has been reached, is to change the shape of the
model from the hemispherical punch to the elliptical punch, and eventually to the

tapered square, validating the results through experimentation.

If the correlation between the experimental and numerical results for the three
punch conﬁgurations is not adequate then the development of a specialized ﬁnite
element code for the hydroforming of composite materials process is warranted.
To accurately model the forming process of composite materials, it is imperative
to study the macroscopic and microscopic behavior of the material. Since
composite microstructures are very complex, the homogenization method, as
deﬁned by Hsiao and Kikuchi [4], for composite materials, is a possibility for this

analysis. Homogenization, in the broad sense, is replacing a complicated model

78

 

 

with a simpler, equivalent model. The use of the homogenization method makes
it possible to predict both the overall and local properties of processes in
composites. This is accomplished in two steps. The ﬁrst is to solve the
appropriate local problem on the unit cell (microscopic level) and then to use this

solution in the solution of a boundary value problem for a homogenized material.

There are two distinct advantages to the use of the homogenization method.
First, the analysis of the unit cells at the microscopic level can be used to
determine the material properties and the macroscopic constitutive equations.
Secondly, the homogenization method allows for a localization procedure to be

used in the evaluation of the microscopic ﬁeld of deformation mechanics.

Current numerical analyses of the composite processing technologies all tend
to have the same basic principles. There has not been a signiﬁcant amount of
research conducted on the micromechanical behavior of thermoplastic material
as the material temperature ﬂuctuates during the forming process. By adapting
the homogenization method [4], and applying it to the hydroforming process, a
numerical analysis could be developed that accounts for the thermal differences
of the part during the shaping process, as well as the changes and interactions of

the microstructure of the composite material.

79

Chapter 7

CONCLUSIONS

Fiber-reinforced composite materials are gaining popularity as substitutions
for many of the weight critical components in the aerospace and automotive
industries. Currently there exists a need for forming and shaping methods that
can produce complex structures utilizing random ﬁber, continuous-ﬁber or
woven-ﬁber composites with limited wrinkling and distortion. One manufacturing

process that could achieve this desired result is the stamp hydroforming process.

The process of hydrofoming, unlike conventional stamping, involves
supporting the bottom of the sheet with a bed of viscous ﬂuid during the stamping
process. This external support provides a through-thickness compressive stress
that will improve the formability of the sheet by delaying the tensile instability (i.e.
necking). Also, this external support reduces the formation of wrinkles due to

tensile frictional forces.

Through a series of preliminary experiments using a specially designed. die
set a complication associated with material sag arose. Through the use of a thin
vinyl diaphragm material the beneﬁt of a hydrostatic pressure for the processing
of thermoplastic materials was demonstrated. A new die has been designed that
should eliminate the material sag issue and allow for the application of a

localized ﬂuid pressure as the material is being formed.

80

 

A numerical analysis for the hydroforming process was conducted using the
commercial code MARC. The numerical results correlated very well with the
experimental results and exhibited the same material sag complications. Further
modeling will be conducted in order to add an equalizing ﬂuid pressure on the

punch side of the material thereby simulating the new die design.

Further experimentation and modeling will need to be conducted in order to
optimize the process with regard to the rupturing instabilities. The next step will
be the evaluation of pure wrinkling instabilities and then the evaluation of a
combination of wrinkling and rupturing instabilities. The end goal is to optimize
the process with regard to both wrinkling and rupturing and to determine the
optimum ﬂuid pressure-punch stroke path that will lead to the production of high
quality parts. Overall the experimental results, coupled with the numerical
modeling, showed that the stamp hydroforming process is a viable processing
method for thermoplastic materials that warrants additional attention based on

the signiﬁcant advantages in cost savings and part production accuracy.

81

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82

 

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~

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