NASA Contractor Report 177958

NASA-CR-177958 19850026930

CHEMOVISCOSITY MODELING FOR THERMOSETTING RESINS - II

T. H. Hou

PRC Kentron, Inc.

Aerospace Technologies Division Hampton, Virginia 23666

Contract NASl-18000

August 1985

NI\SI\ Natronal AeronautiCS and Space Adrrun,stratlon

Langley Research Center Hampton, VirglnlB 23665

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https://ntrs.nasa.gov/search.jsp?R=19850026930 2020-02-22T20:22:25+00:00Z

I 2 Government Acceulon No 1 Report No NASA CR-177958

ChemoV1scoS1ty Model1ng for Thermosett1ng ReS1ns - II

5 Report Oate August 1985

6 Performing Orglnlzltlon Code

7 Author(s) 8 Performing OrglnlZltlon Report No

r..-_T_._H_._H_O_u ______________________ """""I 10 Work Unit No 9 Performlnll Organization Name and Address

PRC Kentron, Inc. Aerospace Technolog1es D1v1s1on 3221 N. Armlstead Avenue

11 Contract or Grant No

NASl-18000 t-_H_a_m_p_t_o_n_,_VA __ 2_3_6_6_6 __________________ "'"""i 13 Type of Repon and Period Covered

Contractor Report 12 Sponsorlnll Agency Name and Address

Natlonal Aeronautlcs and Space Adm1n1strat1on Washlngton. DC 20546

15 Supplementary Notes Langley Technical Monltor: R. M. Baucom F1nal Report

16 Abstract

14 Sponsoring Agency Code 505-33-33-01

A new analyt1cal model for simulat1ng chemov1scosity of thermosett1ng reS1n has been formulated. The model 1S developed by mod1fying the well-established W1lliams-Landel-Ferry (WLF) theory 1n polymer rheology for thermoplastlc materlals. By assumlng a llnear relationship between the glass transltlon temperature Tg{t) and the degree of cure a{t) of the resin system under cure, the WLF theory can be mod1f1ed to account for the factor of reactlon t1me. Temperature-dependent functlons of the mod1fled WLF theory constants C1{T) and C2 (T) were determlned from the lsothermal cure data of Lee, Loos, and Sprlnger for the Hercules 3501-6 reSln system. Theoretlcal predlct10ns of the model for the resin under dynam1c heat1ng cure cycles were shown to compare favorably w1th the exper1mental data reported by Carpenter. Th1S work represents progress toward establishlng a chemov1scos1ty model Wh1Ch 1S capable of not only descr1bing V1SCOSlty profiles accurately under varlOUS cure cycles, but also correlat1ng V1SCOSlty data to the changes of phys1cal propert1es assoc1at~d w1th the structural transformations of the thermosett1ng reSln systems dur1ng cure.

17 Key Words (Suggested by Author(sl) Thermoset, Chemoviscos1ty, Autoclave, WLF Theory, Cure

18 Distribution Statement UnclaSSlf1ed - Unlimlted

19 Security Olulf (of thIS report) UnClaSSlfled

20 Security CIIUlf (of thIS Plge) UnClaSS1fled

Subject Category 24

21 No of PIgIS

37 22 Price

A03

N-305 For sale by the National Technical Information SerVice, Springfield, Virginia 22161

Chemoviscosity Modeling for Thermosetting Resins - II

ABSTRACT

FOREWORD

I. INTRODUCTION

LIST OF SYMBOLS

II. THEORY

Ill. EXPERIMENTAL DATA

Degree of Cure a(t,T)

ChemoVlscosity n(t,T)

TABLE OF CONTENTS

. . . . . . . . . . . . . . . .

· . . . . . . . . . . . . . . · . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . · . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

IV. MODEL PREDICTIONS AND DISCUSSION . . . . . . . . . Isothermal Case

Dynamlc Heatlng Case

V. CONCLUSIONS

REFERENCES

. . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . APPENDIX - GENERALIZED NEWTON'S METHOD ••

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

LIST OF COMPOSITES PROCESSING LABORATORY RESEARCH REPORTS •

PAGE

iii

v

1

3

4

7

7

9

11

11

13

18

19

20

21

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ABSTRACT

A new analytical model for simulating chemoviscosity of thermosetting

reS1n has been formulated. The model is developed by modifying the

we1l-establ1shed W1ll1ams-Landel-Ferry (WLF) theory in polymer rheology for

thermoplastic mater1als. By assum1ng a linear relat10nship between the glass

transition temperature Tg(t) and the degree of cure a(t) of the resin system

under cure, the WLF theory can be modified to account for the factor of

react10n time. Temperature-dependent functions of the modified WLF theory

constants C1(T) and C2(T) were determ1ned from the lsothermal cure data of

Lee, Loos, and Spr1nger for the Hercules 3501-6 reS1n system. Theoretical

pred1ctions of the model for the resin under dynam1c heating cure cycles were

shown to compare favorably with the experimental data reported by Carpenter.

Th1S work represents progress toward establ1shing a chemoviscosity model which

lS capable of not only descr1b1ng v1scosity prof1les accurately under various

cure cycles, but also correlat1ng V1SCOS1ty data to the changes of physical

propert1es assoc1ated w1th the structural transformations of the thermosetting

reS1n systems during cure.

iii

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FOREWORD

This work, performed at NASA - Langley Research Center (LaRC), was

supported by the LaRC Polymeric Materials Branch (PMB) under Contract

NASl-l8000. ThlS is a progress report on an ongoing research project toward

the chemoviscosity modeling for thermosetting resins, and ;s monltored by

R. M. Baucom (PMB). Technlcal guidance provlded by Dr. N. T. Wakelyn (PMB)

and W. T. Freeman (PMB) with regard to the uses of LaRC IAF computing

faCllltles and helpful discussions with Or. J. A. Hlnkley (PMB) during the

course of thlS study are gratefully acknowledged.

v

CHEMOVISCOSITY MODELING FOR THERMOSETTING RESINS - II

I. INTRODUCTION

There are two dlfferent basic approaches in chemoviscosity modeling of

thermosettlng reSln. One approach, tYPlcally represented by the work of

Roller [lJ, lS to emplrically formulate a rate equation which relates the

change of chemovlscosity with reactlon tlme. For a reSln system cured under a

dynamlc heatlng cure cycle (as commonly encountered in autoclave processlng

for composlte materlals), such an approach usually Ylelds a model Wh1Ch 1S

1nadequate in descrlblng accurately the nonlinearity of chemoviscoslty as a

functlon of reactlon time. As TaJlma and Crozler [2J pointed out, such a

modellng approach renders ltself to the llmitatlon of batch-spec1fic. The

model parameters cannot be readily related to the chemical and rheologlcal

propertles of the reactlng system as well.

The second approach is based upon a modlflcation to the well-establlshed

V1SCoslty-temperature relationship eXlstlng ln polymer rheology for

thermoplastlc materlals. The parameters in such an equation can be expressed

in terms of polymerlzation k1netlcs, and the chemoviscosity profiles as a

function of reactlon tlme can then be modeled for thermosetting reSln systems.

The appllcablllty of the modlfied Wllllams-Landel-Ferry (WLF) theory [3]

ln chemovlscoslty modellng for thermosettlng reSln has been studled by TaJima

and Crozler [2,4J, Aplcella et al. [5J, and Hou [6J among others. It has been

extenslvely documented ln the llterature that temperature-dependent ViscoSlty

of thermoplastic material can be accurately descrlbed by the WLF equatlons

w1th1n 1000 K above its glass trans1tion temperature (Tg). For a

thermosetting resin system under cure, 1t is reasonable to assume that Tg(t)

of the material is always within 1000 K lower than the cure temperature. The

WLF equat10n should then be appl1cable to every instant state of the resin

system under cur1ng. The central theme in mod1fying the WLF theory to

descr1be the chemov1~cosity of thermosettlng reS1n 1S to take 1nto account the

react10n t1me factor.

In an earl1er paper [6J, two assumptions were proposed, namely, that the

rate constant of reaction, kT' at any temperature T, 1S (i) diffusion

controlled and 1S, therefore, inversely proportional to the viscosity

nT(t) of the reactlve med1um, and (11) d1rectly proport1onal to the rate

of change of glass transition temperature Tg(t). The modified WLF equat10n

becomes a f1rst order ord1nary nonl1near differential equation. Numer1cal

solutions have also been shown to compare favorably w1th the experimental

results for several thermosett1ng systems under 1sothermal and dynamic heat1ng

cure condit10ns. It has been concluded that the flexibil1ty demonstrated by

the mod1f1ed WLF theory [6J can be conveniently explo1ted to establ1sh an

analyt1cal model with h1gh degree of accuracy for the chemoviscosity of any

thermosett1ng resin system under var10US cure cycles. The phys1cal

slgn1f1cances of the mater1al parameters selected for the model were, however,

d1ff1cult to extract for the particular resin system under investigat10n.

As a next step toward the 1mprovement of the chemoviscosity model1ng for

a thermosetting resin system, a new mod1ficat1on of the WLF theory 1S proposed

1n th1S report. Comparisons between the theoretical predictions and

experimental data for chemov1scos1ty of a reS1n system (Hercules 3501-6) under

both lsothermal and dynam1c heating cure cond1t1ons will be d1scussed.

2

li st of Symbols

a,b,c,d

B

DSC

R

T

t

t.t

WLF

nT(t)

a(t)

Materlal parameters (min-I) speclfied in Table 1

Constants used in Eq. (5)

Materlal parameter specified ln Table 1

Temperature-dependent WLF constants defined by Eqs. (7) and

( 8)

Differentlal Scanning Calorimeter

Actlvation energles (J/mol) speclfied in Table 1

Materlal constants (min-I) deflned ln Eqs. (3) and (4)

Universal gas constant (=1.987 Cal/gm-mole/oK)

Temperature (OK)

Cure temperature (OK), Tc = Tg{m)

Glass transition temperature of the reSln system

under cure (OK)

Glass transition temperature of the resins system at

completion of cure (OK)

Glass transltion temperature of the uncured resin g

Cure time (minutes)

Tlme (mlnutes) deflned in Eq. (6)

Tlme required for completion of cure (minutes)

Time interval (minutes) used ln solving Eq. (9)

Wllliams-Landel-Ferry

Chemoviscosity at temperature T (poises)

Degree of cure of the thermosetting resin durlng cure

as determlned by DSC thermal analysis

3

II. THEORY

The W1lliam-Landel-Ferry (WLF) theory [3] is given by

(1)

C1 and C2 are two mater1al constants, and nT represents v1scosity at

temperature T of the glven thermoplastic mater1al Wh1Ch possesses a glass

trans1tion temperature Tg• The normal use of the WLF equat10n for

thermoplastic materials requ1res that Tg be constant wh1le the temperature T

1S var1ed for the specif1c polymer under study. However, during cure of

thermosett1ng resins, the monomers are initially polymerized and crosslinks

are formed later. Th1S is a system where Tg{t) 1S changing and the curing

temperature T 1S held constant (In an isothermal cure case, for example). The

glass trans1tion temperature Tg r1ses cont1nuously and may eventually

approach the curing temperature. Over the entire curing cycle, the material

structure actually undergoes cont1nuous phase transformations from a low

molecular weight llQU1d to a h1gh molecular we1ght polymer1c melt, and

eventually transforms to a crossl1nked network. It 1S reasonable to assume

that Tg{t) of the mater1al 1S always lower than the cure temperature T, and

that (T-Tg{t)) 1S always w1th1n lOOoK. The WLF theory {Eq. (I)) should then

4

be applicable to all of the different polymeric structure phases during cure.

Before Eq. (l) can be applied to describe the chemoviscosity of the curing

resin, however, modlfications need to be made in order that reaction time, t,

of the thermosetting resin system lS properly taken into account. This can be

accompllshed as follows:

A simple assumption that Tg{t) lS a linear functlon of the degree of

cure a{t) of the thermosetting reSln can be made, WhlCh gives:

Tg{t) = TO + (T _TO) a(t) 9 c g

(2)

where T~ = Tg(O) lS the glass transitlon temperature of the unreacted reSln

system, Tc lS the cure temperature ln OK, and t is the reaction time in

minutes. Equation (2) should satisfy the boundary conditions, namely,

T = TO a = 0 at t = 0 g g'

and

where tf lS the tlme required for completlon of cure. The degree of cure

a(t) for the resin system can be determlned by means of thermal analysis. It

is assumed that the degree of cure at tlme t lS equal to the fractlon of heat

released as measured by a OSC up to time t for the thermosetting materlal

under cure. The total heat of reaction can be determined for the experlments

uSlng dynamlc temperature scanning. The degree of cure a(t) can then be

5

determ1ned for dlfferent isothermal cure cond1tions [7,8J. The a's thus

determ1ned are funct10ns of curlng temperature and tlme.

Equations (1) and (2) const1tute a mod1fled WLF theory for simulat1ng

chemoviscosity of thermosett1ng reS1n. Among the f1ve mater1al parameters, C1

and C2 can be determined as a funct10n of temperature T by fitting w1th

lsothermal cure n(a) data, nT = 10 13 poises lS given by Gordon and 9

Slmpson [9J for many polymer1c mater1als at T = Tg, and T~ can be determlned

by DSC thermal analys1s. In an 1sothermal cure case, Tc of Eq. (2) 1S equal

to cure temperature. In the dynam1c heating case, however, Tc lS d1ff1cult

to spec1fy exactly and 1S the only adJustable var1able 1n the present mod1fied

WLF theory.

6

III. EXPERIMENTAL DATA

For the purpose of evaluating model pred1ctions of this modified WLF

theory, experimental data on Hercules 3501-6 epoxy reS1n reported in the

llterature by Lee, Laos, and Springer [8] and Carpenter [10] were selected.

These data will be summarlzed br1efly.

Degree of Cure a{t,T)

Lee et al. [8] performed thermal analyses on the epoxy resin system using

a Different1al Scanning Calorimeter (DSC). The degree of cure a and the rate

of degree of cure da/dt were determined from the results of the isothermal

scanning experiments. Eight d1fferent temperatures were selected, and the

results are reproduced 1n Figure 1. It is noted from the f1gure that both

h1gher values of the degree of cure and rate of degree of cure can be obtained

at higher cure temperatures. The rate of degree of cure 1S a decreasing

funct10n of cure t1me t, and eventually levels off at a low rate value (< 0.1)

when a h1gh degree of cure 1S reached. The follow1ng equations were found to

describe these temperature-dependent data accurately:

for a < 0.3 (3)

da df = K3 (l-a) for a > 0.3 (4)

where

7

KI = Al exp (-l1E I/RT)

K2 = A2 exp (-l1E 2/RT)

K3 = A3 exp (-l1E 3/RT)

Values of constants in Eqs. (3) and (4) are shown in the Table below.

Comparisons between the measured values of da/dt and the values calculated by

Eqs. (3) and (4) are also shown 1n F1gure 1.

Table 1. The values of the constants of Eqs. (3) and (4) for Hercules 3501-6 Resin System [8J

B = 0.47

Al = 2.101 X 10 9 m1n- 1

A2 = -2.014 X 10 9 min- I

A3 = 1.960 X 10 5 m1n- 1

l1E 1 = 8.07 X 104 J/mol

l1E 2 = 7.78 X 104 J/mol

l1E 3 = 5.66 X 104 J/mol

Eqs. (3) and (4) can be integrated prov1ded that the temperature is kept

constant. The following relat10nships between a and t are obtained:

a K2 t = K; Ln (1 + K7 a) - b Ln (I-a) - c Ln (1- f) (5)

t = 1 Ln (I-a) + t -K; 0.7 c (6)

8

where

a = K2 (B-l)/d 2

b = - (K 1+K 2)/d

c = (K 1+K 2B)/d

d = (K 1+K 2) [K 1B2+(K 1-K 2) B-K 1 ]

and tc is the t1me given by Equat10n (5) for a = 0.3.

ChemOV1scoS1ty n(t,T)

ChemOV1scoS1ty of the reS1n under an lsothermal cure cond1t1on were

measured by Lee et. al. [8] on a Rheometr1cs parallel d1SC and plate

mechan1cal spectrometer Model 605. The rad1us of the disc was 25 mm and the

gap between the d1SC and the plate was 0.5 mm. A frequency of 1.6 Hz was

employed. For a glven cure temperature, the n(t) measured can be related to

a(t) obtained from DSC thermal analys1s. The results are plotted 1n F1gure 2

for three d1fferent lsothermal cure cases. It lS again noted that at a h1gher

cure temperature, h1gher values of the degree of cure can be reached. For a

glven a, the decrease 1n V1SCOS1ty 1S attributed to the temperature effects.

ChemOV1scos1t1es of the 3501-6 epoxy resin cured under dynam1c heat1ng

cond1t1ons were reported by Carpenter [10]. Carpenter measured chemov1sco­

slt1es at d1fferent rate of 1ncrease 1n temperatures and reported the measured

values as a funct10n of cure t1me. The experimental data shown here are for

reS1ns cured at constant heat1ng rates of 10 K/min (f1gure 5), 2.17 and 5°K/min

(F1gure 6) and a cure cycle (F1gure 8) slm1lar to the one typ1cally found 1n

autoclave processes for compos1te materials.

9

The procedure used for model evaluations will be as follows:

1. Model parameters of Eqs. (1) and (2) will be determlned first by the

experimental data of Lee et al. [8] under isothermal cure conditlons.

Temperature-dependent materlal constants C1(T) and C2 (T) can thus be

determined.

2. The chemoviscoslty model n(t,T) establlshed by isothermal cure data under

procedure 1 wlll then be made to follow varlOUS dynamic heating cure

cycles T(t). The viscosity values thus calculated will be compared with

the experimental data reported by Carpenter [10].

10

IV. MODEL PREDICTIONS AND DISCUSSION

Isothermal case

Gordon and Simpson [9] pointed out that glass-forming substances

generally have the same shear viscosity of nT = 10 13 poises at their g

Tg, and this has also been conf1rmed for polymer systems. By specifying TO

T8 = 3000 K (27°C) 1n Eq. (2), the model (l.e., Eqs. (l) and (2)) can then be

f1tted to the experimental data n(a) as shown in Figure 2 provided that proper

values of material constants C1 and C2 are selected. C1 and C2 determined for

different temperatures are tabulated below, and the model predictions are

drawn as solid llnes 1n the figure.

Table 2. Values of material constants C1 and C2 1n the modi fled WLF Theory for Hercules 3501-6 reS1n system as determined by the isothermal cure data.

Tc(OK) C1 C2(OK)

375 21.1 53.0

400 17.1 33.6

425 18.5 46.0

The model is capable of descr1bing the nonl1near relationship between

V1SCOS1ty, n, and the degree of cure, a, as shown in Figure 2, especially for

11

the case of h1gher cure temperature. Th1S 1S cons1dered a slgn1f1cant

improvement over the emp1r1cal 11near model used by Lee, Loos, and Spr1nger

[8]. An arrhen1us type of plot 1S arb1trar11y chosen for C1 and C2 as shown

in F1gure 3. The data 1S rather scattered. Due to the (unfortunate)

11m1tat1on on size of the exper1mental data and the w1de range 1n temperatures

covered by the dynam1c heat1ng cure exper1ments (as w11l be d1scussed later),

a 11near least squares flt was chosen. The straight lines are represented,

respectively, by:

log C1 = 186.02 (liT) + 0.8084 (7)

and

log C2 = 212.16 (liT) + 1.106 (8)

It 1S noted that 1n the analysis descrlbed above, the glass trans1tlon

temperatures Tg(t) for the varYlng molecular structures of the reSln cured

at dlfferent tempreatures are chosen as reference temperatures. C1 and C2 are

therefore treated as "unlVersal constants" ln the present context. Val ues of

C1 and C2 reported ln Table 2 are close to the values of 17.44 and 51.6,

respect1vely, once reported by Will1ams et ale [3] as the unlversal constants

for all polymer1c materials sytems. Eqs. (7) and (8) wlll still be used,

however, to account for temperature-dependences of C1 and C2 1n chemovlscoslty

slmulatl0n under dynam1c heat1ng cure cond1tlons.

The theoretical assumptlons as descrlbed above, WhlCh Yleld close values

for the WLF constants C1 and C2 , respectlvely, among three d1fferent

12

1sothermal cur1ng temperatures, are also supported by the parallellsm among

experimental data observed 1n Figure 2 for a < 0.3. Data of higher values of

both n and a are d1fficult to be measured, and could be considered less

accurate.

Dynam1c Heat1ng Case

In the case of dynamic heating cure conditions, 1ntegrations of Eqs. (3)

and (4) are very difficult to perform. If one assumes that within any t1me

1nterval lI,t = t2 - t l' the temperature Tc 1S uniform, and 1 s equal to

(Tl+T 2)/2, where Tl and T 2 are temperatures at t 1 and t2 respectively as

def1 ned by the cure cycle, Eqs. (3) and (4) become:

lI,t = t 2 - tl

(9)

where

a K2 f (a,Tc ) = K2 Ln (1 ~l a) - b Ln{1 - a) - c Ln (1 - f), for a < 0.3

and

f (a, Tc) = 1 Ln (1 - a) + t - K3 0.7 c for a > 0.3

13

The parameters a, b, c, and tc are the same as defined before in Eqs. (S)

and (6). The value of the increased degree of cure a2 1n Eq. (9) can be

calculated by the Generalized Newton's Method. Deta1ls of the solution

schemes are summarized 1n the Appendix.

Values of a(t} determined by the scheme descr1bed above depend heavily on

the t1me 1nterval ~t chosen. Theoret1cally more accurate a(t} can be

determined numerically when a smaller ~t 1S used. On the other hand, a

smaller ~t could increase dramatically the numer1cal round-off errors. A

series of ~t values were selected, and a(t} was calculated from Eq. (9) for a

cure cycle w1th a constant heat1ng rate of SOK/min. The results are plotted

1n F1gure 4. It can be seen that numer1cal round-off errors become dom1nant

when ~t < O.OS m1n. It is also noted that numerical values of a(t} calculated

for ~t = O.S and 1.0 minute, respect1vely, are almost 1ndistingu;shable.

Consequently, ~t = O.S m1nute was chosen for all calculations discussed below.

Chemov1scosities of the Hercules 3S01-6 epoxy resin system under dynamic

heating cure cond1t10ns were reported by Carpenter [10J. Data for these

constant rates of heating experiments are reproduced in F1gures Sand 6. The

heat1ng rates are 1.0, 2.17, and S oK/min respect1vely. All cure cycles

started from 3000 K (27°C). Temperature-dependent C1 (T) and C2(T) as def1ned

by Eqs. (7) and (8) are followed 1n the slmulation. Values of the rest of the

parameters used 1n the model are tabulated below:

14

Table 3. Values of model parameters used 1n simulat1ng chemov1scosity under rate of heating cure condit1ons

Heat1ng rate nT (poises) TO (0 K) T c (0 K) (0 Klm1 n) g g

1 10 13 300 415

2.17 10 13 300 430

5 10 13 300 450

The model predictions are shown as solid curves in F1gures 5 and 6. It is

noted that the theoret1cal calculations compared favorably with the

exper1mental data for all three cases.

Theoret1cally, Tc 1S equal to Tg(~) at T + ~ or a + 1 (see Eq. (2)).

Under the dynam1c heat1ng cure cond1tions, however, Tc 1S d1ff1cult to

spec1fy. Values of Tc (In Table 3) 1n the above calculations were

selected arb1trar1ly such that model pred1ct1ons are 1n reasonably good

agreement w1th the exper1mental data. Nevertheless, h1gher values of Tc

(Table 3) resulting from the slmulat10n of higher rates of heating

experiments, are 1n agreement w1th phys1cal observat1ons for thermosett1ng

res1ns.

The calculated degree of cure a{t) for all three cases 1S plotted 1n

F1gure 7. These calculated a(t) are based on the exper1mental data for the

resln under 1sothermal cure condlt1ons [8J, and are lndependent of the

arbltrarlly selected values of Tc d1scussed above. Values of da/dt go

15

through maXlma for all three cases. The arrow marks shown in the figure

denote the times when chemoviscositles approach inflnity during cure. These

arrow marks are located approxlmately at a(t) = 0.75 ~ 0.05, and are near the

lnflection pOlnts of the curves as well. Physical slgnificances of these

observatlons are unclear at the present time, and further research in the

future lS required.

Chemoviscosity was also measured by Carpenter [10] for the 3501-6 resin

system under a typlcal cure cycle used in autoclave processlng for composite

materials. The experimental data is reproduced ln Figure 8. Values of model

parameters used are the same as those lncluded in Table 3 and Eqs. (7) and

(8), except that Tc = 375°K. The theoretical predictlons, shown as solid

curves, are seen in reasonably good agreement with the experimental data. The

model, however, falls to describe the chemoviscosity "shoot-up" near the end

of the cure cycle. The reasons are unclear at the present time. It could be

due to the inadequate definitlons of C1(T) and C2 (T) by Eqs. (7) and (8); or

due to different reaction mechan1sms appeared 1n the h1gh cur1ng temperature

reg1me. Calculated values of a(t) are plotted in Flgure 9. The arrow mark

shown denotes the time when chemov1scosity "shoot-up" occurs. Features of the

a(t) curve discussed above for isothermal cure cases are again noticeable in

th1S f1gure.

Temperature ranges covered by Carpenter [10] in dynam1c heating cure

experiments, as shown by dotted lines 1n Figure 3, far exceed the ranges

covered by Lee et ale [8] in isothermal cure experiments (shown by solid lines

in the figure). Accurate deflnitions of the crucial temperature-dependences

of C1(T) and C2(T) needed for the model thus suffer from serious data

16

extrapolatlon errors. The results of the present lnvestigations, although

encouraglng, can only demonstrate the feaslbillty of the approach of modlfying

the WLF theory in chemoviscosity modeling for thermosetting resin. Detailed

studies such as the preclse deflnitlons of Tg{a) (Eq. (2», and the

functlons of C1{T) and C2 {T) over the full temperature range by experlmental

measurements for the reSln system under lnvestigation have to be pursued In

the future.

17

v. CONCLUSIONS

A new analytlcal model, based upon modiflcatlons of the WLF theory, has

been formulated. The model assumes that the glass transltlon temperature

Tg{t) of the reSln system under cure is llnearly related to the degree of

cure a{t) determined by DSC thermal analysis. Theoretlcal predlctlons of the

chemovlscoslty compare favorably wlth the experlmental data reported ln the

llterature for both lsothermal and dynamic heatlng cure condltions.

Conslderlng that data are available only ln the relatlvely narrow temperature

range used in lsothermal curing experlments by Lee, Loos, and Sprlnger [8J,

the agreement between theoretlcal predlctions and experlmental data reported

by Carpenter [10J for dynamlc heating cure cycles are partlcularly

encouraglng. Due to the limltations In Slze of the data avallable, the

successful analysls reported here has establlshed the feaslblllty of the

proposed approa~h WhlCh slmulates chemovlscoslty for thermosettlng reSln by

modlfYlng the wldely used WLF theory In polymer rheology.

18

REFERENCES

1. Roller, M. B.: "Characterization of the Time-Temperature-Viscosity

Behav10r of Cur1ng B-Staged Epoxy Resin," Polym. Engr. Sci.,.!,?, 406,

1975.

2. Taj1ma, Y. A.; and Croz1er, 0.: "Chemorheology of an Amine Cured Epoxy

Res1n," SPE ANTEC Conference Proceedings, 274, 1984.

3. Williams, M. L.; Landel, R. F.; and Ferry, J.D.: "The Temperature

Dependence of Relaxat10n Mechan1sms in Amorphous Polymers and Other

Glass-Forming Liquids," J. Amer. Chern. Soc., 72, 3701, 1955.

4. TaJima, Y. A.; and Crozier, 0.: "Thermokinetic Modeling of an Epoxy Resin

1. Chemov1scos1ty," Polym. Engr. Sci., Q, 186, 1983.

5. Apicella, A.; N1cola1s, L.; and Halp1n, J. C.: "The Role of the

Process1ng Chemo-Rheology on the Ag1ng Behav10r of H1gh Performance Epoxy

Mat ri ces," 28th Nat i ona 1 SAMPE Sympos i um, 518-527, 1983.

6. Hou, T. H.: "Chemov1scos1ty Model1ng for Thermosetting Res1ns - I,"

NASA-Langley Research Center, CR-172443, November, 1984.

7. Sourour, S.; and Kamel, M. R.: "01 fferenti al Scanning Calorimetry of

Epoxy Cure: Isothermal Cure K1netics," Thermochimica Acta, .!.i, 41-59,

1976.

8. Lee, W. I.; Loos, A. C.; and Springer, G. S.: "Heat of React1on, Degree

of Cure, and V1SCOS1ty of Hercules 3501-6 Resin," J. Compo. Matl., 16,

510-520, 1982.

9. Gordon, M.; and Slmpson, W.: "The Rate of Cure of Network Polymers and

the Superposition Pr1nc1ple," Polymer, ~, 383-391, 1961.

10. Carpenter, J. F.: "Process1ng Science for AS/3501-6 Carbon/Epoxy

Compos1tes," Technl cal Report NOOOI9-81-C-0184, McDonnell Ai rcraft Co.,

1983. 19

•

Appendix - General1zed Newton's Method 1n Solving a2 from Eq. (9)

Eq. (9) can be rearranged to become:

(a)

and

(b)

where g'(a2) = dg/da2, and f'(a2,Tc ) = df/da2' The Generalized Newton's

Method sets up the follow1ng recursion formula to solve for a2 1n Eq. (a):

(c)

prov1ded that g'(a2)/tO; where w 15 called the over-relaxat1on factor. A good

cho1ce for w can be determ1ned, 1n general, only by experimentation. A cho1ce

of w d1fferent from un1ty often can 1ncrease the convergence rate of the

rout1ne apprec1ably. In this study, W = 0.1 was used for all calculations.

Iterat10n5 are continued unt1l lan+1 - anl~ 10- 6 •

20

li st of F; gures

F1gure 1. Rate of degree of cure vs. degree of cure reported by Lee, Loos, and Springer [8J for Hercules 3501-6 reS1n system under 1sothermal cure cycles. Solid lines were calculated using Eqs. (3) and (4).

F1gure 2. Chemoviscosity as a function of degree of cure for Hercules 3501-6 resin system under isothermal cure cycles. Symbols represent experimental data reported by Lee, Laos, and Springer [8J. Solid lines were calculated by the model, Eqs. (1) and (2).

Figure 3. Temperature-dependences of the WLF constants C1 and C2 determ1ned by the isothermal cure data of Lee et ale [8J for the Hercules 3501-6 resin system.

Figure 4. Simulated degree of cure data for the Hercules 3501-6 resin system cured under constant rate of heating condition, 5°K/min. Various time intervals fit were used 1n solving Eq. (9).

Figure 5. Chemoviscosity of the Hercules 3501-6 resin system cured under constant rate of heating condition of 10 K/min. Circles denote experimental data by Carpenter [9J. Solid curve denotes the model predictions of Eqs. (1) and (2).

F1gure 6. Chemov1scos1ty of the Hercules 3501-6 resin system cured under constant rates of heating condit1ons of 2.17 and 5°K/min, respectively. Circles denote the experimental data by Carpenter [9J. Solid curves denote the model pred1ctions of Eqs. (1) and (2) •

F1gure 7. Simulated degree of cure for the Hercules 3501-6 reS1n system cured under constant rate of heat1ng conditions 1ndicated.

Figure 8. Chemov1scos1ty of the Hercules 3501-6 resin system cured under the cure cycle shown. Circles denote the experimental data by Carpenter [9J. SOlld curve was calculated by the model, Eqs. (1) and (2).

Figure 9. Simulated degree of cure data for the Hercules 3501-6 reS1n system cured under the cure cycle included.

21

Composite Processing laboratory Research Reports

Polymerlc Materlals Branch, Langley Research Center Natlonal Aeronautics and Space Admlnlstratlon

CPl1. "A Theoretical Study of Resln Flows for Thermosetting Materials

Durlng Prepreg Processing," NASA CR-172442, July, 1984, by T. H. Hou

(Kentron).

CPl2. "Chemovlscoslty Modeling for Thermosettlng Reslns - I," NASA

CR-172443, November, 1984, by T. H. Hou (Kentron).

CPl3. "Correlation of Dynamic Dlelectrlc Measurements with V1SCOSity 1n

Polymerlc Res1n Systems," 30th National SAMPE Sympos1um and

Exh1b1t1on, Anaheim, CA., March, 1985, pp 638-648, by D. Kranbuehl,

S. Delos, E. Y1, J. Mayer (W&M), T. H. Hou (Kentron), and W. P.

Wl nfree (LaRC).

CPl4. "On the Appllcations of WLF Theory to Thermosett1ng Resins," SPE

ANTEC, Washlngton, D.C., Aprll, 1985, pp 1253-1255, by T. H. Hou

(Kentron).

CPl5. "Chemov1scos1ty Model1ng for Thermosetting Reslns - II," NASA

CR-177958, August, 1985, by T. H. Hou (PRC Kentron, Inc.)

22

-'C ...... tS 'C .. W 0: ::> u lI-0 W W 0: (!) W 0 lI-0

0.1 400K o..5~450K

I o Data - Calculated

o oh:am.1

425K 465K

430K 470K

440K 475K

o O~LJ~~~~ OL--....L-~----='O.'-:'4---0:;::"'.6 0 0.2 0.4 0.6 DEGREE OF CURE.a

Flgure 1. Rate of degree of cure vs. degree of cure reported by Lee, Loos, and Springer [8J for Hercules 3,01-6 reSln system under lsothermal cure cycles. SOlld llnes were calculaterl using Eqs. (3) and (4).

23

uP

104 VI Q) VI ·0 c.. :;: c:: Q) u

c

103

006 Hercules 3501-6 resin (Lee, Loos & Springer)

- Model prediction

a, degree of cure

Flgure 2. Chemovlscoslty as a functlon of degree of cure for Hercules 3501-6 reSln system under lsothermal cure cycles. Symbols represent experlmental data reported by Lee, Loos, and Sprlnger [8J. Solid llnes were calculated by the model, Eqs. (1) and (2).

24

500 450 400 350 300 1oor------.-I-------.I-----------.-�------------~I-.

r -~~ -

~ ~ --~ --- -O ---50 r _--

~ I- _ - C2 --I.-- 0

-

-

-

20 -

--------0 __ -- -----

_---~1 ,.--

-

10~ _____ ~1 _____ ~1 _____ ~1 _____ ~1 ____ ~1 ______ ~1 ____ ~

lO l2 l4 l6 l8 10 12

1fT, oK x 103

Flgure 3. Temperature-dependences of the WLF constants C1 and C2 determlned by the lsothermal cure data of Lee et al. [8J for the Hercules 3501-6 reSln system.

25

14

a(t)

10°r---~----~----~----~--~----~----~ I T 1 I I I

10 -1 t-

D 0

10-5 I I I I

0 4 8 12 16 t, min

o o o

at, min 0.001 0.005 0.010

[). 0. 050 ~ 0.100 D 0. 500 0

0

<)

I

1000 5.000

10. 000

I

-

-

-

-

20 24 28

Flgure 4. Slmulated degr~e of cure data for the Hercules 3501-6 reSln system cured under constant rate of heatlng condltlon, 5°K/mln. Varlous tlme lntervals fit were used in solvlng Eq. (9).

26

8

7

6

~ 5 I 0 ->< VI Q) 4 VI

'0 Co

= C Q) u 3 c:

2

1

o

Hercu les 3501-6 0

Heating rate: 10K/min 0

0 Experimental data

- Model prediction 0

0

0 0

0

0

0

20 40 60 80 t, min

Flgure 5. Chemovlscoslty of the Hercules 3501-6 reSln system cured under constant rate of heatlng condltion of l°K/mln. Clrcles denote experlmental data by Carpenter [10]. Solid curve denotes the model predictions of Eqs. (1) and (2).

27

160

~ I 0 -)( VI C1) VI ·0 c..

:;::; c C1) u . c

8

Hercules 3501-6

7 0 Experimental data

- Model predictions

6 Heating rate: 2. 170K/min SOK/min

0 0

S

4

3

2

1

o 20 40 60 80 90 0 20 40 t, min t, min

F1gure 6. Chemov1scos1ty of the Hercules 3501-6 resin system cured under constant rates of heating connlt10ns of 2.17 and 5°K/m1n, respectlVely. C1rcles denote the exper1mental data by Carpenter [10]. S011d curves denote the model pred1ct10ns of Eqs. (1) and (2).

28

60

L 00 .-------J'{llr-------::-o-<;>-----~ Hercules 3501-6 0

.75

a(t) .50

.25

o

o 0 o

to .0 o 0

50K/min 0 o o

o o

o o

o o

o

o o

50

o

o o 2. 17oK/mln

o o

o

6 6

6

6666 6

6

6

6

66 LOOK/min 6

100 t, min

Flgure 7. Slmulated degree of cure for the Hercules 3501-6 reSln system cured under constant rate of heatlng condltlons indlcated.

29

..

150

y 0 ...-4

>< VI Q) VI

'0 c..

:;:; c: Q) u

c

T OK ,

8

Hercu les 3501-6 7 0

0 Experimental data

6 0 - Model prediction

5 o

4

3 o

2

1

0

700 600 500 400 300 200

0 20 40 60 80 100 120 140 t, min

Flgure 8. Chemovlscoslty of the Hercules 3501-6 reSln system cured under the cure cycle shown. Clrcles denote the experlmental data by Carpenter [10]. SOlld curve was calculated hy the model. Eqs. (1) and (2).

30

· 75 I-

a(t) .50 I-

.25 I-

o 'CIIDQ"()

Hercules 3501-6

° (")0

I

-

-

-

I

700~-------------~1-------------'-1--------/-"~-' /

600 ~ / -/.L:J2.7SoK/min

/ '----~--------

/// Cure cycle 400 I- _f'

/.LJ2. 7SoK/min 300 ~

500 >- -

--

200L-__________ ~1L_ __________ ~1 ____________ ~

o 50 100 t. min

Flgure q. Slmulated degree of cure data for the Hercules 3501-6 resin system cured under the cure cycle included.

31

150

End of Document