VIRGINIA TECH 

CENTER FOR 

COMPOSITE MATERIALS 

AND STRUCTURES 

[HAS&-CR-176439) TBEBBDPLASTIC HATBIX N86-21619 

COBPOSXTE PEDCESSHNG EODE k [Virginia 

Bo~ytecknic Inst, and State Univ,] 151 p 

MC A88/fif a01 CscL %ID anclas 

G3J24 "1567 

Thermoplastic Matrix Composite Processing Model 

Philip He Dara 

Alfred C. Loos 

Virginia Polytechnic 

Institute 

and 

State University 

Blacksburg, Virginia 
College of Engineering 

Virginia Polytechnic Institute and State University 

Blacksburg, Virginia 24061 

September 1985 

Thermoplastic Matrix Composite Processing Model 

Philip H. ~aral 

Alfred C. ~oos* 

Department of Engineering Science & Mechanics 

Interim Report 57 

The NASA-Virginia Tech Composites Program 

NASA Cooperative Agreement NAG-1-343 

Prepared for: W. T. Freeman, Jr. 

Polymeric Materials Branch 

National Aeronautics and Space Administration 

Langley Research Center 

Hamptan, VA 23665 

l~raduate Student, Department of Engineering Science & Mechanics 

2~~si stant Professor, Department of Engineering Science & Mechanics 
THERMOPLASTIC MATRIX COMPOSITE PROCESSING MODEL 

(ABSTRACT) 

The effects the processing parameters pressure, temperature, and 

time have on the quality of continuous graphite fiber (AS4) reinforced 

0 thermoplastic matrix (UDEL P1700) composites have been quantitatively 

accessed by defining the extent to which intimate contact and bond 

formation has occurred at successive ply interfaces. Two models are 

presented predicting the extents to which the ply interfaces have 

achieved intimate contact and cohesive strength. The models are based 

on experimental observation of compression molded laminates and neat 

resin conditions, respectively. Identified as the mechanism explaining the phenomenon by which the plies bond to themselves is the theory 

of autohesion (or self diffusion). Theoretical predictions from the 

"Reptation Theory" between autohesive strength and contact time are 

used to explain the effects of the processing parameters on the observed experimental strengths. The application of a time-temperature 

relationship, in the WLF manner, for autohesive strength predictions 

is evaluated. A viscoelastic compression molding model of a tow was 

developed to explain the phenomenon by which the prepreg ply interfaces develop intimate contact. The intimate contact model contains 

sub-models defining the degree of nonuniformity of tow heights across 

the width of a prepreg, viscoelastic mechanics model simulating the 

response of tows to a compressive load, and an empirical relationship 

of the influence of fibers on the neat resin viscosity. 
Acknowledgements 

The authors would like to express thanks for support of this work 

from the NASA-Virgi ni a Tech Composites Program through NASA Grant 

NAG1-343, and the faculty and students of the program. 
Table of Contents 

Page 

ABSTRACT ............................................................ ii 

ACKNOWLEDGEMENTS .................................................. iii 

TABLE OF CONTENTS ................................................... iv 

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

LIST OF TABLES ...................................................... xi 

1.0 INTRODUCTION ................................................... -1 

2.0 AUTOHESION-AU ................................................... 5 

2.1 Introduction-Au ........................................... -5 

2.2 Literature Review-Au ....................................... 9 

2.2.1 Mechanism Explaining the Autohesion 

Phenomenon .......................................... 9 

2.2.2 Experiment/Theory for Quantifying Autohesion ....... 12 

2.3 Experiment-Au ............................................. 19 

2.3.1 Description ........................................ 19 

2.3.2 Sample Preparation ................................. 23 

2.3.3 Testing Program .................................... 27 

2.4 Results and Discussion.Au ......... ........................ 32 

2.4.1 Original Data . ..................................... 33 

2.4.la Effects of Contact Pressure on 

Autohesion .................................. 33 

2.4.lb Effects of Contact Time on Autohesion ....... 35 

2.4.1~ Effects of Temperature on Autohesion ........ 43 

2.4.ld Interrelationship Between Contact Time 

and Temperature on Autohesion ............... 47 
Tab1 e of Contents (continued) 

Page 

3.0 INTIMATE CONTACT.IC... ......................................... 53 

3.1 Introduction-IC ........................................... 53 

3.2 Experiment-IC ............................................. 56 

3.2.1 Description ........................................ 56 

3.2.2 Sample Preparation ................................. 57 

3.2.3 Testing Procedure .................................. 62 

3.3 Results and Discussion-IC ................................. 64 

3.3.1 Original Data and Data Reduction ................... 64 

3.3.2 Intimate Contact Sub.Models ........................ 68 

3.3.2a Mathematical Description of Prepreg's 

Geometric Nonuniformity-Sub-Mode1 ........... 69 

3.3.2b Compression Modeling of a Single 

Tow-Sub-Model ............................... 74 

3.3.2~ Rheological Material Properties ............. 81 

3.3.3 Intimate Contact Model ............................. 85 

3.3.3a Problem Formulation ......................... 85 

3.3.3b Mathematical Model ......................... 87 

3.3.4 Intimate Contact Model/Experiment Correlation ...... 89 

3.3.4a Discussion ..............................*... 89 

3.3.4b Influences of the Prepreg Geometric 

Nonuniformity on DIC ........................ 95 

3.3.4~ Observation of the Model .................... 97 

4.0 COMPUTER MODEL ................................................ 101 
Tab1 e of Contents (continued) 

Page 

5.0 SUMMARY AND CONCLUSION ....................................... -113 

REFERENCES ......................................................... 120 

APPENDIX A . RHEOLOGICAL PROPERTIES OF UDE P PI700 RESIN ........... 123 

A.l Introduction ............................................. 123 

A.2 Experiment ............................................... 123 

A.3 Test Data Results and Discussion ......................... 125 

A.3.1 Dynamic Testing ................................... 125 

A.3.2 ' Linear Check ...................................... 130 

A.4 Viscoelastic Theory ...................................... 134 

A.4.1 Cox Merz Rule ..................................... 134 

A.4.2 WLF Theory-Master Curve ...... ...........,,........ 135 
List of Figures 

Figure Page 

2.1 

2.2 

2.3 

2.4 

Physical Picture of Autohesion Phenomenon.. ................. .7 

Reptation Model .............................................lo 

Reptat ion at an Interface. ................................. .I5 

Cohesive Tear Strength as a Function of Pealing Rate 

at Several Constant Temperatures (Hamed and Shieh [15]). 

The dashed line shows a slope of 1/2 as predicted by Wool 

for chain pullout failure mechanism to occur [ll] .......... .18 

Testing Apparatus - Rheometrics Series Systems Four.... ..... 24 

Testing Fixture with Close-up of Test Specimen .............. 25 

Sample Preparation - P1700 Bead to Thick Film 

Transformation. .............................................26 

Test Specimen Preparation ................................... 29 

Typical Autohesive Strength Testing Format 

and Procedure.. .................................*.......... .31 

Evaluation of.P,, and Effects of Contact Pressure on the 

Autohesive Strength .........................................34 

Autohesive Load versus Fourth Root of Contact Time 

at T = 200°C (39Z°F), and P = P ........................... 36 m 

Autohesive Load versus Fourth Root of Contact Time at 

T = 210°C (410°F), 220°C (428"F), 230°C (446"F), 240°C 

(464"F), 250°C (48Z°F), 260°C (500°F), and P = P ......... .37 m 

Degree of Autohesion Versus Fourth Root of Contact Time 

at T = 210°C (410°F), 220°C (428"F), 230°C (446"F), 

250°C (48Z°F), 260°C (500°F), and P = P .................. .40 m 

Summary Plot of Degree of Autohesion vessus Fourth Root 

of Contact Time. ............................................41 

Evaluation of Arrhenius Constants for Autohesion 

Temperature Dependency ...................................... 44 

Comparison Between Arrhenius Law and the Degree of 

Autohesion Test Data for Evaluation of Temperature 

Relationship ................................................45 
Li st of Figures (continued) 

Figure Page 

2.17 Parametric Study Between Temperature and Contact Time 

(a) Autohesive Load versus Temperature at Contact 

Times of 10, 100, and 500 Seconds (b) Degree of 

Autohesion versus Temperature at Contact 

Times of 10, 100, and 500 Seconds.. ................... .46 

2.18 WLF Theory, (a) Shift of Original Data at Respective 

Temperature to the Reference Temperature, (b) 

Evaluation of WLF Constants................. ................ 49 

2.19 Compari son between the WLF Time-Temperature 

Relationship, and the Degree of Autohesion Test Data ........ 51 

3.1 C-Scan Technique Detection of Spacial Gaps After 

Cure of Unidirectional Graphi te/Epoxy Composite. ......... .. .58 

3.2 Intimate Contact Testing (a) Specimen Preparation, 

(b) Testing Apparatus.. .................................... -60 

Model Formulation Flow Diagram .............................. 70 

Schematic of Prepreg Geometry ............................... 71 

Weibull Density Model of Prepreg Geometric 

Nonuniformity with Histogram ................................ 73 

Geometry of a Single Tow Subject to Uniform 

Compressive Loading Normal to XY Planes of Top and 

Bottom Surfaces. ............................................ 75 

Complex Viscosity versus Frequency and Steady Shear 

Viscosity Versus Rate of Strain Using Cox-Merz Rule,........83 

Intimate Contact Model Formulation of Prepreg 

Geometry .................................................... 86 

Comparison Between Intimate Contact Theory and 

Test Data.......... ......................................... 92 

Effects of Temperature on Fiber Reinforced Resin 

Viscosity Parameters. ....................................... 94 

Effects of Probabi 1 istical ly Skewed Distributions of 

Tow Height Nonuniformity Across the Width of a Prepreg 

with the Degree of Intimate Contact....... ................ 36 

viii 
List of Figures (continued) 

Figure Page 

Effects of Probabi l i stical ly Deviated Normally 

Distributed Tow Height Nonuniformity Across the Width 

of a Prepreg with the Degree of Intimate Contact...........,98 

Observations of Model Concerning (a) Tow Height versus 

Contact Time, and (b) the Rate of Decreasing Tow 

Height due to Compression Loading versus Tow Height ......... 99 

Distribution of the Degree of Autohesion Over the 

Area in Intimate Contact for Several Processing Times......l06 

Cumulative Distribution of Areas in Intimate Contact 

Having a Minimum Degree of Autohesion at Several 

Processing Times.... ...............,..,..................... 108 

Summary Plot of the Minimum Degree of Autohesion 

Versus the Degree of Intimate Contact at Processing 

Times of 50 and 1000 sec.. ........,....................... .I10 

Effects of Temperature and Pressure on the Final 

Processing Time Required to Achieve Full Intimate 

Contact and Cohesive Strength .....,........................ 112 

8 Linear Viscoelastic Complex Viscosity Data of UDEL 

P1700 Resin at 20°C Intervals from 220°C to 400°C 

and Frequency Range from 0.1 to 100 Radianslsec ............ 127 

@ Linear Viscoelastic Shear Storage Modulus of UDEL 

PI700 Resin at 20°C Intervals from 220°C to 400°C 

and Frequency Range from 0.1 to 100 Radianslsec ..........-. 128 

G9 Linear Viscoelastic Shear Loss Modulus of UDEL 

PI700 Resin at 20°C Intervals from 220°C to 400°C 

and Frequency Range from 0.1 to 100 Radianslsec ............ 129 

Linear Check of Viscosity, Data of ,,UDE i? PI700 Resin at 

T = 260°C, Plots of Q*, G , and G versus Percent Strain 

at Frequencies 0.5 rad/sec (top graph), 5 -0 rad/sec 

(center graph), 50.0 radlsec (bottom graph). .............. .I31 

0 Linear Check of Viscosity,Data of,,UDEL P1700 Resin at 

T = 320°C, Plots of TI*, G , and G versus Percent Strain 

at Frequencies 0.5 rad/sec (top graph), 5.0 rad/sec 

(center graph), 50.0 radlsec (bottom graph). .............. .I32 
List of Figures (continued) 

Figure Page 

Q A.6 Linear Check of Viscosity,Data of,UDEL PI700 Resin at 

T = 360°C, Plots of TI*, G , and G versus Percent 

Strain at Frequencies 0.5 rad/sec (top graph), 5.0 

rad/sec (center graph), 50.0 rad/sec (bottom graph). . . . . . . .I33 

A.7 Master Curve of Complex Viscosity Data Using WLF 

Time-Temperature Superposition at a Reference 

Temperature, Trefl = 220°C .................................. 136 
List of Tables 

Tab1 e Page 

2.1 Autohesion Test Matrix.. ........... .. ...................... -21 

3.1 Material Properties ......................................... 61 

3.2 Intimate Contact Test Matrix ................................ 63 

'3.3 Degree of Intimate Contact Data ............................. 67 

4.1 Input Parameters ........................................... 103 

A . 1 Viscosity Test Conditions .................................. 126 
1.0 Introduction 

Increased damage tolerance and decreased cost are the main 

drivers behind the interest in development of thermoplastic matrix 

composites over thermosetting matrix composites. However, currently, 

no processing theory exists that would assure the quality of a 

composite for a given set of the processing parameters pressure, 

temperature, and time. To eliminate the trial and error approach 

taken to date, this study attempts to; 1) understand the phenomena 

occurring during processing; 2) identify the mechanisms expl ai ni ng the 

phenomena; and 3) re1 ate the processing parameters with the mechanisms 

to define the state of some properties that define a known quality. 

The type of thermoplastic matrix composite under study has made 

of a prepreg material composed of a thermoplastic resin (matrix 

material) reinforced with a high percentage of continuous 

unidirectional fibers. The methods commonly used to process the 

prepreg material into a composite uses either a matched metal die 

press or an autoclave. In both methods the prepreg sheets are 

orientated, shaped, and processed under an applied pressure and 

elevated temperature condition for a given length of time, called the 

processing cycle. The applied pressure is the driving force causing 

the prepreg ply interfaces to coalesce. The elevated temperature 

controls the rate at which the ply interfaces bond together by 

influencing the mobility of the molecular chains of the polymer. The 

molecular chain mobility influences the material properties of 

viscosity and self diffusion. The magnitude of the applied 
temperatures and pressures significantly affect the performance of the 

f i ni shed part. 

In the making of prepregs, a solvent must be introduced to the 

thermoplastic matrix material to allow the resin to wet out the 

f i bers . In general, the lowest attainable thermoplastic 

4 viscosity (> 10 poise), already exceeds the gel point of an epoxy 

resin (i.e. gel point is where epoxy resin solidifies). The lower 

viscosity allows the fibers to be thoroughly wetted with resin and 

evenly distributed. However, the solvent must be bled from the 

prepreg prior to processing so that good mechanical properties can be 

attained. 

The motivation for using thermoplastic matrix composites in lieu 

of thermosetting matrix composites is the potential for increasing the 

toughness of composites in order to improve damage tolerance, and for 

lowering the fabrication cost by reducing processing time and a1 lowing 

for high speed production. Other advantages are: its abilities to be 

postformed and reformed making use of metal forming techniques; 

reduced storage cost by eliminating refrigeration; reduced scrappage; 

and it is easily weldable and repairable. The interested reader is 

referred to the industrial reports listed as references 1-5. 

The motivation for studying thermoplastic matrix composites is 

the desire to define a processing state (i.e. interfacial contact 

area, degree of cure for thermosets, etc.) through the processing 

parameters pressure, P, temperature, T, and tqme, t, from a scientific 

approach and not the presently used empirical method. At the present 

time no model exists that relates the interfacial bonding, and 
interfacial deformation phenomena that occur during processing of 

thermoplastic matrix composites. In an analogous fashion just as the 

steam tables are to the thermodynamicist, so should the thermoplastic 

matrix composite model be to the processing engineer (i .e. given any 

two processing parameters (P, 1, t) the third parameter is 

automatically defined, as well as, all the processing states.) 

@ In studying the processing of UDEL P1700 Polysulphone/AS4 

graphite fiber thermoplastic matrix composites, one must address four 

problem areas: 1) the solvent removal from the matrix material, 2) 

the strength of the fiber/matrix interface, 3) the bonding 

(consolidation) of the ply interfaces to one another, and 4) the 

formation of intimate contact (coalescence) at the 1 ami nate ply 

interfaces. The last two problem areas are addressed in this study. 

The third problem mentioned, the bonding of ply interfaces to one 

another, is addressed in Section 2.0. The phenomenon was identified 

as autohesive bonding. The mechanism describing the autohesive 

phenonenon has been described by the "Reptation Theory" where 

molecular chain movement across the ply interface was related to time, 

depth of chain penetration, and resulting bond strength. An 

experimental investigation of neat resin interfacial strength was 

undertaken at temperature conditions above the glass transition 

temperature of the resin (Tg = 194°C (381.Z°F)). Several interesting 

results occur as a result of performing strength tests at the elevated 

temperatures differing from most other studies. 

The fourth problem, the formation of intimate contact at the 

laminate ply interfaces, is addressed in Section 3.0. A time 
dependent model was formulated that simulates the vi scoel astic 

response of a fiber bundle impregnated with resin (i .e. tow) subjected 

to- uniform compressive loading normal to the top and bottom 

surfaces. This model was used as the basis for describing the 

flattening of nonuniform tow height distributions across the width of 

a prepreg. The model combines the viscoelastic properties of the 

fiber reinforced resin, the distribution of tow height nonuniformity, 

and the processing parameters pressure, temperature, and time to 

describe the degree of intimate contact. The model was verified 

experimentally, where [O, 90, 0IT cross-ply laminates were processed 

under several processing conditions and ultrasonically C-scanned for 

presence of spacial gaps at the two-ply interfaces. 

In Section 4.0 an overall thermoplastic processing model is 

constructed by combining the autohesion model of Section 2.0 with the 

Intimate Contact model of Section 3.0. 

Lastly, Section 5.0 presents the conclusions and recommendations 

for further study. 
2.1 Introduction-Au 

In studying the processing of thermoplastic matrix composites it 

has been observed that individual prepreg plies consolidate into a 

laminate by bonding themselves to one another at the interfaces. The 

bond strength for thermoplastic matrix composites has been shown to be 

dependent upon the processing parameters pressure (P), temperature 

(T), and contact time (t,). The degree at which bond formation has 

occurred at the interface, as a function of the processing parameters, 

is the subject of this section of the report. Thus, this study 

addresses only the neat resin at the interface in which bond formation 

occurs. It is assumed that strong bond formations on the neat resin 

will result in strong bond formations at the interface of a composite. 

Before the bonding of the ply interfaces can be modelled, the 

mechanism explaining the phenomenon must be identified. A special 

type of bonding, called autohesion, has been identified as the 

mechanism by which neat thermoplastic resins bond to themselves. 

Autohesion, or self diffusion, is the type of adhesion used to 

explain the phenomenon high polymers possess when two surfaces of the 

same material are placed in contact with each other, resulting in the 

formation of a strong bond at the interface [6]. The term selfdiffusion implies the time dependency of the bond formation process 

and its eventual asymptotic convergence to some final state of bond 

strength. A requirement for autohesion is that the materials placed 

in contact be similar. 
Autohesion is distinguishable from adhesion in that autohesive 

bond strength is the result of diffused chain segments across the 

interface. In the case of adhesion, bond strength is due to the 

chemical bonding of two dissimilar materials present at the interface 

(i.e. metal to high polymer.) Also, thermoplastic matrix composites 

distinguish themselves from thermosetting matrix composites in the 

manner by which the plies consolidate, even though the materials at 

the interface in both cases are identical (i .e. 

polysul fone/polysul fone and epoxy/epoxy, respectively.) Thermopl astic 

matrix composites rely strictly on the strong autohesive properties of 

the neat resin to consolidate the plies. Thermosetting matrix 

composites rely on the polymerization of the neat resin to bond the 

plies and not on its weaker autohesive strength properties. 

It has largely been accepted in the field that the mechanism by 

which autohesion occurs is attributed to two characteristics of high 

polymers: 1) a random chain network consisting of entanglements, and 

2) flexible macromolecules able to move within the bulk polymer [6]. 

Schematically outlined in Fig. 2.1 is the autohesion phenomenon 

for an amorphous polymer above its glass transition temperature, . 

g 

At the initial contact (Fig. 2.la) of the two surfaces, localized 

deformation occurs so that macroscopic fitting of the surfaces takes 

place. At some intermediate time (Fig. 2.lb) partial diffusion has 

occurred across the interface. This is due to free chain movement, 

resulting from the increased molecular free volume at temperatures 

above the Tg. This is the stage at which the increased penetration 

depth of the diffusing chain occurs, resulting in increased 
Autohesion Phenomenon 

r Chain Like Molecules 

Initial Contact 

t = 0 

Partially 

Diffused 

Completely 

Diffused 

t = t, 

Figure 2.1 Physical Picture of Autohesion Phenomenon 
entanglements, causing increased bond strength. At long contact times 

(Fig, 2.1~) the interfacial diffusion process has been completed and 

the interface can no longer be distinguished from the bulk material 

Experimental evidence has shown that autohesion is largely a time 

and temperature dependent problem. This is due to the diffusive and 

viscoelastic nature of the material. Also, the pressure required to 

achieve good contact at the interface of the neat resin is very much 

less than the pressure needed to process a fiber reinforced 

thermoplastic matrix composite. This is because macroscopic fitting 

of the smooth neat resin surfaces in the study of autohesion requires 

pressures much less than the pressures required to deform irregular 

\ 

fiber reinforced resin surfaces. 

Two major approaches for quantifying the autohesion phenomenon 

have been cited in the literature: 1) mechanical strength testing of 

the polymer's interface, and 2) radioactive doping of the polymer 

chains and measurement of the rate at which the tracer progresses 

through the polymer. The present study of the autohesive bond 

formation made use of the mechanical strength approach. 

The mechanical strength approach assumes a definite correlation 

exists between the contact (entanglement) time to form the bond and 

the disentanglement period required to cause failure. The 

entanglement process is the time required for molecular entanglements 

to form through increased penetration of diffused chain lengths across 

the interface. The disentanglement process is the time span during 

which the interface is loaded until failure. The failure mechanism 
can either be chain pull-out or chain fracture depending upon the 

depth of penetration of molecular chains and the molecular free 

volume. Strain rate effects must be accounted for when comparjng the 

absolute values of the autohesive strengths above the glass transition 

temperature because of the viscoelastic nature of the material. 

2.2 Literature Review-Au 

2.2.1 Mechanism Explaining the Autohesion Phenomenon 

Molecular Dynamics of Random-Coil Chains 

The "reptation theory" of Pierre-Gi 1 les de Gennes [8,9] has been 

used to model the motions of individual linear random-coil chains in 

amorphous solid state bulk materials. The major points of the theory 

will be presented here. Wool gives a good summary of the reptation 

theory [ 10 ] . The premise of the reptation model is that the chain-like 

molecules can change shape and move, but cannot intersect each 

other. Thus, the chain is confined to an imaginary tube within which 

all motion takes place (Fig. 2.2a). The tube represents the 

constraints imposed by adjacent macromolecules preventing transverse 

motion. The chain moves in a snake-like motion within this tube but 

cannot go outside the tube boundary except at the ends. The local 

snake-like motion causes the molecular chain to slip out of the 

original tube over a period of time. Simultaneously, as the original 

tube length decreases a new tube of equal length is being formed. 

Figure 2.2b schematically shows the transition from snake-like motion 

to macroscopic motion. It is this snake-like motion back and forth in 

the tube, coupled with the gradual loss of memory, that allo-ws for the 

formation of new tube orientations and macromolecular motion. This 

apparent loss of memory by the polymer is characteristic of- high 

polymers due to the viscoelastic nature of the material. Considering 

long time intervals, the details of the snake-like motion may be 

ignored and a macroscopic viewpoint may be taken. This macroscopic 

viewpoint entails the movement of the chain as a whole [8]. This 

macromolecular motion acts initially at the chain's ends and works 

towards the center of mass of the original chain where some memory has 

still been maintained [Ill. 

With this physical model, de Gennes formulated relationships 

between chain length, chain-tube mobility, chain length diffused, and 

time. Of major importance in the study of autohesion is the 

relationship shown in Eq 2.1 between the 'random walk' (i.e. mean 

2 

square path (< >)) of the chain length diffused <a > and the depth of 

the resulting penetration of chain lengths across a plane within the 

2 bulk material >. 

Equation 2.1 describes the random progress of the chain's uncertain 

path to that resulting in a preferred direction on the average of many 

chains. 

The relationship between x and time (t) via a double random walk 
process as proposed by de Gennes becomes: 

x-t 1/4 

Where the introduction of time is made through the application of 

2 Einstein's diffusion equation <a > = 2Dt to the motion of the chain 

within the tube, where D is the microscopic diffusion coefficient. 

These relationships describing the polymer's chain motions in an 

entangled melt are the basis of Wool's [12] and Jud's [13] work 

addressing crack healing and welding of polymers. 

Presented in the next section are the testing methods used by 

Wool and Jud for quantifying autohesion along with their extensions of 

the reptation model for autohesive strength predictions. 

2.2.2 Experimentflheory for Quantifying Autohesion 

Several mechanical strength approaches for quantifying autohesion 

are presented here. Compact tension tests (CT) of thick films were 

used to study the welding time and crack healing times of like 

polymers. Peel and double cantilever beam tests were also used to 

study crack healing of like polymers. Wool et. al. [Ill carried out 

welding and crack healing studies. Studies were carried out on neat 

resin, as well as continuous and short fiber reinforced resin 

coupons. No remarks concerning the influences of the reinforcement on 

autohesive strength were reported. 

Jud et. al. [13] studied the autohesive strength properties 

through the use of the compact tension test. Razor edge cracks were 
introduced into the exposed edges. The sample was then fractured in a 

tensile machine at room temperature. Smooth, clean fractured surfaces 

resulted. The fractured specimens were put back together under a 

light compression to assure good contact. The temperature of the 

sample was then raised above the Tg for the desired length of 

contacting time and then cooled to room temperature. The sample was 

then fractured again. The peak load at fracture defined the fracture 

toughness KIc (or autohesive strength (Au) (111) resulting from the 

temperature and contact time conditions during autohesion. Jud [13] 

used the above CT test in the studying of welding. Smooth virgin 

surfaces were brought into contact at a given temperature (> glass 

transition temperature) and contact time in order for autohesion to 

occur, The sample was then returned to room temperature, notched with 

a razor's edge, and tested until fracture. 

The theory presented by Jud relates a diffusion model similar to 

the reptation theory of de Gennes, where the number of physical 1 inks 

per unit area is proportional to the average depth of penetration of 

molecules. Jud assumes that the strength is proportional to the 

number of links and that the Einstein diffusion equation holds 

2 true <a > = 2Dt. Jud has shown good agreement between experiment and 

theory . 

Jud observed in both studies a linear relationship between 

fracture toughness and the fourth root of time, (tc 'I4) and that 

specimens healed or welded at a higher temperature required less time 

to achieve the same toughness. Also, welded specimens with polished 

surfaces required longer contact times in order to attain a given 
fracture toughness than those observed in the crack healing study, 

where fractured surfaces were healed as is. This was attributed to 

the different initial conditons of molecular chain-orientations at the 

interface. 

Wool et. al. [10,11,12] studied the autohesion phenomenon in a 

similar fashion to Jud and observed similar relationships between 

autohesive strength, contact time, and temperature. In addition to 

the compact tension test Wool also added the double cantilever beam 

and peel test. These tests were also conducted at room temperature 

conditions in similar fashion to the CT test described above. 

Wool extended de Gennes' reptation theory of macromolecular 

motion within the bulk of the polymer to that of macromolecular motion 

across a polymer-polymer surface (Fig. 2.3). Thus, Wool assumes that 

the molecular chain entanglement density near and at the interface has 

the same influence on chain motion as does the bulk's entanglement 

density . 

Wool asserts that the autohesive strength (Au) is proportional to 

the square root of the average interpenetration length a shown in Eq 

2.3 and proportional to the average interpenetration depth, x, given 

in Eq 2.4 and defined in the reptation theory by de Gennes. 

(2.3) 

AU - x (2.4) 

With this assumption, Wool used a strain energy approach to 
Self Diffusing Molecular Chain Segments 

Figure 2.3 Reptation at an Interface 
derive relationships between: 1) autohesive strength and contact time 

(Eq 2.5), 2) autohesive strength and strain rate for a chain pull-out 

failure mechanism (Eq 2.6), and 3) autohesive strength and strain rate 

for a chain fracture failure mechanism (Eq 2.7). 

These equations were a1 so supported by experimental evidence [ 10- 

141. The strain energy approach assumes a uniaxial stress is applied 

normal to the interface. A unit surface area contains a finite number 

of molecular chains intersecting the interface with various depths of 

penetration. The chain is assumed to be held within a tube by a 

molecular friction coefficient, resisting longitudinal loading (i .e. 

direction para1 lel to tube end.) The molecular friction coefficient 

similates the chain's entanglement with other chains. The stored 

strain energy resulting from a longitudinal load can either cause 

chain fracture or chain pull-out, depending upon the magnitude of the 

applied load, the strain rate, and the depth of the penetrating 

chains. Chain pull-out is favored for slow strain rates, high 

temperatures, short contact times, and shal low depths of 

penetration. As shown in Eq 2.5, Wool's study of polymer welding and 

crack healing predicts a 1 inear relationship between Au and t:l4 up to 
the green strength (i.e. cohesive strength) after which the strength 

becomes independent of processing time. The green strength 

corresponds to that state within the polymer in which the interface 

has become indistinguishable from the surrounding bulk polymers. Wool 

assumes that the autohesive strength data approaches the green 

strength of the material linearly with the fourth root of 

1/4) time (tc . 

Wool (111 states that contact time-temperature relationships for 

the diffusion coefficients (D) may behave according to the theory of 

Williams, Landel, and Ferry (commonly referred to as WLF). 

Experimentally determined temperature-dependent self-diffusion 

coefficients become independent of strain rate provided the autohesive 

failure data results from chain pull-out and are normalized to the 

cohesive strength under identical temperature and strain rate 

conditions. This observation was supported by the following 

experimental work done by Hamed et. a1 . [ 15 I. 

Hamed and Shieh [15] reported cohesive tear strength data versus 

peel rate at several constant temperatures above the Tg as shown in 

Fig. 2.4. The results support Wool's theoretical predictions of 

strain rate effects on autohesive strength for failure mechanisms of 

chain pull-out (Eq 2.6) and chain fracture (Eq 2.7). Three important 

observations of Fig. 2.4 are pointed out here which will be used in 

Section 2.4.lb. First, an increasing strain rate results in an 

increasing percentage (0 to 100%) of chain fracture failure, and that 

a decreasing strain rate results in an increasing percentage of chain 

pull-out failures. Second, at temperatures just above the Tg, chain 
Figure 2.4 Cohesive Tear Strength as a Function of Peallng Rate 

at Several Constant Temperatures (Hamed and Shieh [ 151 ) . The dashed line shows a slope of 1/2 as predicted by Wool 

for chain pullout failure mechanism to occur Ill] 
failure due to fracture predominates over a large range of strain 

rates. Three, the curves exhibit a time-temperature relationship in a 

WLF manner for the disentanglement process. 

The reason the above observations occur is that the molecular 

free volume increases with temperature; thus, shorter disentanglement 

times (i.e. faster strain rates) are required for chain fracture to 

occur at higher temperatures. Also, the slower the strain rate, the 

longer the time the chain entanglements have to untangle, and so the 

greater the occurrence of chain pull-out. 

With these findings by Jud et al. and Wool et. al. a test program 

for quantifying autohesion for PI700 neat resin was undertaken with 

three goals: 1) to see if the linear relationship between Au 

and t:I4 exists up to the cohesive strength of the material, 2) to 

reduce amount of scatter in the mechanical strength data as observed 

by Wool and Jud by conducting mechanical strength tests at the 

temperatures at which the autohesion phenomenon occurs, and 3) to 

determine if a contact time-temperature relationship for the diffusion 

coefficient exists in a WLF manner. The last goal would greatly 

reduce the number of tests by simulating the autohesion phenomenon at 

low temperatures above Tg requiring long contact times with the higher 

temperature test data requiring short contact times. 

2.3 Experiment-Au 

2.3.1 Description 

Measuring the progress of the polymer's state of interfacial 
diffusion has been qualitatively and quantitatively obtained using 

numerous approaches. Some of the strength approaches have been peel 

strength, tensile strength, and shear strength tests as reported in 

Section 2.2.2. The following experimental method for quantitatively 

assessing the effect of the processing parameters P, T, and tc on 

autohesion is based on the premise that the distance of the diffused 

polymer chain across the interface is proportional to interfacial 

strength given in Eq 2.4. Processing is concerned with the time 

required to achieve a certain degree of autohesion OAu, defined in Eq 

2.8 as the ratio of the autohesive strength to cohesive strength. 

Strength measurements were made on pol y su 1 f one (Uni on Carbi de ' s 

UDEL@ P1700) material. The measurements included the following: 1) 

effects of contact pressure on autohesion, 2) effects of material 

temperature on autohesion, and 3) the effects of contact time on 

autohesion. Table 2.1 1 ists the testing temperature and contact times 

during the autohesion phenomenon and the temperature conditions during 

the strength test. 

To determine the degree of autohesive strength an interfacial 

tensile test approach at elevated processing temperatures above the Tg 

was used. 

The reasons for the high temperature testing approach are 

threefold: 1) to reduce the inherent error caused by the temperature 

transitions of going from room temperature to processing temperature 
Table 2.1 Autohesion Test Matrix 

Autohesion Strength Test 

Temperature OC/"F tc (set) Temperature OC/"F 
and back down to room temperature for testing, 2) to devise a test 

method so that a standard test apparatus (Rheometrics System Four 

rheometer) common to most processing facilities could be used for 

evaluating autohesion properties, and 3) to evaluate the possibilites 

of expanding the data through time and temperature superposition. 

As pointed out in Section 2.2.2 the failure mechanism is a 

function of both strain rate (L) and temperature. Thus, if high 

temperature testing is used, it becomes imperative that the failure 

mechanism be constant throughout the contacting time spectrum for each 

set of temperature data. It is also necessary that failure be due 

totally to chain pull-out throughout the temperature range for which 

time-temperature superposition is used [ 1 . The reason for these 

restrictions is that no additional influences caused by differences in 

the type of failure mechanism are allowed to affect the relationship 

between the failure load and the depth of penetrating chain lengths 

(i.e. testingldisentanglement time and contacting/entanglement time, 

respectively). The cause for a possible change in the failure 

mechanism is that as the penetrating chain length increases with 

increasing contacting time a higher probability of chain fracture 

results unless the disentanglement time (i.e. d) is sufficiently slow 

or temperature sufficiently high. 

For the above reasons and the inability of the test apparatus to 

produce more than one strain rate, the useful temperature range is 

expected to have a lower bound above the Tg while the upper 

temperature i s bounded by material 1 imitations. 

The evaulation of autohesion required the following capability: 
1) an oven temperature range of 200 - 260°C (392-500°F), 

2) a constant cross-head rate, and 

3) monitoring of compressive and tensile loads as a function of 

time 

The Rheometrics System Four rheometer (used for obtaining shear 

viscosity data for non-Newtoni an fluids) meets the above 

requirements. The oven, servo motors and test fixtures (para1 lel 

plates) designed primarily for shearing flows are versatile enough to 

be used for the autohesion experiment. The instrument is very 

accurate in monitoring temperature, compressive and tensile normal 

loads, and is capable of storing data as a function of time. However, 

limitations of the test rig are having only one crosshead speed (2.2 

mm/min. (.0215 in./min.)), and a maximum normal load capacity of 1000 

grams. 

A picture of the Rheometrics System Four is shown in Fig. 2.5 

along with a close-up detailing the transducer and test fixture in 

Fig. 2.6. 

2.3.2 Sample Preparation 

Test samples were prepared in the following manner: 

1) starting with UOEL@ P1700 in bead form, beads were placed 

between ,0762 mm (0.003 inch) thick Kapton films in a mold cavity with 

shims set at the desired specimen thickness, (Figure 2.7) 

2) the mold was placed in a vacuum oven with enough dead load to 

assure adequate flow of beads during melt, 

3) heat mold to 220°C (428°F) (Tg = 194°C (382°F)) while under a 

vacuum (heating above the T was required to ensure flow, and use of !3 



vacuum was required to reduce contamination,) 

Note: The final temperature was approached very slowly (-6 hrs.) to 

allow moisture to diffuse out of the polysulfone beads before the 

onset of flow. Use of a higher heating rate during specimen 

preparation would cause the formation of bubbles. 

4) cool sample down below T and remove from oven, 9 

5) keep sample stored in vacuum desiccator heated to 100°C 

(21Z°F), and 

6) remove Kapton film from samples just before testing. 

2.3.3 Testing Program 

The test program was divided into three sub-programs: 1) sizing 

the area of resin contact of the test specimen to the maximum load 

limits of the normal force transducer on the rheometer, 2) evaluating 

the effects of preloading the contact area (i .e. contact pressure) to 

assure intimate contact at the interface, and 3) evaluating the 

effects of contact time on the autohesive strength of the neat resin 

for various isothermal temperatures above the Tg. 

Sizing the Specimen 

The following procedure was used to determine the allowable area 

of resin contact of the specimen so as not to exceed the limit of the 

force transducer (1000 grams). The largest autohesive strength is 

expected to occur at the longest contact time (tc = 1200 sec) and 

lowest test temperature (210°C (400°F)) expected to be tested. At 

these conditions the autohesive strength is expected to have the 
maximum value because the depth of penetrating chains are at their 

maximum in addition to the molecular free volume being at its minimum. 

Specimens 12.7 rnm (0.5 in.) in diameter were punched from a flat 

sheet of PI700 thermoplastic resin. The protective Kapton films were 

then removed from the specimens surfaces. Holes were punched in the 

center of two 25.4 mm (1.0 in.) diameter Kapton films 2.54E-4 mm 

(0.001 inch) thick. The two identical Kapton films were placed 

between two Pl7OO specimens as shown in Fig. 2.8. Assembling the test 

specimens in this manner ensured that the load required for adhesive 

failure between the PI700 resin and the metallic parallel plate 

fixtures was greater than the load required to cause autohesive or 

cohesive failure of the P1700 resin at temperatures above the T The 9 ' 

test specimen was placed between the parallel plates of the rheometer 

and heated to 260°C (500°F) in a nitrogen purged atmosphere for over 

twenty minutes. The coupon was then placed under a compressive load 

of 750 grams to assure good adhesion between the metallic plate and 

the P1700 resin. The specimen was slowly cooled to 210°C (410°F) and 

pulled apart at the constant crosshead rate. The Kapton film hole 

diameter (5.08 mm (.20 in.)) was adjusted to ensure that the maximum 

load to cause failure would not exceed 1000 grams (the maximum load 

cell capacity. ) 

Effect of Pressure on Autohesive Strength 

The first processing parameter that must be measured is the 

pressure (P rn ) required to achieve intimate contact for a particular 

temperature and contact time. The 1 owest temperature (210°C (410°F) ) 

and time (10 sec) expected to be measured were used in determining the 

saturation pressure. This would provide the largest P over the m 

enti re test spectrum.. The contacting pressure was increased for 

successive tests and the resulting autohesive strength was recorded. 

The pressure corresponding to the maximum autohesive strength at a 

given T and tc is the saturation pressure P . This saturation m 

pressure was used for all the tests listed in Table 2.1. 

Effects of Contact Time and Temperature on Autohesive Strength 

Table 2.1 lists the various temperatures and contact times tested 

for autohesive strength. The tests were conducted such that the 

entire contact time spectrum was run with one specimen for each 

isothermal temperature condition. Figure 2.9 shows the applied load 

as a function of time for a typical test run. The two piece specimen 

was allowed to reach the isothermal test temperature, and then brought 

into contact at the saturation contact pressure, Pa, for the duration 

of the contacting time (t,). The specimen was then put under tensile 

loading at the constant crosshead rate of the test apparatus. The 

maximum load was recorded and termed the autohesive load obtained for 

that T and tc. Because the specimen's resin contact area was held 

constant for all tests, the autohesive loads for different tests can 

be compared directly to each other as if they were strength values. 

The specimen is then allowed to attain its initial conditions of chain 

entanglement density and orientations at the surface before contact 

was made again. This period of time is called the reentanglement time 

(tr) shown in Fig. 2.9. 

The reentanglement time was determined by repeating the above 

test at T = 210°C (410°F) and tc = 1200 sec, and increasing t, until 

the autohesive strengths were approximately equal on succesive runs. 

The tr was found to be one hour and twenty minutes (1 hr. 20 min.) and 

was used for all other tests. 

2.4 Results and Discussion-Au 

The relationships between pressure, temperature, and contact 

time, and autohesive strength (Au) are discussed here. Autohesion is 

also a function of the elongational strain rate, sample geometry, 

molecular weight of the polymer (M), memory capability of the polymer, 

and the failure mechanism at the interface. Wool's and Jud's 

theoretical predictions (Section 2.2.2) between autohesi ve strength 

and contact time shown in Eq 2.5 are used to explain the effects of 

the processing parameters on the observed experimental strengths. 

Wool's assertion that the self-diffusion coefficient may be 

temperature dependent in a WLF manner is then evaluated. Lastly, a 

master curve defining the degree of autohesion as a function of 

contact time and temperature is derived. This was done by extending 

the data obtained at high temperatures, requiring short contact times 

to simulate the degree of autohesion obtained at the long contact 

times required for low temperature conditions. An explanation of the 

effects that the processing parameters have on the experimental 

results are discussed next. An application of the "free volume 

theory" to contact time and temperature data is used as its basis. 
Autohesion strength data will be addressed in a relative sense. 

Recalling Eq 2.8, the degree of autohesion was defined as the ratio of 

autohesion strength at a given temperature and contact tlme to that of 

the maximum autohesive strength (i.e. cohesive strength) at the same 

temperature. This ratio compares the state at which interfacial 

diffusion has progressed relative to the state of cohesive strength 

(i.e. Au at tm, where t is the time required to achieve cohesive m 

strength ), 

2.4.1 Original Data 

This section presents a comparison between theory and 

experimental results obtained for the various processing parameter 

conditions listed in Table 2.1. First, the data used to 

evaluate P is presented. Second, the experimental data addressing m 

effects of contact time on autohesive strength are compared to the 

autohesive strength theory. Third, the temperature effects on 

autohesive strength are discussed. 

Because the area of contact was kept constant for all the tests, 

the autohesive load at failure is reported in lieu of its ultimate 

stress. Thus, the terms autohesive strength are used interchangeably 

with autohesive load. 

2.4.la Effects of Contact Pressure on Autohesion 

Figure 2.10 shows that autohesion increases in an asymptotic 

fashion up to a saturation pressure where autohesion becomes a 

maximum. Thus, autohesion is invariant with contact pressures above 
Fit to quadratic regression 

EMPERATURE=Z 1 OC(41 OF) 

CONTACT TIME= 1 0 seconds 

Figure 2.10 Evaluation of P_, and Effects of Contact Pressure on the 

Autohesive Strength 
the saturation pressure. This fact has previously been noted by Wool 

[ll] and Voyutskii [6]. As previously mentioned, this behavior is due 

to the area .of contact at the interface increasing with increasing 

pressure unti 1 full intimate contact is achieved. Initially the 

surface must rearrange and deform as full intimate contact is 

approached. 

Because P is very small compared to the pressures normally used m 

in processing, its importance lies only in the autohesion testing 

procedure where intimate contact must be assured for all tests. 

The value for P given in Fig. 2.10 corresponds to the lowest m 

temperature and the shortest contact time in the test matrix. It can 

therefore be expected that intimate contact on the neat resin is 

achieved at all the temperature and contact time conditions tested as 

explained in Section 2.3. 

2.4.lb Effects of Contact Time on Autohesion 

Wool and Jud have derived theoretically and shown experimentally 

that autohesive strength increases in proportion with the fourth root 

of contact time Thus, on a plot of autohesive strength versus 

the fourth root of contact time, the experimental data should fall on 

a straight line. Figures 2.11 and 2.12 show the experimentally 

measured autohesive strength data in comparison with the theory of 

Wool and Jud for the various temperature conditions listed in Table 

2.1. The constant of proportionality relating Au and t:I4 was 

determined by a linear regression curve fit. The cohesive strength 

region was not always achieved at the lower temperatures because of 

ORIGINAL PAGE IS 

OF POOR QUALm 

min. 1.0 min. 2.0 min. 2 min. 10 min. 20 min. 

50 25 1 UDE~?PI~OO - 

AVlOHESWE 

T-21 OC(410F) T=220C(428F) 

0 dola 0 data 

, - Linear Regression - Linear Regression 0 0 

- Linear RegreasIan 0 

- Linear Regreasion 

0 

0 1 2 3 4 5 6 

CONTACT TIME (reel/* ) 

T=240C(464F) 

- Linear Ragreaaion 

T=260C(500F) 

0 data -/%- - Linear Regression 

CONTACT TIME (secl/4 ) 

Figure 2.12 Autohesive Load versus Fourth Root of Contact Time at 

T = 210°C (410°F), 220°C (428"F), 230°C (446"F), 240°C 

(464"F), 250°C (48Z°F), 260°C (500°F), and P = P m 
insufficient durations of contact time. The acquisition of autohesive 

strength data at high temperatures was limited by the human capability 

to test for autohesion strength at short contact times. An explanation 

of each one follows. 

Figure 2.11 shows that at T = 200°C (392°F) (Tg+5"C (10°F)) the 

autohesive data deviates increasingly wfth t;l4 from the prediction by 

theory. It can also be seen that the theory is conservative in the 

prediction of autohesive strength. The cause of this disagreement 

between theory and experiment is that for the given strain rate (too 

high) and temperature (too 1 ow) condition an increasing proport ion of 

chain failures due to fracture are occurring. Failure due to chain 

fracture corresponds to a higher failure load, and so the net effect 

is an increase in autohesive load for longer contact times. This 

increased incidence of chain fracture is due to an increased chain 

penetration depth at longer contact times. The theory requires that 

the fracture mechanism be constant throughout the test (i .e. the same 

proportion between fractured chains and pul led out chains), Thus, the 

200°C (392°F) temperature cannot be used to evaluate the degree of 

autohesion and is placed as the lower limit for the test matrix. If 

lower temperatures are to be used for evaluating the degree of 

autohesion then a slower stain rate must be used to produce the 

desired failure by chain pull-out. 

In Fig. 2.12 the T = 210°C (410°F) data shows good correlation 

between theoretical response and experiment for the autohesive 

region. However, the comparison between theory and experiment is 

inconclusive in determining the transition from the autohesive region 
to the cohesive region. The slight deviation of the two data points 

at the largest contact times may be attributed to either experimental 

error in the transition to cohesive failure or to error resulting from 

the test conditions being so close to the conditions at which the 

reentanglement time (tr) was determined, thus, causing different 

initial conditions of the molecular structure and affecting the 

diffusion mechanism and disentanglement period, The T = 220°C (420°F) 

data shows good correlation between theoretical response and 

experiment for the autohesive and cohesive strength regions. The last 

data point is indicating the plateau of cohesive strength. The T = 

230°C (446°F) data shows fair correlation between theoretical response 

and experiment when comparing the theoretical response with the next 

higher and lower temperature data results. The T = 240°C (464°F) data 

shows good correlation between theoretical response and experiment for 

both regions of failure. The apparent curvature of data in the knee 

section separating the autohesive and cohesive regions, may be 

attributed to error in the experiment. The T = 250°C (482°F) and 

260°C (500°F) data show good correlation between theoretical response 

and experiment for both regions of failure. 

Figure 2.13 shows the degree of autohesion versus t:I4 for the 

same processing temperature conditions of Fig. 2.12. The solid line 

indicates the theoretical response (autohesion region fit by 1 inear 

regression) of the autohesive and cohesive regions of failure. 

Figure 2.14 summarizes the effects between contact time and the 

degree of autohesion where the theoretical responses (autohesion 

region fit by linear regression) and the data from Fig. 2.13 are 
2 rnin. 10 rnin. 2.0 rnin. 

UDEPP 1 700 /Yr{ AUTOHESNE DOMAIN 

T-21 OC(41 OF) 

doto 

- Linear Regreasion 

- Linear Regreadon 

0 

- 

- 

2 min. 1.0 rnin. 2.0 rnin. .-" 

T=220C(428F) 

0 data 

- Linear Regression 

r 

- 

- 

CONTACT TIME (rscl/r ) CONTACT TIME (recV4 ) 

T-240C(464F) 

data 

- Linear Regression 

7 I r 

1 - 

z 

0 In 

Y 

0 

2 

I. 0 

I 

X 

0- 

Figure 2.13 Degree of Autohesion Versus Fourth Root of Contact Time 

at T = 210°C (410°F), 220°C (428"F), 230°C (446"F), 

250°C (482"F), 260°C (500°F), and P = P m 

0 1 2 3 4 5 

T 

6 0 1 2 3 4 5 6 

" -

TmZSOC(482F) 

data 

Linear Regression 

- - 0 - 

T=2WC(500F) 

0 data 

- Linear Regrerdon 

shown. It is observed that as temperature increases, a greater degree 

of autohesion can be achieved for a given contact time. 

Jud [ 131 observed that the experimental ly determined macroscopic 

diffusion coefficients (D), proportional to the slopes of the strength 

versus fourth-root of time curves for various temperatures, can be 

represented by an Arrhenius law shown in Eq 2.9: 

where Ea is the activation energy, k is the Boltzmann constant, T is 

the absolute temperature, and Do is a constant with the units of 

meters square per second (in2/sec). 

Thus, from the Fig. 2.14 the degree of autohesion can be written 

as: 

where DAu is the initial degree of autohesion at t = 0 (zero in this 

0 

study) and K(T) is a temperature dependent parameter with dimensions 

of DAu. K(T) is defined as that product of a proportional i ty constant 

times the self diffusion coefficient. The Arrhenius law has been 

rewritten as: 
The parameters KO and Ea (Eq 2.11) are determined by plotting the 

natural log (Ln) of the slopes of the curves in Fig. 2.14 versus 1/T 

as shown in Fig. 2.15. The slope determines the value of Ea while the 

intercept determines the value of KO. The constants were found to be; 

KO = 1922 (dimensionless), and Ea = 6.0902E-20 Joules (5.7772E-23 

BTU). The value of Ea is used strictly in an empirical manner. 

With the use of Eq 2.11, the validity of Eq 2.10 can be compared 

to the experimental results. Shown in Fig. 2.16 are the experimental 

data while the solid lines are those curves obtained from Eq 2.11. 

Fair agreement between the empirical formulation given by Eq 2.10 

using the Arrhenius law (Eq 2.11) and the experimental data is 

observed. The empirical formulation overpredicts the time required to 

achieve a given degree of autohesion at the higher temperatures. 

However, the contact times observed at the higher temperature data are 

very short and may be, in reality shifted to longer or shorter contact 

times because of experimental procedure. 

Thus, Eqs 2.10 and 2.11 describe completely the degree of 

autohesion as a function of temperature and contact time up to the 

cohesive state. 

2.4. lc Effects of Temperature on Autohesion 

Figure 2.17a is a plot of Au versus temperature at the saturation 

contact pressure and several contact times. It has been observed that 

on an absolute scale the autohesive strength at any one time is 

greater at the lower temperature condition than at the higher 

temperature condition. However, in the relative sense, it has been 

min. 

CONTACT TIME (sEc~/~ ) 

Figure 2.16 Comparison Between Arrhenius Law and the Degree of 

Autohesion Test Data for Evaluation of Temperature 

Relationship 
210 220 230 240 250 260 

TEMPERATURE ('c) 

Figure 2.17 Parametric Study Between Temperature and Contact Time 

(a) Autohesive Load versus Temperature at Contact Times of 

10, 100, and 500 Seconds (b) Degree of Autohesion versus 

Temperature at Contact Times of 10, 100, and 500 Seconds 
observed that the degree of autohesion at any time less than t is m 

greater at the higher temperature condition than at the lower 

temperature condition. This occurs because of the increased molecular 

mobility at higher temperatures allowing greater self diffusion for a 

given length of time. One must remember that just as it is easier for 

molecules to penetrate across the interface, the higher the 

temperature, it is just as easy to pull them out. Thus, one must use 

the definition of the degree of autohesion (Eq 2.8) to observe the 

effects of temperature on autohesion. Figure 2.17b is a plot 

of DAu versus T. 

2.4.ld Interrelationship Between Contact Time and Temperature on 

Autohesion 

Wool [ll] has suggested that the autohesion phenomenon may 

exhibit a time-temperature relationship provided that the failure 

mechanism is due to chain pull-out as stated in Section 2.2.2. 

Observation of the data in Fig. 2.12 has shown this to be true. 

However, the 200°C (392°F) temperature data shown in Fig. 2.11 has 

been shown to exhibit a combined failure mode of chain pull-out and 

chain fracture. With this stated, a brief explanation of the WLF 

theory is made, followed by its application as a contact timetemperature relationship for the degree of autohesion. 

It is widely accepted that temperature affects self diffusion 

because of its effects on the molecular free volume [6,7,11]. As T 

increases so does the molecular mobility. The premise of the 

molecular free volume as proposed by William, Landel and Ferry is that 
a given state a polymer possesses at T1 and tl is not necessarily 

unique. There are a range of corresponding temperatures and times 

having an identical state of some physical property u (e.g. modulus, 

viscosity, etc.). This concept is written mathematically in Eq 2.12, 

and has been shown true for a wide choice of polymers. 

Replotting Fig. 2.14 on a log-log scale, shown in Fig. 2.18a, it 

has been observed that the slopes of the autohesive region are all 

0.25 as predicted by the theory shown in Eq 2.5. Also from Fig. 

2.18a, it was observed that for a given degree of autohesion (Au) at 

T1 and tl the same degree of autohesion could be achieved at a shorter 

contact time if the temperature is increased. The contrary is also 

true. A longer contact time would be needed to achieve the same 

degree of autohesion if processed at a lower temperature. 

The fol lowing mathematical observation was made of Fig. 2.18a: 

loglO tc - log t = aT 

lo 'ref 

where; tc is any contact time, t is the contact time at some Cref 

reference temperature (Tref) , and a,- is the shift factor and is a 

function of temperature. 

Equation 2.13 is the basis of the WLF theory and can be written 

in the WLF form shown in Eq 2.14: 
Figure 2.18 WLF Theory, (a) Shift of Original Data at Respective 

Temperature to the Reference Temperature, (b) 

Evaluation of WLF Constants 
where; 

The constants C1 and C2 were determined by the shifts required to 

superimpose all the temperature data to one master curve. The 

constants have significance concerning the mol ecu 1 ar free volume; 

however, no further interest other than those previously implied are 

made here for this study. Figure 2.18b plots the shifts as a function 

of temperature in such a way that the constants C1 and C2 were 

evaluated to be 2.604 and 47.682, respectively, for the reference 

temperature of 210°C (410°F). 

With the WLF Eq 2.14, Eq 2.10 can be written as: 

I 

- ] 1/4 

D~u ' Ko . [a~ tc ref 

where; K: = 0.1953 sec-'I4 is the slope of the curve in Fig. 2.14 at 

210°C (410°F). Figure 2.19 shows fair correlation over the entire 

temperature test spectrum between the experimental data and the timetemperature relationship evaluated in the WLF manner. The increasing 

apparent error in the high temperature results may be attributed to 

either, an error in estimating the actual time autohesion has occurred 

during the very short time intervals, or error in the assumed cohesive 

strengths of the low temperature tests. In both cases a shift in the 

data would result. It was uncertain whether the high 

temperature/short contact times or low temperature/long contact times 

tests produce the largest error. Thus, the well defined cohesive 

regions of the higher temperature data can be used to help evaluate 

the cohesive regions at lower temperatures requiring long contact 

times. One equation now describes the degree of intimate contact for 

any contact time and temperature. 
3.0 Intimate Contact-IC 

3.1 Introduction-IC 

In the previous section, the mechanism by which a thermoplastic 

matrix composite consolidates to form a laminate was attributed to 

autohesive bond formation between plies. However, the autohesion 

phenomenon can only occur after the two surfaces have coalesced (i .e. 

are physically in intimate contact). Macromolecules cannot diffuse 

across spacial gaps at the interface. The study in this section 

identifies the mechanisms by which the interfaces of a thermoplastic 

prepreg coalesce (not to be confused with consolidate) resulting in 

intimate contact. The effect of the various processing parameters on 

the degree of intimate contact is discussed. 

The presence of spacial gaps between prepreg plies prior to 

processing is evident in both thermosetting and thermoplastic matrix 

composites. Unlike thermosetting epoxy matrix composites, which rely 

on low viscosity flow and wetting ability of the resin to coalesce the 

ply interfaces, thermoplastic matrix composites must be physically 

deformed to cause coalescence. The viscosity of epoxy decreases 

substantially when heated, resulting in its ability to wet out the 

interface even with the presence of fibers. However, the neat 

thermoplastic matrix resin, when heated, still maintains a zero shear 

rate viscosity greater than the viscosity of the epoxy at its gel 

point (i.e. when the epoxy begins to set). The amount of wetting 

which occurs during the processing of a thermoplastic matrix composite 

is therefore minimal. 
It has been visually observed that spacial gaps between the 

laminate ply can be present before, during, and after the processing 

cycle. The extent of these spacial gaps will depend on the processing 

parameters: pressure (P), temperature (T), and contact time (t,). A 

brief explanation follows as to the nature of the prepreg's geometric 

non-uniformity of tow heights across the width of the prepreg sheet, 

and how the effect of this nonuniformity can be minimized through the 

judicious choice of the processing parameters. 

A prepreg is made up of single tows laid side by side. The tows 

have constant cross-sectional areas and fiber/matrix fractions. 

However, the tow thickness varies across the width of the prepreg. 

Thus, when the prepreg plies are stacked on top of each other, spacial 

gaps are present. 

It has been observed during processing that specific combinations 

of pressure, temperature and contact time result in varying degrees of 

intimate contact at the laminate ply interfaces. However, these 

processing conditions are not unique. The same degree of contact can 

be obtained for different processing parameter combinations. The 

present study will attempt to quantify the relationships between the 

processing parameters and the degree of contact at the ply interfaces. 

Surface mechanicians have shown experimentally that increasing 

areas of contact can be achieved by increasing the applied load across 

the interface [16,17]. Local elastic and plastic deformations of 

surface irregularities are attributed to the cause of increasing areas 

of contact. Thus, one would also expect an increase in the processing 

pressure to increase contact area. However, because of the 
viscoelastic nature of the matrix, some time dependency can also be 

expected. Also, the temperature of the material during processing 

will greatly influence the rate at which the area of contact increases 

because of its influence on the properties of the matrix. 

If viscoelastic effects are present during the processing of the 

composite then intuitively the following can be said: 

1) surface contact area wi 11 increase with increasing pressure 

(P) for a constant T and tc, 

2) surface area will increase with increasing temperature (T) 

for a constant P and tc, and 

3) surface area will increase with increasing time (tc) for a 

constant P and T. 

Based upon these observations, an intimate contact- (IC) model is 

presented which simulates the phenomenon by which the interfaces of 

the stacked plies coalesce. The model incorporates the viscoelastic 

properties of the material. However, certain engineering material 

properties were not obtainable to allow absolute ~er~ification of the 

model. Thus, the proposed mechanistic approach must be reduced to an 

empirical one, until these properties can be obtained. Nevertheless, 

the empirical constants used to fit the data show the expected 

viscoelastic responses of the physical material properties they have 

replaced. 

The following are presented below: 1) experimental procedure and 

test matrix, 2) the data reduction scheme, 3) sub-model formulation, 

4) IC model formulation, 5) theory and experiment correlation, 6) 

parametric study of processing parameters and the prepreg's geometric 
non-uniformi ty, and 7) viscoelastic observations of the model and 

empirical constants. 

3.2.1 Description 

The purpose of studying intimate contact is to determine the 

relationships between the contact area at the ply interfaces to the 

processing parameters. Reported here are the experimental approach, 

procedure, and data reduction scheme for accompl i shing this task. 

It is desired to determine a certain combination of P, T, and tc 

which will provide maximum ply interfacial contact. Thus, given any 

two processing parameters the third parameter can be defined for any 

desired state of ply interface contact (usual ly 100%). 

Towards this end, laminates were fabricated using various 

combinations of the processing conditions. Several means of defining 

the area of contact at the ply interfaces are currently in use. They 

are: 1) C-scan, 2) thermal diffusivity, 3) ultrasonics, and 4) 

dielectric analysis. Only the first of these methods was used for the 

current study. The latter three methods are current ongoing research 

projects being pursued at NASA-Langley . The C-scan approach has been we1 1 established, however, it is not 

without difficulties. The true area of contact observed by the C-scan 

is subject to the threshold chosen for the relative attenuation 

values. The threshold chosen for this investigation was based on 

experience gained in locating cracks after mechanical loading and 
spacial gaps after processing in graphite/epoxy laminates. It is 

necessary to assume that damage detected by the C-scan represents a 

lack of coalescence at the ply interfaces and not damage within the 

plies. Because the laminates are not subject to any loading before 

being C-scanned, this appears to be a reasonable assumption. Figure 

3.1 shows the use of the C-scan technique used to locate the areas of 

spacial gaps in unidirectional graphite/epoxy laminates shown as black 

areas. These areas were sectioned and photomicrographed to show 

validity of the approach. 

3.2.2 Sample Preparation 

The test samples used in evaluating intimate contact were 

laminates with ply orientations of [0,90,0]T. The crossply laminate 

provides a worst case situation in that no nesting of tows occurs as 

in the case of unidirectional laminae. The presence of two interfaces 

creates a need for a statistical interpretation of the data. This 

will be discussed in detail in Section 3.3.1. 

The reinforcement material used in this study was AS-4 graphite 

fiber, manufactured by Hercules Inc. The matrix material used was 

polysul fone polymer UDEL@ PI700 (beadform) manufactured by Union 

Carbide Corporation. The U.S. Polymeric division of Hitco was chosen 

to prepreg the AS-4 graphite fiber with the P1700 resin. The 

prepreging process required the use of a solvent to allow impregnation 

and wetting of the resin onto the graphite fibers surfaces. The 

solvent used was cyclohexanone. The prepreg received required the 

removal of the solvent before the processing study was undertaken. 
ORlG!NAL PAGE IS 

OF WOR QUNm 

PHOTOMI CROGRAPHS 

C-scan Detection of Spacial Gaps 

Spacial Gaps 7 

Unidirectional Laminate 

Graphite/Epoxy 

Figure 3.1 C-Scan Technique Detection of Spacial Gaps After 

Cure of Unidirectional Graphite/Epoxy Composite 
The solvent was removed by vacuum stripping individual (i.e. not 

stacked) prepreg sheets at a temperature above the glass transition 

temperature of the resin for a 12 hour period of time. All materials 

were kept dry in a heated vacuum (102"C/215"F) desiccator until 

tested. The pertinent material properties are listed in Table 3.1. 

The test samples were prepared in the following fashion: 

1) Three 76.2 mm x 76.2 mm (3" x 3") square sheets of AS4/P1700 

prepreg (solvent free and dry) were cut from a roll of 

prepreg. By matching the prepreg size with the mold cavity, 

fiber washout was prevented. Thus, only local deformation 

at the ply interfaces was allowed (i.e. global movement of 

resin and fibers through the thickness of the prepreg was 

inhibited.) 

2) The prepregs [0,9090]T were sandwiched between layers of 

Kapton film 0.0762 mm (0.003 inch) that had been treated 

with a release agent (Fig. 3.2a). 

3) The specimen was placed in the mold cavity. 

4) The punch was then placed in the mold cavity and the 

assembly placed between preheated press platens (at testing 

condition temperature) (Fig. 3.2b). 

5) The temperature of the mold and prepreg were monitored 

during the test. The mold and prepreg were held at the 

desired temperature for a period of time sufficient to 

ensure a uniform temperature. 

6) Pressure was then applied and the contact time was measured, 

starting when the desired pressure was reached. 
w C, C, In 

Elcdw 
Tab1 e 3.1 Materi a1 Properties 

PropertylDescription Value (ave.) 

AS-4 graphite fiber specific gravity 1.74 

number of fibers per tow 12,000 

fiber sizing G 

P1700 polysulfone 

(bead) resin 

sol vent-cycl ohexanone 

Prep reg 

specific gravity 1.24 

glass transition 

temperature-Tg 194°C (381°F) 

structure of polymer amorphous 

boiling point 68.7"C (155.6"F) 

width 304.8 mm (12 in.) 

dry resin content by wt 32.3% 

volatile content by wt 19.05% 

areal fiber wt 148.8 gm/m2 
7) The pressure was released after the desired contact time had 

been attained. 

8) The mold was removed and allowed to cool slowly to between 

23.9"C - 37.8"C (75-100°F) below the Tg of the resin. 

9) The sample was removed and C-scanned. 

3.2.3 Testing Procedure 

The C-scan data was obtained as a function of position over the 

top surface of each test specimen. The magnitude of the signals 

recorded were compared to the threshold (determined as showing spacial 

gaps in graphite/epoxy) indicating the locations of contact and 

spacial gaps at the interfaces over the entire width and length of the 

specimen. Plots of black and white profiles were made of each 

specimen reproducing the areas of contact as white and the areas of 

spacial gaps as black. This procedure works very well in showing the 

top areal view of contacting and non-contacting areas; however, it 

cannot be used to locate which of the two interfaces present in the 

[0,90,0]T laminate are not in contact, if not both. Thus, the C-scan 

provides only a qualitative measure of the true area of contact. A 

statistical interpretation of the black area is needed since it 

results when either of the two interfaces, or both are in contact. 

The test matrix for determining the effect of the processing 

parameters on contact area is given in Table 3.2. The test matrix 

provides a temperature range from just above the T to a maximum '3 

allowable temperature before noticeable degradation in the properties 

of the prepreg are observed. The pressure range covers a range from 
Table 3.2 Intimate Contact Test Matrix 

TEMPERATURE 

tc = 20 min t = 15 min t, = 10 min 

172KPa 10 5 5 

(25 psi) 5 2 2 

2 1/2 1 

1 1/2 

112 

tc = 20 min t, = 15 min t, = 10 min 

10 5 5 

344KPa 5 

PRESSURE (50 psi) 2 

1 

tc = 5 min t, = 15 min t, = 40 min 

688 KPa 2 5 20 

(100 psi) 1 2 2 

1/2 1 1 

1/2 
64 

above vacuum bag pressures to a typical autoclave pressure. 

3.3 Results and Discussion-fC 

This section presents experimental data showing the variation of 

intimate contact area over the range of the processing parameters P, 

T, and tc presented in Table 3.2. Also presented is a model of 

intimate contact area of a [0,90,0]T laminate as a function of the 

processing parameters. The IC model is comprised of three submodels: 1) formulation of the viscoelastic deformation of a single 

tow; 2) a statistical distribution describing the prepreg geometric 

nonuniformity; and 3) experimental data of the neat resin viscosity is 

empirically extended to include the influence of the fiber on the 

viscoelastic response of the resin. 

3.3.1 Original Data and Data Reduction 

Black and white C-scans were taken of each of the specimens 

listed in Table 3.2. The specimens tested have two interfaces. One 

on each side of the middle ply in the [0y90yO]T laminate. The white 

areas of the C-scanned specimens are areas where intimate contact is 

achieved throughout the specimen thickness (i.e. both interfaces); 

however, the black areas do not define areas of total interfacial 

spacial gaps. Three conditions of spacial gaps are possible that will 

cause black areas to show up in the C-scan approach used. First, that 

both interfaces are not coalesced. Second, the top interface is not 

coalesced while the bottom is. Third, the bottom interface is not 

coalesced and the top is. 
A statistical interpretation of the data will be required because 

the C-scanned data was obtained from specimens with two interfaces in 

series, and it is desired to obtain the outcome of the experiment as 

if one interface had been used. Intuitively, the occurrence of 

contact and no contact areas forming during processing will have an 

equal probability at either of the two interfaces. Further, one would 

also expect the two occurrences to be probabilistically independent 

and not mutually exclusive as a first approximation. 

With these assertions the probability (Pr) of a contact event 

occurring at the top and bottom interfaces may be written as: 

The joint probability of achieving contacts directly on top of one 

another of the two interface system may be written as: 

PrJ(joint top and bottom) = Pr,. - Prg (3.2a) 

The joint probability is identically defined as the ratio of the white 

area to the total white and black areas of the C-scan data. The joint 

probability may then be written as: 

where WC and BC denotes the white and black areas, respectively. 

Equation 13.3a may also be rewritten in terms of the fractions of the 
white (E) and black (m) areas to a unit area such that: 

Therefore, the following relationship results: 

Since the C-scan data will allow the direct computation of the 

joint probability, PrJ, the probability of contact occurrences of the 

top and bottom interfaces independent of one another can be evaluated 

by taking the square root of the joint probability. Thus, the degree 

of intimate contact for one surface, DIG, may be written as: 

Table 3.3 reports the statistical degree of intimate 

contact DIG. Plots of the data will not be presented here nor a 

discussion until after the model is presented. A thorough 

investigation and interpretation will then be made. 
h 

0. 

m- ul 

Ll P 

dW 

hN 

eum 
3.3.2 Intimate Contact Sub-Model s 

An approximate model is presented for relating the processing 

parameters to the degree of intimate contact DIG. This IC model 

incorporates the use of 3 sub-models: 

1) a statistical distribution describing the prepreg geometric 

non-uniformity of tow heights; 

2) a mechanics model similating the viscoelastic response of 

the fiber reinforced resin to the compressive loading 

typical of thermoplastic matrix composite processing; and 

3) an assumed constitutive relationship for the viscosity of 

the resin, as well as, an assumed relationship simulating 

the fibers influence on the viscosity of the neat resin. 

These sub-models have been merged in a final IC model 

formulation. 

The model has been constructed from physical reasoning of the 

observations made while processing, as well as, from some intuitive 

specu 1 at i on. 

No global flow (i.e. fiber washout or resin bleed) of the 

laminate was observed for the processing conditions tested; therefore, 

the coalescence must be occurring as a local deformation at the ply 

interfaces. Because the laminates were thin, (3 ply) the prepreg 

geometric non-uniformity showed up on the outer surfaces by scattering 

the ambient light nonuniformly when underprocessed. Increased areas 

of contact were observed to grow para1 lel to the fiber by C-scan and 

surface reflection methods. This resulted in a checkerboard pattern 
in the case of cross-ply laminates. The formation of the checkerboard 

pattern occurred in a random piecewise manner over the areal surface 

of the laminate and not necessarily uniformly. For these reasons the 

IC model should incorporate for its foundation a sub-model that 

simulates the uniformly distributed compressive loading of a single 

unidirectional tow, normal to the top and bottom surfaces. The local 

deformation model must also be a function of the viscoelastic 

properties of the resin and fiber. 

Intuitively, one would expect prepregs of greater or lesser tow 

uniformity to influence the quality of the laminate for a given set of 

processing parameters (i.e. prepregs of greater nonuniformity are 

expected to take longer to process to achieve quality laminates). For 

this reason the model should also include a description of the 

prepreg's tow geometry as input. 

Figure 3.3 shows a flow chart of the model formulation. A 

detailed description of each sub-model follows. 

3.3.2a Mathematical Description of Prepreg's Geometric 

Nonuniformity-Sub-Model 

The importance of tow heights varying across the width of a 

prepreg has already been pointed out. Presented here is the method 

for obtaining the tow height distribution for the prepreg. 

Figure 3.4 shows the assumed geometry of the prepreg tow crosssection. The cross-sectional area Ai of each tow is constant, while 

the subscript i denotes the tow number and q is the number of tows. 
INTIMATE CONTACT MODEL FLOW DIAGRAM 

I Compression Molding 

of a Single Tow 

Sub-Model I 

I Intimate Contact 

Model 

Figure 3.3 Model or mu la ti on Flow Diagram 

The heights in the model are also assumed to be constant along each 

tow width although in reality this is not true. 

The prepreg tow heights were measured with a micrometer to the 

nearest thousandth of an inch. Each tow height was measured across a 

twelve inch width prepreg sheet perpendicular to the fibers. 

Measurements were made once every foot over a five foot length of 

prepreg. No appreciable difference in tow height variation was 

observed along the length of a single tow. The tow heights, ai, were 

then normalized to the largest tow height 6, according to Eq 3.5. 

A histogram of the tow height data is shown in Fig. 3.5. This 

figure shows the percent tows within the interval of tow heights 

shown. A two parameter Weibull function was fit to the histogram 

shown as the solid line in Fig, 3.5. The Weibull density 

function, g(z), is defined in Eq 3.6 along with the values of the 

constants used to fit the data 

g(7) = (t) ($)"-I exp 

where: a = 2.25 shape parameter 

s = 0.1108, scale parameter 

The cumulative distribution (Eq 3.7) is defined as: 

L 

G(7) = 5 g(s)ds - 1 - exp [- (%)"I 

0 
Figure 3.5 Wei bull Density Model of Prepreg Geometric 

Nonuniformity with Histogram 
The function G(?) defines the total number of tows having height 

greater than or equal to si. As will be pointed out later, G(?) is 

the degree of intimate contact as a function of tow height or 7. The 

viscoelastic response of a single tow subjected to compression loading 

normal to the fiber direction will couple G(2) with time through the 

time dependency of ?(t). 

3.3.2b Compression Molding of a Single Tow-Sub-Model 

Presented here is the derivation of the viscoelastic flow 

response of a single tow subjected to compression molding as a 

function of the processing parameters, pressure, temperature (>T ) and 9 

contact time. This sub-model is the foundation of the intimate 

contact model. It defines the rate at which the tow deforms (i.e. 

f i ber/resin squeezes) between two para1 lel and uniformly di stri buted 

compressive loads through the inherent temperature sensitive 

viscoelastic material properties. 

Figure 3.6 shows the coordinate system used for the sub-model. 

Based on experimental observations during compression molding of 

laminate samples, the fol lowing postulates were assumed in the 

derivation: 

1) The combined fiber/resin deformation perpendicular to the 

fiber direction (x-direction) dominates any local resin flow 

taking place parallel to the fiber. 

2) Negligible resin flow from the tow occurs in all directions, 

maintaining the same fiberlmatrix distribution within a 
Uniformly Distributed Compressive Load 

on Top and Bottom Surfaces 

of a Sinale Tow /// 

Fiber Orientation = Y Direction 

Figure 3.6 Geometry of a Single Tow Subject to Uniform 

Compressive Loading Normal to XY Planes of Top and 

Bottom Surfaces 
P~Y * This is due to the high fiber volume 

fraction uf = 68%, and the high viscosity of the resin. 

These two observances are untypical for most thermosetting resin 

composites in that the lowest viscosity of the P1700 resin exceeds the 

gel point of an epoxy matrix composite. 

The analysis that follows is based on the assumption that the 

problem can be treated as a viscometric flow. In viscometric flows 

time-dependent elastic effects are not considered. If the fluid 

relaxation time is small with respect to the time required for the 

fluid to deform around fibers, the fluid will accommodate quickly and 

no elastic effects would be observed [18]. 

In an analogous study of neat polymer flows under squeeze 

loading, (i .e. para1 lel plate plastometer) Grimm [19] has shown 

experimentally that by restricting the test to slow squeezes, the 

assumption of steady shear was found to be adequate, and that useful 

viscosity measurements could be obtained. 

The derivation presented here parallels the derivation presented 

by Bird et. al. 1201 in the study of the viscosity properties of 

polymers under squeeze loading between parallel plates. The 

coordinate system for that study was cylindrical. Dienes and Klemm 

[21] have derived the rheological equations for a Newtonian fluid 

subject to the parallel plate plastometer loading. Kataoka et. al. 

[22] derived rheological equations for a power-law fluid. Dealy [23] 

gives a good history in the development of squeezing flow rheology. 

From the previously described observances, assumptions shown in 

Eq 3.8 are made regarding the velocity field and the pressure: 
From the assumed velocity field the components of the rate-of-strain 

tensor are: 

Also, assuming that the non-Newtonian effects result predominately 

from the shearing components rather than the elongational effects, the 

diagonal components in Eq 3.9 can be neglected. Therefore, the rateof-strain tensor reduces to the following: 

The equation of continuity is: 
The equations of mot ion are (neglecting inertia terms) ; 

x-direction 

z-direction 

The 1st dashed-underlined term in Eq 3.13 is dropped because the flow 

is assumed to be locally and instantaneously under steady shear 

between two fixed planes, (i .e. uniform x-dir .) . The remaining dashed 

underlined terms in Eqs 3.12 and 3.13 are elongational stresses which 

are assumed to have minor importance compared to the shear stress. 

The constitutive equation assumed is the power-law fluid. It is 

a ' general ized Newtonian fluid ' (GNF) constitutive equation which 

assumes: 1) the viscosity is strain rate dependent, 2) only shear 

strain rate components exist, and 3) the shear strain rate is 

independent of time. The power-law equation is written as: 

where m (units of shear viscosity-poise) and n (dimensionless) are 

constants used to describe the shear rate dependency of the polymer. 

Kataoka [22] has shown this approximation to be acceptable if a test 

does not span too wide a range of low shear rates. The value of n is 

evaluated from the constant slope of the log-log plot of TI versus ;. 

An assumed velocity distribution given by Eq 3.15 
will satisfy the equation of continuity. Integrating the equation of 

continuity (Eq 3.11) over the boundary from 0 to h/2 (tow height) and 

0 to x (1/2 tow width), and observing quarter symmetry it is shown: 

where; h = vz at z = h/2. 

Substituting the power-law Eq 3.14 in to the x-direction equation of 

motion yields: 

- X Substituting - for ixz from Eq 3.10, integrating with respect to z, a z a v 

X and imposing the boundary conditions = 0 at z = 0 and vx = 0 at 

z = h/2 it is shown: 

Substituting Eq 3.18 into Eq 3.16b it is shown: 
Substituting Eq 3.19 into Eq 3.18 it is shown: 

Integrating Eq 3.19 for pressure with the boundary condition p = p at 

x, p = pa at x = X (X = 112 tow width) it is shown: 

Evaluating the force f applied to the tow shown in Fig. 3.6, and 

integrating over the top and bottom surfaces of the tow it is shown: 

where T~, was determined to be zero at z = h/2 by previous 

assumptions, as we1 I as, mathematical 1y by substitution of the 

constitutive equation (Eq 3.14) into the equation of continuity (Eq 

3.11). Thus r,, at z = h/2 can be written as: 

Substituting Eqs 3.21 and 3.23 into Eq 3.22 and evaluating f it is 

shown : 
Although the applied force is constant over time, X(t) is not. 

However, noting that the cross-sectional area Ai of the tow remains 

constant with time Eq 3.25 can be substituted into Eq 3.24 to 

eliminate X(t) as a function of time. 

2h(t) . X(t) = A; A = constant for t 2 0 

Therefore, 

Equation 3.26 describes the compression of a tow as a function of the 

strain rate dependent viscosity, the applied force, the tow height, 

and time. Thus, all processing parameters are now related through the 

rheological flow phenomena and the viscoelastic properties of the 

resin. 

3.3.2~ Rheological Material Properties 

This section presents the shear viscosity data of the neat PI700 

resin data as a function of shear rate. The temperature effects on 

viscosity are presented by the WLF Eq 3.27. Also presented is an 

assumed relationship for viscosity, simulating the effects of fiber 

reinforcement on the polymer observed by investigators in the field of 

rheology [24). A detailed explanation addressing the experiment, and 

data reduction scheme is given in Appendix A. 
* Figure 3.7 presents the steady (Q(;)), and complex (11 (u)) viscosity as a function of the rate-of-strain (y) or frequency (w). As a 

first approximation, use of the Cox-Merz Law allows a direct 

relationship between the complex viscosity and steady shear viscosity 

with the frequency and the rate of shear strain, respectively. The 

viscosity/temperature relationship for the P1700 resin is expressed by 

the WLF equation given by Eq 3.27 

where; T is the temperature being observed, Tref is the reference 

temperature (220°C(428" F)) , and nref i s the viscosity at the reference 

temperature and is the viscosity at temperature T. 

Various researchers [24,25,26] have studied the influences of 

particle and fiber reinforcements on the viscosity of the neat 

resin. The shear rate dependence of the viscosity of the reinforced 

polymer is additionally complicated because the non-Newtonian property 

of the resin is superposed on the non-Newtonian effect due to the 

reinforcement . Bartenev and Zakharenko [27] have observed that higher 

concentrations of carbon black in polyisobutylene resulted in 

approaching infinite shear viscosity at low shear stresses and 

exhibiting a yield value. However, White et. al. [26] reported that 

yield values are not present in all reinforced systems as Chapman 
8 wer Law Region 

n 

7 m -* I Cl = 5.714 

V 1 C2 = 54.309 

F=l .I 6 

m 

3 *F 

u 

"5 0 

primed alphabet denotes 

4 

LOG ( wl ) 

Figure 3.7 Complex Viscosity versus Frequency and Steady Shear 

Viscosity Versus Rate of Strain Using Cox-Merz Rule 
and Lee [28] have observed with glass fiber and bead reinforced high 

polymers. Matsumoto [29] reported that the concentration effects on 

viscosity may be temperature sensitive. Kataoka et. al. [24] has 

experimentally shown that the viscosity of fiber (length to dia. ratio 

of carbon fiber = 600) and particle reinforced polymers increases and 

acts more non-Newtoni an (i .e. more strain-rate dependent) at lower 

shear rates relative to the neat polymer. Also shown, was that higher 

concentrations of reinforcement of the polymer 4 resulted in higher 

magnitudes of viscosity. Def i ni ng, nr as the ratio of the fiber 

reinforced resin viscosity to the neat resin viscosity, Kataoka et. 

a1 . [24] have shown good superposition of vi scosi ty versus shear rate 

data at increasing concentrations of reinforcement (0 < @ < 0.65). 

From the above cited works, the effects of fiber reinforcement on 

the neat resin viscosity (Fig. 3.7) are assumed to take the following 

form as a first approximation. For a power-law fluid defined in Eq 

3.14 the curves in Fig. 3.7 shift to higher viscosities at lower shear 

rates for the higher fiber concentration present in the study 

(Y, = 68%). This shift is shown as the temperature (T) and 

concentration (4) dependent variable c (reinforcement/viscosity 

influence factor) in Eq 3.28 which is analogous to the reduced 

viscosity defined earlier. 

- (T (fiber filled resin) c(T,+) - 

(T,o) (neat resin) 

This model will be taken as is. Its use in the intimate contact 

model is only for illustrating viscoelastic tendencies for model 
justification. Obviously, future work in the area is needed to obtain 

a better understanding of the influence of fiber reinforcement on the 

resin viscosity. 

3.3.3 Intimate Contact Model 

3.3.3.a Problem Formulation 

Presented here is a physical interpretation by which prepregs 

coalesce at the interfaces during the processing of a thermoplastic 

matrix composite laminate. Recalling the three sub-models that make 

up the intimate contact model (refer to Fig. 3.3) construction can now 

begin. 

Figure 3.8 shows the geometry of the prepreg as applied to the 

intimate contact model, and implies the following: 1) all tows are 

not in contact initially, but progressively increase with time, 2) the 

tows act independently concerning the disruption of flow, however, not 

independently concerning the input of loading, and 3) only slow, 

steady, and small deformations exist. 

The first assertion seems justified from the non-uniformity of 

coalesced interfacial surfaces observed from the C-scan data. The 

first statement of the second assertion was assumed to allow for a 

closed form solution as a first approximation. Its justification lies 

in the already assumed exi stence of slow, steady, small deformations 

as stated in the third assertion. The later statement of the second 

assertion seems justified on the grounds that only shear thinning 

viscosity reponses were experimentally observed on the neat resin, 
. cs 

On'% 

COO 

'-gc 

om0 

s'iZ,Y' 

L 

L.+ 

Eao a 

OOQ, 

LLt-v, 

II II II 
(Fig. 3.7) (also expected of fiber reinforced viscosity [24,26,29]) 

and that, if the force per tow was kept constant with time then 

dilatent viscosity responses would be the result. 

3.3.3b Mathematical Model 

Figure 3.8 shows the progressive nature of the distribution of 

the applied force F (constant in time) to the individual force per 

tow, f, as a function of time. It is assumed that F is distributed 

evenly to those tows in contact only. Thus, the following definition 

is given in Eq 3.29 where the viscosity coefficient m (Eq 3.14) will 

now be premultiplied by the c (the reinforcement/viscosity influence 

factor given in Eq 3.28) to simulate the tow's viscosity: 

4 6i < h(t) f = 0 

F = i f[h(t),bi) ; if { i=l 

6. 1 L h(t) f = finite 

where; 

f E is the load per tow, 

bi E is the individual tow height, 

h(t) E is the spacing between the plates as a function of time, 

q r is the total number of tows across the specimen width 

Knowing that the cumulative distribution function ~(2) discerns 

between tows in contact and tows not in contact Eq 3.29 can be written 

as: 
where; 

NI = initial fraction of tows in contact (3% for all test) 

G = Eq 3.7 

- 

z = Eq3.5 

f =Eq3.26 

Writing Eq 3.30 in full form we have: 

Equation 3.31 is the intimate contact formulation relating the 

processing parameters, and the viscosity to the degree of intimate 

contact DIG via the squeeze flow phenomenon of a prepreg. The 

pressure P enters into the solution through F, the temperature T 

enters into the solution through its influence on the viscosity, the 

viscosity q(;,T,4) enters into the solution through the parameters 

m, c(4,T), and n, and the prepreg's geometry enters into the solution 
in the form of 6'. 6' is the degree of intimate contact numerical ly 

solved for as a function of time (Eq 3.32). 

I 

G (t) = DIC(t) 

3.3.4 Intimate Contact Model/Experimental Correlation 

3.3.4a Discussion 

This section presents a comparison of the intimate contact model 

(Section 3.3.3) with the experimental data (Section 3.3.1). The 

following discussions are addressed: 1) the method by which the model 

was fitted to the data through the assumed viscosity relationships, 2) 

the validity of the observed viscoelastic responses of the viscosity 

relationships with those responses expected by rheological theory, 3) 

the influences of the processing parameters on the degree of intimate 

contact, and 4) the influences of the prepreg's geometric 

nonuniformity on the degree of intimate contact. 

Because of the lack of experimental data for the shear viscosity 

of the fiber reinforced P1700 resin, the values of c and n were 

determined by fitting the model's response to the intimate contact 

test data over the range of the processing parameters. The viscosity 

coefficient m, represents the viscosity of the neat resin, which is a 

function pf temperature. The values of c and n cannot be uniquely 

determined from one set of pressure and temperature processing 

conditions. However, certain expected trends should be observed for 

the relative values of c and n when comparing whole sets of 
experimental data at different temperature and pressure processing 

conditions. 

The variable c is expected to be a function of temperature 

[26]. The value of n is expected to be a function of the pressure 

since increasing pressure results in expanding the range of shear 

rates 'present during the testing period. Kataoka et. al. [24] has 

shown that n may be a function of test time depending on the pressure 

and material tested. This assertion seems justified in that the 

power-law constitutive equation, Eq 3.14, describes only the straight 

portion of the viscosity data shown in Fig. 3.7, and does not allow 

for zero shear rate viscosity or characteristic time (i.e. horizontal 

portion of curve and transition region respectively [19,22)). 

Nevertheless, the power-law relationship will be used for the current 

study. 

Since the absolute values of c and n are not deterministic from 

the intimate contact data for the present model (i.e. two unknown 

constants for every set of processing P and T conditions) the powerlaw exponent n was arbitrarily set to one (i .e. Newtonian n = 1) for 

the lowest pressure studied (P = 172 KPa (25 psi)) for each 

temperature condition. 

The choice of n = 1 for the P = 172 KPa (25 psi) data allows the 

higher processing pressures to be evaluated in a relative sense for 

non-Newtonian shear thinning responses. The higher pressure data 

should exhibit a more non-Newtonian response. 

With the selection of n = 1 for each set of intimate contact data 

having a specified temperature and an applied pressure of 172 KPa (25 
psi), the value of c was then obtained by fitting the model to the 

data. This was repeated for each set of temperature data with P = 172 

KPa (25 .psi). Also, because c is a function of T, the values were 

kept constant for each processing temperature while the value of n was 

used to fit the data for the higher processing pressures. 

Figure 3.9 plots the degree of intimate contact versus the 

processing contact time at the various pressure and temperature 

conditions listed in Table 3.1. Shown on each plot are the power-law 

exponent n and the reinforcement/viscosity influence factor c used to 

fit the data, and the power-law viscosity coefficient m obtained from 

the neat resin data. The statistical distribution defining the 

prepreg's geometric non-uniformity, g(?), was held constant for a1 1 

the tests. The effects of pressure (holding temperature constant) can 

be observed by comparing the plots forming a vertical column. The 

effects of temperature (holding pressure constant) can be observed by 

comparing the plots forming a horizontal row. The better fit to data 

is observed at higher pressures when a greater shear rate dependent 

viscosity is used. This is to be expected. Good correlation exists 

between theory and experiment over the entire spectrum of contact time 

for each set of pressure and temperature conditions. It is observed 

that both pressure and temperature have a dramatic influence on the 

time required to achieve 100% intimate contact. 

The values of n and c were determined by fitting the data, and 

cannog, be obtained using the present model and testing method. 

However, the relationships between the power law exponent, n with P, 
E 

PC, 

W 

0 Q, Vk 
and the reinforcement/viscosity influence factor, c with T have 

viscoelastic significance. 

Concentrating on the values of n first, it is noted that within 

the realm of experimental error n decreases with increasing pressure 

for each set of temperature data, exhibiting increasing shear thinning 

with P [24]. This is expected if too large a range of shear rates is 

covered over the test period, as observed by Kataoka. Also, because n 

is not constant among the three applied processing pressures tested, 

the tests were not in the typical power-law region shown in Fig. 3.7, 

but extended into the transition zone (i .e. knee portion of the curve 

separating Newtonian responses from non-Newtoni an). Thus, correct 

viscoelastic responses are observed in the pattern of the values of n 

with pressure, with higher pressures exhibiting greater non-Newtonian 

response than the lower pressures. Remembering that the selection of 

n = 1 at the lowest applied pressure was arbitrary, nothing can be 

said as to where the response lies within the transition zone, as n is 

bounded by n = 1 to 0.07 where n = 0.07 is the value for the neat 

resin. 

Addressed here are the observed values of c for similating the 

influence the fiber has on the neat resin viscosity. Figure 3.10a 

plots the values of c as a function of temperature. The effective 

viscosity (c m) is plotted against temperature in Figure 3.10b where 

it is shown that although c increases with temperature the effective 

viscosity does not, as would be expected. However, is the response of 

c to temperature realistic? No reports in literature were found that 

addressed the temperature effects over such a large range; however, 
TEMPERATURE ( 'c) 

Figure 3.10 Effects of Temperature on Fiber Reinforced Resin 

Viscosity Parameters 
Pisipati [30] has shown c to increase at the lower shear rates (as 

assumed here) but reverses at the high shear rates for a 20% glass 

f i ber-reinforced nylon. As stated in the previous sections, the 

theory and experimental work are still in their developmental 

stages. Interested readers are referred to the work by Pisipati. 

In summary, the values of c and n seem arbitrary when correlated 

to single sets of pressure and temperature data; however, when the 

responses of c with T, and n with P are observed over an entire 

spectrum of applied pressures and temperatures, viscoelastic material 

responses are observed. Further work is needed if the values of c and 

n are to be quantified, as we1 1 as their responses. 

3.3.4b Influences of the Prepreg Geometric Nonuniformity on DIC 

Intuitively, the greater the nonuniformity of the prepreg (i.e. 

the greater the difference between tow heights) the greater the 

contact time required to achieve a given state of DIG. The following 

study was made addressing the effects of tow nonuniformity on the 

degree of intimate contact. This study was divided into two parts: 

1) the effects of statistically skewed distributions (i.e. heavily 

populated thin or thick tows) and 2) the effect of statistically 

deviated tow uniformity (i.e. greater or lesser tow height 

uniformity). The processing conditions used for this study were 

chosen as P = 172 KPa (25 psi) and T = 240°C (465°F). 

Statistically Skewed Tow Nonuniformity 

Shown in Fig. 3.11a are three conditions of skewness of tow 
I (A) HEAVILY WEIGHTED THICK TOW DISTRIBUTION 

a= 2.25 P=.1 108 g,=.084 

. (8) BASELINE 

a= 3.50 @=.I 108 g,=. 122 

(C) HEAVILY WEIGHTED THIN TOW DISTRIBUTION 

a= 4.75 @=.I 108 g,=.162 

PROCESSING CONDITIONS: 

PRESSURE= I 72KPa(25psi) 

TEMPERATURE=240C(465F) 

0- I I 

0 

I 

600 1200 

CONTACT TIME (sec) 

Figure 3.11 Effects of Probabi 1 istically Skewed Distributions of Tow 

Height Nonuniformity Across the Width of a Prepreg with 

the Degree of Intimate Contact 
nonuniformity: 1) curve A is the tow distribution in the present 

study which simulates a heavily populated thick tow distribution, 2) 

curve B is the normal distribution of curve A by setting a = 3.50, and 

is used as the baseline in both the skewness and deviated tow 

nonuniformity studies, and 3) curve C simulates a heavily populated 

thin tow distribution. 

Figure 3.11b shows that a heavily populated thin tow prepreg 

results in a faster initial growth of DIG followed by a slower growth 

as 100% contact is approached. The opposite is true of prepregs being 

heavily populated with thick tows. 

Statistically Deviated Tow Nonuniformity 

Shown in Fig. 3.12a are two conditions of deviated normal 

distributions of tow nonuniformity: 1) curve D is the baseline curve 

B used in Fig. 3.11 simulating a large deviation in tow uniformity, 

and 2) curve E is a normally distributed prepreg simulating greater 

tow uniformity, 

Comparing curves D and E in Fig. 3.12b, it is found, as expected, 

that the smaller the standard deviation (curve E) the shorter the 

contact time required to achieve the same DIG. 

3.3.4~ Observations of the Model 

As a final word about the intimate contact results, reference is 

made to Figs. 3.13a and 3.13b. Had plate separation been monitored as 
PROCESSING CONDITIONS: 

PRESSURE= 1 72KPd25psi) I 

1 - 

d: 

\ 

n 

IN 

w 

rT 

0- 

600 1200 

CONTACT TIME (sec) 

(D) BASELINE 

a= 3.50 P=.1108 g,=.122 

(E) GREATER TOW THICKNESS UNIFORMITY 

a= 3.50 /3=.0708 g,=.190 

I I I I I 

Figure 3.12 Effects of Probabi 1 istical ly Deviated Normally Distributed 

Tow Height Nonuniformity Across the Width of a Prepreg 

with the Degree of Intimate Contact 
PROCESSING CONDITIONS: 

PRESSURE=688KPa(l OOpsi) 

TEMPERATURE=240C(465F) 

PREPREG- TEST CONDITION 

600 1200 

TIME (sec) 

LOG(h) (mm) 

(inch) -2.2 -2.0 

Figure 3.13 Observations of Model Concerning (a) Tow Height versus 

Contact Time, and (b) the Rate of Decreasing Tow 

Height due to Compression Loading versus Tow Height 

- -3.5 

@ 

- 

r' 

3 

0 

3 a 

0 

u 

- 

- -6.5 

- 2- 

- 3- 

- 4- 

- 5- 

I 

PROCESSING CONDITIONS: 

PRESSURE=688KPa(l OOpsi) 

TEMPERATuRE=~~OC(~~~F) 

PREPREG- TEST CONDITION 

I 
a function of time in lieu of C-scanned area as a function of time, 

then the following responses would have been realized according to the 

model. Plate separation h versus tc is shown in Fig. 3.13a while log 

(dh/dt) versus log (h) is shown in Fig. 3.13b. The rate at which the 

plates approach each other (Fig. 3.13b) has two physically distinct 

regions. 

The first region has the characteristics of a decreasing plate 

separation rate. This similates the force per tow decreasing with 

time (i .e. the area of contact increasing with time as the force is 

kept constant). Whether or not this response is valid must still be 

evaluated. The model cannot predict transient conditions, only steady 

state conditions as assumed in the formulation. In other words, the 

stress overshoot typical of vi scoel astic material s cannot be predicted 

as new tows come into contact and start their flow process. 

The second region is the steady state region where 100% contact 

has been achieved at the interfaces and a global squeeze flow 

occurs. The slope of this portion of the curve is 1/6 for Newtonian 

fluids. If other than 1/6 the material is non-Newtonian where the 

slope of the power-law region can be evaluated. Because of the mold 

cavity, no global squeeze was allowed nor would this region be 

possible to evaluate using the C-scan technique. 
4.0 Computer Model 

A computer code was developed which can be used to calculate the 

degree of autohesion, DAu , and the degree of intimate contact, DIG, at 

the interface of a thermoplastic matrix composite during processing. 

The model is 1 imited to constant temperature (greater than the Tg of 

the resin) and constant pressure conditions throughout the laminate. 

With the pressure and temperature conditions specified, of major 

interest are the states of autohesion and intimate contact as a 

function of the processing time, tp (i .e. total elapsed time) and more 

specifically the processing time required to achieve full intimate 

contact and cohesive strength of the interface. 

Intuitively, coalescence at the interfaces of stacked plies is 

expected to be quicker for unidirectional laminates, than for angle 

ply and cross-ply laminates due to the nesting of tows. Thus, because 

the intimate contact model was formulated using data obtained from 

cross-ply laminates, the computer model presented here is expected to 

give conservative results for laminates other than cross-ply. 

The computer code provides the user with the following 

information about processing: 

1) the degree of intimate contact (i .e. fraction of interfacial 

area in contact) as a function of processing time, 

2) the distribution of the degree of autohesion over the 

interfacial area in contact, and 

3) the minimum degree of autohesion of a total interfacial area 

in contact as a function of processing time. 

Up to now, the autohesion and intimate contact models were 

f ormu 1 ated i ndependent 1 y . However, during the processing of 
thermoplastic matrix composites, the two time dependent phenomena 

occur simultaneously. 

The computer code couples the autohesion model with the intimate 

contact model through the observation that autohesive bonding cannot 

begin until intimate contact is achieved. As processing time 

progresses the total area in contact increases (i.e. DIG). Because 

the total area in contact (1.. DIG) is the cumulation of smaller 

areas, dIC9 achieving contact previous to the processing time in 

question, the set of dIC1s at a given processing time will each have a 

unique degree of autohesion. This is due to the differences in the 

length of time that each dIC has been in contact. The model 

distinguishes between the length of time (tIC) required for each 

successive element of area to come into contact, and the length of 

time (tAu) each successive element has been in contact. Thus, the 

following equation was used in the computer model formulation: 

where t,,, tIC9 and tAu are defined previously. 

Solution of the autohesion model (Section 2) and intimate contact 

model (Section 3) requires that the input parameters be specified. 

The input parameters are shown in Table 4.1, and are grouped in the 

fol lowing catagories: I) Processing Cycle, I I) Prepreg Properties, 

and 111) Resin Properties. 

The input parameters describing the temperature and pressure 

conditions are specified by the user. The parameter denoted by a 
Table 4.1 Input Parameters 

I) Processing Cycle 

a) Constant temperature condition 

b) Constant pressure condition 

I I ) Prepreg Properties 

c) Initial distribution of geometric nonuniformity of tow 

heights* (see Eq 3.7) 

d) Fiber volume fraction of composite vf = 68% 

e) fiber reinforced resin viscosity parametersf* (see Eq 3.28) 

f) Cross-sectional area of a single tow 

g) Glass transition temperature - Tg 

I I I) Resin Properties 

I 

h) Resin dynamic viscosity r~ (T,u) 

(see Appendix A) 

i) Autohesion parameters (K(T), or K; and aT(T))*** 

(see Eqs 2.11, 2.14, and 2.15) 

* measured by user 

** empirically .determined by fitting IC theory to experimental data 

*** material property experimentally measured 
single astrisk (*) must be measured by the user. The method used to 

obtain this parameter can be found in Section 3.3.2a. The parameter 

denoted by a double asterisk (**) was determined by fitting the theory 

to experimental data as described in Section 3.3.4. The material 

property denoted by a triple asterisk (***) was determined 

experimentally as described in Section 2.0. All other parameters are 

either specified by the manufacturer or can be found in the open 

literature. 

With the input parameters specified, Eqs 2.10 (or 2.15) and 3.31 

are solved numerically. 

Three cases were run on the computer to show the relationship 

between the degree of intimate contact and the degree of autohesion 

for various processing conditions. The computer model was used to 

calculate the degree of intimate contact, the degree of autohesion, 

and the total processing time of a fiber-reinforced thermoplastic 

matrix composite under different processing conditions. The material 

properties of AS4/P1700 prepreg were used as input data to the model. 

Case I - P = 172 KPa (25 psi), T = 240°C (465"F), t = 0 + 3000 sec P 

Case I1 - P = 344 KPa (50 psi), T = 240°C (465"F), t = 0 + 3000 sec 

P 

Case 111 - P = 172 KPa (25 psi), T = 227°C (440°F), t = 0 + 3000 sec 

P 

The degree of intimate contact was calculated as a function of 

the processing time for cases I, 11, and 111, independent of the 

autohesion phenomenon. However, at each processing time a whole 

distribution of DAu values exist because of the progressive nature of 

intimate contact with time. By plotting the degree of autohesion 

versus the percent of contacted area (i .e. dIC, density of contacted 
area) shown in Fig. 4.1, the distribution of autohesion over the area 

in contact is obtained for all three cases. The solid curves 

represent the distributions of autohesion (for 1% intervals of DAu) at 

different processing times up to but not including, a degree of 

autohesion of 1.0. The table on the graph shows the values of the 

percent of contacted area having a degree of autohesion equal to 

1.0. For case I, at short processing times (i.e. P = 10 sec) it is 

shown that no areas in contact have occurred that have a DAU greater 

than 00.63, and that at point iiA1' approximately 0.8% of the contacted 

area has a DAu between .395 and .405. As expected, at longer 

processing times greater percentages of contacted area coexist with 

the higher degree of autohesion. This observation is obvious for 

curves "a" and "b" but somewhat disquised for curves Ncil through 

Ii j". This is because at the long processing times an increasing 

percentage of the contacting area has a degree of autohesion equal to 

one. These values are shown in the tables on Fig. 4.1. 

The effects of pressure and temperature on the distribution of 

autohesion over the contacted area are shown in Fig. 4.1 by comparing 

the top and center graphs and top and bottom graphs, respectively. By 

comparing the results from Case I and Case 11, the effect of a 50% 

increase in pressure (holding temperature constant) can be observed. 

It is shown that the distribution of autohesion is skewed upward for 

the higher pressure condition indicating a more rapid growth in areas 

coming into contact and a less uniform distribution of autohesion at 

any one processing time. However, this observation on the skewness is 

somewhat insensitive at long processing times. Also, the increase in 
0 * of total interfacial area I I I I I 

DISTRIBUTION OF AUTOHESION OVER AREAS IN CONTACT 

* of total interfacial area 

OCDk < 1 

13 

CASE I 

T=240C(465F) 

I P- 172KPo(25psi) I 81 

1 

CASE Ill 

T=227C(440F) 

P= 172KPa(25psi) 

roo 0.0 (ojz 

250 51.0(12)% 

500 80.2 29)% 

1 000 91.9[49)% 

1500 95.4(61)% 

t, (sac) 

lo 

50 

100 

250 

500 

1000 

1500 

2000 

2500 

3000 

04 * of total interfacial area I I I I I I 

0 1 2 3 4 5 

DA, = 1.0(*) 

0.0 (o)a 

0.0 (O)% 

49.0(10 7: 

84.2(29{% 

93.3 47)% 

97.4{67)% 

98.6(78)% 

99.3(85)% 

99.4(90 % 

99.6(93{% 

PERCENT OF CONTACTED AREA 

Figure 4.1 Distribution of the Degree of Autohesion Over the 

Area in Intimate Contact for Several Processing Times 
pressure results in greater percentages of contacting area having a 

D~u = 1 at long processing times. 

The effect of temperature on the distribution of autohesion can 

be observed by comparing Case I with Case 111 (holding pressure 

constant) where Case I11 is 13°C (25°F) lower as shown in Fig. 4.1. 

The 13°C (25°F) decrease in temperature results in suppressing the 

distribution to lower degrees of autohesion, as well as, lower 

percentages of contacted areas. This is a result of temperature 

affecting both the viscosity and autohesive properties of the resin 

thereby influencing the growth of contacting area, and the growth of 

autohesion. 

Shown in Fig. 4.2 is a plot of the minimum degree of autohesion 

versus the degree of intimate contact at several processing times. 

This curve was obtained by integrating the curves in Fig. 4.1 at each 

processing time. The curves show the coexistence of DAu and DIG at a 

given processing time. This cumulative distribution will provide the 

user with the minimum degree of autohesion expected for a given area 

in intimate contact (i.e. DIC) at any processing time. These curves 

show the cumulative distribution of contacted area to the total area 

up to a given DAu Thus, using tp = 100 seconds as an example point 

"8" shows that ~20% of the total interfacial area is in intimate 

contact, point "C" shows that ~10% of the interfacial area is in 

intimate contact with a DAu = 1.0, and point "Dli shows that 

approximately 17% of the interfacial area in contact has a value of 

DAu of 0.70 or greater. At very long processing times the lines 
MINIMUM DEGREE OF AUTOHESION MINIMUM DEGREE OF AUTOHESION 

5 

5 

25 

w - 

n -I 

~n-nn-nn u II ~~~~~~& PN 

+ 

0 

a wmw-- ulm= 

O~ovIovlm- - ofn 000000W0~-. -0 7 

0000000000 V OD. - 

MINIMUM DEGREE O

0 

--wQpG*z 

---YYY-- 

uwm-2 

8E8g8gEGW-

000000000
appear more vertical because of the compressing time scale with 

increasing DIC (i.e. DIC does not increase linearly with time). 

The effect of pressure is shown in Fig. 4.2 by comparing the top 

and center graphs. It is shown that the higher pressure results in 

higher degrees of intimate contact for any one processing time. No 

pressure effects were expected nor observed on the autohesive values 

as observed by the intercepts of curves "an and "b" with DAu at the 

initial contact area. 

The effects of temperature are shown in Fig. 4.2 by comparing the 

top and bottom graphs. It is shown that the lower temperature results 

in smaller degrees of intimate contact at any given processing time. 

This result is expected since the viscosity increases with a decrease 

in temperature thus suppressing the rate of deformation and the growth 

of intimate contact. Also observed, is the influence of temperature 

on the degree of autohesion. At the lower temperature and at any 

processing time a greater percentage of the areas in contact have a 

degree of autohesion less than 1.0. This is because a decrease in 

temperature decreases the molecular mobility of the diffusing 

molecular chains thus suppressing the degree of autohesion for any 

unit of time. 

Figure 4.3 summarizes cases I through I11 showing the effects of 

temperature and pressure od DIC and DAu at tp equal to 50 and 1000 

seconds. More easily seen than in Fig. 4.2 is the increasing range of 

DIG values as processing time is increased, The effect of pressure on 

DIC and DAu can be observed by comparing cases I and 11. For the same 

temperature, a 172 KPa (25 psi) pressure increase results in 
t =50 sec P t =I 000 sec 

0- P 

1 I I v I I I I I 

DEGREE OF INTIMATE CONTACT 

Figure 4.3 Summary Plot of the Minimum Degree of Autohesion Versus 

the Degree of Intimate Contact at Processing Times of 50 

and 1000 sec. 
higher values of DIG with no observed effects on DAu as expected. 

In summary, the length of processing time required to achieve 

full intimate contact and cohesive strength of the interfacial area is 

subjected to the processing temperature and processing pressure 

conditions selected. The time frames of the intimate contact model 

and autohesion model are related to the processing time frame by Eq 

4.1. Figure 4.4 shows the length of processing time required to 

achieve DAu = 1.0, and DIG = 1 for a given temperature and pressure. 

Because the temperatures tested for intimate contact are well above 

the T of the resin the influence of autohesive time to the overall 9 

processing time played a very minor role (refer to Eq 4.1). While the 

increase in pressure may decrease the time required to achieve 100% 

intimate contact the effect on the final processing time may not be as 

dramatic at temperatures lower than those tested. As pointed out in 

Section 2.0, at temperatures just above the T of the resin a degree 9 

of autohesion equal to one could only be obtained only after long 

autohesive contact times (-20 minutes). The nonlinearity of these 

curves shows the importance of just minor changes of the processing 

conditions with the final processing time. 
0 1000 2000 3000 4000 

PROCESSING TIME (sec) 

Figure 4.4 Effects of Temperature and Pressure on the Final 

Processing Time Required to Achieve Full Intimate 

Contact and Cohesive Strength 
5.0 Conclusfons 

The following major tasks were completed during the course of 

this investigation: 

1) Models were developed to simulate the processing of 

cont i nuous fiber (AS4 graphite) reinforced thermoplastic 

matrix (PI700 polysulfone) composites. The models 

successfully describe the ply interfacial bonding phenomenon 

(cons01 idat ion) and the ply interfacial deformation 

(coalescence) phenomenon through mechanisms attributed to 

autohesion and squeeze flow, respectively. 

Autohesion Model/Experiment 

a) The autohesion model predicts the experimentally 

determined autohesion strength of the neat resin to be 

proportional to the fourth root of contact time, 

b) A testing method for obtaining autohesive strength data 

at the same elevated temperature that the autohesion 

phenomenon occurred was successfully developed. The 

test method reduces the overall testing time required 

for room temperature testing. 

c) Time-temperature superposition of the experimental ly 

determined autohesive strength data was successfully 

applied in an empirical Arrhenius format and also in a 
WLF method thereby coupling testing time to testing 

temperature. 

Intimate Contact Model/Experiment 

a) Black and white C-scans were obtained of [0,9090]T 

laminates processed at several pressures, temperatures 

and times. The C-scan settings were set to indicate 

spacial gaps at the ply interfaces. The theory of 

probabilistics was applied to the C-scan data to 

distinguish between areas in contact and spacial gaps 

at the top and bottom interfaces. 

b) A model was developed to simulate the growth of 

interfacial areas obtaining intimate contact. 

- The model accounts for; 1) the extent of tow 

height nonuniformity across the width of a 

prepreg, and 2) the viscoelastic response of the 

deformation of a single tow subjected to a 

uniformly distributed compressive load over the 

top and bottom surfaces. 

- The results of the model Yits the experimental 

data quite well because of an assumed empirical 

formulation to indicate the fiber's influence on 

the neat resin viscosity. Further work is needed 
to el iminate the experimetal ly determined 

constants for complete model verification. 

However, the expected vi scoel ast ic response was 

observed between the processing parameters and the 

formation of intimate contact areas. 

c) Experimental ly measured dynamic viscosity data was 

obtained for the PI700 polysulfone neat resin over the 

temperature range from 220°C to 400°C in 20°C 

intervals. The frequency range was 0.1 to 100.0 

rad ./sec. 

- Steady shear viscosity results were obtained by 

applying the Cox-Merz rule to the dynamic 

viscosity data. 

- A master curve of the original viscosity data was 

constructed in the WLF manner, The results are an 

expanded frequency (or shear rate range) from 

3.OE-06 to 100. rad/sec at 220°C. 

2) A computer code was developed from the autohesion and 

intimate contact models. This code can be used to generate 

the following information for flat plate composites: 

a) the degree of intimate contact, DIG, as a function of 

processing time, 
b) the degree of autohesion, DAuy as a function of the 

length of time certain percentages of the interface 

have been in contact and the processing time. 

3) The following input parameters required in the computer code 

for the solution of the models were specified: 

a) shear viscosity of the neat resin, n, was obtained 

experimentally as a function of shear strain 

rate, ;, and temperature, T, 

b) shear viscosity parameters of the fiber reinforced 

resin, c and n, were obtained experimentally as a 

function of temperature, T, and pressure, P, 

respectively, 

c) the autohesion diffusion coefficient, KO, was obtained 

experimentally as a function of temperature, 

d) the prepreg's geometric non-uniformity, g(y), was 

measured and defined statistically. 

4) The computer model quantitatively confirms the intuitive 

speculation that decreased processing time can be realized 

by either increasing temperature, or pressure, or both. 

With the user defining any two of the three processing 

parameters (P, T, and t) the computer model will define the 

third parameter required to achieve a completely contacted 

and bonded i nterf ace. 

5) A parametric study was performed on the extent of tow height 

nonuniformity to illustrate how the models and the 
associated computer code can be used to determine the 

appropriate processing parameters for achieving a uniformly 

processed composite in the shortest time. 

Normally Distributed Tow Height Nonuniformity 

Prepregs having greater or lesser extents of tow height 

nonuniformity have been shown to greatly influence the final 

processing time required to achieve full intimate contact 

and full bond strength. 

Skewed Distribution of Tow Height Nonuniformity 

Prepregs having a greater number of tows that are thick 

require longer processing times than prepregs having a 

greater number of thin tows due to the changing load per tow 

distribution of the constant applied processing pressure. 

The f 01 lowing recommendat ions are made concerning the outcome of 

this study: 

1) that autohesive strength be measured on actual laminates at 

room temperature in order to observe any differences in the 

development of the degree of autohesion and the contact time 

with the neat resin test, 

2) that the effects of strain rate and shear strain on the 

cohesive strength be obtained at temperatures just above glass 

transition temperature, 
It has been observed that if a steep thermal gradient 

through the thickness in the three ply laminate (10,90,0IT) 

is imposed, greater or lesser extents of warpage (out of 

plane curvature) of a symmetric lay-up can be obtained. It 

is the extent of warpage that leads one to believe that 

varying shear strains are taking place during this 

trans1 tory period (a1 so resu 1 ti ng in varying thermal 

stresses). This can be explained since the material is 

still capable of motion during the transition period when 

cooling from the processing temperature to the Tg of the 

resin (unlike thermosets which solidify). 

It is the varying extent of shear strain and its rate that 

can place areas of reduced autohesive strength at the 0"/9Q0 

ply interface as the fibers contract or expand to different 

extent. It is believed that the varying amounts of shear 

strain will also result in a varying loss of autohesion 

strength and a different initial condition from which 

autohesion formation is to restart. The autohesion process 

occurs very slowly at temperatures just above the Tg of the 

resin leading one to believe that a limiting factor may be 

this cooling down period if the shortest processing time is 

desired. 

3) Lastly, that a faster and more accurate means of measuring the 

degree of intimate contact, than the C-scan method used here, 
may be realized through the measurement of processing plate 

separation as a function of time. Also, the use of dielectrics 

may be very useful in monitoring the formation of intimate - 

contact by monitoring the change in signal with the increasing 

area of contact. 
References 

1. May, L. C., and Goad, R. C., tlManufacturing Methods for 

Fabrication and Assembly of Advanced Composite Primary 

Structure,Ii U.S. Air Force Materials Laboratory Report Nr. AFMLTR-75-111, July, 1975. 

2. Hoggatt, J. T., and VonVolki, A. D., "Evaluation of Reinforced 

Thermoplastic Composites and Adhesives," Naval Air Systems 

Command Final Report - Contract N00017-7A-C-0026, March, 1975. 

3. Hill, S. Gey et. al., "Advanced Thermoplastic Composite 

Development," Final Report on Contract N00019-77-C-0561, Boeing 

Aerospace Company, Seattle, Washington, May, 1979. 

4. Husman, and Hartness, J., "Polyphenyl Sulfone Matrix 

 composite^,^^ 24th National SAMPE Symposium and Exhibition, 

Volume 24, Book 2, p. 21 (1979). 

5. Hartness, J., iiPolyphenylene Sulfide Matrix composite^,'^ 25th 

National SAMPE Symposium and Exhibition, Volume 25, pg. 376 

(1980) . 6. Voyutskii, S. S., Autohesion and Adhesion of High Polymers, 

Volume 4, Polymer Reviews, Interscience Publishers, New York, 

7. Bothe, L., and Rehage, G., "Autohesion of Elastomers," Rubber 

Chemi stry and Technology, 55, 1308 (1981). 

8. De Gennes, P. G., "Reptation of a Polymer Chain in the Presence 

of Fixed ~bstacles," Journal of chemical Physics, 55, 572 

(1971). 

9. De Gennes, P. G., "Entangled Polymers," Physics Today, pp. 33- 

39, June, 1983. 

10. Wool, R. P., "Molecular Aspects of Tack," Rubber Chemistry and 

Techno1 ogy , 57, 307 ( 1983). 

11. Wool, R. P., and OtConnor, K. Me, "Theory of Crack Healing in 

 polymer^,^^ Journal of Applied Physics, - 52, 5953 (1981). 

12. Wool, R. P., "Relations for Healing, Fracture, Self-Diffusion, 

and Fatigue of Random Coil Polymers," ACS Polymer Preprints, 23 

I1)-, 62 (1982) . 

13. Judy K., Kausch, H. H., and Williams, J. G., "Fracture Mechanics 

Studies of Crack Healing and Welding of polymer^,^^ Journal of 

Materials Science, 16, 204 (1981). 
14. Skewis, J, D., "Self-Diffusion Coefficients and Tack of Some 

Rubbery Polymers," Rubber Chemistry and Technology, - 39,217 

(1966). 

15. Hamed, G. R., and Shieh, C. H., "Relationship Between the 

Cohesive Strength and the Tack of elastomer^,'^ Journal of 

Polymer Science, Polymer Physics Edition, 21, 1415 (1983). 

16. Ling, F. F., "The Properties of Random Surfaces in Contact," 

Surface Mechanics, ASME Winter Annual Meeting, p. 36, November, 

16-21, 1969. 

17. Blakely, J. Me, Surface Physics of Materials, Volume 2, pp. 475- 

487, Academic Press, New York, (1975). 

19. Grimm, R. J., "Squeezing Flows of Polymeric Liquids," AIChE 

Journal, 24(3), 427 (1978). 

20. Bird, R. B., Armstrong, R. C., and Hassager, O., Dynamics of 

Vol . 1, pp. 223-226, John Wi ley and Sons, New 

21. Dienes, G. J., and Klemm, H. F., "Theory and Application of the 

Para1 lel Plate Plastometer," Journal of Applied Physics, - 17,458 

(1946). 

22. Kataoka, T., Kitano, T., and Nishimura, T., "Utility of 

Parallel-Plate Plastometer for Rheological Study of Filled 

Polymer Melts," Rheologica Acta, - 17 0, 626 (1978). 

23. Dealy, J. M., Rheometers for Molten Plastics, pp. 174-177, Van 

Nostrand Reinhold Company, New York, (1982). 

24. Kataoka, T., Kitano, T., Sasahara, M., and Nishijima, K., 

"Viscosity of Particle Filled Polymer Melts," Rheologica Acta, 

17(21, 149 (1978). 

25. Mooney, M., "The Viscosity of a Concentrated Suspension of 

Spherical Particles," Journal of Colloid Science, 5, 162 (1951). , 

26. White, J. L., Czarnecki, L., and Tanaka, He, "Experimental 

Studies of the Influence of Particle and Fiber Reinforcement on 

the Rheolog.ica1 Properties of Polymer Melts," Rubber Chemistry 

and Technology, 3, 823 (1980). 
27. Bartenev, G. M., and Zakharenko, N. V., "The Viscosity and Flow 

~echanism of polymer-~i 1ler ~ixtures," Kol loidn. ZH., 24, 121 

(1962) . 

28. Chapman, F. M., and Lee, T. S., "Effect of Talc Filler on the 

Melt Rheology of P~lypropylene,~~ SPE Journal, 26(1), 37 (1970). 

29. "A Modified Casson Equation for Dispersion," Transactions of the 

Society of Rheolou, 14(4), 617 (1970). 

30. Pisipati , R. M., "A Rheological Characterization of Particle and 

Fiber Filled Nylon 6,6 Melts and Its Application to Weld-Line 

Formation in Molded Parts," Ph.D. Thesis, VPI&SU, 1983. 
Appendix A 

@ Rheological Properties of UDEL PI700 Resin 

A. 1 Introduction 

Experimentally obtained dynamic viscosity data was obtained for 

neat P1700 polysulfone resin using a parallel plate testing fixture 

within the frequency range from 0.1 to 100.0 radians per second at 

temperatures from 200°C to 400°C in 20°C intervals. The viscosity 

data was tested to be linearly viscoelastic over the test spectrum. 

Also, , the viscosity data was evaluated for time-temperature 

superposition in the WLF manner. All temperature conditions fit quite 

well with the WLF theory except for the temperature conditions above 

the 360°C data, where prolonged exposure to a nitrogen purged 

atmosphere was found insufficient to prevent degradation of the 

polymer. 

Presented here are the experimental procedure (Section A.2), the 

original test data (Section A.3), application of the Cox-Merz rule to 

obtain steady shear viscosity from the dynamic viscosity data (Section 

A.4.1), and the construction of a master curve from the WLF theory 

relating time and temperature with viscosity (Section A.4.2). 

A.2 Experiment 

The dynamic viscosity data were taken using the Rheometrics 

System Four rheometer (Fig. 2.5) using a parallel plate test fixture 

I 

(Fig. 2.6). The dynamic viscosity, ri (u), shear storage 

1 I I 

modulus, G (u), and shear loss modulus, G (w), were obtained from 
amplitudes of oscillation of the driven top plate and the non-driven 

bottom plate and the phase angle between the oscillations of the two 

I I (I 

plates. The equations relating TI ,.G , and G with the measured 

quantities of torque, M, frequency, w, and phase angle, e for the 

parallel plate plastomer are as follows: 

rl I =- poise 

W 

,.l I1 =- G' poise 

W 

I 

G = K . [Real M/e] Dynes/cm 2 

I1 

G = K [Imag M/e 1 Dynes/cm 2 

u = frequency 

II * 

q = is the out of phase component of Q 

* 

q = is the complex viscosity 

H = is the plate spacing (mrn) 

R = is the radius of the plates (mm) (12.5 rnm) 

e = is the phase angle (radians) 

(A. la) 

(A. lb) 

(A. lc) 

(A. 2) 

M = is measured torque 

All PI700 sample disks used in the test were prepared in a similar 

fashion to the thick film preparation used for autohesion sample 
preparation described in Section 2.3,2, All viscosity measurements 

were made in a nitrogen purged oven. At temperatures of 360°C and 

greater, nonrepeatable data were observed with the same specimen. 

This was attributed to the degradation of the polymer as greater 

discoloration of the polymer was observed with prolonged times at 

higher temperatures. Using several different specimens all other 

temperature data showed good repeatability. No effects of plate 

separation from 1.0 mm to 1.70 mm were observed in the viscosity 

response. 

Shown in Table A.l are the conditions of the dynamic viscosity 

test and the conditions used to verify the test as being linear 

viscoelastic. 

A.3 Test Data Results and Discussion 

A.3.1 Dynamic Testing 

Shown in Fig. A.1, A.2, and A.3 are the linear viscoelastic 

* I 

complex viscosity, (n ), the shear storage modulus, G (u), and the II 

shear loss modulus, G (u) for the test conditions shown in Table A.l, 

respectively. Smooth and continuous data curves are obtained at all 

temperatures over the entire frequency range except at the very low 

frequencies and high temperature data. This slight fluctuation is 

attributed to the very low torque output signals produced at these 

conditions. The greater fluctuations are present in the measurement 

of GI because of the magnitude difference with G'. As expected there 

is a greater shear dependent response of viscosity with frequency 
126 

Table A.1 Viscosity Test Matrix 

Dynamic Test 

PI ate N2 L i near 

Oven Temp. Frequency % Strain Spacing Purge Check 

Yes 

Yes 

Yes 

Yes 

Yes 

Yes 

Yes 

Yes 

Yes 

Yes 

Linear Check 

PI ate 

Oven Temp. Frequency 2 X Strain Spacing Purge 

260" C 0.5 rad/sec 1-20% 1.145 mm Yes 

5.0 1-20 1.145 Yes 

50. 1-20 1.145 Yes 

320°C 0.5 1-20% 1.693mm Yes 

5.0 1-20 1.693 Yes 

50. 1-20% 1.693 Yes 

- - 

Yes 

-- 

- - 

Yes 

- - 

Yes 

- - 

360" C 0.5 rad/sec 1-40% 1.145 mm Yes 

5.0 1-40 1.145 Yes 

50. 1-40 1.145 Yes 
Y VI >w 

a: 

-In 

-I-d 

Kh 

a0 

(do 

L 
U 

0 

w 

T V) .r 

-r V) 

>w 

a 

*r 

Fh0 

(do 

L 

.-I 

-In 
Figure A.3 Linear Viscoelastic Shear Loss Modulus of UDEL" 

P1700 Resin 
(i.e. shear rate) at the lower temperatures and a greater extent of 

the Newtonian domain over the frequency range tested at high 

temperatures. 

A.3.2 Linear Check 

Checks for 1 inear viscoelastic material response of the dynamic 

viscosity data were made at temperatures of 260°C, 320°C and 360°C and 

are shown in Figs. A.4, A.5, and A.6, respectively. These linear 

checks involved measuring the viscosity response at a given frequency 

(i.e. time) and varying the percent of strain. Theoretically, as 

shear strain is increased for a given shear rate, a greater 

entanglement density is realized resulting in increased material 

resistance to deformations. This results in fracture on the molecular 

level and a further decrease in resistance. The test was repeated for 

three frequencies spanning the range of frequencies tested. The 

linear portion of the viscosity versus percent strain response 

separates the domai ns of the 1 i near and nonl i near vi scoel ast i c 

materi a1 responses. The percent strain value indicating the 

transition provided the limit of strain in the dynamic testing 

procedure. Once again, some scatter is observed at the start up of 

the test at the low shear strain. Further limitations of the test, 

not present in any theory for linear viscoelasticity, are the capacity 

of the torque load cell being exceeded at higher shear strains and 

rates and the material being extruded from between the plates at large 

strains and frequencies, 
%: Strain 

Figure A.4 Linear Check of Viscosity,Data of ,,UDEL* PI700 Resin at 

T = 260°C, Plots of n*, G , and G versus Percent Strain 

at Frequencies 0.5 rad/sec (top graph), 5.0 rad/sec 

(center graph), 50.0 rad/sec (bottom graph) 
% Strain 

Figure A.5 Linear Check of Viscosity, Data of ,,UOEL" PI700 Resin at 

T = 320°C, Plots of II*, G , and G versus Percent Strain 

at Frequencies 0.5 rad/sec (top graph), 5.0 rad/sec 

(center graph), 50.0 rad/sec (bottom graph) 
Linaor Check 

0.5 rod/sec 

rl* 1~360 c ................... 

Z Strain 

Figure A.6 Linear Check of Viscosity, Data O~,,UDEL@ PI700 Resin at 

T = 360°C, Plots of n*, G , and G versus Percent 

Strain at Frequencies 0.5 rad/sec (top graph), 5.0 

rad/sec (center graph), 50.0 rad/sec (bottom graph) 
A.4 Viscoelastic Theory 

Presented here are the application of the Cox-Merz rule allowing 

the approximation of steady shear viscosity from the dynamic viscosity 

and the application of the WLF theory of time-temperature 

superposition to the dynamic viscosity data. In both instances the 

theory is well developed and will be used to evaluate its usefulness 

to the P1700 material response. 

A.4.1 Cox Merz Rule 

The empirical rule of Cox and Merz [20] has been used to 

approximate the steady shear viscosity from dynamic viscosity data in 

the absence of actual steady shear viscosity by the use of the complex 

viscosity. It has been observed experimentally that both the steady 

shear viscosity and dynamic viscosity converge to the same value as 

the shear rate and frequency respectively go to zero. However, at the 

high shear rates and frequencies it is found that the steady shear 

viscosity exceeds the value of that of the dynamic viscosity. This is 

expected since a greater degree of chain entanglements will be 

realized for continuous shear conditions in lieu of an oscillating 

one. 

The Cox-Merz rule is shown as Eq A.4 where the relationship 

empirically predicts that the magnitude of the complex viscosity is 

equal to the steady shear viscosity at equal values of frequency and 

shear rate: 

Figure A.7 Master Curve of Complex Viscosity Data Using WLF ., Time-Temperature Superposition at a Reference 

Temperature, Tref = 220°C 
"ref = reference viscosity 

C1 = 5.714 experimetal ly determined constant 

C2 = 54.309 experimentally determined constant, 
Thermoplastic Matrix Composite Processing Model 

Virginia Polytechnic Institute & State University 

Engineering Science and Mechanics 

17b. Idcntificrs/Open-Ended Terms 
VIRGINIA TECH CENTER FOR 

COMPOSITE MATERIALS AND STRUCTURES 

The Center for Composite Materials and 

Structures is a coordinating organization for 

research and educational activity at Virginia 

Tech. The Center was formed in 1982 to 

encourage and promote continued advances in 

composite materials and composite structures. 

Those advances will be made from the base of 

individual accomplishments of the thirty-four 

founding members who represent ten different 

departments in two colleges. 

The Center functions by means of an 

Administrative Board which is elected yearly. 

The general purposes of the Center include: 

collection and dissemination of information about composites activities at Virginia 

Tech, 

contact point for other organizations and 

individuals, 

mechanism for collective educational and 

research pursuits, 

forum and mechanism for internal interactions at Virginia Tech. 

The Center for Composite Materials and 

Structures is supported by a vigorous program 

of activity at Virginia Tech that has developed 

since 1963. Research expenditures for investigations of composite materials and structures total 

well over five million dollars with yearly 

expenditures presently approaching two million 

dollars. 

Research is conducted in a wide variety of 

areas including design and analysis of composite materials and composite structures, 

chemistry of materials and surfaces, characterization of material properties, development of 

new material systems, and relations between 

damage and response of composites. Extensive 

laboratories are available for mechanical 

testing, nondestructive testing and evaluation, 

stress analysis, polymer synthesis and characterization, material surface characterization, 

component fabrication and other specialties. 

Educational activities include eight formal 

courses offered at the undergraduate and 

graduate levels dealing with the physics, 

chemistry, mechanics, and design of composite 

materials and structures. As of 1982, some 33 

Doctoral and 37 Master's students have 

completed graduate programs and several 

hundred Bachelor-level students have been 

trained in various aspects of composite 

materials and structures. A significant number 

of graduates are now active in industry and 

government. 

Various Center faculty are internationally 

recognized for their leadership in composite 

materials and composite structures through 

books, lectures, workshops, professional society 

activities, and research papers. 

FOUNDING MEMBERS OF THE CENTER 

Aerospace and Ocean Engineering Science and Industrial Engineering 

Engineering Mechanics and Operations Research 

Raphael T. Haftka Hal F. Brinson Joel A. Nachlas 

William L. Hallauer, Jr. John C. Duke, Jr. Materials Engineering Eric R. Johnson Daniel Frederick David W. Dwight 

Chemical Engineering Robert A. Heller D. P. H. Hasseiman 

Donald G. Baird Mmund G. Henneke, I1 Charles R. Houska 

Carl T. Herakovich Chemistry M. R. Louthan, Jr. 

Michael W. Hyer James E. McGrath Robert M. Jones Mathematics 

Thomas C. Ward Manohar P. Kamat Werner E. Kohler 

James P. Wightman Alfred C. Loos Mechanical Engineering 

Civil Engineering Don H. Morris Norman S. Eiss, Jr. 

Raymond H. Plaut Daniel Post Charles E. Knight 

Electrical Engineering J. N. Reddy S. W. Zewari 

loannis M. Besieris Kenneth 1. Reifsnider 

Richard 0. Claus C. W. Smith 

Wayne W. Stinchcomb 

Inquiries should be directed to: 

Center for Composite Materials & Structures 

College of Engineering 

Virginia Tech 

Blacksburg, VA 24061 

Phone: (703) 961 -4969