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thesis entitled
Selective Size Reduction of poly(viny1 chloride)
and poly(ethylene terephthalate) by Impact Grinding

presented by

Janet Lynn Green

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SELECTIVE SIZE REDUCTION OF POLY(VINYL CHLORIDE) AND
POLY(ETHYLENE TEREPHTHALATE) BY IMPACT GRINDING

By

Janet Lynn Green

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

DOCTOR OF PHILOSOPHY

Department of Chemical Engineering

1996

ABSTRACT

SELECTIVE SIZE REDUCTION OF POLY(VINYL CHLORIDE) AND
POLY(ETHYLENE TEREPH’I'HALATE) BY IMPACT GRINDING

By

Janet Lynn Green

The separation of post-consumer thermoplastics for recycling is often dificult in
cases where significant physical property difl‘erences between the materials do not exist.
One instance of this is the separation of Poly(ethylene terephthalate) from Poly(vinyl
chloride). This research has investigated a method to selectively grind Poly(ethylene
terephthalate) and Poly(vinyl chloride) in a hammer mill to difi‘erent particle sizes and
shapes for classification. Process variables, namely impact rate and temperature, have
been related to the failure mechanisms for each thermoplastic. Single and multiple particle
breakage patterns have been examined. The brittle-ductile transitions have been compared
with those predicted by tensile and compressive tests, and the B-transition process. Izod
impact and ballistics testing were also conducted to explore differences in low and high
speed impact. High speed videography was used to examine particle flow and breakage
within the hammer mill. The surfaces of the particles were viewed by scanning electron
microscopy for failure mechanism identification.

Failure mechanisms suggested by tensile and compressive deformation diagrams
proved to be poor indicators of the failure mechanisms of PVC and PET during impact

grinding. Izod impact testing and the B-relaxation temperature provided correlating

brittle-ductile transition information for PVC cornminution, but not for PET. The ductile
behavior of PET at cryogenic conditions is not fully understood.

An empirical two parameter equation proved useful in describing the size reduction
behavior of PVC and PET. The model coefficients could be related to the grinding
temperature, impact rate and screen size. The product sizes of PVC particles decreased
with increasing impact rate and decreasing temperature, and the breakage changed fi'om
bimodal cascade failure to monomodal catastrophic failure. For PET the product size was
independent of temperature, and only decreased slightly with increases in impact rate.

At cryogenic temperatures, PVC can be selectively ground to smaller particle sizes
than PET. This is due to PVC particles fracturing in a brittle fashion, while PET fails in a
ductile fashion. Separation of the two materials based on size is possible, however,

optimintion to increase purity and yield is still necessary.

   
  
    
    
 

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ACKNOWLEDGMENTS

My appreciation and indebtedness to those who contributed to this work are
limitless. My sincere thanks to my advisor, Dr. Eric A Grulke, whose assistance,
guidance, and support over the years have been invaluable. My gratitude to my advisor,
Dr. Charles A Petty, who stepped right in with enthusiasm, insuring the success of this
project with his unrivaled ideas. To the Department of Chemical Engineering, who gave
me the opportunity and support to complete this work.

I would like to thank Dr. Syed Ali for all of his assistance in obtaining the
necessary equipment and guidance at the start of this project. I would like to give special
thanks to Dr. Serban Peteu for his help with the high speed videotaping and so many other-
aspects of this research. His tireless efi‘orts and kindness will always be remembered.
Thanks to Eric Cheslek, whose assistance with experimentation at the close of this project
was immensely appreciated.

I would also like to acknowledge the Office of Naval Research, Research
Excellence Fund, American Plastics Council, Michigan Materials Processing Institute, and
the Summer Acceleration Fellowship Fund, for their financial support

Finally, to my parents, Rev. Havious and Mrs. Julia Green, and my sisters, Dr.
June Rivers, PhD., Dr. LaClaire Bouknight, M.D., Dr. Constance Price, Ph.D., Dr. Hazel
Young, MD, Dr. Valeria Jackson, PhD., Dr. Chiarina Owens, Ph.D., and Dr. Carmen
Green-Lee, M.D., who provided the prayers, example, direction and vision. To Eric
Hopson, whose fiiendship, support, and companionship has made this journey an
adventure. To Drewy, who helped me learn what faith, hope, and love really mean.

TABLE OF CONTENTS

List of Tables
List of Figures
List of Symbols
List of Abbreviations
Chapter
1. INTRODUCTION
l-l. Problem Description
1-2. Background
1-2.1 Plastic Recycling
l-2.2 Thermoplastic Properties and Grinding
1-3. Objectives
14. Methodology and Scope of the Study
1-5. Engineering Significance
1-6. References
2. SURVEY OF RELEVANT LITERATURE
2-1. Introduction
2-2. Size Reduction
2-2.1 Fracture Mechanics

2-2.2 Impact Grinding
2-2.3 Thermoplastics

Page

a.

10

10

10
12
14
15

2-2.4 Predicting Particle Size and Shape

2-3. Failure Mechanisms
2-3.1 Types of Failure Mechanisms
2-3.2 Dependence on Loading Rate, Temperature, and
Material Properties

2-4. Separation by Grinding
2-5. References
FAILURE MECHANISM DIAGRAMS: PVC AND PET
3-1. Introduction
3-2. Strain Rate - Velocity Relationship
3-3. Tensile and Compressive Failure
3-3.2 Tensile Failure Mechanism Diagrams
3-3.2 Compressive Failure Mechanism Diagrams
3-3.3 Sensitivity Analysis of Model Coefficients on
Brittle-Ductile Transition
3-4. Izod Impact Failure
3-4.l Materials
3-4.2 Izod Impact Testing
3-4.3 Limitations
3-4.4 Results and Discussion
3-5. High Speed Ballistics
3-5.l Materials

3-S.2 Ballistics Testing
3~S.3 Results and Discussion

3-6. Impact Transition Temperature Estimations from
B-Relaxation Process

3-7. Conclusions
3-8. References

IMPACT GRINDING OF THERMOPLASTICS: SIZE
DISTRIBUTION FUNCTION MODEL

4-1. Introduction

17
l7
19

21

24
24
25
26
27

34
38

40
42
42
47
47
47
47

50

53

54

55

55

4—2.

4-4.

4-5.

Experimental

4-2.1 Materials

4-2.2 Hammer Mill

4-2.3 Particle Size Determination
4-2.4 Optical Microscopy

4-2.5 Limitations

Results and Discussion

4-3.1 Empirical Breakage Models
4-3.2 Characteristic Particle Size
4-3.3 Particle Breakage Mechanism

Conclusions

References

IMPACT GRINDING OF THERMOPLASTICS: EFFECT OF
PROCESS VARIABLES ON PARTICLE COMMINUTION

5-1.

5-2.

5-4.

5-5.

Introduction

Experimental

5-2.1 Materials

5-2.2 Hammer Mill

5-2.3 Particle Size Determination
5-2.4 Size Distribution Representation
5-2.5 High Speed Videography

5-2.6 Scanning Electron Microscopy
5-2.7 Limitations

Results and Discussion

5-3.1 Effect of Temperature

5-3.2 Effect of Impact Rate

5-3.3 Efl‘ect of Feed Particle Size

5-3.4 Efi‘ect of Screen Size

5-3.5 Breakage Mechanism Identification

5-3.6 Predicting Particle Size

5-3.7 Selective Size Reduction of PVC and PET

Conclusions

References

CONCLUSIONS

55
56
56
56
58
58

58
58
62
63

74

75

76

76

77
77
79
82
82
83
85
85

85
86
88
91
95

105
121

123

125

I26

RECOMMENDATIONS
APPENDICES
Appendix A: Izod Impact Data

Appendix B: Impact Grinding Data

129

131

131

132

Table
1.1
1.2
2.1
2.2
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11

3.12

LIST OF TABLES

Thermoplastic Separation Techniques

Properties of Typical Consumer Waste Therrnoplastics
Factors Promoting Brittle Fracture

Mechanical Properties of Select Therrnoplastics

Values of Strain Rate and Velocity for Various Stress Types
Constants for Tensile Brittle Behavior Model

Constants for Tensile Yield Behavior Model

Constants for Tensile Viscous Behavior Model
Brittle-Ductile Transition Temperatures for Tensile Failure
Thermal Properties

Requirements for Adiabatic Heating

Constants for Compressive Brittle Behavior Model
Constants for Compressive Yield Behavior Model
Sensitivity of Tensile Failure Strength to Model Coeficients
Sensitivity of Compressive Failure Strength to Model Parameters

B-Relaxation Temperature and Activation Energy

Page

20
20
26
30
30
30
33
33
33
35
35
39
39

51

4.1

4.2

4.3

4.4

5.1

5.2

5.3

5.4

Coefficients for Cumulative Size Distribution Models for PVC
Coefficients for Cumulative Size Distribution Models for PET
Efi‘ects of Temperature and Impact Rate on PVC Comminution
Effects of Temperature and Impact Rate on PET Comminution
Apparatus for Grinding and Analytical Systems

Physical Data for PVC and PET

Process Variable for Impact Grinding

Brittle-Ductile Transition Temperatures (C) for PVC

61

61

73

74

78

78

80

124

LIST OF FIGURES

Figure

2.1 Schematic Diagram of Incipient Flaw

3.1 Tensile Failure Mechanism Diagram for PVC

3.2 Tensile Failure Mechanism Diagram for PET

3.3 Brittle-Ductile Transition for Tensile Failure

3.4 Compressive Failure Mechanism Diagram for PVC

3.5 Compressive Failure Mechanism Diagram for PET

3.6 Brittle-Ductile Transition for Compressive Failure

3.7 Schematic of Izod Apparatus

3.8 Izod Impact Strength of PVC and PET at Various Temperatures
3.9a SEM (x 50) of PVC Izod Test Specimen Impacted at -40°C
3.9b SEM (x 1,000) of PVC Izod Test Specimen Impacted at -40°C
3.10a SEM (x 50) of PVC Izod Test Specimen Impacted at20°C
3.10b SEM (x 1,000) of PVC Izod Test Specimen Impacted at 20°C
3.11a SEM (x 50) of PET Izod Test Specimen Impacted at 20°C

3.1 lb SEM (x 1,000) of PET Izod Test Specimen Impacted at 20°C

3.12 SEM of PVC Ballistics Sample Impacted at 398 m/s

Page

31
31
32
36
36
37
41

42

45

45

49

3.13

3.14

3.15

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

4.10

4.11

4.12

4.13

4.14

4.15

SEM of PET Ballistics Sample Impacted at 369 m/s
Brittle-Ductile Transition Predicted by B-Relaxation Temperature

Brittle-Ductile Transition Based on the B-Temperature in Temrs of
Strain-Rate

Schematic of Hammer Mill

Comparison of Cumulative Size Distribution Functions Modeling Ground
PVC Particles

Comparison of Cumulative Size Distribution Functions Modeling Ground
PET Particles

Cumulative Size Distribution of PVC Ground in a Hammer mill

Progeny PVC Particles from Single Particle Impact at 53.3 m/s and 22°C
Progeny PVC Particles fi'om Single Particle Impact at 93.2 m/s and 22°C
Progeny PVC Particles from Single Particle Impact at 93.2 m/s and 0°C
Progeny PET Particles from Single Particle Impact at 53.3 m/s and 22°C
Progeny PET Particles fi'om Single Particle Impact at 93.2 m/s and 22°C
Progeny PET Particles fiom Single Particle Impact at 93.2 m/s and 0°C

Optical Microscopy Photograph of PVC Particle Ground at 92.3 m/s and
0°C

Optical Microscopy Photograph of PET Particle Ground at 92.3 m/s and
0°C

Density Distribution for Multiple Particle Breakage of PVC at 53.3 m/s
and 22°C

Density Distribution for Multiple Particle Breakage of PVC at 93.2 m/s
and 22°C

Density Distribution for Multiple Particle Breakage of PVC at 93.2 m/s
and 0°C M.O.T.

49

52

52

57

63

65

65

67

67

68

68

70

70

71

4.16

4.17

4.18

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

5.10

5.11

5.12

5.14

Density Distribution for Multiple Particle Breakage of PET at 53.3 m/s
and 22°C

Density Distribution for Multiple Particle Breakage of PET at 93.2 m/s
and 22°C

Density Distribution for Multiple Particle Breakage of PET at 93.2 m/s
and 0°C M.O.T.

Cumulative Particle Size Distribution of Fwd Thermoplastic Flakes

Bantam Mikro-Pulverizer Hammer Mill

Experimental Setup for High Speed Videography of the Grinding Process

Cumulative Particle Size Distribution for PET at Various Temperatures
Cumulative Particle Size Distribution for PVC at Various Temperatures
Efi‘ect of Mill Outlet Temperature on PVC Comminution

Cumulative Particle Size Distribution for PVC at Various Impact Rates
At Room Temperature

Cumulative Particle Size Distribution for PET at Various Impact Rates
At Room Temperature

Cumulative Particle Size Distribution for PVC at Various Impact Rates
At 0°C M.O.T.

Cumulative Particle Size Distribution for PET at Various Impact Rates
At 0°C M.O.T.

71

72

72

79

81

87

87

88

89

89

Cumulative Particle Size Distribution PVC for Various Feed Particle Sizes 93

at Room Temperature

Cumulative Particle Size Distribution PET for Various Feed Particle Sizes 93

at Room Temperature

Cumulative Particle Size Distribution PVC for Various Feed Particle Sizes 94

at 0°C M.O.T

Cumulative Particle Size Distribution PET for Various Fwd Particle Sizes 94

at 0°C M.O.T

5.15

5.16

5.17

5.18

5.19

5.20

5.21

5.22

5.23

5.24

5.25

5.26

5.27

5.28

5.29

5.30

5.31

5.32

5.33

5.34

Self-similar size distribution of PVC for Various Feed Particle Sizes at
0°C M.O.T

Cumulative Particle Size Distribution PET for Various Retaining Screen
Sizes at Room Temperature

Cumulative Particle Size Distribution PVC for Various Retaining Screen
Sizes at Room Temperature

Cumulative Particle Size Distribution PET for Various Retaining Screen
Sizes at 0°C M.O.T.

Cumulative Particle Size Distribution PVC for Various Retaining Screen
Sizes at 0°C M.O.T.

SEM (x1,000) of PVC Particle Ground at Room Temperature

SEM (x1,000) of PET Particle Ground at Room Temperature

SEM (x1,000) of PVC Particle Ground at 0°C M.O.T.

SEM (x1,000) of PET Particle Ground at 0°C M.O.T.

SEM of PET Particle Shape

SEM of PVC Particle Shape

High Spwd Videography of Particle Prior to Impact

High Speed Videography of Particle at the Point of Impact

Dependence of Characteristic Product Size on Feed Temperature for PET
Dependence of Characteristic Product Size on Feed Temperature for PVC
Dependence of Uniformity Index on Feed Temperature for PET
Dependence of Uniformity Index on Feed Temperature for PVC
Dependence of Characteristic Product Size on Impact Rate for PET
Dependence of Characteristic Product Size on Impact Rate for PVC

Dependence of Uniformity Index on Impact Rate for PET

95

97

97

98

98

101

101

103

103

106

106

107

107

109

110

5.35

5.36

5.37

5.38

5.39

5.40

5.41

5.42

5.43
5.44
5.45

5.46

5.47

5.48

Dependence of Uniformity Index on Impact Rate for PVC

Dependence of Characteristic Product Size on Feed Particle Size for PET
Dependence of Characteristic Product Size on Fwd Particle Size for PVC
Dependence of Uniformity Index on Feed Particle Size for PET
Dependence of Uniformity Index on Feed Particle Size for PVC
Dependence of Characteristic Product Size on Screen Size for PET
Dependence of Characteristic Product Size on Screen Size for PVC
Dependence of Uniformity Index on Screen Size for PET

Dependence of Uniformity Index on Screen Size for PVC
Self-similar Size Distribution for PVC
Self-similar Size Distribution for PET

Cumulative Size Distributions for Separated PVC/PET Ground Mixture

Mass Percentage of Particles of Each Thermoplastic Retained on Sieve
Size

Size Separation of PVC/PET Mixture Ground at -20°C M.O.T.

110

112

112

113

113

115

115

116

116
118
118

122

122

123

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LIST OF SYMBOLS

Thermal diflirsivity (cmzlsec)
Incipient crack length (m)

Heat capacity (kJ/kg-K)

WLF constants (K)

Particle thickness (mm)
Young’s Modulus (N/mz)
Modulus at 0 K (N/mz)
Frequency (Hz)

Activation energy (J/mol)
Critical stress intensity factor (N/m”)
Distance from center (cm)
Particle length (mm)
Characteristic particle size (mm)
Uniformity index

Tensile load (N)

Universal gas constant (J/mol-K)
Time to failure (sec)
Exponential time constant (sec)
Temperature (K)

Glass transition temperature (K)
B-relaxation temperature (K)
Activation energy (kJ/mol)
Velocity (m/s)

Fractional difference between compressive and tensile strengths
Temperature coeflicient of the modulus

Surface free energy per unit area (N/m’)

Strain rate (sec‘l)

Pro-exponential for strain rate (sec'l)

Boltzmann constant (J/K)

Sm (N/mz)

On
0a
ago

711-.
V

Brittle tensile stress (N/mz)
Draw stress (N/mz)

Fracture stress at 0 K (N/mz)
Yield stress at 0 K (N/mz)
Viscosity at Tg (N-sec/mz)
Stress activation volume (m3)

B—D

HDPE

M.O.T.
PET
PP
PMMA
PS
PSD
PVC

LIST OF ABBREVIATTONS

Brittle-Ductile Transition
Frames per second

High density polyethylene
Liquid nitrogen

Mill outlet temperature
Poly(ethylene terephthalate)
Polypropylene

Poly(methyl methacrylate)
Polystyrene

Particle size distribution
Poly(vinyl chloride)
Rosin-Rarnmler-Bennett equation
Tetrahydrofuran

CHAPTER 1

INTRODUCTION

l-l. Problem Description
L Plastic recycling has been gaining momentum due to decreasing landfill space,
concerns about environmental contamination, and increasing costs of raw materials. A
major research focus has been to develop technology to separate mixed plastic streams.
The simplest approach to plastics separation is to use difi‘erences in physical properties,
such as density. One technological challenge has been in cases where these differences
between plastics do not exist, thus making separation dificult. The separation of
poly(vinyl chloride) (PVC) fiom poly(ethylene terephthalate) (PET) is an example.

PVC and PET have overlapping density ranges, and due to their similar
appearances and common applications, they are dificult to identify and separate.
However, these materials can be separated if differences in size and shape can be induced
during grinding (F amechon, 1990; Dreissen and F ontein, 1963). Exploratory experiments
at Michigan State University have noted significant differences in the response of PVC and
PET to impact stresses and have produced particle size difi‘erences for classification The
objective of this research is to explore more broadly the size reduction behavior of PVC
and PET over a wide range of temperatures. The approach adopted has provided new
understanding of the failure mechanisms associated with PVC and PET commimrtion
This study has provided a general knowledge of the mechanics of breakage for

thermoplastics during impact grinding.

1-2. Background
1-2,1 Plastic Rmcling

In the past two decades, the market for plastic resins has more than quadrupled in
the United States. With this large increase, plastics still only make up about 7% of
municipal waste. However, with the high cost of waste disposal, the large volume plastic
waste takes up, the increasing cost of petroleum and natural gas (primary constituents of
plastic material), the fear of environmental contamination, and the anticipation of a
significant increase in the use of plastics, there has been incentive enough for the
development and improvement of plastic recycling technologies. With governmental
regulations encouraging and even requiring recycling, the plastic recycling industry is
expanding rapidly. One limitation to this growth industry, however, is an economical
separation technology.

Plastic separation techniques basically fall into three categories: namely
macrosorting, microsorting, and molecular separation. Macrosorting can be defined as
separating plastic waste in its existing form. This is usually done manually, but automated
methods that detect color, shape, and chemical structure also have been developed.
Microsorting is the separation of material that has been reduced by shredders, or
granulators. The separation is usually based on some physical property difi‘erences
between the plastics, such as density. Molecular separation entails separating
macromolecules fi'om each other. A brief summary of some of the techniques can be seen

in Table 1.1. Most of these separation methods are still in the developmental stages.

Table 1.1 Thermoplastic Separation Techniques

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TYPE OF DEVELOPER DESCRIPTION OF ADVANTAGES / STAGE OF
SORTING TECHNI UE DISADVANTAGES DEVEIDPMENT
Macro B. F. Goodrich X-ray fluorescence is Limited Applicability Developmental
(D_r_nge_r' ,1992) used to idengfy‘ vr_ny' 1
Macro Rutgers Light transmission is Contamination Developmental
(Dinger,1992) used to sort plastics by afl‘ects success,
piwt Limited Applicability
Macro Automation Plastics sorted by resin Applicable to all Developmental
(Dinger,l992) Industries, and type and color using common packaging
detectors resins
Macro Eastman Plastics sorted by Need cooperation of Developmental
(Dinger,l992) Chemical and markers placed by entire industry
others manufacturer
Macro Eagldrrook Video cameras used to Difficulty sorting Developmental
(Icaversuch, Plastics sort plastic containers damaged containers
1991) by SEE
Macro - Plastics sorted Costly - time commercialized
manuall consumin
Micro Dev Tech Separation of PET and Limited Applicability Developmental
(Dinger,1992) Laboratories PVC based on
electrostatic mrties
Micro Sepco and Froth flotation - Limited Applicability Pre-
(Dinger’,1992) others surfactants alter commercialintion
plastics floating and
tendencies
Micro Many Sink/ float method Significant density Commercialized
(Kohl991) using separating liquids differences needed
with densities in
between plastics
Micro AKW and Hydrocycloncs separate Significant density Commercialized
(Brewer,l990) others plastics based on difl'erences needed
densities
Micro University of Supercritical C02's Works with density Developmental
(Dinw,l992) Pittsburgh density can be altered differences as little as
bychangingpressureto 0.001 g/qrcm
be between plastics
Micro Micronyl Separation of PET & Does not rely on Developmental
(Famecho PVC based on size density differences
1990) difl‘erences after
successive shock
Micro Herbold PVC(MP-380) and Limited Applicability Developmental
(Modem PET(MP-470) can be
Plastics,1990) separated by melting
them selectiver
Weeular or Rensselaer Selective dissolution of Solvent use may be Pre-
Micro plastics in a solvent at expensive eommeroialintion
M) “was

 

While all of the techniques have their advantages and disadvantages, the following
criteria are often looked for:
1. Economic Feasibility
2. Ease of Operation
3. Broad Applicability
4. Efficiency

5. Purity of Separated Streams

1-22 Thermol 'cPro i an ' in

The vast amount of literature covering comminution deals primarily with the size
reduction of brittle materials. The grinding of polymers is rarely discussed in detail.
However, because of the properties that make them unique, some difi‘erences in their
comminution behavior is expected. Polymers can act as a glassy solid, elastic rubber, or a
viscous liquid, depending on the temperature or time scale of deformation. Thus, the
study of the size reduction of PVC and PET is important, not only for the development of
an approach to recycling, but also to fill a void in the knowledge base of thermoplastics
comminution.

Farnechon (1990) has reported a process for crushing a mixture of PVC and PET
particles to give selective grinding of the PVC. The PET particles are said to be larger at
each stage of the operation. An Australian firm (Mapleston,1991) has reported an impact
grinding process which also accomplishes a size difference. However, the relationship

between the grinding conditions and thermoplastic properties has not been defined.

Whether a material undergoes ductile or brittle failure determines the size and
shape of the comminuted particle. The brittle temperature defines the change between a
brittle and a ductile failure mechanism for a thermoplastic. Ductile failure leads to long
fibrils at the failure surface, higher energy-to-break, and larger particles. Brittle failure
leads to lower energy-to-break and smaller particles. Table 1.2 shows the brittle
temperatures for some commodity thermoplastics, as well as their case of fiacture at
cryogenic conditions. PVC is listed as being easy to fracture, while PET is difficult to
fi'acture at low temperatures. The factors that promote brittle fiacture are: low
temperature, high loading (impact) rate, low molecular weight, high cross-linking, low
crystallinity, high glass transition temperature and low polarity (Braton,l980; Williams,
1984). The factors which are easiest to manipulate during grinding are the polymer
temperature and the impact rate. Thus, these are the process parameters that will be

examined in this study to selectively grind PVC and PET to difi‘erent particle sizes.

Table 1.2 Properties of Typical Consumer Waste Therrnoplastics

at
Transition Cryogenic Temp. (C)
Temp. (C) Temp.

 

The chemical formulas of PVC and PET are, respectively,

[-CH2-CH-] q q
or n [-lC-@-IC-O-CH2-CH2-O-]n

PVC is mainly an amorphous thermoplastic, while PET can have varying degrees of
crystallinity. It is noteworthy that PVC and PET have similar glass transition
temperatures, yet very difi‘erent fracture behavior. Therefore, though often used, the glass
transition temperature (T‘) is not a valid indicator of the brittle-ductile transition. T, is
determined by the measurement of molecular motion in a nondestructive test, while the
actual brittle temperature is defined by the method of fracture. This still does not explain
the behavior of PET at low temperatures. However, suggestions have been made that
PET's ductile behavior in cryogenic environments may be the result of structural changes,
such as strain-induced crystallization or molecular reorientation (see Yano and Yamaolra,

1995; Ward, 1983).

1-3. Objectives

The major objective of this dissertation is to identify conditions under which a
mixture of PVC and PET can be selectively ground to difi‘erent particle sizes. The
grinding conditions will be related to the failure mechanism at the temperature and impact
rate used for each thermoplastic. The subobjectives were to determine tensile,
compressive and impact failure mechanism diagrams for the two homopolymers, and

determine whether either of the first two diagrams could be related to the third.

Experimental data and theoretical models have been assembled in Chapter 3 to
describe the inelastic response of PVC and PET to stress. The data have been
extrapolated to represent conditions of higher strain rates and a broad range of
temperatures in order to determine what deformation mechanism or material property
could be used to estimate the behavior of PVC and PET when subjected to high speed
impact processes.

In Chapter 4, classical mathematical size distribution representations were
appraised for their applicability to describe thermoplastic comminution products. One
function was used, along with single particle grinding tests, to examine the breakage
behavior of PVC and PET. In Chapter 5, the parameters from the size distribution
function were related to changes in process variables for the purpose of evaluating the size

and shape difi‘erences of PVC and PET for a broad range of impact minding conditions.

1-4. Methodology and Scope of the Study

The investigation was approached by attempting to relate the comminution process
to various deformation mechanisms. Impact minding of PVC and PET post-consumer
bottle flakes was carried out in a hammer mill at various temperatures, impact rates, feed
particle sizes, and minder retaining screen sizes. The failure mechanisms were determined
by noting the brittle-ductile transitions for the grinding conditions and observing the failure
surfaces by scanning electron microscopy (SEM). The results were compared to those
predicted by compressive and tensile deformation models. Also, high speed videotaping
of the minding chamber was done in order to gain additional breakage mechanism

information.

1-5. Engineering Significance

This research project will have a direct efi‘ect on the recycling industry by
providing another means for separating PET and PVC. In addition, this research may
have implications in the recycling of composite materials. The controlled minding of
composite materials into distinct shape and sizes will also assist in their separation.

Valuable information needed to understand the comminution of plastics will be
provided by this investigation of particle breakage patterns. By relating these patterns to
particle shape, size, and comminution conditions, improvements can be made in areas

ranging from scrap recovery to producing better polymer powder coatings.

1-6. References

Breton, N., Cryogenic Recycling and Processing, CRC Press, Boca Raton, 1980.
Brewer, G., "Beyond PET and Milk Jug Recycling," Resource Recycling, Jan. 1990, 44.
Dinger, P., ”Automatic Sorting for Mixed Plastics," Biocycle, March 1992, 80.

Dinger, P., "Automatic Microsorting for Mixed Plastics," Biocycle, April 1992, 79.

Dreissen, H., and F. J. Fontein, “Applications of Hydrocyclones and Sieve Bends in Wet
Treatment of Coal, Minerals, and Mineral Products,” S110? T rans., March 1963.

Famechon, R, "Separation of Waste PET and PVC for Recycling," Patent FR2643011,
1990.

Kolb, K., "Method for Separating or Identifying Plastics, " Journal of Chemical
Edwation, 68 (1991) 348.

Leaversuch, R., "Automated Sorting: Key to Success in Recycling," Modern Plastics,
Nov. 1991.

Mapleston, P., "Cryogenics Improve PVC Separation," Modern Plastics, Nov. 1991, 32.
Modern Plastics, "PVC Melt Point Keys Scrap Separation," June 1990, 15.
Modern Plastics, “Resins and Compounds,” Mid-November, 1994.

Ward, 1., Mechanical Properties of Solid Polymers, John Wiley & Sons Ltd., New York
1983.

Williams, 16., Fracture Mechanics of Polymers, Ellis Horwood, Chichester, 1984.

Yano, O. and H. Yamaoka, “Cryogenic Properties of Polymers,” Progress in Polymer
Science, 20 (1995), 585.

CHAPTER 2

SURVEY OF RELEVANT LITERATURE

2-1. Introduction

The study of the selective size reduction of poly(vinyl chloride) and poly(ethylene
terephthalate) has required a review of a number of areas. An understanding of
comminution in terms of fiacture mechanics, modes of size reduction, material property
influences, and mathematical representations were all important. Also, an awareness of
how the failure mechanism of the material is related to the size reduction conditions,
namely temperature and impact rate (hammer velocity), has simrificant relevance. A
survey of other selective size reduction techniques for thermoplastics are also reviewed in
this chapter.

Most available minding data focuses on mineral processing, and very little
information is available for the size reduction of plastics. Transferring minding technology
from minerals to plastics is a key issue, since mineral processing techniques are time-

tested.

2-2. Size Reduction

Despite the fact that particle size reduction is a major unit operation in chemical
engineering, there is not a lot of information available on how the physical properties of a
material relate to the resulting shape and size of the comminuted material. The study of

shape has been limited in the past due to the lack of adequate shape characterization

ll

methods. For instance, it is still being debated whether the equipment, material type, or
the reduction ratio has the biggest efi‘ect on the shape of comminuted particles. Image
analyzers have opened the door to better particle shape determination and study. Particle
size is usually related to mind time, feed size, method of comminution, and impact energy.
The determination of what grinding conditions will give the desired size in the most energy
efficient way seems to be trial and error. Tarasiewicz and Radziszewski (1990) made an
attempt to bridge the gap between process parameters (such as rotation spwd) and
material parameters (such as tensile strength) by way of breakage energy modeling. An
energy balance was done around the breakage event in terms of the elastic strain energy of
the material and the energy added for breakage. This was related to constitutive equations
describing the energy imparted by a ball mill rotating at various rates. Their model was
not verified with experimental data, however, their study reinforces the need for better
understanding of the size reduction behavior of materials. They reported that until a better
relationship is established, it would be diflicult to truly optimize a comminution process.
Recent experimentation investigated the relationship between the temperature and
strain rate to the nature of breakage for some commercial polymers (Ahmad and Ashby,
1988). The strength of the materials were calculated using theoretical models representing
brittle and ductile fiacture, cold-drawing, and viscous flow. This was put in the form of
diamams summarizing mechanical response. They noted that polymers with similar
structures have similar diagrams. This information will be helpful in relating the size and

shape of a size reduced polymer to its brittle temperature and other properties that are

12

specific to polymer type. Thus, following their approach, failure mechanism diagrams

have been developed for PVC and PET as a part of this research.

2-2.1 Fromm Mechanics
2-2.1. 1 Nature of Breaking

In the most general sense, comminution of thermoplastics is the result of the
breakage of secondary valence forces between macromolecules and chain breakage by
tensile stress. Material flaws and crack propagation also affect breakage. Typically, the
Griffith criterion, which defines the minimum tensile stress required for fi’acture, is used to
describe brittle fi'acture. It was derived by doing an energy balance on an idealized
elliptical two-dimensional flaw or crack (see Figure 2.1). The elastically stored energy
within a stressed specimen was equated with the surface energy necessary to propagate
the crack (Ward, 1983). The analysis gives a relationship between the tensile stress, on,

and the incipient crack length, 2c, represented by :

a. = (275/sz (2-1)

P

Figure 2.1 Schematic Diagram of Incipient Flaw

13

where E is Young’s modulus, and y is the surface free energy per unit area of surface.

Over the years, Eq. (2-1) has been transformed to

a, = (K,2 /7tC)m (M)

where K;c is the critical stress intensity factor, which is a function of the load (P) and the
geometry of the material. In polymers there are inherent defects that behave like the
cracks described by the Griflith criteria. However, unlike other material, there is a critical
flaw size below which the fiacture stress is independent of the flaw size. It may be that
the flaws are created by the stress. Once a critical stress around a flaw is reached, a crack
can propagate at velocities of up to 40% of the speed of sound in the material (Prasher,
1987). Excess energy can lead to other cracks as well.

Prasher (1987) presents experimental work on stress patterns in poly(methyl
methacrylate) (PMMA) and steel spheres to compare viscoelastic with elastic material. It
was reported that, in steel, the cracks propagate around curves like onion peels, whereas
in PMMA the cracks run parallel like orange slices when subject to a compressive load.
The difl‘erence is mainly because of the much larger lateral tensile strain that occurs in the
viscoelastic material.

2-2. 1. 2 Progeny Distribution

The sizes and shapes of the daughter particles (progeny distribution) fi'om a size
reduction event can provide many insights into the breakage mechanism. Catastrophic or
cascade breakage can be inferred, as well as characteristic dispersion information, such as

a multimodal particle size distribution. The size distribution from primary breakage is

usually bimodal or even trimodal. There are a few large pieces, and many small particles.
The small particles are a result of a high concentration of stress just below the contact
surface. However, continued grinding (multiple impacts) usually results in monomodal
breakage, as the larger particles are more susceptible to size reduction because of the

following reasons:

0 larger particles have more flaws
0 smaller fragments are often “hidden” by the larger particles
0 smaller particles cannot store enough energy for crack propagation

o the particles are so small that plastic deformation occurs without size reduction

Therefore, for long grinding times, the size of the feed particles should not matter, as
particles are reduced down to nearly the same size.

Prasher (1987) presents a case of PVC being ground in a rotary cutter at room
temperature. The PVC materials had varying amounts of impact modifier (i.e. different
degrees of brittleness). At low rotational speeds and high impact strengths (more ductile),
the product was not only more coarse, but the resulting size distribution was bimodal. At
high impact rates and low impact strengths (more brittle) the particles were smaller and

more uniformly sized. This is ofien indicative of catastrophic breakage.

24 2 I E . 1.
An understanding of the breakage mechanism of particles within the grinder is vital

in order to relate low speed mechanical tests to impact grinding results. On a macroscopic

15

level, the main vehicle of breakage occurs when kinetic energy is transferred between the
hammers and the particles. Stress waves concentrate at areas of weakness due to the
particle being impacted while suspended. Lowrison (1974) reports that particles typically
break immediately as opposed to just leaving residual strains for future crack propagation.
The higher stress concentration is one of the reasons impact mills are commonly used to
comminute sofi products, because there is less deformation.

In terms of the mechano-chernistry of fracture, there is considerable debate as to
the deformation mechanism polymers undergo during impact loading. In Lowrison
(1974), it is reported that tensile strength is the determining parameter in particle
breakage. Prasher (1987) states that impact and compression are actually the same mode
of force application - just at difi‘erent rates. Then, Kausch (1987) reports that deformation
mechanism of impact loading is elastic compression and/or tensile deformation. All of
these mechanisms will be investigated in terms of their relation to impact grinding of PVC

and PET.

2-2.3 Thennoplasg'cs

Though there are some distinct differences between the comminution behavior of
brittle material and viscoelastic materiaL very little information is published on the latter.
A thermoplastic can behave in a brittle fashion, and break without material flow, or in an
elastic manner and withstand large extensions, but return to its original form after being

stressed. It can also behave like a viscous liquid and deform permanently (Ward, 1983).

16

The fact that thermoplastic failures are deformation-controlled will afl‘ect crack
propagation, stress patterns, and the responses to the deformation rate and temperature.

One important characteristic of viscoelastic material in terms of comminution is the
change in deformation behavior caused by changes in deformation rate. “nth higher
velocities, the stress is greater while the deformation is less. This is why this material is
better size reduced by impact rather than by other modes of comminution. Also, plastic
material requires a high amount of energy for crack propagation, and often multiple
impacts are necessary before breakage occurs.

Temperature is also an important component when discussing the comminution of
plastics, both on macroscopic and microscopic levels. The temperature at which size
reduction takes place relates to whether deformation or We will occur. In addition,
with the expenditure of energy for crack propagation, local heating results.

This research will investigate how these characteristics of thermoplastics will afl‘ect
the usage of size distribution representations that have been established chiefly for brittle
material.

One present research initiative on the size reduction of thermoplastics by Khait
(1994) relates to post-consumer plastic recycling as well. This technique uses an
extrusion-pulverizing process to grind commingled plastic waste by applying pressure and
a shear force while rapidly cooling the plastics to temperatures between 15 and 60°C. The
resulting product is used as powder feedstock for a variety of applications. The research
focuses on the microstrucnrral changes in the polymers (e. g. the recombination of

macroradicals formed during comminution that leads to an in situ compatibilizations of

l7

polymer blends), rather than the relationship between process parameters and product
properties that is of interest to this research. However, Khait stated that the latter would

be helpful in the firture development of their process.

2-2.4 Prediging Particle Size and §hape
It has been a long time goal in the comminution industry to be able to predict the

product of a size reduction operation from material property and process parameters.
There has been very limited success. Typically, particle size distributions are represented
by empirical functions. These functions range from equations based on some
characteristic particle size to others based on physical properties, such as fracture initiating
flaws. Prasher (1987) presents an extensive review of each type of mathematical
representation.

This research will investigate the use of some of these equations to describe PVC
and PET comminution. The information will be related to the failure mechanism the
materials undergo at various size reduction conditions. Because thermoplastics behave
difi'erent fi'om the brittle material these models are generally used for, the validity of their

use was of interest.

2-3. Failure Mechanisms
2-3 1 T of F ' M
2-3. 1. 1 Brittle and Ductile Behavior
In describing the failure mechanisms of materials in this research, the terms brittle

or ductile failure will be used. Brittle failure can be defined as catastrophic fracture

18

without any indication of plastic deformation. Conditions of low temperature and high
loading rates usually promote brittle failure. Ductile failure is characterized by yielding of
the material, sometimes resulting in the appearance of a neck. Yielding is associated with
temperatures above the glass transition temperature of the material. Beyond ductile
failure, cold—drawing is the term used when a stabilized neck results in very large
extensions of the material. Though the glass transition temperature (T ,) is ofien used as a
reference point for brittle-ductile transitions, this is not always accurate. PET is known to
exhibit ductile behavior at cryogenic temperatures, despite its T, being around 80°C (Y ano
and Yamaoka, 1995). Allison (1967) noted cold-drawing of PET at temperatures as low
as -50°C.

While the Griflith theory of rupture (see Eq. (2-2)) is used to describe brittle
fi’acture, the Eyring equation is often applied to failure by yield and cold-drawing
(Ward, 1971). The equation is based on the premise that yielding occurs when the internal
viscosity decreases to where the applied strain rate is equal to the plastic strain rate,

leading to Eq. (2.3);
a/ T=Rl v{AH/RT+ln(2a/eo)} (2-3)

a is the applied tensile stress, AH is the activation energy, and v is the activation volume.
2-3.1.2 Adiabatic heating

The occurrence of adiabatic heating is another aspect of interest to this research
At high loading rates, the energy is dissipated as heat at rates too high to be conducted

away fi'om the polymer. Thus, the material undergoes a localized temperature rise which

19

can lead to necking and cold drawing. This phenomena has been associated with PET and

is used to explain its cold-drawing behavior at low temperatures (Marshall, 1954).

2-3,2 Dependenpe on Qading Rate, Temperature and Material Properties
A study of the relationship between the mode of failure (brittle, ductile, viscous

flow) and the temperature and strain rate for various polymers was reported by Ahmad
and Ashby (1988). At temperatures below about 0.8 times the glass transition
temperature, brittle fracture occurs. Depending on the strain rate, ductile fracture
presumably occurs above 0.8T, However, there are many instances when this is not true,
such as in the case of both PET and PVC. Their T 3’s are around 80°C, while the brittle
temperature of PVC is around -20°C and PET does not have a clear brittle-ductile
transition. Newton (1971) reported that at high impact rates polymers in the ductile
region are able to absorb energy by motion, while in the brittle region there is low
mobility, and therefore less energy absorption. Increasing the impact rate has a similar
effect as lowering the temperature inasmuch as it encourages brittle fi'acture.

Shape differences between two materials might be induced by grinding if one
fiactured in a ductile mode and the other fractured in a brittle fashion. Also, because of
the way material handles the impact energy, the breakage size should vary as the mode of
fiacture varies. Some other factors promoting brittle factor can be seen in Table 2.1.
Temperature and impact rate are the parameters easiest to manipulate to afi‘ect the brittle-
ductile properties, and thus, the size and shape distributions of PVC and PET during

impact grinding.

20

Table 2.2 provides some typical mechanical property values for some
thermoplastics at room temperature. It is not obvious from looking at these values, how

PET and PVC will respond to impact grinding. This point will become increasingly clear

as this research is presented.

Table 2.1 Factors Promoting Brittle Fracture

 

 

 

 

Parameters Promoting Brittle Fracture Effects of Additives

Low Temperature Plasticizers Decrease Brittleness
High Rate of Loading Rubbers Decrease Brittleness

Low Molecular Weight Inert Particles Increase Brittleness
High Cross-Linking Fibers Decrease Brittleness

Low Crystallinity (Glass Fibers - Dependent on Resin Type)
Orientation

Rings or Side Groups

Short Linear-Side Chains

High Glass Transition Temperature

Low/No Polari

 

Braton,N. (1980); Williams, J. (1984)

Table 2.2 Mechanical Properties of Select Thermoplastics

 

 

21

2-4. Poly (vinyl Chloride) and Poly (ethylene Terephthalate) Separation by
Grinding

The utilization of the difl‘erence in impact resistance to separate thermoplastics has
gained interest in the past few years. Cryogrind Corporation (Australia) separates PVC
bottle material from other plastics and paper contaminants using granulation under
cryogenic conditions (Mapleston, 1991). Streams of mostly PVC particles are ground with
liquid nitrogen at a temperature below -100°C. PVC particles, less than 500 microns in
diameter are removed by screening from PET and other contaminants. The product is
reported to be more than 99% PVC.

A French patent details the use of the difl‘erences in shock resistance of PET and
PVC to obtain size difl‘erences between the two plastics. Famechon (1990) shows that
successive crushing of the plastics at room temperature can be followed by sieve
separation based on particle size difl‘erences. PET is said to have the larger size at each
stage.

Ultro Pac Inc. (Rogers, Minnesota) uses cryogenic conditions to remove PVC
fi‘om PET and HDPE (Schult, 1993). At -l30°C, PET beverage-bottle and HDPE basecup

flakes are hurled at a steel impact plate. Reportedly 90% of the PVC contaminate can be

removed by screening.

22

2-5. References

Ahmad, Z. and M. Ashby, ”Failure-Mechanism Maps for Engineering Polymers," Journal
of Materials Science, 23 (1988) 2037.

Allison, S., ”The Cold Drawing of Polyethylene Terephthalate," Brit. Journal of Applied
Physics, 18(1967) 1151.

Braton, N., Cryogenic Recycling and Processing, CRC Press, Boca Raton, 1980.

Famechon, R., ”Separation of Waste PET and PVC for Recycling,” Patent FR2643011,
(1990).

Kausch, H., Polymer Fracture, Springer-Vedag, New York, 2nd ed., 1987.

Khait, K., “Novel Elastic-Deformation Grinding Process for Commingled Plastic Waste
Recovery,” ANTEC 94, Vol. 3 (1994) 3006.

Lowrison, G., Crushing and Grinding, Butterworths, Boston, 1974.
Materials Engineering, “Polymer Properties,” December 1992.
Mapleston, P., ”Cryogenics Improve PVC Separation,” Modern Plastics, Nov. 1991.

Marshall, 1., "The Cold Drawing of High Polymers," Proc. Roy. Soc. London, A221
(1954) 541.

Newton, 1., "The High-Speed Impact Strength of Polymers," Applied Polymer Sympositan
No. 17, (1971) 95.

Prasher, C ., Cnashing and Grinding Process Hm, John Wiley & Sons, Chichester
1987.

Schult, 1., ”Cryogenics Remove PVC From PET and HDPE Recycle,” Plastics
Technology, April. 1993. '

Tarasiewicz, S. and P. Radziszewski, ”Comminution Energetics,” Materials Chemistry
wrdPhysics, 25 (1990) 1.

Ward, 1., Mechanical Properties of Solid Polymers, John Wiley & Sons Ltd., New York
1983.

Williams, J., Fracture Mechanics of Polymers, Ellis Horwood, Chichester, 1984.

23

Yano, O. and H. Yamaoka, “Cryogenic Properties of Polymers,” Progress in Polymer
Science, 20 (1995), 585.

CHAPTER3

FAILURE MECHANISM DIAGRAMS: PVC AND PET

3-1. Introduction

Ahmad and Ashby (1988) developed tensile and compressive failure mechanism
diagrams for several homopolymers. Failure regions such as brittle fracture, plasticity and
yielding (ductile fi'acture), adiabatic heating, rubbery flow, viscous flow and elastic
behavior were identified. The brittle-ductile transition temperature occurred at
temperatures below 0.8 times the glass transition temperature. However, the brittle
temperature can be changed either by lowering the temperature of the sample, or by
increasing the impact rate (Newton, 1971). Similar diagrams have been developed for
PVC and PET as a part ofthis research to gain insight into the failure mechanisms that
mightoccurduringimpactminding. Thesizeandshapeofcomminutedmaterialis
dependent onthetypeoffailurethat occursattheminding conditions.

It is unclear what difi‘erences a diagram for impact failure might have fiom one for
tensile or compressive failure. Kausch (1987) has stated that the deformation mechanism
for solid polymers upon minding is compressive yielding, while that during impact loading
specifically is elastic compressive and/or tensile deformation. Prasher (1987) argued that
since the chief difl'erence between impact and compression stress is the strain rate, impact
failure should be similar to compressive failure. The strain rates for tensile and
compression tests are typically less than 1 3'1, while those of the Izod impact test are 100

s‘1 (Kukureka and Hutchings, 1984). The strain rate for impact minding has been

24

25

calculated to be between l0,000-20,000 s‘l. Thus, the failure behaviors of materials for
these loading mechanisms are not expected to be the same at the same temperatures.

In this chapter the failure mechanisms of PVC and PET will be examined in terms
of tensile, compressive, and impact loading. Tensile and compressive behavior have been
predicted for various temperatures and strain rates utilizing theoretical equations of
failure. Experimental data has been extrapolated to include conditions of very high strain
rates and low temperatures for later comparison to the failure behavior seen in high speed
impact minding. It should be noted that tensile and compressive strengths are deformation
properties, while impact strength is a fiacture property. Thus, while they may be related,
their trends are typically different (i.e. reductions in impact strengths are often associated
with increases in yield strengths). Therefore, similarities in their brittle-ductile transition
conditions are of primary interest. Izod and ballistics testing have also been done to study
impact behavior. At the conclusion of this chapter, the B-transition temperature has been
utilized to estimate brittle-ductile transitions, since the strain-rate behavior of polymers has

been related to mechanical relaxations (Foot et al., 1987).

3-2. Strain Rate-Velocity Relationship

It is often helpful to define impact loading in terms of strain rates and vice versa
when comparing mechanical testing and intentional mechanical demadation. Kukureka
and Hutchings (1984) use the following relationship to equate the two in cases of simply-

supported beams:

2:600/ L2 (3-1)

26

where D is the depth of the beam, L is the span of the support points, and v is the velocity
of impact. In a case of a particle being impacted by a hammer, D is the particle thickness

and L is the particle length. Eq. (3-1) was used to calculate the velocities in Table 3.1.

Table 3.1 Values of Strain Rate and Velocity for Various Stress Types

Order of Magnitude
of Strain Rate

(8”)

 

 

 

 

Test
Impact 0.7 5.0 10,000 100
Grinding

Gun Test 76.2 7.62 1,000,000 300

 

 

 

 

 

 

 

3-3. Tensile and Compressive Failure

Failure mechanism diagrams, based on literature data and theoretical equations for
deformation and fracture, were constructed for PET and PVC. Though the diagrams are
based on their possible response to tensile and compressive stresses, the data were
extrapolated to conditions representative of high speed impact testing as well. Thus, the

strain rates are representative ofthose seen in typical tensile and compressive tests, Izod

27

impact tests, and high speed impact minding. The mechanism of failure is determined by

which correlating equation has the lowest calculated stress.

3-3 T ' ° Mec ° Di
The failure mechanisms were modeled using the following equations:
- mam - derived fi'om Grifith criterion (see Ahmad, 1988)
Brittle fracture is defined by a near linear stress-strain response up to the breaking point.
a, .7;

0' =0 — l-a
f f.0[a.y.o( . I;

)1"2 (3-2)

ago and 6330 are the fiacture and yield stresses at OK respectively. A neglimble
dependence on strain rate was assumed for ago and oy’o. arm is the temperature

coeficient of the modulus estimated fiom literature values, using the relationship:

T
E—Eo(1-a. T) (3’3)

8

where E. is the modulus, E, at 0°K.

- Milli! - based on Eyring Theory (see Foot, 1987)

Plasticity is characterized by a drop in the stress prior to fiacture, with some necking of
the material.

. )1+:—Tsinh-‘r(.‘
6'01 2 £02

a", =-"1[-H—'+1n(2 ‘
Vt

 

 

mug—27:» (34)

28

v is the stress activation volume, H is the activation energy, and so is the preexponential
for strain rate. Subscripts l and 2 represent two different activated processes. Process
one represents yielding at high temperatures and low strain rates, while process two is

dominate for low temperatures and high strain rates. These values were obtained fiom

literature data. 2 is the variable strain rate.

- M1101: - (see Ahmad, 1988)
Viscous flow is distinguished by homogeneous deformation with large extensions.

- —2.303C,(T— 7,)

0.=3£nr,exp[ C+T—T ] (3-5)
2 s

 

"T8 is the viscosity at the glass transition temperature, C] and C2 are the WLF constants.

:Adiahstisjjsatim- (866 Ahmad. 1983)

The local temperature rise at high loading rates when heat cannot be conducted away
rapidly enough is termed adiabatic heating. This can lead to cold-drawing of polymers,
where a stabilized neck results in very large extensions.

The two requirements for adiabatic heating are:
a, >10C,p/c (3'5)
c>2all2 (3-7)

Wmcpistheheatcapacity.pisthedensity,eisthestraiaaisthethemardimm~

and [is the distance from center of sample. 04 is the drawing stress, which can be

29

represented by Eq. (3-4) for plastic yielding. The strain in Ineq. (3-6) can be assumed to
be unity.

Figures 3.1 and 3.2 illustrate the possible failure mechanisms for PVC and PET
materials in tension at various temperatures and strain rates. They were constructed using
Eqs. (3-2) through (3-5), using the values in Tables 3.2 - 3.4. Of, 0,, and 0., were
calculated, and the one resulting in the lowest failure strength is considered the dominant
mechanism. As the temperature and strain rate changes, the dominant mechanism
changes. The change from brittle failure to ductile failure is denoted in the diagrams. A
summary of the brittle-ductile transition temperatures is presented in Table 3.5, with
comparisons to experimental data.

The brittle-ductile transition of PET is much lower than that of PVC, which means
PET will began to exhibit ductile behavior at lower temperatures than PVC. As the strain
rate is increased, the transition fiom brittle to ductile behavior occurs at higher
temperatures.

The regions where adiabatic heating may occur were not placed in the diagrams
due to the fact that from the rudimentary calculations, an adiabatic temperature rise may
take place at any of the conditions where ductile failure occurs for both PVC and PET.
However, adiabatic heating seems more likely to occur in PET because more plastic work
must be done for failure to occur due to its higher tensile strength. The thermal properties

and requirements for adiabatic heating can be seen in Tables 3.6 and 3.7, respectively.

30

Table 3.2 Constants for Tensile Brittle Behavior Model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Polymer Tg (K) am crf’o (N/mz) ow, (N/mz) E0 (N/mz)
PVC 352 0.295' 1.27x10glr 1.90x105' 9 94x10all
PET 337 0.295' 2.82x103” 3.69x103‘ 1 00x1015'
;Assumed.
cEstirrutted.
‘Calculatedfi'omeq. 3-4.
. Extrapolated, using data from Polymer Handbook
aminedfromEDD Database.
Table 3.3 Constants for Tensile Yield Behavior Model
rolymer v1(m5)_ v2 (m5) H1(J/mol) H2 (J/mol) 301(sec‘I) e02 (see-1)
rvc 3.1x10-5'7' 2.15x10-5'7 2.95x10 5.86x104 1.0x1053 2.35x109_
rm“ 1.21x10-27 0.86x10-27 1.88x105 7.15x104 1.2sx10fl 1.94x1014

 

 

 

 

 

 

 

 

PVCdatafromBauwem—Crowetetal,l969.

PETdamfimFomaal, 1987.

Table 3.4 Constants for Tensile Viscous Behavior Model

 

 

 

 

 

 

Polymer "T8 (N-sec/mf) C1 (K) C2 (K)
PVC 1x10”. 174' 51.6'
PET 1x1015' 15.1b 75.7b

 

 

 

‘Amurned.

bFromDuckettet. a1, 1970.

Tensile Strength (NIm‘Z)

31

 

 

 

 

 

 

 

 

 

 

12E+8
8.0E+7
4.0E+7
0.0E+0

-300 -200 400 0 100 200 300
Temperature (C)

Figure 3.1 Tensile Failure Mechanism Diamarn for PVC

3.0E+8
'3" Shin Rue (1lsec)
s ‘—O—0.1
g 2.0E+8 I 100
e A 10000
.5.
i 1.0E+8
I
E
p.

0.0E+0

-300 -200 -100 0 100 200 300

Temperature (C)

Figure 3.2 Tensile Failure Mechanism Diagram for PET

32

Another way of presenting the failure mechanisms of PVC and PET is by
determining the brittle-ductile transitions explicitly in terms of temperature and strain rate.
This has be done in Figure 3.3. The diagram illustrates B-D transition lines for which
tensile deformation at conditions to the lefi of each line would lead to brittle fracture, and
to the right, ductile failure. Thus, with the objective of causing PET and PVC to fail in
different ways, the conditions of stress should lie between the two lines. In this case, PET

would fail in a ductile fashion and PVC would fail in a brittle manner.

10000
1000

100

Strain Rate (1Isec)

 

-200 -100 0 100 200
Temperature (C)

Figure 3.3 Brittle-Ductile Transition for Tensile Failure

33

Table 3.5 Brittle-Ductile Transition Temperatures for Tensile Failure

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Strain Rates (see-1) PVC PET
Predicted Literature Predicted Literature
(Vincent, (Foot, 1987)
1960)
0.1 -48/-23 0C -25°C -98/-73 0C -80 0C
100 2/27 oC 0 °C -48/-23 0C -20 oC
10,000 52/77 0C -- 2127 °C ~—
Table 3.6 Thermal Properties
Material k(W/m-K) p(g/cm3) C,(lekg-K)
PVC 0.160 1.40 0.957
PET 0.147 1.38 1.13
Table 3.7 Requirements for Adiabatic Heating
Material Strain Rate Required for Drawing Stress Required for
Adiabatic Heating (secl) Adiabatic Heatin lm
PVC 0.006 1.34X10
PET 0.005 1.56x10’

 

 

 

 

 

 

34

3-3,2 QQmW' Fgl' ure Mghanism
The compressive failure-mechanism behavior was modeled using Eqs. (3-8) and
(3-9). Eq.(3-8) is derived fi'om the Grifith criterion for brittle fiacture (see Ahmad,

1988). Eq. (3-9) is a simplification of the Eyring theory. The mechanisms are represented

 

 

asfollowing:
imam
0 T
a =0 ..[—’—(1- a.—)1"’ (3-8)
I f 0'", T:
~21 . .
_ 2+a RT, 1 c _
a, —0,,. ——2 )[1+( H XT )ln( . )l (3 9)

3 8'

where a. is the fi'actional difi‘erence between compressive and tensile strengths given by:

or = 2(oc - (IO/(6c + at) (3.10)

0,; and at are the compressive and tensile strengths. The values of the parameters used in
these equations can be seen in Tables 3.8 and 3.9. Figures 3.4 and 3.5, which illustrates
the compressive failure behavior these equations predict for PVC and PET, were
constructed in the same manner as the tensile failure diamams.

For compressive failure, the brittle-ductile transitions for PET are slightly higher

than for PVC, implying that PET will still exhibit brittle behavior at temperatures where

35

PVC will began to act in a ductile fashion. This is the opposite of what the tensile
diagrams illustrated. Also, the brittle-ductile transitions occur at much higher temperature

for compressive failure.

Table 3.8 Constants for Compressive Brittle Behavior Model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Polymer Tg (K) am 050 (N/m2) a”, (N/mz) Eo (N/m2)
PVC 352 0.295‘ 1.27x103' 1.90x105' 9.94x109'
PET 337 0.295 ' 2.82x103" 3.69x103‘ 1.00x1010'_
: Assumed.
c Estimated.
a Calculated from eqn. 3.
. Extrapolated, using data from Polymer Handbook
Obtained from .D Database.
Table 3.9 Constants for Compressive Yield Behavior Model
Polymer ac (N/rfi)‘ at (N/mir H (J/mol) e0 (sec-1)
PVC 5.52m? 4.07x1<V 2.95x10f 1.0x1055 ;
PET 7.58x107 4.83x107 1.88x105 1.2srr1022
' Modern Plasties, Encyclopedia 1993.

PVCdatafiomBauwens-Crowetet.al,l969.
PE’I'datafmmFootet.al,l987.

36

2.0E+8

 

 

 

 

 

ST
‘2
g
a Stra'n Rate (1/sec)
C
52-, 1.oe+a +01
o + 100
13 10000
2
i
o

0.0E+0

-300 -200 400 0 100 200

Temperature (C)

Figure 3.4 Compressive Failure Mechanism Diamam for PVC

 

 

 

 

 

5.0E+0
a
<5 40E+8
Z .
g Shin Rate (1Isec)
: 3.0E+8
§ +0.1
+100
2.0E+8
I; CI 10000
2
5 1.01m .
O
o
0.0E+0
-300 -200 -100 0 100 200 300

Temperatun (C)

Figure 3.5 Compressive Failure Mechanism Diamam for PET

37

Figure 3.6 represents the brittle—ductile transition in terms of strain rate and
temperature only. Deforming PVC and PET at conditions between the B-D line of each
would result in PVC failing in a ductile mode and PET fi'acturing in a brittle fashion This
is the opposite of what is seen during impact minding, which has a strain rate of about
10,000 sec". This will be discussed further in Chapter 5. It should be noted that Figure

3.6 is a function of the compressive strength of the materials, though that cannot be seen

explicitly.

Strain Rate (1Isec)

 

0 50 100 150 200
Temperature (C)

Figure 3.6 Brittle-Ductile Transition for Compressive Failure

38

3-3 3 ' 'vi i f M el ci n n Bri Ductile Tran ition

Data are not readily available over the range of temperatures that were needed for
the failure mechanism models. Thus, many estimations were made. In order to assess
possible errors introduced by these estimations, the efl'ect of a 20 % change in the material
property values on the tensile strength and brittle-ductile transition were evaluated. This
sensitivity analysis reveals that the values of Ofo and oyo have the greatest efi‘ect on the
failure strengths and brittle-ductile transitions calculated. Tables 3.10 and 3.11 summarize
the influence of these coeficients on the material response.

The failure strength of PVC is more sensitive to error than PET, but both are
significantly affected. However, as seen in Table 3.5, the brittle-ductile transitions were

fairly close to those determined experimentally.

39

Table 3.10 Sensitivity of Tensile Failure Strength to Model Coeficients

 

 

 

 

 

 

 

 

 

 

 

 

Parameter Efl‘ect on 0 Effect on Brittle- Example: 20%
Ductile Transition increase in
Parameter
°fo A0 at: Aajo An increase Decreases transition
decreases transition by as much as 75°
temperature for PET and 200°
for PVC
“yo Ao- cc 1 / M An increase Increases transition
increases transition by as much as 25°
temperature for PET and 50°
for PVC
Table 3.11 Sensitivity of Compressive Failure Strength to Model Parameters
Parameter Efl‘ect on o Efl‘ect on Brittle- Example: 20%
Ductile Transition increase in
Parameter
Ofo A0 0: A010 An increase Decreases transition
decreases transition by as much as 25°
temperature for PET and 75°
for PVC
°yo Ad's1e f (Aayo) in An increase Increases transition
brittle region; increases transition by as much as 25°
A0 at Acne in temperature

 

ductile region

 

 

 

 

 

3-4. Izod Impact Failure
34 erial

Poly(ethylene terephthalate) post-consumer bottle flakes were utilized for these
experiments. The flakes were dried and then injection molded at about 260°C into impact
specimens for the Izod impact tests. The poly(vinyl chloride) impact specimens were
injection molded at about 185°C fiom general purpose GEON PVC containing 25%
recycled content. The specimens had a width of 12.7 mm (0.5 in), a length of 63.5 nun

(2.5 in.), and a thickness of 3.17 mm (0.125 in.).

34 T

A notch cutter (Testing Machine Inc., Model TMI 22-05) was used to produce the
indented impact site on the samples. The samples were impacted on an Izod impactor
(Testing Machines Inc., Model 43-02). A 10 lb. pendulum was used for the PVC samples,
whilea 1 lb. pendulumwasused forthe PET samples. Thefiacture surfaceswere
evaluated using a JEOL T-330 Scanning Electron Microscope (SEM) to obtain fiacture
mechanism information.

The impact testing was conducted according to ASTM-D256 standard test for
impact resistance. The Izod apparatus is illustrated in Figure 3.7. The desired test
ternperatureswereobtainedbyplacingthesamplesinaNalgeneDewarcontainingaheat-
transfermediafor3 minutes. Thetemperaturewasadjustedbyplacingdryiceina
methanol bath below room temperature and an immersion heater in a water bath above

roomternperature. Atemperaturerangefiom-400Cto 80°Cwasused.

41

' oint of Impact

u'

 

Digital Display\

 

E

Impact Specimen\

 

 

 

 

 

 

 

Figure 3.7 Schematic of Izod Apparatus

42

3-4.3 Limitations
Though the testing was done as quickly as possible, the temperature of the test specimens

may not be exactly as recorded at the time of the tests.

3-4.4 Results Ed Diggssion

PQM vinyl thgride). The data for the Izod impact strength versus testing
temperature are shown in Figure 3.8 (see tabular data in Appendix A). The amount of
energy required to break a PVC test specimen varies widely with temperature. At
temperatures less than -10 0C, the impact strengths were low and were all less than 27
J/m. Photomicrographs of the fracture surface showed characteristics typical of brittle
fi'acture. Figure 3.9 a and b show the surface for samples tested at -40 0C. The lower
magnification (Fig. 3.9a; x 50) shows a sharp fi'acture edge, and no obvious necking at
higher magnifications (Fig 3.9b: x 1000). Both observations are consistent with brittle

fracture.

hipaet Enemy (Jan)

 

$a°asaa

Tam paratute (C)

Figure 3.8 Izod Impact Strength for PVC and PET at Various Temperatures

43

There is a step change in PVC Izod impact strength over the temperature range,

0 0C < T < 20 0C. The impact energy increases by an order of magnitude. Inspection of
the samples for PVC specimens above 0 °C showed that only partial breaks occurred.
Fracture surfaces were whitish in color from deformation during impact, which is
consistent with a ductile failure mechanism. Photomicrographs taken for sampr tested at
O, 20 and 80 0C all showed ductile fracture. Figure 3.10 a and b (20 0C) show obvious
necking at low and high magnifications. The circular depressions in Fig. 3.10a aresimilar
in size to PVC suspension macroparticles. At temperature above 20 0C, the Izod impact
strength is independent of temperature and ductile failure occurs.

PM Mien; Terephthalate), The PET impact test specimens all break via a
brittle fi'acture mechanism over this temperature range. Photomicrographs of fracture
surfaces taken over the entire range were all quite similar (Figure 3.11 a and b), showing
no obvious necking even at high magnification.

 

Figure 3.9a SEM (x 50) of PVC Izod Test Specimen Impacted at -40°C

 

Figure 3.9b SEM (x 1,000) of PVC Izod Test Specimen Impacted at -40°C

fl

 

SOOPM 200001

Figure 3.10a SEM (x50) of PVC Izod Test Specimen Impacted at 20°C

 

Figure 3102: SEM(x1,000) of PVC Izod Test Specimen Impacted at 20°C

1
0
0
0
0.
.2

 

Figure 3.11a SEM (x50) of PET Izod Test Specimen Impacted at 20°C

 

Figure 3.11a SEM (xl,000) of PET Izod Test Specimen Impacted at 20°C

47

3-5. High Speed Ballistics

The velocities of impact for Izod impact testing are much smaller than those seen
during impact grinding. For Izod testing, the specimens are impacted at 3.4 m/s compared
with nearly 100 m/s during impact grinding. Therefore, ballistics testing was done at room

temperature in order to evaluate the impact failure mechanisms at higher speeds.

3-5.1 Maggifls
PET and PVC material molded into 9.53 mm (.375 in) diameter rods were cut to

lengths of 38.1 mm (1.5 in.), 57.15 mm (2.25 in), and 76.2 mm (3 in.) and used as

projectiles.

3-5 2 B ' ' T
The PVC and PET cylinders were shot fiom a gun at velocities of 300 to 600 m/s
into a wall. The final lengths and appearances of the samples were noted. SEM was used

to observe the failure mechanism of the materials.

gamma:

The failure mechanisms of PVC and PET were the saine as observed for Izod
impacting at room temperature. The PVC samples deformed and decreased in length,
while the PET samples shattered. The SEM photographs in Figures 3.12 and 3.13 depict

the yielding of the PVC material, and the brittle fiactured surface of the PET material.

48

The PVC material flowed, as if stretched, while the PET material has blunt edges, fi'om

stable crack propagation.

 

Figure 3.13 SEM of PET Ballistics Sample Impacted at 369 m/s

50

3-6. Impact Transition Temperature Estimations from B-Relaxation Process

As the temperature of a polymer is lowered, various molecular motions (or
relaxations) occur. The secondary relaxation, known as the B-relaxation process, and its
corresponding temperature, Tp, have been related to transitions that are observed in impact
behavior with changes in loading rate and temperature (Foot et al., 1987: Yano and
Yamaoka, 1995). The B-relaxation temperature occurs at the secondary peak, below that
of the glass transition temperature, and is associated with the motion of polymer side-
groups. This process is evaluated by determining the dynamic mechanical responses at
various temperatures using a the oscillating torsion pendulum. A method for estimating
the brittle-ductile transition using the B-relaxation temperature as a function of the time to
failure and temperature has been presented by Menges and Boden (1986). The time to

failure is give as
tr= 1/(21tf) (3-11)

where f is the fiequency of the torsion test. The time to failure, which is the inverse of the

strainrate, isrelatedtothetemperatureby

AU

1"! = r an" 1 (3-12)

where AU is the activation energy. The reference temperature, T..;, was chosen to be the
B—transition temperature, T3, at] Hz. The variable tn; is the time to failure at T3, Values

for T9 and AU are listed in Table 3.12. To determine the B-D transitions, the time

51

constant, to, was calculated for TB and a strain rate of 0. 160 sec'1 (1 Hz). Eq.(2-12) was

rearranged to calculate the B-temperatures for a range of times to failure.

Table 3.12 B-relaxation Temperature and Activation Energy

 

 

 

 

 

 

 

 

 

Material T,3 at 1 Hz AU t.
4K) (kJ/mol) (sec)
PVC 218‘ 54.4' 1.46x10'“
PET zoo" 715° 3.39x10'”
5
Armeniades

°Foot

Figure 3.14 illustrates the brittle—ductile transition for PVC and PET as predicted
by the B-relaxation temperature in terms of the time to failure. The region of brittle
fixture is to the right of the transition line. The estimates for the ED transitions for PVC
are -80 and -3 5°C for times to failure equivalent to those for tensile and Izod testing,
respectively, while those for PET were -85 and -60°C. According to these values, PET
will began to exhibit ductile behavior at lower temperature than PVC. At a time to failure
of 1 x 10" see, which is comparable to the time scale for impact grinding, the BB
transition for PVC is estimated to be about 12°C for PVC and -3 5°C for PET. Figure
3.15 is a replot ofFigure 3.14 in terms ofthe strain rate. It can be easily compared to the
tensile and compressive B-D transition diagrams presented earlier in this chapter. This

information will be referred to in Chapter 5.

52

1 .0E+00

1 .0E-02

1 .0E—04

Time to failure (sec)

 

1 .OE-OB
3.05-03 4.0E-03 5.0E-03 6.0E-03

Reciprocal Temperature (1IK)

Figure 3.14 Brittle-Ductile Transition Predicted by B-relaxation Temperature

1 .0E+02

Straln nu (1lsec)

 

-100 -50 O 50 100

Figure 3.15 Brittle-Ductile Transition Based on the B-Ternperature in Terms of Strain-
Rate

53

3-7. Conclusions

The values for the brittle-ductile transition temperatures as estimated by the tensile
failure diagrams and that determined by the Izod impact test are in agreement for PVC,
but not for PET. Both give a B-D transition of around 0 to 20°C for PVC. The value
predicted for PVC by the B-relaxation temperature is somewhat lower than observed.
PET does not appear to have a clear brittle-ductile transition for the range of temperatures
tested by Izod impact. In the SEM photographs, PET appears to be consistently brittle,
while the tensile theoretical failure diagrams and B-relaxation process predict PET to be
ductile for these temperatures. Ballistics tests also indicate brittle behavior for PET at
room temperature.

The brittle behavior of PETspecimens in Izod and ballistics tests at room
tmperature may be due to property changes during the specimen molding process.
Another possible explanation is that the failure behavior of PET is too complex to be
modeled by one mechanism While extrapolating tensile failure models seemingly works

for PVC, very high strain rates appear to cause PET to behave in an unexpected manner.

54

3-8. References

Ahmad, Z. and M Ashby, Journal of Materials Science, 23 (1988) 203 7.

Armeniades, C. and I. Kuriyama, “Mechanical Behavior of Poly(ethylene terephthalate) at
Cryogenic Temperatures,” in Serafini, T. and J. Koenig, ed. Cryogenic Properties of
Polymers, Marcel Dekker, Inc., New York, 1968.

Bauwens-Crowet, C., Bauwens, J.C. and G. Homes, Journal of Polymer Science: Part A-
2, 7 (1969) 735.

Duckett, RA, Rabinowita S., and I.M. Ward, Journal of Materials Science, 5 (1970)
909.

Foot, 18., Truss, RW., Ward, I.M., and RA. Duckett, Journal of Materials Science, 22
(1987) 1437.

GE Plastics, Engineering Design Database, 1992.
Kausch, H., Polymer Fracture, Springer-Verlag, Berlin, 1987.

Kukureka, S.N., and I.M. Hutchings, International Journal of Mechanical Science, 26
(1 ll12), (1984), 617.

Menges, G. and H. Boden, “Deformation and Failure of Thermoplastics on Impact,” in
Brostow, W. and R Corneliussen, ed. Failure of Plastics, New York, 1986.

Modern Plastics Encyclopedia ‘93, Mid-December. 1992.

Newton, 1., ”The High-Speed Impact Strength of Polymers," Applied Polymer .Sjmrposiran
No. 17, (1971) 95.

Prasher, C.L., Crushing and Grinding Process Handbook, Wiley, New York, 1987.

Yano, O. and H. Yamaoka, “Cryogenic Properties of Polymers,” Progress in Polymer.
Science, 20 (1995), 585.

CHAPTER 4

IMPACT GRINDING OF THERMOPLASTICS: SIZE DISTRIBUTION FUNCTION
MODEL

41-] Introduction

It has long been a goal of the comminution industry to be able to predict product
particle size distributions. Various mathematical filnctions have been modified to model
comminution results with some success. However, it is unclear how well these functions
would describe the breakage of thermoplastics, due to their dependence on breakage
mechanism.

It is the objective of this chapter to develop and demonstrate empirical breakage
mechanisms and models for impact minding of plastics. Results from multiple and single
particle breakage in a hammer mill will be utilized. This information will assist in bridging
the gap between material properties and process parameters and their relationship to

commimrtion results.

4-2. Experimental

PET and PVC chipped bottles (typically 80 grams) were ground in a laboratory
hammer mill at temperatures ranging from 496°C to room temperature. The bottle flakes
were soaked in liquid nitrogen prior to minding and liquid nitrogen was also added
continuously into the minding chamber, for the low temperatures. The temperature of the
minding chamber was measured using a thermocouple probe. Temperatures are reported

55

56

in terms of the mill outlet temperature (M.O.T), and not necessarily the exact temperature
of the flakes. The impact rate of minding was varied from 53 m/s (8,000 RPM) to 93 m/s
(14,000 RPM) by changing pulleys controlling the hammers. The particle size
distributions of the mound particles were determined by sieving. Most of the minding
results are the average of eight replicated experiments. The tabular data are in Appendix

B.

ill—mirage:
Post-consumer PET and PVC bottle flakes were used. The characteristic size of

the PET and PVC flakes were 4.6 and 7.4 mm, respectively.

$21M
A laboratory hammer mill was used for minding the particles. The model CF

Bantam Mikro-Pulverizer (Micron Powder Systems) contains six swing hammers on a
rotor disc. The minding chamber is 130 mm in diameter. The maximum speed is 14,000
RPM (93.2 m/s). A retaining screen size of3.175 mm was used for these experiments. A

schematic ofthe equipment canbe seeninFigures 4.1.

l 2 3 E . 1 5° 12 . . n
Aseries onyler sievesrangingfiom212 umto 8 mm(70-21/2Mesh)wasused
to determine the particle size distributions (PSD). The set of sieves were subjected to a

sieve shaker for size classification.

57

HOPPER
LINER _ /

1

Rolollon

 

 

 

 

 

 

 

 

 

 

 

 

 

MAIN BODY A . FEED SCREw
\ MECHANISM
ROTOR o 0
000
O 0
SCREEN o o
BASE
I I/ I T O O
HAMMER l//
/——OUTLET
L// BAG -

 

 

 

 

Figure 4.1 Schematic ofHammerMill

58

43W
An optical microscope (Olympus BH-2) was use to examine the surface structure

of mound particles. This was done to gain insight into the breakage mechanism of PVC

and PET. Surface mamrifications of 50 x were photographed.

4.2 E I o o lo I
The collection of particle fines is often diflicult. Though only a small amount of

fines is typically lost, this can afl‘ect the data’s representation by empirical models.

4.3. Results and Discussion
4.3,], Empirig Brflagg Mflels

Four mathematical functions were examined for their usefirlness in describing PVC
and PET breakage in an impact minder. The models were fitted to the data by the least-
squares method. The data are tabulated in Appendix B. Because sieves were used to
determine the particle size distributions and the number of particles per impact were low,
cumulative particle size distributions were use to interpret the results.

The following cumulative size distribution representations were used (see Prasher, 1987):

- ' -B
F(I) = 1 _ e-(l/L..)' ln(5) (4.1)
mm

17(1) = (II L,,,)" (4-2)

59

Mad—MM

 

F(l) = 1’ "Hf" (+3)
1- e
mm
F(l)=l—(l—I/Lroo)n (4‘4)

where l is the particle size, and n is a power exponent sometimes referred to as the
uniformity index. Small values of 11 mean the distribution is broad, while large values of n
signify uniform-sized particles. Leo and Ltoo represent, respectively, the characteristic size
for which 80% and 100% of the particles are smaller. The equations are bound by the
lower limit F(l) = 0 at l=0, and F(l)=l at I=Ltoo.

It should be noted that Eq. (4-1) is a modification of the Rosin-Rammler-Bennett
function The equation presented here has been altered for use with a characteristic size
based on 80% passing rather than the original 63.2% passing. The reason for this choice
will be discussed in the next section

InFigures4.2 and4.3, it canbeseenthateach firnctionfitsthedatawithvarying
success. Coeficient values were determined by minimizing the error between the data and
the models. This was done using the Solver program by Microsoft Excel. The values of
the coeficients for PVC and PET can be seen in Tables 3.1 and 3.2. The Rosin-Rammler-
Bennett gives the best overall fit. However, the Gaudin-Meloy and the Gaudin-

Schuhmann firnctions give a better fit for the fines.

Mass 96 underalzo

  

 
 
  

   

 

     
  

 

 

“at,
steamer, ”it ..

 

We»?

 

 

   

2 3

Figure 4.2 Comparison of Cumulative Size Distribution Functions Modeling Multiple

 

 

 

 

Particle Breakage of PVC Particles
1!)
+H
8)
5 --—Rtin
5 m
g “WNW
3‘ o
g ----audnt
m coo-op”.
O

 

“dam

Figure 4.3 Comparison of Cumulative Size Distribution Functions Modeling Multiple
Particle Breakage of PET Particles

  
   
  

61

Table 4.1 Coeficients for Cumulative Size Distribution Models for PVC

 

 

 

 

 

 

Model Characteristic Size, Uniformity Index, Error Sum of
L; 11 Squares
Rosin-Rammler— 2.14 2.67 42.8
Bermett
Gaudin-Meloy 1.56 0.20 2.92
Broadbent-Callcott 3.74 - 955.78
Gaudin-Schuhmann 2.48 1.64 59.93

 

 

 

 

Table 4.2 Coeficients for Cumulative Size Distribution Models for PET

 

 

 

 

 

 

Model Characteristic Size, - Uniformity Index, Error Sum of
L; n Squares
Rosin-Rammler- 2.60 2.07 4.18
Bennett
Gaudin-Meloy 1.47 0.15 6.04
Broadbent-Callcott 4.63 - 472
Gaudin-Schuhmann 2.86 1.50 39.57

 

 

 

 

The two fitted coeficients for the RRB firnction describe the data well. The

standard deviations of replicated data for Leo are 0.07 and 0.12 for PVC and PET,

respectively. The standard deviations for n are 0.35 for PVC, and 0.21 for PET.

 

 

62

4.3 ' ' Parti le Siz

The various mathematical models utilize difl‘erent characteristic particle lengths.
The most common are L50, 143.2, Leo, and L100, with the subscripts representing the
percentage of particles under the sieve size denoted by Lt. Although Leo is generally
thought to better characterize a particle size distribution (Lowrison, 1974), most values
are chosen out of convenience or by default fi'om the mathematical function employed. In
using the appropriate variations of the Rosin-Rarnrnler-Bennett equation, the same fit is
obtained for either L50, 1.53.2, or Lao. This is not surprising inasmuch as the particle size
distributions are self-similar (Prasher, 1987). Thus, there exists a transformation between
each of the RRB modifications because the characteristic lengths are proportional to one

another. Eqs. (4-5) and (4-6) represent RRB when 1.633 and L50 are used.

17(1) = 1_ e'U/LGJJ) I (*5)

17(1) = 1_ e-(l/L”)'ln(2) (4-6)

When the cumulative distribution is plotted logarithmically (see Figure 4.4) a nearly
straight line is obtained up to 80%. This observation partially motivates the arbitrary

selection of Lao as a characteristic size parameter.

63

wmumuneemmw aaaaaa

       

% mass underslze

mtgssttttmmess
a fifi

as
ii

 

Sieve size (mm)

Fimrre 4.4 Cumulative Size Distribution of PVC Ground in a Hammer mill

4-3,3 ng'clg Brgkage Mechanism

Progeny particles from single particle minding experiments and density
distributions determined fiom multiple particle testing were analyzed to obtain information
about the breakage mechanisms for PVC and PET. The results are sometimes discussed
in terms of coarse or fine particles, meaning particle sizes of 1-10 mm or 01-] mm,
respectively. Monomodal and multimodal behavior has been identified. Also, evidence
suggesting catastrophic (i.e. an impact producing many fine particles) vs. cascade (i.e.
repeated impacts needed to reduce particle to screen size) breakage is examined.
4-3. 3. 1 Single Particle Grinding

Single post-consumer bottle flakes, roughly 6 mm in length, were subjected to

impact minding in order to gain information about the progeny particles. The impact rate

64

of minding was controlled by varying the rotation rate of the mill. Single particles were
dropped directly into the minding chamber. At the lowest impact rate of 53.3 m/s, the
progeny PVC particles were made up of a few (~6) nearly equally sized coarse particles
and some fines (Figure 4.5). At 93.2 m/s the framnents were made up of a few coarse
pieces and quite a few fines (Figure 4.6). Grinding done at a M.O.T. of 0°C (feed
conditions typically below -196°C) and a rotational speed of 93.2 m/s resulted in mostly
midsize to fine particles (Figure 4.7). Single particle tests for PET produced a few (~6)
coarse particles at room temperature and 53.3 m/s (Figure 4.8). At 93.2 m/s the PSD is
broad, but is made up of mostly a number of larger particle (Figure 4.9). A liquid nitrogen
soaked PET particle broke into quite a few coarse and fine particles (Figure 4.10).

As the impact rate is increased and the temperature decreased, the PVC particles
mound to smaller and more uniform sizes. This seems to infer that the breakage
mechanism changes from being cascade to catastrophic. The results for PET are difl‘erent
in that at low temperatures and high impact rates, the size of the mound particles are still
comparatively large, though there are more fines. Cascade breakage may be ocairring at
these conditions.

Examination by optical microscopy of PVC and PET particles mound at 93 m/s
and a M.O.T. of 0°C, gives firrther clues about the breakage mechanism. In Figure 4.11,
PVC appears to break perpendicular to the bottle surface. The edges are blunt. However,
PET seems to craze throughout the sample (see Figure 4.12). This seems to give

credence to catastrophic break for PVC and cascade breakage for PET at low

temperatures.

65

 

Figure 4.5 Progeny PVC Particles from Single Particle Impact at 53.3 m/s and 22°C:
3.175 mm Retaining Screen, Mamrification x 5.8

 

Figure 4.6 Progeny PVC Particles from Single Particle Impact at 92.3 m/s and 22°C:
3.175 mm Retaining Screen, Mamrification x 5.8

 

Figure 4.7 Progeny PVC Particles from Single Particle Impact at 92.3 m/s and 0°C
M.O.T: -196°C Feed Temperature, 3.175 mm Retaining Screen, Magnification x 5.8

 

Figure 4.8 Progeny PET Particles from Single Particle Impact at 53.3 m/s and 22°C:
3.175 mm Retaining Screen, Mamlification x 5.8

67

 

Figure 4.9 Progeny PET Particles from Single Particle Impact at 92.3 m/s and 22°C:
3.175 mm Retaining Screen, Mamlification x 5.8

 

Figure 4.10 Progeny PET Particles fiom Single Particle Impact at 92.3 m/s and 0°C
M.O.T. : -196°C Feed Temperature, 3.175 mm Retaining Screen, Mamlification x 5.8

68

 

Figure 4.11 Optical Microscopy Photomaph of PVC Particle Ground at 92.3 m/s and 0°C
M.O.T: -l96°C Feed Temperature, 3.175 mm Retaining Screen, Mamlification x 50

 

Figure 4.12 Optical Microscopy Photomaph of PET Particle Ground at 92.3 m/s and 0°C
M.O.T: -196°C Feed Temperature, 3.175 mm Retaining Screen, Mamrification x 50

69

4-3.3.2 Density Distributions

One method for determining changes in breakage mechanism is to observe density
(or differential) distributions. Density distributions are the derivatives of cumulative
distributions. They ofl‘er the advantage of revealing multimodal behavior. Thus,
information about the number and size of progeny particles fiom multiple particle impact
minding can be obtained. This information should correlate with what is seen in single
particle testing.

PVC and PET flakes were mound at impact rates of 53 and 93 m/s and at room
temperature and a M.O.T. of 0°C (feed temperature below -l96°C, see Section 4-2). The
resulting size distributions were arranged in the form of the change in % mass undersize
divided by the change in the representative sieve sizes. PVC exhlbits bimodal
characteristics and coarser particles at room temperature for impact rates of 53.3 and 93.2
m/s, though at the higher impact rate there is a decrease in the bimodal component (see
Figures 4.13 and 4.14). At a M.O.T. of 0°C, the PVC density distribution is monomodal
(Figure 4.15). The narrowness of the peak suggests a more uniform distribution, and
possibly catastrophic failure. In Figures 4.16 - 4.18, PET appears to exhibit monomodal
breakage at room temperature, but is slightly bimodal, with finer particles at 0°C. This
bimodal distribution may be the result of cascade breakage or PET may be exhibiting both
ductile and brittle behaviors, leading to both fine and coarse size particles.

Though these density plots are based on actual data, it is interesting to note that of
the PSD functions presented at the beginning of this chapter, only the RB equation gives

a difl‘erential distribution which represents the data.

70

16 mass per millkmter

 

0 1 2 3
Parflcle size (mm)

Figure 4.13 Density Distribution for Multiple Particle Breakage of PVC at 53.3 m/s and
22°C: 3.175 mm Retaining Screen

 

0 1 2 3
Particle size (nun)

Figure 4.14 Density Distribution for Multiple Particle Breakage of PVC at 93.2 m/s and
22°C: 3.175 mm Retaining Screen

71

Sumner“

 

0 1 2 3
Particle slze (mm)

Figure 4.15 Density Distribution for Multiple Particle Breakage of PVC at 93.2 m/s and
0°C M.O.T: -l96°C Feed Temperature, 3.175 mm Retaining Screen

96 mass per mllllmeter

 

0 1 2 3
Particle size (111111)

Flgt:te4.16 DensityDistribution forMultiple Particle Breakage ofPET at 53. 3 m/s and
22' C: 3. 175 mmRetainingScreen

72

 

i
5 40
E
I.
a
g 20
a!

0

0 1 2 3
Particle size (mm)

Figure 4.17 Density Distribution for Multiple Particle Breakage of PET at 93.2 m/s and
22°C: 3.175 mm Retaining Screen

 

0 1 2 3
Particle size (mm)

Figure 4.18 Density Distribution for Multiple Particle Breakage of PET at 93.2 m/s and
0°C MO.T : -l96°C Feed Temperature, 3.175 mm Retaining Screen

 

73

The coemcients for the RRB equation representing each condition given in the
density distributions are presented in Tables 4.3 and 4.4 for PVC and PET, respectively.
Leo decreases with increasing impact rate and decreasing temperature for PVC. The
uniformity index, n, for PVC increases with increasing impact rate and decreasing
temperature. Leo follows the same trend for PET as for PVC except to a smaller extent.
However, the uniformity index for PET decreases with increasing impact rate and
decreasing temperature. The fact that It increases with decreasing temperature and
increasing impact rate for PVC, by definition, means the distribution is more uniform,
again suggesting a change toward catastrophic failure. By the same logic, since it
decreases for PET for these conditions, the distribution is becoming increasingly scattered,
implying multiple breakage mechanisms. Thus, the behavior for PET at low temperatures

is quite different fiom that of PVC.

Table 4.3 Efl‘ects of Temperature and Impact Rate on PVC Comminution

 

 

 

 

 

Impact Rate Outlet Temperature Characteristic Size, Uniformity Index,
(tn/8) (C) Let (M) n
53.3 22 3.12 2.52
93.2 22 2.14 2.67
93.2 0 1.17 3.25

 

 

 

 

 

74

Table 4.4 Effects of Temperature and Impact Rate on PET Comminution

 

 

 

 

 

Impact Rate Outlet Temperature Characteristic Size, Uniformity Index,
(m/s) (C) Leo (mm) 11
53:3 22 2.67 2.89
93.2 22 2.57 2.09
93.2 0 2.41 1.68

 

 

 

 

 

4-4. Conclusions

The Rosin-Rammler-Bennett equation adequately models PVC and PET behavior
over the entire range of the cumulative size distribution. The two fitted coeficients, Leo
and n, describe the data well. The breakage mechanism for multiple particle size reduction
amee with what is seen in single particle breakage. PVC breaks in a bimodal fashion at
room temperature, and in a monomodal fashion at low temperatures. The breakage
behavior of PET is the reverse. Grinding at low temperatures and/or high impact rates
appears to cause PVC flakes to break catastrophically, while the breakage pattern for PET

seems to be both catastrophic and cascade at those conditions.

75

4-5. References
Lowrison, G., Cntshing and Grinding, Butterworths, Boston, 1974.

Prasher, C., Crushing and Grinding Process Hancfiook, John Wiley & Sons Ltd., New
York, 1987.

CHAPTERS

IMPACT GRINDING OF THERMOPLASTIC S: EFFECT OF PROCESS VARIABLES
ON PARTICLE COMMINUTION

S-l. Introduction

The impact failure behavior of thermoplastics is generally described in terms of
their responses to low speed tests at room temperature. However, failure behavior is
dependent on the rate of impact loading, and on the temperature. Very little work has
been done at high impact rates and low temperatures. For various applications, whether
exposed to intentional or inadvertent impact stresses, information at these condition is
very important.

In this chapter the failure behavior of PVC and PET will be examined during high
speed impact minding. The effect that process variables, namely impact rate, tanperature,
retaining screen size, and feed particle size, have on the comminuted product will be
discussed. The particle size distribution (PSD) data are represented by the Rosin-
Rammler-Bennett (RRB) distribution.

Due to the self-preserving nature of particle size distributions, a similarity solution
exists that is only disrupted with changes in the mode and/or mechanism of size reduction
In addition, beyond initial minding periods the observed similarity behavior is independent
of minding time. Since each of the process variables has an effect on the residence time of

the particles, this is an important fact.

76

77

The breakage and failure mechanisms have been observed using scanning electron

microscopy and high speed videomaphy.

5-2. Experimental
The minding experiments were carried out on a Bantam Mikro-Pulverizer impact

minder with cryogenic apparatus made by Micron Powder Systems. The temperatures of
the bottle flakes (ranging fl'om -196 to 80°C) were lowered using liquid nitrogen or
refiigeration, and raised by heating in an oven. The flakes were placed on a vibratory
feeder and fed into the hopper of the impact minder. The hammer speed was varied
between experimmts fi'om 53 to 93 m/s. The retaining screens, with slots ranging fi'om
0.254 to 3.175 mm, were also varied. The mound material was collected, and the particle
size distribution was determined. The data and the curves representing the empirical size
distribution model are presented as cumulative mass percent of particles under a given
sieve size. The data, in tabular form, are presented in Appendix B. Scanning electron
microscopy was employed to determine shape and failure mechanism information Table

5.1 lists the apparatus employed.

W
Post-consumer PET and PVC bottle flakes were used. Relevant physical property
data are summarized by Table 5.2. The initial cumulative size distributions of the flakes

are plotted in Figure 5.1.

78

Table 5.1 Apparatus for Grinding and Analytical Systems

 

 

 

 

EQUIPMENT MAKE MODEL
Testing Sieve Shaker Tyler RO-TAP Model B
High Speed Motion Eastman Kodak EKTAPRO EM
Analyzer
Scanning Electron Joel T-330
Microscope

 

Micro-Pulverizer Hammer Micron Powder Systems BANTAM
Mill

 

 

 

Electromamretic Vibratory Syntron FTO-C

Feeder

Thermocouple McMaster Carr Model C, Type K
Thermometer

 

 

 

Table 5.2 Physical Data for PVC and PET

 

 

Material Density Glass Melting Characteristic Particle
(glcm’) Transition Temperature Feed Particle Thickness
Temperature (C) Length (mm)
(C) (m)
PET ~1.30-I .40 80 250-255 4.6 0.68

 

 

PVC ~l .30-1 .35 85 150-200 7.4 0.72

 

 

 

 

 

 

 

 

79

96 mass undersize

 

2.0 4.0 6.0 8.0

Sieve size (mm)

Figure 5.1 Cumulative Particle Size Distribution of Feed Thermoplastic Flakes

5-2,2 Ems; Mill

A laboratory hammer mill containing six “'1'” head swing-hammers was used for
minding the particles. The hammers are attached to a rotor in the 12.7 cm diameter
minding chamber. The hammer speed, which is the circumference of the minding chamber
multiplied by the number of revolution of the rotor per min. (RPM), can be varied by
changing pulleys and belts. The minding chamber has a liquid nitrogen purge for lowering
the temperature. There are retaining screens of difl‘erent slot sizes that fit in the bottom of
the chamber. Herringbone perforated screens were used for this experimentation A
herringbone screen has a series of slotted holes at 45 demees to the length of the screen

The opening without a screen is 5 cm x 12 cm. There are multiple deflector liners which

80

supplement the impacts of the hammers. A list of the process variable can be seen in

Table 5.3. A photomaph of the equipment can be seen in Figures 5.2.

Table 5.3 Process Variables for Impact Grinding

 

 

 

 

 

 

 

 

 

VARIABLE TYPE OR RANGE

Material PVC, PET

Impact Rate 53 m/s (8,000 rpm), 67 m/s (10,000 rpm),
93 m/s (14,000 rpm)

Screen Slot Size 0.254 mm, 1.57 mm, 2.36 mm, 3.175 mm,
no screen (50mm)

TWG -l96°C to 80°C

Screen Type Herringbone

Feed Size up to 8 mm

Feed Rate up to 100 mmin.

 

 

 

81

 

Figure 5.2 Bantam Mikro-Pulverizer Hammer Mill

82

5-2.3 Pm'cle Size Determination

The particle size distributions of the feed and product were determined by standard
sieving methods. The representative size of the particles in a sample was taken to be that
of the sieve screen size through which 80% of the particles passed. This size is thought to
more accurately characterize the material, without placing too much emphasis on the
larger or smaller size fractions (Lowrison,1974). The large size fractions may contain
particles that have not been reduced or just odd particles that are not representative
of the batch Smaller size fi'actions (i.e. below 50% undersize) neglect some characteristic
particles.

A series onyler sieves ranging fi'om 212 pm to 8 mm (70 - 2 1/2 Mesh) were
used to determine the size distributions. The set of sieves were subjected to a sieve shaker

for size classification.

5- 4 ' 5 Di ' ' n r

A number of mathematical equations have been used to represent particle size
distributions. Though empirical in nature, they are often vary useful for mapping changes
in size distributions with changes in design parameters and operating conditions. They are
also helpfiil in exposing changes in the mode and the mechanism of comminution

In the previous chapter, the Rosin-Rammler-Bennett equation (Eq. 5-1) was
determined to adequately model PVC and PET comminution. Thus, the RB equation

will be used to represent the size distribution data presented in this chapter:

83
F“) ____ 1_ e-(l/Lso)"ln(5) (5_1)

F0) is the cumulative size distribution function. Leo is the fineness index representing the
characteristic 80 % passing size, and the exponent n is the uniformity index. Large values
of n imply nearly uniform particle sizes, while smaller values denote a scattered
distribution (Prasher, 1987). Note that when l= Lao, Eq. (5-1) implies that F(L.o)=0.80.
The measured PSD are given as cumulative plots of mass percentage of particles

below a given sieve size.

5- Vi h

A high speed motion analyzer was used to observe the particles within the minding
chamber, which was retrofitted with a 12 mm thick transparent acrylic window. The
comminution was recorded at LOGO-6,000 fiames per second (fps) using a 67 mm
diameter lens with a macro focusing zoom - The objective for using high speed

videomaphy was to capture the following:

- number of impacts to break a particle;
- number ofirnpacts to break a particle to screen size;
- number of fi'amnents per impact (i.e. catastrophic or cascade breakage) and,

- the breakage mechanism (i.e. particle-particle, particle-hammer, particle-wall).

The setup for the high speed videomaphy is illustrated in Figure 5.3

 

 

 

 

 

 

114/

A I —
/ $130mm 200 mm
90'
3
S . 400mm
4
6

 

 

 

-]—L Kodak Eirtapro 1012 Motion Analyzer

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Key.
1. 'ropvleworgtlndcrrrrodel caulcrot‘r Powder 6. rermlencwitltmacrotocusrtgzoom
Meme, Sllmmlt, NJ) 7. Processor
2. Oscilatory harmler ' 8. \fideo monitor
3. Transparert window 9. Super-VHS VCR
4. Quartz lamp will dicltrole reflector 10- Video cow War

5. light-speed vide‘o irlager. 192x239 NMOS pixel "- WP“
array

Fimrre 5.3 Experimental Setup for High Speed Videomaphy of the Grinding Process

85

flLMmflflQLMi—EM

The intensity of the secondary electrons is monitored to form the image from the
specimen topomaphy. The sample is gold-covered to obscure emission variations due to
surface composition and surface charging. Magnifications up to 1,000 times were used.

Particle shape and the We mechanism were observed.

5-2.7 Lm ' 'ggs

Whenliquid nitrogenwasusedasthecoolingmethod, itwasaddedtothefeed
prior to processing and was also fed directly into the minding chamber during testing.
The actual temperature of the plastic flakes was not known. Thus, the temperature was
measured just outside the minding chamber using a thermocouple probe, and is reported

as the mill outlet temperature (M.O.T).

5—3 Results and Discussion

The influence of temperature, impact rate, feed particle size, and retaining screen
size on PVC and PET minding have been evaluated. This has been done in terms of
cumulative size distribution plots, surface morphology photomaphs, and the assessment of
breakage model parameters. High speed videotaping of the minding event was also done

to examine particle breakage.

5-3 1 f tur

Using a 3.175 mm retaining screen and an impact rate of 93.2 m/s, PVC and PET
flakes were mound in the hammer mill. The temperature of the feed was varied fiom
-196 to 80°C. Temperature plays only a small role in the particle size distribution for PET.
As seen in Figure 5.4, the PSD at room temperature nearly coincides with that at a MO.T.
of 0°C for the coarser particles. For PVC, the size distribution remains relatively
unchanged for room temperature and above, but changes quite a bit at 0°C (Figure 5.5).
Nearly 100 % ofPVC is under 1.4 mm, while only about 50 % ofPET is under that size at
0°C.

When liquid nitrogen was used, the actual temperature of the flakes during
minding was not known. Thus, the mill outlet temperature was varied by adjusting the
amount of liquid nitrogen injected into the mill to determine whether the flakes were near
or at liquid nitrogen (LEI) temperature (-196°C). From Figure 5.6, the amount of LIN

injected does not appear to change the PSD significantly for sizes below L50.

87

ttmaesunderelze

 

 

.0 M.O.T.
A220
x800

 

 

 

 

Sieve (mm)
Temperature L” n
0°C M.O.T. 2.41 1.68
22°C 2.57 2.09
8_1_)°C 2.6_1 2.22

 

 

Figure 5.4 Cumulative Particle Size Distribution for PET at Various Temperatures: 3.175

mmretaining screen, 93.2 m/s

Stmaeeunderelae

 

 

 

 

0 1 2 3 4
Sieve (mm)
Temperature 1.. n
0°C M.O.T. 1.17 3.25
22°C 2.14 2.67
80°C 2.19 2.21

 

 

Figure 5.5 Cumulative Particle Size Distribution for PVC at Various Temperatures: 3.175

mm retaing screen, 93.2 m/s

 

 

 

.M.o.r.=oc
“M.O.T. =-2oc
xM.o.r.=.4oc

 

 

 

SSmaeeundereiae

 

 

0 1 2 3
Sieve (m 111)
Temperature 1.0 n
0°C M.O.T. 1.17 3.25
-20°C M.O.T. 1.69 2.58
40°C MO.T. 1.32 2.51

 

 

 

Figure 5.6 Effect of Mill Outlet Temperature on PVC Comminution: 3.175 mm retaining
screen, 93.2 m/s

5-3,2 Efl‘g of Irnpgg. Rate

Bottle flakes were mound at impact rates of 53.2, 66.6, and 93.2 m/s using a 3.175
mm retaining screen. This was done at both room temperature and a M.O.T. of 0°C.
Changes in the impact rate appear to affect PVC and PET in roughly the same way at
room temperature (see Figures 5.7 and 5.8). The size reduction increases with increasing
impact rate, as expected. At lower temperatures, the impact rate seems to have a meater
effect on PVC (Figure 5.9), and a lesser efl‘ect on PET (Figure 5.10). PVC particles are
mound to a much smaller size, with 100% of the particles being under 2 mm at 93.2 m/s,

and 70% of the PET particles being smaller than that size.

89

 

 

 

 

 

 

100
80
60 053.3 mle
.683 mle
3 ‘° .932 mls
8 20
0.00 1.00 2.00 3.00 4.00
Sieve (mm)
Impact Rate (m/s) 140 n
53.3 3.12 2.52
66.6 2.48 2.64
93.2 2.14 2.67

 

 

 

Figure 5.7 Cumulative Particle Size Distribution for PVC at Various Impact Rates at
Room Temperature: 3.175 mm retaining screen

 

 

 

 

 

 

053.3 mle
I66.6 mle
A 93.2 mle
0.00 2.00 4.00 6.00
Sieve(mrn)
Impact Rate (m/s) [.0 n

53.3 2.76 2.89

66.6 2.68 2.15

_9_3.2 2.42 23.02

 

 

 

Figure 5.8 Cumulative Particle Size Distribution for PET at Various Impact Rates at
Room Temperature: 3.175 mm retaining screen

 

 

 

 

 

 

3
§ 953.3 mle
, l66.6 mle
a .932 mle
E
a!
0.00 1.00 2.00 3.00
Sieve (mm)
Impact Rate (m/s) 1..., n
53.3 2.05 3.24
66.6 1.69 3.25
23.2 1.17 3.25

 

 

 

Figure 5.9 Cumulative Particle Size Distribution for PVC at Various Impact Rates at 0°C
MO.T. : 3.175 nrrn retaining screen, -l96°C Feed Temperature

 

 

 

 

 

 

3
g o 53.3 mle
:1 .666 mle
a A932 mle
a!
0.00 2.00 4.00 6.00
Sieve (mm)

Impact Rate (m/s) 1.0 n

53.3 2.57 2.31

66.6 250 1.78

93.2 2.41 1.6_8

 

 

 

Figure 5.10 Cumulative Particle Size Distribution for PET at Various Impact Rates at 0°C
M.O.T. : 3.175 mm retaining screen, -196°C Feed Temperature

91

- Eff f P i la '

As minding proceeds, breakage changes from multimodal to monomodal (Prasher,
1987). In primary breakage, the particles break in many small fiamnents and fewer large
pieces (bimodal breakage). With continued comminution (or longer residence time in the
minding chamber), the larger pieces are preferentially broken, both because larger
particles are weaker due to the existence of more flaws, and because the smaller particles
are often shielded. This leads to more uniform-sized particles (monomodal breakage).
Thus, the product size distribution should be independent of the feed size distribution for
extendedmindingtimes. To examinewhetherthisistrue, thefeed streamsweresievedto
narrow size fiactions. Particle fi'actions close to sizes of 2 mm, 2.36 mm, 3.35 mm, 4.0
mm, and 6.3 mmweremound separatelyusinga3.175 mmretainingscreen Thiswas
done at room temperature and a mill outlet temperature of 0°C. PVC appears to be
independent of the size of the feed particles at room temperature (Figure 5.11), while this
is not the case for PET (Figure 5.12). The reverse appears to be true at low temperatures
(Figures 5.13 and 5.14). At a MO.T. of 0°C, PVC is more dependent on feed particle
size than PET.

This information seems to contradict the breakage pattern results presented in the
last chapter (see Section 4-3.3). At conditions for which bimodal breakage was predicted,
the feed particle size does not afl‘ect the product size distribution When monomodal
breakage occurs, feed particle size does appear to affect the resulting product distribution
However, Figure 5.15 illustrates that the curves for the difl‘erent feed particle sizes

collapse on one curve when plotted against a dimensionless size l/L80, which represents

92

the sieve size over the characteristic particle size. This means that the feed size effect is a
residence time issue perhaps linked to a breakage mechanism change. Ifit were simply a
breakage mode or mechanism change, this self-preserving nature would not be seen. The
reason for monomodal breakage for short residence times may be a result of catastrophic

breakage, as oppose to cascade breakage at other conditions.

93

 

 

 

 

 

 

1 00
80 o 2 mm
30 A 3.35 mm
x 4 mm
g 40 + 8.3 mm
at 20
0
Sieve (mm)
Feed Particle Size (mm) 1.0 n
2.00 1.88 3.13
3.35 2.02 2.72
4.00 2.03 2.74
6.3 2.3 2.70

 

 

 

Figure 5.11 Cumulative Particle Size Distribution PVC for Various Feed Particle Sizes at
Room Temperature: 3.175 mm retaining screen, 93.2 m/s

 

 

 

 

 

 

100

E 80 02 mm
g 60 A335 mm
2 40 *4 mm
+6.3 mm
a. 20
0
Feed Particle Size (mm) 1.0 n

2.00 2.29 2.37
3.35 2.33 2.07
4.00 2.74 1.93
6.3 3.01 2.10

 

 

 

Figure 5.12 Cumulative Particle Size Distribution PET for Various Feed Particle Sizes at
Room Temperature: 3.175 mm retaining screen, 93.2 nl/s

 

 

xmaseurrderslze

 

 

 

 

 

 

02.38 mm
A 3.35 mm
x4mm
Feed Particle Size (mm) 140 n
2.36 1.42 3.39
3.35 1.03 4.07
4.00 1.22 3.35

 

 

Figure 5.13 Cumulative Particle Size Distribution PVC for Various Feed Particle Sizes at
0°C MO.T: 3.175 mm retaining screen, 93.2 m/s, -196°C Feed Temperature

 

 

 

 

 

5 0 2.36 mm
g A 3.35 mm
3 *4 mm
a!
Feed Particle Size (mm) 1.0 n
2.36 2.34 1.44
3.35 2.43 1.39
4.00 2.6_0 1.48

 

Figure 5.14 Cumulative Particle Size Distribution PET for Various Feed Particle Sizes at
0°C M.O.T: 3.175 mm retaining screen, 93.2 m/s, -196°C Feed Temperature

 

 

95

 

 

 

 

 

 

3 +2.36 mm
3 a 3.35 mm
3 +4 mm

3

3‘

Feed Particle Size (mm) L” n

2.36 1.42 3.39
3.35 1.03 4.07
4.00 1.22 3.35

 

 

 

Figure 5.15 Self-similar size distribution of PVC for Various Feed Particle Sizes at 0°C
M.O.T: 3.175 mm retaining screen, 93.2 m/s, -196°C Feed Temperature

5-3,4 Efl‘gt 9f Sm SQ

Grinding was done with herringbone screens, with varying slot sizes, placed at the
base of the minding chamber. It was expected that the product particles would have sizes
close to that of the screen used. The screen slot sizes ranged from 0.889 to 3.175 mm.
Grinding was also done without a screen, thus leaving a 50 m exit space for the
particles. Figures 5.16 and 5.17 illustrate the effect minder screen size has on the particle
size distributions of PET and PVC when mound at room temperature. The size
distnbutions are nearly identical for the two materials at that condition, with the particles
basically minding closer to the size of the screen as the screen size decreases. At 0°C
M.O.T, it can be seen that with the larger screen, PET (see Figure 5.18) is much less

inclined to mind than PVC (Figure 5.19). This shows that in order to produce the largest

96

difl‘erence between the average particle sizes of the two plastics, a larger screen size will
likely work best. Nearly 90% ofthe PVC is mound to a size smaller than 1.40 mm,
compared to 40% of the PET particles for the 3.175 mm retaining screen Therefore no

screenisneeded.

 

00.869
A1.57

83.175
+None

 

 

 

 

 

Sieve (mm)
Screen Size (mm) 1..., n
0.889 0.86 2.51
1.57 1.50 2.14
3.175 2.57 2.09
none 4.11 2.0_9

 

 

 

 

Figure 5.16 Cumulative Particle Size Distribution PET for Various Retaining Screw
Sizes at Room Temperature: 93.2 m/s

 

00.866
A157

33.175
+None

 

 

 

 

 

Sieve (mm)
Screw Size (mm) 1.0 71
0.889 0.67 2.04
1.57 1.42 1.4
3.175 2.14 2.67
none 4.28 1.92

 

 

 

Figure 5.17 Cumulative Particle Size Distribution PVC for Various Retaining Screw
Sizes at Room Temperature: 93.2 m/s

96 mass Moraine

 

03.175
‘none

 

 

 

Sieve (m m)
Screen Size (mm) L” 71
3.175 2.41 1.68
none 4.22 1.94

 

 

Figure 5.18 Cumulative Particle Size Distribution PET for Various Retaining Screw

Sizes at 0°C M.O.T. : 93.2 m/s, -196°C Feed Temperature

 

 

 

100
80
3
g 60
a 03.175
An
3 40
a!
20
0
8.
N V
Sieve (mm)
ScrewSize(mm) 140 n
3.175 1.17 3.25
none 1.98 2.15

 

 

Figure 5.19 Cumulative Particle Size Distribution PVC for Various Retaining Screw

Sizes at 0°C M.O.T. : 93.2 m/s, -196°C Feed Temperature

99

5-3,5 Brflge Mechanism Identificatign
5-3. 5. 1 Failure Mechanisms

The mound particles were examined by scanning electron microscopy to determine
the type of flacture that occurred for each minding condition. At room temperature PVC
particles failed in a ductile manner, with obvious aims of plastic yielding, as documented
in Figure 5.20. PET also showed signs of yielding at room temperature (Figure 5.21). At
a mill outlet temperature of 0°C, the PVC particles had more distinct crack patterns
identifiable with brittle fi'acture (Figure 5.22). PET particles appear to have some
characteristics of brittle failure and some of ductile (Figure 5.23). It is not well
understood why PET would exhibit ductile behavior at cryogenic conditions. Yano et a1.
(1995) reported that studies have indicated that a nodular structure and small isometric
crystallites might increase the ductility of PET by providing an wergy absorbing structln'e.
Adiabatic heating is another possible cause. At the high strain rates of impact minding,
there is insuficient time for heat fi'om energy dissipation to be conducted away.

Therefore, local heating may occur, leading to plastic yielding.

101*! 110500

R
fil'rSKu xr.oaa 5“”

 

Figure 5.21 SEM (x1,000) of PET Particle Ground at Room Temperature

WI

 

15KU X1r000

Figure 5.23 SEM (x1,000) of PET Particle Ground at 0°C M.O.T.

102

5-3.5.2 Dtflerences in Particle Shcpes

The fi'acture mechanisms of PET and PVC not only have an effect on their particle
size distributions, but on their particle shapes as well. Because of the ductile mode in
which PET fails during minding, its particles have a high aspect ratio due to elongation
(see Figure 5.24). PVC particles have a low aspect ratio because of their brittle fiacture,
as sew in Figure 5.25. The particles were comminuted after being soaked in liquid

nitrogen, andatanimpact rate of93 m/s. A3175 mmscreenwasused.

5-3. 5. 3 Particle Firm and Breakage

High speed videotaping of impact minding of PVC and PET revealed two key
points. The first being that particle are caught up in the air flow and often avoid being hit
by the hammers. The second revelation is that the particles appear to be impacted many
times before actual breakage takes place, though PVC particles seem to require fewer hits
than PET particles. It was dificult to determine how many impacts that were required
and the number of progeny particles that resulted because of the speed of the comminution
action and the limited viewing area Each viewing frame represented between 0.5-1 ms.
After initial breakage the progeny particles appeared to be hit many more times before
falling through the retaining screen Figures 5.26 and 5.27 illustrate a particle prior to and

at the point of impact, respectively.

1m

 

Figure 5.24 SEM of PET Particle Shape: 93.2 m/s, 0°C M.O.T.

200002

 

Figure 5.25 SEM of PVC Particle Shape: 93.2 m/s, 0°C M.O.T.

104

 

Figure 5.26 High Spwd Videomaphy of PVC Particle Prior to Impact: 93.2 m/s, 22°C,
2000 fps

 

Figure 5.27 High Speed Videomaphy of PVC Particle at the Point of Impact: 93.2 m/s,
22°C, 2000 fps

105

5-3.6 Predicting Particle Size

The two coemcients, Leo and n, of the Rosin-Rammler-Bennett equation have been
evaluated in terms of the process variables (see Chapter 4 for further discussion). Since
temperature seems to be a key variable, all of the other process parameters have been
evaluated in relation to temperature as well. It should be noted that the standard
deviations for Leo and n for PET is 0.12 and 0.21, respectively, while those for PVC are

0.07 and 0.35. These values were obtained by doing a statistical analysis on eight

replicated experiments.

5-3. 6. 1 T emperature

Below the glass transition temperature of 80°C, the product size of PET appears to
be nearly independent of temperature (Figure 5.28). Leo is generally around 2.5 mm
However, the characteristic particle size of PVC decreases significantly as the temperature
decreases fi'om 22°C to about -196°C (Figure 5.29). Above room temperature, Leo
remains relatively constant. PVC appears to undergo a brittle-ductile transition between
0°C and -20°C.

The uniformity index for PET decreases with decreasing temperature (Figure
5.30), while the uniformity index for PVC increases with decreasing temperature (Figure
5.31). This indicates that the PVC particles are becoming more uniformly sized as they
become more brittle with decreasing temperature. The slight decrease in n for PET may
be related to the partial ductile nature observed at cryogenic temperatures, leading to a

broader size distribution.

106

L80 (mm)

 

0
400460420780 -40 0 40 80

Temperature (C)

Figure 5.28 Depwdence of Characteristic Product Size on Feed Temperature for PET:
3.175 mm Retaining Screen, 93.2 m/s

L80 (mm)

 

-200-160-120-80 -40 0 40 80
Temperature(C)

Figure 5.29 Depwdwce of Characteristic Product Size on Feed Temperature for PVC:
3.175 mm Retaining Screw, 93.2 m/s

 

~200-160-120-80 40 0 40 80
Temperature(C)

Figure 5.30 Depwdence of Uniformity Index on Feed Temperature for PET: 3.175 mm
Retaining Screen, 93.2 m/s

 

-200-180-120-60 -40 0 40 80
Temperturew)

Figure 5.31 Depwdwce of Uniformity Index on Feed Temperature for PVC: 3.175 mm
Retaining Screen, 93.2 m/s

108

5-3. 6.2 Impact Rate

PVC is afi‘ected more by impact rate than PET. This fact was not obvious when
looking at cumulative plots. Lao decreases slightly with increasing impact rate for PET
(Figure 5.32). In Figure 5.33 it can be seen that there can be as much as a millimeter
difi‘enence in product particle size for a change in impact rate from 53 m/s to 93 m/s for
PVC. Increasing the impact rate has a similar afl'ect as lowering the temperature - the
particles break in an increasingly brittle fashion. This is a result of the higher
concentration of stress, and the less time for molecular mobility.

For PET, the uniformity index decreases significantly with a change in the impact
rate fi’om 53 m/s to 66 m/s, then remains relatively unchanged with a further increase in
the impact rate to 93 m/s (Figure 5.34). This seems to indicate a mechanism change.
However, as with the anomalous response of n to decreasing the grinding temperature, the
decrease in n with increasing impact rate signifies a broader distribution, possibly the
result of the both brittle and ductile properties of PET observed by SEM Increases in
impact rate have virtually no efi‘ect on n for PVC (Figure 5.35). No apparent failure
mechanism change occurs over the range of impact rates tested.

The data summarized by Figures 5.32-5.34 at 0°C were obtained for feed material

which was pretreated with liquid nitrogen (see Section 5.2-7).

+0 C M.O.T.
+22 C

 

Impact Rats (mle)

Figure 5.32 Dependence of Characteristic Product Size on Impact Rate for PET: 3.175
mm Retaining Screen

+0 C M.O.T.
+22 C

 

Figure 5.33 Dependence of Characteristic Product Size on Impact Rate for PVC: 3.175
mm Retaining Screen

110

+0 C M.O.T.
+22 C

 

Figure 5.34 Dependence of Uniformity Index on Impact Rate for PET: 3.175 mm
Retaining Screen

+0 C M.O.T.
+22 C

 

Figure 5.35 Dependence of Uniformity Index on Impact Rate for PVC: 3.175 mm
. . S

111

5-3. 6.3 Feed Particle Size

The characteristic product particle size for PET, as illustrated in Figure 5.36,
increases slightly with increasing feed particle size for both room temperature and low
temperature. Leo is nearly independent at room temperature for PVC (Figure 5.37). At a
M.O.T. of 0°C (i.e., feed temperature -196°C) the trend for Leo is unclear.

It should be noted again that the size of the feed particles is actually an estimate
fi'om a narrow particle size distribution. As a result, the value of Lao for PET for a 2 mm
feed is slightly above 2 mm. This may indicate that no size reduction occurred and the
particles simply fell through the retaining screen.

The uniformity indexes for both PET and PVC (see Figures 5.38 and 5.39) are
nearly independent of feed particle size except for the smallest size of 2 mm. Once again,

an explanation is unclear.

112

L30 (mm)

 

Food Siz. (m)

Figure 5.36 Dependence of Characterisu'c Product Size on Feed Particle Size for PET:
3.175 mm Retaining Screen, 93.2 m/s

 

 

 

 

 

E +22c
75 +0 c M.O.T.
3
2 4 a
and Size (mm)

 

Figure 5.37 Dependence of Characteristic Product Size on Feed Particle Size for PVC:
3.175 mmRetaining Screen, 93.2 m/s

113

+22 C
+0 C M.O.T.

 

Food Size (mm)

Figure 5.38 Dependence of Uniformity Index on Feed Particle Size for PET: 3.175 mm
Retaining Screen, 93.2 m/s

 

Figure 5.39 Dependence of Uniformity Index on Feed Particle Size for PVC: 3.175 mm
Retaining Screen, 93.2 m/s

114

5-6. 6. 4 Retaining Screen Size

WhennoscreenwasusedtheopeningisS cmx 12cm, however, thescreensize
was taken to be the size of the characteristic feed particle size. Both PET and PVC
particles grind to just under the screen size at room temperature (Figures 5.40 and 5.41).
However, at a M.O.T. of 0°C (i.e., feed temperature -196°C), PVC particles grind to well
below the retaining screen size, again signifying the brittleness of the particles at these
conditions and, thus, more willingness to fracture. The uniformity index for PET increases
with decreasing screen size, while that for PVC fluctuates quite a bit (Figures 5.42 and
5.43). For both PVC and PET there seems to be a transition point at screen size 1.57 mm,
where Lao is no longer a function of temperature, and the particles become more

uniformly-sized.

115

+0 C M.O.T.
+22 C

 

+0 C M.O.T.
+22 C

L80 (mm)

 

0 2 4 6 8
Screen size (mm)

Figure 5.41 Dependence of Characteristic Product Size on Screen Size for PVC: 93.2 m/s

116

 

Figure 5.42 Dependence of Uniformity Index on Screen Size for PET: 93.2 mls

+22 C
A 0 C M.O.T.

 

0 2 4 6 8
Screen Size (mm)

Figure 5.43 Dependence of Uniformity Index on Screen Size for PVC: 93.2 mls

117

5-3. 6.5 Similarity Solution

One implication of the empirical models presented in the last section is that,
because of their self-preserving nature, there exist a single dimensionless curve that is
independent of impact rate and temperature, unless there is a change in mode and/or the
mechanism of size reduction. However, if the change in mode and/or the mechanism is a
firnction of residence (or minding) time, the change is incorporated in the normalizing
parameter 140, and the similarity solution is preserved (Prasher, 1987). The empirical
model is then presented as the mass % undersize verses the sieve size made dimensionless
by the characteristic particle size. In Figures 5.44 and 5.45 the similarity solutions for
PVC and PET can be seen Regardless of temperature or impact rate, the dimensionless
curve for PVC is basically the same. However, there is some variance for PET. This
indicates that there is a factor in the breakage mechanism of PET that cannot be related to
minding time. For PVC, the breakage mechanism changes caused by changes in
temperature and impact rate are expressed in a time scale factor incorporated in L». In
the case of PET, since plastic yielding occurs for all of the minding conditions tested, Ln
may be a more complex function of this yielding, thus, making it insuficient as a minding
time scale factor.

These difl‘erences between PVC and PET observed in this examination of the
similarity solution suggests some key difi‘erences in the comminution behavior of brittle
and ductile materials. That is, the relationship between plastic yielding and the size of the
resulting particle is needed for ductile material if the similarity solution is to be used to

map the particle size distribution for various minding conditions.

 

118

Stmasamderslze

 

 

+513 mls. r.t.
A 93.2 mls. r.t.

 

 

 

 

I 93.2 mls, 0 C
IIL00
Impact Rate (mls) Temperature (C) Lao n
53.3 22 3.12 2.52
93.2 22 2.14 2.67
93 .2 0 MO.T. 1.17 3.25

 

 

Figure 5.44 Self-similar Size Distribution for PVC

96 mass underslu

 

 

 

+533 mle. r.t.
X 93.2 mle. Lt
+932 mls, 0 C

 

 

 

Impact Rate (mls) Temperature (C) I40 11
5 . 22 2.76 2.89
93.2 22 2.57 2.09
93.2 0 MO.T. 2.41 1.68

 

Figure 5.45 Self-similar Size Distribution for PET

 

119

5-3. 6. 6 Scaling Laws

The relationships between the characteristic product size, Lao, and the impact
minding conditions were presented in graphical form in the previous sections. The
existence of a similarity solution by which the product size distribution could be mapped
with changes in temperature and impact rate was also presented. The missing component
to predicting particle size distributions is a empirical relationship between Lao (and, the
uniformity index n) and the process variables. Thus, a scaling analysis was done to try to
bridge this gap for Lao.

The cumulative particle size distribution modeled with the RB equation can be

presented in the following form by normalizing the particle size with Leo:
F = F(l/L.o, n) (5‘2)

Ingo is assumed to depend on the thermal energy required for breakage (i.e., ~ KT, where

x is the Boltzmann), the density p, and the impact rate u, then

f (I40, KT, p, u) = 0 (5-3).

Thus, by dimensional reasoning, the thermal energy of the particle should be proportional

to the kinetic energy of the particle. Hence,

KT

—— = C (5—4)
V 2

V2 ,p.

120

where V, is the volume of the particle, and is proportional to L330, and C is some constant.
Rearranging Eq. (5-4) gives the following scaling relationship between Leo and the
minding temperature and impact rate:

L, = arm/um (5-5).
Over the range of temperatures and impact rates studied, this relationship works for the
size reduction of PVC, but not for PET. This may be due to the ductile nature of PET.
The following examples illustrate how the characteristic product size can be determined

for PVC at various minding temperatures and impact rates fi'om a knowledge of Lao at one

set of conditions.

Examples of Scaling Law Utilization for PVC
MM
Lao azac = Leo u-zooc(sz/T-2ooc)1/3
= 2.05(295"K/73°I<)"3
= 3.26 mm

Experimentally, Lao .mc = 3.12 mm (see Figures 5.7 and 5.9)

mm Rate; L80 ~ 3;”
Leo and. = Lao a 533 ds [(11533 mid/(1193.2m)]2’3

= 3.12 (53.3/93.2)”3

=2.15mm

Experimentally, Lfio‘”.2-/. = 2.14 mm (see Figure 5.7)

121

Empirical relationships can be developed fi'om this scaling analysis for PVC.
However, the relationships between L30 and the minding conditions for PET need to be

investigated firrther.

5-3.7 l ' ' Reducti n f PVC an PET

A 50/50 mixture of PVC and PET flakes were pre-soaked in liquid nitrogen and
mound at a MO.T. of -20°C using a 3.175 mm retaining screen and an impact rate of 93.2
mls. The PVC and PET particles were separated by dissolving PVC in tetrahydrofuran
(THF). Since PET is insoluble in THF, the quality of the size separation could be
evaluated by determining the weight of the remaining particles. In Figure 5.46, the
cumulative size distributions for the mound mixture can be seen. The values for Lao
determined fi'om these distributions were 2.55 and 0.92 for PET and PVC, respectively.
The values for n were 1.57 and 3.07. These values are close to what was obtained when
PET and PVC were mound separately.

Most of the fines fi'om the mound mixture were PVC particles, while the coarser
particles were mainly PET, as illustrated in Figure 5.47. This was an expected and
necessary result for size separation. The purity and yield of PET can be seen in Figure
5.48. However, with the understanding of how the process variables afi‘ect the product

size, future optimization is possible.

122

d

$maeaunderahe
8 6 8 8 8

 

0 2 4 6
Steve (mm)

Figure 5.46 Cumulative Size Distributions for Separated PVC/PET Ground Mixture: 93.2
mls, 3.175 mm Retaining Screen, -20°C MO.T.

+Pvc
—I—PET

Mass 96 slave size

 

Slave (nun)

Figure 5.47 Mass Percentage of Particles of Each Thermoplastic Retained on Sieve Size:
93.2 mls, 3.175 mm Retaining Screen, -20°C M.O.T.

123

+% Pun'ty
+96 Yidd

 

Figure 5.48 Size Separation of PVC/PET Mixture Ground at -20°C M.O.T.

5—4. Conclusions

There are conditions for which PVC bottle flakes will mind finer than PET flakes.

Temperatures below 0°C and high impact rates produce the most substantial size
difi‘erences. Shape differences are also created at these conditions. PET has a much
higher aspect ratio than PVC due to the ductility of PET. Using larger size screens also
seems to improve the size difi‘erences. PET is insensitive to temperature or impact rate,
while the opposite is true for PVC.

It is possible to estimate the characteristic particle product size from the
relationships between L» and the minding temperature, impact rate, and retaining screen

size. The scaling laws validate this for PVC. The characteristic product size has been

124

found to be proportional to the 1/3 power of the temperature, and inversely proportional
to the 23 power of the impact rate. Once empirical modeling has been completed, these
relationships can be used to optimize the particle size difl‘erences between the two
materials.

The breakage behavior of PET is somewhat anomalous in that PET exhibits
seemingly ductile and brittle characteristics at cryogenic temperatures and high strain
rates. This behavior cannot be expressed in terms of a time-dependent scale factor, as in
the case of PVC.

Tensile and compressive failure mechanism behaviors do not predict the failure
mechanisms seen during impact minding, though the tensile failure mechanism diagram
accurately predicts the brittle-ductile transition for PVC (see Table 5.4). The Izod impact
experiments also predicts the brittle-ductile transition for PVC, as well as the failure
mechanisms. They also show that the impact behavior of PET is not afl‘ected much by
temperature. However, the SEM photographs show that PET Izod impact specimens fail

in a brittle fashion, while PET fails in a ductile fashion during impact minding.

Table 5.4 Brittle-Ductile Transition Temperatures (C) for PVC

 

 

 

 

 

 

 

 

 

 

 

Strl'ain Rate Tensile' Compressive' Izod" B-Relaxation' Grinding"
(8. )

0.1 48/-23 52/77 - -80 -
100 2’27 77/102 0/20 -35 -
10,000 52/7 7 102/ 127 - 12 -20
'Estimated

 

125

5-5. References
Lowrison, G., Crushing and Grinding, Butterworths, Boston, 1974.

Prasher, C., Crushing and Grinding Process HWIC, John Wiley & Sons Ltd., New
York, 1987.

Yano, O. and H. Yamaoka, “Cryogenic Properties of Polymers,” Progress in Polymer
Science, 20 (1995), 585.

CHAPTER 6

CONCLUSIONS

This research has provided a fi'amework for studying thermoplastics comminution.
The applicability of using theoretical deformation processes and conventional mechanical
testing to model impact minding result was examined. The suitability of various
mathematical representations to model particle size distributions fi'om the size reduction of
PVC and PET was also investigated. Lastly, the development of relationships between
impact minding process variables to the size of the resulting particles was desired. The
purpose of these undertakings were for the ultimate goal of selectively minding mixtures
of PVC and PET material to difi‘erent particle sizes and shapes.

Classical impact theory developed for low speed mechanical testing is not
suficient to predict the high speed impact behavior of thermoplastics. While the brittle-
ductile transitions for PVC at various temperatures and impact rates were forecasted,
those for PET could not be anticipated. Tensile and compressive theoretical models were
not useful in describing PVC and PET behavior at high strain rates. The brittle-ductile
transition temperatures determined fiom Izod impact testing and the B-relaxation
temperature were comparable to the failure mechanism transition‘seen during impact
minding for PVC. However, neither of these methods, nor high speed ballistics testing,
predicted the ductile behavior of PET at cryogenic conditions. This could be due to the

uniqueness of thermoplastics as viscoelastic material. Factors such as notch sensitivity and

126

127

sample thickness must be taken into consideration. In the latter case, orientation afl‘ects
for thinner samples may afl‘ect the failure mechanism.

Empirical breakage mechanism and model information was developed from single
and multiple particle comminution in a hammer mill. A two parameter empirical model
was used to describe PVC and PET comminution at various conditions. One parameter,
Leo, provided information about how the characteristic particle product size varied with
temperature, impact rate, and screen size. The other parameter, n, described the
uniformity of the particles and whether the breakage was catastrophic or cascade in
nature. The product sizes of PVC particles decreased with increasing impact rate and
decreasing temperature, as expected. The breakage changed fiom bimodal cascade failure
to monomodal catastrophic failure as the temperature decreased and the impact rate
increased. For PET, the product size was independent of temperature, and only decreased
slightly with increases in impact rate. The breakage mode changed fiom monomodal to
bimodal as temperature was decreased and the impact rate increased.

Empirical models can be constructed to estimate a characteristic product particle
size using the relationships established between 140 and the process variables. The
characteristic product size, Lao, was found to be proportional to the one-third power of
temperature, and inversely proportional to the two-thirds power of the impact rate. A
complete particle size distribution can be determined for PVC based on a similarity
solution However, further information about the yield behavior of PET (i.e. the
elongation at break) is needed to model its complete particle size distribution for various

process parameters.

128

At cryogenic temperatures, PVC can be selectively mound to smaller particles
sizes tlmn PET. This is due to PVC particles fiacturing in a brittle fashion, while PET
particles fail in a ductile fashion. Separation of the two materials based on size is possible,
however, optimization to increase purity and yield is still necessary. Shape differences can
also be created, with PET having a larger aspect ratio than PVC.

The failure behavior of PET at low temperatures and high impact rates is
somewhat anomalous to what was expected. Even though PET is known to exhibit some
ductility at cryogenic conditions, PET seemed to display just as much, or perhaps even
more ductile behavior at these conditions than at room temperature. This could be due to

factors such as stress-induced crystallization, chain reorientation, or adiabatic heating.

CHAPTER 7

RECOMMENDATIONS

This work has provided a fi'amework for studying the conuninution of
thermoplastics, in addition to presenting a method for selectively minding mixed
component streams for classification. However, a number of areas of this research invoke
the need for further investigations. One of the key questions that remains is how can
material be evaluated to gain insight into the probable failure mechanisms that will occur
during comminution? This can be examined by studying the material properties and
deformation behaviors of other thermoplastics, such as polyethylene and polypropylene.
Further high speed mechanical testing at low temperatures also needs to be done to
understand brittle-ductile transitions at those conditions.

Using the relationships developed between the process variables and the
characteristic product size, empirical equations should be developed. The scaling analysis
provided the starting point for this empirical modeling. Then the optimal conditions for
afl‘ecting the desired separation can be estimated and verified through experimentation

The ductile behavior of PET at cryogenic conditions should be examined more
thoroughly to determine causes, such as strain-induced crystallization or molecular
reorientation. Experimentation, such as minding spherical shape particles rather than

flakes, could provide information about morphological changes, since the inclination for

129

130

structural changes are alien related to sample thickness. Thermal analysis on mound
material could give insight to whether changes in crystallirrity are occurring.

The final recommendation is that the actual separation of PVC and PET by size
and/or shape should be carried out in a hydrocyclone, by sieving, or some other method.
This research provided some answers to why this is possible. Now it needs only to be

done.

APPENDICES

APPENDIX A

131

APPENDIX A

IZOD IMPACT DATA
PET
Temperature Impact Strength STD.
(0) (Jim) DEV.
-40 5.29 1.512
-30 4.81 1.836
-20 3.94 0.594
-10 4.27 1.026
0 4.64 0.54
10 4.59 0.378
20 3.02 0.756
30 4.86 0.702
40 5.83 1.566
50 4.75 1.188
60 3.56 0.648
70 4.97 0.756
80 2.97 0.54
PVC
Temperature Impact Strength STD.
(C) (Jim) DEV.
-40 10 2.538
-30 19 18.63
-20 19 4.536
-10 22 8.316
0 31 13.122
10 178 37.314
20 256 22.14
30 255 33.372
40 275 28.782
50 241 23.328
60 251 27.756
70 240 28.404
80 287 19.872

APPENDIX B

132

APPENDIX B
IMPACT GRINDING DATA
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PVC 23 M.O.T. 93.2 3.175 7.4
Sieve Size (mm) Mass °/o undersize RRB Model
2.36 86.85 87.98
2 73.85 72.14
1.4 33.44 34.93
0.85 9.67 8.93
0.5 3.65 1.8
0.212 0.79 0.13
CharacteristicProductSize,L.o=2.16 Uniformitylndex, n-=3.06
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PVC 22 93.2 3.175 7.4
Sieve Size (mm) Mass % undersize RRB Model
2.36 91.49 92.42
2 79.78 78.53
1.4 38.68 39.68
0.85 10.59 10.11
0.5 3.37 2.01
0.212 0.48 0.14

Characteristic Product Size, Lao = 2.03 Uniformity Index, 11 = 3.12

Material Temperature Impact Rate /"’ Screen Size Characteristic Feed Size
(C) (mls) (mm) (Inn)
we 22 93.2 3.175 7.4
Sieve Size (mm) Mass%undersize RRBModel
2.36 86.56 85.96
2 73.61 72.25
1.4 36.72 40.06
0.85 15.25 13.20
0.5 7.05 3.55
0.212 1.31 0.40

CharacteristicProduct Size,1..o=2.1s Uniformityinder.n=2.57

133

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm (mm)
PVC 22 93.2 3.175 7.4
Sieve Size (mm) Mass °/o undersize RRB Model
2.36 85.23 84.55
2 72.03 70.59
1.4 35.16 38.89
0.85 15.03 12.88
0.5 7.71 3.50
0.212 1.57 0.40
Characteristic Product Size, Loo = 2.23 Uniformity Index, a = 2.55
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PVC 22 93.2 3.175 7.4
Sieve Size (mm) Mass % 1mdersize RRB Model
2.36 90.36 88.12
2 11.07 77.38
1.4 35.03 49.56
0.85 22.40 20.64
0.5 9.38 7.03
0.212 7.6 1.12
CharacteristicProdnctSize,L.p=-2.07 Uniformitylndex,n=2.17
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PET 22 93.2 3.175 4.6
Sieve Size (mm) Mass 9’. undersize RRB Model
2.36 72.97 72.82
2 63.27 62.82
1.4 41.45 42.13
0.85 20.48 21.24
0.5 10.79 9.41
0.212 3.03 2.35

CharacteristicProductSize,L.o-2.68 Uniformitylndex,n=l.66

134

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (In/S) (In!!!) (In!!!)
PET 22 93.2 3.175 4.6
Sieve Size (mm) Mass % undersize RRB Model
2.36 70.10 74.47
2 59.20 58.27
1.4 34.42 33.05
0.85 11.30 12.63
0.5 2.79 4.15
0.212 0.53 0.64

CharacteristicProduct Size, Lgo= 2.65 Uniformitylndex, n=2.18

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (Inn) (mm)
PET 22 93.2 3.175 4.6
Sieve Size (mm) Mass 9’. undersize RRB Model
2.36 70.07 71.42
2 59.21 58.27
1.4 34.44 33.12
0.85 11.39 12.71
0.5 2.91 4.20
0.212 0.66 0.66

ChmactaisficProdrmtSWLgo=265 Uniformitylnkx,n=2.l7

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (Inn) (mm)
PEI‘ 22 93.2 3.175 4.6
Sieve Size (mm) Mass % undersize RRB Model
2.36 71.25 72.69
2 60.39 59.44
1.4 35.21 33.79
0.85 11.55 12.88
0.5 2.75 4.21
0.212 0.41 0.65

CharacteristicProductSize,I.p-2.60 Uniformitylndex, n=2.20

135

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PET 22. 93.2 3.175 4.6
Sieve Size (mm) Mass % undersize RRB Model
2.36 75.53 77.02
2 64.89 64.02
1.4 38.70 37.32
0.85 13.30 14.45
0.5 3.32 4.75
0.212 0.53 0.74
Characteristic Product Size, Lao = 2.46 Uniformity Index, 11 = 2.20
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm
PET 22. 93.2 2.36 4.6
Sieve Size (mm) Mass % undersize RRB Model
2.36 88.28 89.05
2 79.24 79.17
1.4 53.38 52.67
0.85 23.31 23.31
0.5 7.51 8.44
0.212 1.01 1.47
CharactefistichductSize,l...y—=2.02 Uniformitylnderan=2.08
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (min)
PVC 22 93.2 2.36 7.4
Sieve Size (mm) Mass % undersize RRB Model
2.36 96.61 94.14
2 91.32 87.33
1.4 59.84 64.75
0.85 31.64 33.00
0.5 19.00 13.48
0.212 3.93 2.76

CharacteristicProduct Size, I.” = 1.76 Uniformity Index, 11 =1.92

136

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PET 22 93.2 0.254 4.6
Sieve Size (mm) Mass % undersize RRB Model
2.36 100.00 100
2 100.00 100
1.4 100.00 100
0.85 99.39 99.99
0.5 96.34 96.34
0.212 23.78 23.78

CharacteristicProdnct Size,Lgo =0.39

Material Temperature Impact Rate
(C) (mls)
PVC 22 93.2
Sieve Size (mm) Mass % undersize
2.36 100.00
2 99.17
1.4 98.33
0.85 99.17
0.5 97.5
0.212 38.33

CharacteristicProductSize,L.o= 0.35

Material Temperature Impact Rate
(C) (In/S)
PVC -20 M.O.T. 93.2
Sieve Size (mm) Mass % undersize
2.36 98.99
2 97.36
1.4 82.16
0.85 39.82
0.5 11.93
0.212 2.64

CharacteristicProdnct Size,Lgo= 1.37

Uniformity Index 11 = 2.91

Screen Size Characteristic Feed Size
(mm) (mm)
.254 7.4

RRB Model
100
100
100
99.99
97.50
38.33
0.35
Uniformity Index, 11 = 2.37

Screen Size Characteristic Feed Size
(mm) (mm)
3.175 7,4

RRB Model
99.79
98.35
81.93
39.58
12.79

1.65

Uniformity Index, n = 2.45

137

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PVC 0 M.O.T. 93.2 3.175 2.36
Sieve Size (mm) Mass % undersize RRB Model
2.36 97.98 99.99
2 96.42 99.40
1.4 78.38 78.23
0.85 25.19 24.49
0.5 2.18 4.54
0.212 0.16 0.25

CharacteristicProduct Size, Lao= 1.42

Material Temperature

Impact Rate
(C) (In/S)
PVC 0 M.O.T. 93.2
Sieve Size (mm) Mass % undersize
2.36 100.00
2 100.00
1.4 94.54
0.85 51.97
0.5 6.55
0.212 0.44

CharacteristicProductSize,I..o= 1.04

Material Temperature Impact Rate
(C) (mls)
PVC 0 M.O.T. 93.2
Sieve Size (mm) Mass % undersize
2.36 98.80
2 98.29
1.4 90.75
0.85 39.55
0.5 4.28
0.212 0.34

CharactefisticProdrrctSizelgoa 1.22

Uniformity Index, 11 = 3.39

ScreenSize CharacteristicFeed Size
(M)
3.175

(M)
3.35

RRB Model
100.00
100.00
99.58
51.33
7.98
0.25

UniformityIndex, n=4.07

Screen Size Characteristic Feed Size
(mm) (mm)
3.175 4.00

RRB Model
100.00
99.98
92.06
37.79
7.69
0.45

Uniformity Index, 11 = 3.36

138

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (m/S) (mu!) (Inn!)
PVC 0 M.O.T. 53.3 3.175 7.4
Sieve Size (mm) Mass % undersize RRB Model
2.36 90.35 91.97
2 78.09 77.12
1.4 37.49 37.14
0.85 7.74 8.80
0.5 1.01 1.64
0.212 0.10 0.10

Characteristic Product Size, L” = 2.05

Material Temperature Impact Rate
(C) (In/S)
PVC 0 MO.T. 93.2
Sieve Size (mm) Mass % undersize
2.36 99.48
2 98.83
1.4 90.64
0.85 48.63
0.5 7.15
0.212 0.13

CharacteristicPIoductSize,I..o= 1.17

Material Temperature

Impact Rate
(C) (mls)
PVC 0 M.O.T. 66.6
Sieve Size (mm) Mass 9’. undersize
2.36 96.66
2 91.99
1.4 58.21
0.85 10.15
0.5 0.27
0.212 0.00

CharacteristicProdrrctSizelqo= 1.69

3.175

Uniformity Index, 11 = 3.24

Screen Size
(In!!!)
3.175

Characteristic Feed Size
(mm)
7.4

RRB Model
100.00
99.99
94.29
43.19
9.59
0.62

Uniformity Index, 11 8 3.25

Screen Size Characteristic Feed Sin

(mm) (mm)

7.4

RRB Model
99.14
93.80
58.20
15.83
3.03
0.19

Uniformity Index, 11 = 3.25

Material Temperature Impact Rate
(C) (In/S)
PVC ~20 Refig. 53.3
Sieve Size (mm) Mass °/o undersize
2.36 60.73
2 42.52
1.4 20.75
0.85 13.21
0.5 8.05
0.212 1.01

Characteristic Product Size, Leo = 3.03

Material Temperature Impact Rate
(C) (In/S)
PVC -20 Refig.. 66.6
Sieve Size (mm) Mass % undersize
2.36 82.79
2 66.24
1.4 28.98
0.85 12.29
0.5 6.60
0.212 1.03

CharacteristieProduct Size, Loo= 2.31

Material Temperature Impact Rate
(C) (mls)
PVC -20 Refig.. 93.2
Sieve Size (mm) Mass % undersize
2.36 92.87
2 83.83
1.4 45.30
0.85 17.24
0.5
0.212

CharacteristicProdIrctSizelao= 1.96

139

Screen Size Characteristic Feed Size
(mm) (mm)
3.175 7.4

RRB Model
57.48
44.97
24.08

8.91
2.91
0.45

Uniformity Index, a = 2.36

Screen Size Characteristic Feed Size
(mm) (mm)
3.175 7.4

RRB Model
81.96
65.73
32.25

9.02
2.08
0.18

Uniformity Index, n = 2.34

ScreenSize CharacteristicFeed Size

(mm) (mm)
3.175 7.4

RRB Model
92.70
81.59
48.40
16.29

Uniformity Index, 11 = 2.63

140

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PVC 22 53.3 3.175 7.4
Sieve Size (mm) Mass % undersize RRB Model
2.36 54.62 51.84
2 37.95 40.45
1.4 18.95 21.91
0.85 1 1.67 8.41
0.5 6.41 2.88
0.212 0.77 0.49
Characteristic Product Size, 1.0 = 3.13 Uniformity Index, n = 2.52
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (Inn) (Inn!)
PVC 22 66.6 3.175 7.4
Sieve Size (mm) Mass % undersize RRB Model
2.36 77.27 75.81
2 60.22 60.01
1.4 25.98 30.04
0.85 12.72 9.12
0.5 7.71 2.33
0.212 1.35 0.24

CharacteristicProductSize,L.o-2.48 Uniformitylnderen=2.64

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (In/8) (Inn!) (min)
PVC 22 93.2 3.175 7.4
Sieve Size (mm) Mass 96 undersize RRB Model
2.36 88.03 87.77
2 76.07 74.12
1.4 36.87 40.69
0.85 15.24 12.90
0.5 7.55 3.30
0.212 1.28 0.34

ChmacteristichdlrctSinlqo=2J4 Uniformitylndergn=2.67

141

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PVC 40. 53.3 3.175 7.4
Sieve Size (mm) Mass % undersize RRB Model
3.35 88.20 80.24
2.36 60.42 69.32
2.00 43.51 44.99
1.4 30.97 20.57
0.85 13.37 8.01
0.50 8.78 1.61
CharacteristicProduct Size, Im=2.35 Uniformitylndex, n= 1.91
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (In/S) (mm) (mm)
PVC 40 66.6 3.175 7.4
Sieve Size (mm) Mass % undersize RRB Model
2.36 75.42 73.01
2 58.82 58.96
1.4 27.03 32.15
0.85 15.06 11.42
0.5 9.14 3.46
0.212
CharacteristicProductSize,L.o=2.58 Uniformitylndergn=2.33
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (Inn!)
PVC 40 93.2 3.175 7.4
Sieve Size (mm) Mass % undersize RRB Model
2.36 88.67 87.83
2 77.21 75.24
1.4 39.45 43.76
0.85 17.45 15.35
0.5 9.11 4.36
0.212

CharacteristieProductSize,L.o=2.12 UniformityIndex,n=2.48

142

Material Temperature Impact Rate Screen Size
(C) (mls) (mm)
PVC 60 53.2 3.175
Sieve Size (mm) Mass % undersize
2.36 52.56
2 37.48
1.4 21.23
0.85 15.47
0.5
0.212

Characteristic Product Size, Loo = 3.32

Material Temperature

PVC

Sieve Size (mm)

2.36
2
1.4
0.85
0.5
0.212

CharacteristicProdrrctSizem=268

Characteristic Feed Size
(min)
7.4

RRB Model
53.51
41.42
21.84

8.00

Uniformity Index, n = 2.17

Material Temperature Impact Rate
(mls) (mm)
PVC 93.2 3.175
Sieve Size (mm) Mass % undersize
2.36 85.34
2 72.79
1.4 39.63
0.85 22.59
0.5
0.212
Characteristic Product Size, Loo = 2.24

Impact Rate Screen Size Characteristic Feed Size
(mls) (mm) (Inn!)
66.6 3.175 7.4
Mass % undersize RRB Model
71.82 70.22
54.65 56.87
28.05 31.82
18.35 11.97
Uniformity Index, n = 2.21

ScreenSize CharacteristicFeed Sin

(mm)
7.4

RRB Mow
83.37
71.63
44.46
18.34

UniformityIndex, n=2.14

Material Temperature

PVC

Sieve Size (mm)

2.36
2
1.4
0.85
0.5
0.212

CharacteristicProduct Size, Lao= 3.13

Material Temperature

PVC

Sieve Size (mm)

2.36
2
1.4
0.85
0.5
0.212

CharacteristicProduct Size, Lgo= 2.58

Material Temperature

PVC

Sieve Size (mm)

2.36
2
1.4
0.85
0.5
0.212

CharacteristicProductSize,I4o=2.l4

Impact Rate
(In/8) (mm)
93.2 3.175

143

Mass 9’. undersize
86.14
75.74
41.08
21.05

Impact Rate Screen Size Characteristic Feed Size
(mls) (mm) (mm)
53.2 3.175 7.4
Mass % undersize RRB Model
57.22 57.29
41.48 44.35
21.46 23.08
14.69 8.18
Uniformity Index, 11 = 2.25

Impact Rate Screen Size Characteristic Feed Size
(mls) (mm) (mm)
66.6 3.175 7.4
Mass % undersize RRB Model
75.1 73.23
58.45 59.52
29.23 33.08
17.56 12.11
Uniformity Index, 11 = 2.28

ScreenSize CharacteristicFeed Size

(mm)
7.4

RRB Model
93.23
84.47
72.83
45.31

Uniformity Index, n = 2.26

144

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (In/S) (mm) (mm)
PET 0 M.O.T. 53.2 3.175 4.6
Sieve Size (mm) Mass % undersize RRB Model
2.36 72.14 73.46
2 60.95 59.56
1.4 32.85 32.80
0.85 11.8 11.81
0.5 2.07 3.63
0.212 0.24 0.51

CharacteristicProduct Size, Lao: 2.57

UniformityIndex,n=2.3I

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (In/S) (mm) (min)
PET 0 M.O.T. 66.6 3.175 4.6
Sieve Size (mm) Mass % undersize RRB Model
2.36 74.36 76.7
2 66.23 66.24
1.4 47.32 43.80
0.85 21.56 21.13
0.5 4.34 8.83
0.212 0.13 1.99

CharacteristicProduct Size, Loo= 2.50

UniformityInderr,n=I.7s

ScreenSize CharacteristicFeed Size

Material Temperature Impact Rate
(C) (mls) (mm) (mm)

PET 0 M.O.T. 93.2 3.175 4.6
Sieve Size (mm) Mass % undersize RRB Model

2.36 76.73 78.97

2 68.37 69.29

1.4 51.63 47.71

0.85 26.01 24.45

0.5 5375 10.86

0.212 0.13 2.68

CharacteristicProduct Size, 14032.41

Uniformity Index, n=1.68

(C)
PET -20 Refig.
Sieve Size (mm)
2.36
2
1.4
0.85
0.5
0.212

Characteristic Product Size, 14.0 = 2.81

Material Temperature
(C)
PET -20 Refig
Sieve Size (mm)
2.36
2
1.4
0.85
0.5
0.212

CharacteristicProduct Size, 140:2,59

(C)
PET -2o Refig
Sieve Size (mm)
2.36
2
1.4
0.85
0.5
0.212

CharacteristicProduct Size, 1.0:: 237

ImpactRate

ImpactRate

145

1mm Rate Screen Size
(mls) (mm)
53.2 3.175

Mass °/o undersize
65.43
48.04
21.55
9.54
5.05
1.46

Screen Size
(mls) (mm)
66.6 3.175

Mass °/o undersize
71.93
60.37
32.17
11.68
3.85
0.87

(mls) (mm)
93 .2 3 . 175

Mass%undersize

78.82
69.29
47.24
21. 18
7.29
2. 12

Characteristic Feed Size
(mm)
4.6

RRB Model
64.14
48.87
23.57
7.20

1.90
0.21

Uniformity Indus n = 2.56

Characteristic Feed Size
(M)
4.6

RRB Model
72.86
59.07
32.66
1 1.89
3.69
0.53

Uniformity Index, n = 2.28

ScreenSize CharacteristicFeed Size

(mm)
4.6

RRB Model
79.81
69.25
45.71
21.61
8.74

1.86

UMUW n= 1.84

Material Temperature
(C)
PET 22
Sieve Size (mm)
2.36
2
1.4
0.85
0.5
0.212

CharacteristicProduct Size, Lao= 2.76

Material Temperature
(C)
PET 22
Sieve Size (mm)
2.36
2
1.4
0.85
0.5
0.212

Characteristic Product Size, Lao = 2.68

146

Impact Rate Screen Size Characteristic Feed Size
(In/S) (mill) (Inn!)
53.2 3.175 4.6

Mass % undersize RRB Model
64.76 63.98
46.08 46.89
19.02 20.20
7.31 5.19
3.06 1.14
0.93 0.10
Uniformity Index, 11 = 2.89
Impact Rate Screen Size ' Characteristic Feed Size
(mls) (M) (min)
66.6 3.175 4.6
Mass % undersize RRB Model
71.74 70.51
57.42 57.47
30.05 32.73
13.94 12.65
7.29 4.22
2.17 0.68

Material Temperature Impact Rate Screen Size
(C) (mls) (mm)
PEI‘ 23 M.O.T. 93.2 3.175
Sieve Size (mm) Mass % undersize
2.36 78.51
2 68.6
1.4 41.74
0.85 15.70
0.5 4.41
0.212 0.69

CharacteristicProduct Size, Lao = 2.36

Uniformity Indere n= 2.15

Characteristic Feed Sim

(mm)
4.6

RRB Model
80.00
67.62
40.79
16.42
5.57
0.90

Uniformitylndex n= 2.15

147

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PET 40 53.2 3.175 4.6
Sieve Size (mm) Mass °/o undersize RRB Model
2.36 67.8 65.91
2 50.22 51.17
1.4 23.08 25.82
0.85 10.99 8.40
0.5 6.29 2.36
0.212

Characteristic Product Size, L” = 2.78 Uniformity Index, 11 = 2.45

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PET 40 66.6 3.175 4.6
Sieve Size (mm) Mass % undersize RRB Model
2.36 71.93 72.86
2 60.37 59.07
1.4 32.17 32.66
0.85 11.68 11.88
0.5 3.85 3.69
0.212 0.87 0.53
Characteristic Product Size, 1...) = 2.48 Uniformity Index, 11 = 2.06
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (In/S) (min) (mm)
PET 40 93.2 3.175 4.6
Sieve Size (mm) Mass % undersize RRB Model
2.36 78.82 79.81
2 69.29 69.25
1.4 47.24 45.71
0.85 21.18 21.61
0.5 7.29 8.74
0.212 2.12 1.86

Characteristic Product Size, Loo '3 2.42 Uniformity Index, 11 = 2.03

148

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PET 60 53.2 3.175 4.6
Sieve Size (mm) Mass % undersize RRB Model
2.36 62.47 61.04
2 43.83 45.36
1.4 19.65 20.70
0.85 8.69 5.89
0.5
0.212
Characteristic Product Size, Loo = 2.88 Uniformity Index, 11 = 2.69
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (tn/S) (Inn!) (min)
PET 60 66.6 3.175 4.6
Size (mm) Mass % undersize RRB Model
2.36 70.07 68.35
2 54.8 54.52
1.4 27.34 29.42
0.85 12.07 10.53
0.5
0.212
CharacteristicProductSize,L.o=2.73 Uniformitylndergn=229
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PET 60 93.2 3.175 4.6
Size (mm) Mass % undersize RRB Model
2.36 79.00 78.34
2 67.2 65.96
1.4 38.25 39.74
0.85 16.75 16.15
0.5
0.212

Clmracter'isticProductSize,Lgo=2.42 UniformityIndex,n=2.12

149

Material Temperature Impact Rate
(C) (mls)
PET 80 53.2
Size (mm) Mass % undersize
2.36 63.35
2 46.1
1.4 22.17
0.85 9.45
0.5
0.212

Characteristic Product Size, 15.0 = 2.86

Material Temperature Impact Rate
(C) (mls)
PET 80 66.6
Size (mm) Mass % undersize
2.36 66.58
2 50.26
1.4 23.65
0.85 9.64
0.5
0.212
Characteristic Product Size, 1.40 = 2.78
Material Temperature Impact Rate
(C) (In/S)
PET 80 93.2
Size (mm) Mass % undersize
2.36 73.31
2 85.4
1.4 31.35
0.85 15.16
0.5
0.212
Characteristic Product Size, Loo = 2.61

Screen Size Characteristic Feed Size

(M) (M)
3.175 4.6

RRB Model
62.65
47.53
22.81

6.97

Uniformity Index, 11 = 2.56

ScreenSize CharacteristicFeed Size

(mm) (mm)
3. 175 4.6

RRB Model
65.68
50.58
24.95

7.85

Uniformity Index, n = 2.52

ScreenSize CharacteristicFeed Size

(mm) (mm)
3.175 4.6

RRB Model
72.39
58.98
33.24
12.48

Uniformity Index, a = 2.22

150

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (M) (M)
PET 0 MO.T. 93.2 3.175 2.36
Size (mm) Mass % undersize RRB Model
2.36 77.42 80.43
2 70.18 72.35
1.4 58.42 53.69
0.85 35.94 31.32
0.5 9.78 16.07
0.212 0.38 4.97
Characteristic Product Size, Lao = 2.34 Uniformity Index, 11 = 1.44
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (M) (M)
PET 0 MO.T. 93.2 3.175 _ 3.35
Size (mm) Mass % undersize RRB Model
2.36 74.55 78.60
2 68.99 70.61
1.4 57.88 52.52
0.85 36.05 31.05
0.5 9.56 16.27
0.212 0.78 5.23
Characteristic Product Size, Lao = 2.43 Uniformity Index, 11 = 1.39
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (M) (M)
PET 0 M.O.T. 93.2 3.175 4.00
Size (mm) Mass % undersize RRB Model
2.36 71.34 75.16
2 65.33 66.40
1.4 53.47 47.46
0.85 29.74 26.49
0.5 5.53 13.10
0.212 0.46 3.87

CharacteristicProductSize,Igo=2.60 Uniformitylndex,n=l.48

Material Temperature
(C)

PET 22

Size (mm)
2.36
2
1.4
0.85
0.5
0.212

Characteristic Product Size, Leo = 1.50

Material Temperature
(C)

PVC 22

Size (mm)
2.36
2
1.4
0.85
0.5
0.212

CharacteristicProduct Size, Loo= 1.42

Material Temperature
(C)
PET 22

Size (mm)
4.75
4.00
3.35
2.80
2.36
2.00

CharacteristicProductSize,L.o=4.l2

ImpactRate

151

Impact Rate Screen Size Characteristic Feed Size
(In/S) (M) (M)
93.2 1.57 4.6

Mass % undersize RRB Model
98.14 98.59
95.35 94.91
75.3 75.09
37.18 38.04
15.41 14.29
2.12 2.44
Uniformity Index, 11 = 2.14

Impact Rate Screen Size Characteristic Feed Size
(mls) (M) (M)
93.2 1.57 7.4

Mass % undersize RRB Model
98.21 96.20
96.57 92.51
77.35 79.20
49.03 54.12
36.81 3091

9.24 10.49

(mls) (M)
93.2 none

Mass % undersize
88.69
78.27
64.42
51.08
39.77
29.86

UniformityIndex,n=1.4o

ScreenSize CharacteristicFeed Size

(mm)
4.6

RRB Model
88.59
78.02
64.83
51.22
39.46
29.87

Uniformity Index, r1 = 2.09

152

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (tn/S) (M) (M)
PVC 22 93.2 none 7.4
Size (mm) Mass % undersize RRB Model
4.75 84.2 85.89
4.00 75.33 75.73
3.35 64.75 63.26
2.80 52.09 50.81
2.36 40.34 , 40.01
2.00 28.85 31.05
Characteristic Product Size, Loo = 2.73 Uniformity Index, n = 2.29

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (mm) (mm)
PVC 0 M.O.T 93.2 2.36 7.4
Size (mm) Mass % undersize RRB Model
2.36 99.47 99.72
2 97.6 97.75
1.4 77.39 77.09
0.85 31.91 32.47
0.5 9.84 9.17
0.212 1.33 0.98
CharacteristicProductSize,L.o=1.47 UniformityIndex,n=2.65

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (M) (M)
PET 0 M.O.T. 93.2 2.36 4.6
Size (mm) Mass % undersize RRB Model
2.36 80.19 80.41
2 69.66 70.62
1.4 49.54 48.38
0.85 25.70 24.37
0.5 8.36 10.56
0.212 0.93 2.50

CharacteristicProductSInlqo=234

Uniformity Index n = 1.73

153

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (tn/S) (M) (M)
PET/PVC 22 93.2 3.175 -
Size (mm) Mass % undersize RRB Model
2.36 85.87 86.61
2 75.72 74.53
1.4 44.20 44.90
0.85 16.67 17.01
0.5 6.52 5.28
0.212 1.09 0.73
Characteristic Product Size, Leo = 2.14 Uniformity Index, 11 = 2.33
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (M) (M)
PET/PVC 0 M.O.T. 93.2 3.175 -
Size (mm) Mass % undersize RRB Model
2.36 83.28 86.95
2 77.70 78.19
1.4 60.28 55.67
0.85 28.57 28.71
0.5 8.71 12.47
0.212 1.05 2.90
CharacteristicProductSize,I.oo==2.06 Uniformitylndex,n=1.76
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (In/8) (M) (M)
PET/PVC ~20 M.O.T. 93.2 3.175 -
Size (mm) Mass % undersize RRB Model
2.36 85.03 87.69
2 78.91 79.77
1.4 62.59 59.02
0.85 32.99 32.61
0.5 12.58 15.28
0.212 2.38 4.00

CharacteristicProductSize,L.o=2.01 Uniformitylndex, n= 1.63

154

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (m/S) (M) (M)
PVC 0 MO.T 93.2 0.889 7.4
Size (mm) Mass % undersize RRB Model
2.36 100 100
2 100 99.99
1.4 100 99.83
0.85 86.19 87.88
0.5 49.72 47.66
0.212 6.08 9.14
Characteristic Product Size, Lao = 0.75 Uniformity Index, 11 = 2.23
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (M) (M)
PET 0 M.O.T. 93.2 0.889 4.6
Size (mm) Mass % undersize RRB Model
2.36 99.62 100
2 99.62 99.99
1.4 98.86 99.88
0.85 87.55 87.69
0.5 45.28 45.05
0.212 7.17 7.60
Characteristic Product Size, Lao = 0.76 Uniformity Index, 11 - 2.36
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (M) (M)
PVC -20 M.O.T. 93.2 3.175 7.4
Size (mm) Mass % undersize RRB Model
2.36 99.34 99.80
2 98.34 98.59
1.4 85.43 85.16
0.85 46.02 46.18
0.5 16.89 17.08
0.212 3.64 2.67

CharacteristicProductSize,L.o= 1.30 Uniformitylndex, n=2.25

Material Temperature
(C)
PVC -40 M.O.T.
Size (mm)
2.36
2
1.4
0.85
0.5
0.212

CharacteristicProduct SizeLao=1.32

155

Impact Rate Screen Size Characteristic Feed Size
(mls) (M) (M)
93.2 3.175 7.4

Mass % undersize RRB Model

99.06 99.90
97.59 98.93
83.91 84.31
42.35 41.07
11.26 13.02

1.34 1.60

Uniformity Index, 11 = 2.51

Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (mls) (M) (M)

PET -20 M.O.T. 93.2 3.175 4.6
Size (mm) Mass % undersize RRB Model

2.36 79.06 80.68

2 71.79 71.89

1.4 53.42 51.64

0.85 29.49 28.31

0.5 11.11 13.51

0.212 2.14 3.72

CharacteristicProductSize,L.o=2.32 UniformityIndexn=L56
Material Temperature Impact Rate Screen Size Characteristic Feed Size
(C) (tn/s) (M) (M)

PET -40 M.O.T. 93.2 3.175 4.6
Size (mm) Mass % undersize RRB Model

2.36 78.16 79.09

2 69.97 70.56

1.4 52.56 51.26

0.85 30.72 28.94

0.5 12.29 14.35

0.212 2.05 4.22
CharacteristicProductSize,L.o=2.40 UniformityIndex,n=l.49

Material Temperature
PET -20 M.O.T.

Size (mm)

2.36
2
1.4
0.85
0.5
0.212

Characteristic Product Size, Loo = 2.97

Material Temperature
PET/PVC -20 M.O.T.

Size (mm)

4.75
2.36
1.40
0.85
0.5
0.212

CharacteristicProductSize,I.o=1.67

Impact Rate
(tn/s) (M)
93.2 3.175

156

Impact Rate Screen Size
(mls) (mm)
53.2 3.175

Mass%undersize

65.66
56.57
35.35
17.17
7.07
1.68

Characteristic Feed Size
(M)
4.6

RRB Model
66.20
55.77
35.69
17.05
7.22

1.70

Uniformity Index, 11 = 1.72

Mass%undersize

99.47
87.73
71.91
51.80
17.02

ScreenSize CharacteristicFeed Size

(M)

RRB W
99.96
93.24
70.72

44
22.97
6.93

Uniformity Index, n =1.so