Creep Behavior of Amine-Cured Epoxy Networks - ACS Publications

13 Creep Behavior of Amine-Cured Epoxy Networks: Effect of Stoichiometry 1

S. L. KIM , J. A. MANSON, and S. C. MISRA

Downloaded by UNIV OF PITTSBURGH on May 4, 2015 | http://pubs.acs.org Publication Date: December 3, 1979 | doi: 10.1021/bk-1979-0114.ch013

Materials Research Center, Coxe Laboratory #32, Bethlehem, PA 18015

Creep studies are not only important in the theory of viscoelasticity but also of great practical importance in any engineering application in which the polymer must sustain loads for long times. With a thermoset resin, creep can vary a great deal, depending on the degree of crosslinking, the perfection, and the morphology of the network structure. While many studies of the effects of crosslinking on behavior have been made, most have been restricted in scope and many have used relatively uncharacterized materials. For this reason, a systematic examination was conducted to elucidate the effects of crosslink density and its distribution on a wide range of properties including basic viscoelastic response, stress-strain and impact behavior, and fatigue crack propagation. The same base prepolymer type and curing agent were used throughout, and a given crosslink density was obtained by changing the stoichiometry and by changing the molecular weight of the prepolymer at constant stoichiometry. Related Studies In some epoxy systems ÇL,_2) , i t has been shown that, as expected, creep and s t r e s s r e l a x a t i o n depend on the s t o i c h i o m e t r y and degree of cure. The time-temperature s u p e r p o s i t i o n p r i n c i p l e (3) has been a p p l i e d s u c c e s s f u l l y to creep and r e l a x a t i o n behavior i n some epoxies (4-6)as w e l l as to other mechanical p r o p e r t i e s (5-7). More r e c e n t l y , K i t o h and Suzuki (8) showed that the W i l l i a m s - L a n d e l - F e r r y (WLF) equation (3) was a p p l i c a b l e to networks (with equivalence of f u n c t i o n a l groups) based on n i n e t e e n carbon a l i p h a t i c segments between c r o s s l i n k s but not to t i g h t e r networks such as those based on bisphenol-A-type prepolymers cured with m-phenylene diamine. R e l a x a t i o n i n the l a t t e r r e s i n followed an Arrhenius-type equation. C u r r e n t address: F i b e r and Polymer Product Research Goodyear T i r e & Rubber Co., Akron, Ohio 44316.

Division,

0-8412-0525-6/79/47-114-183$05.00/0 © 1979 American Chemical Society

In Epoxy Resin Chemistry; Bauer, R.; ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

184

EPOXY RESIN CHEMISTRY

In t h i s study, the i m p e r f e c t i o n of the networks was v a r i e d by v a r y i n g the s t o i c h i o m e t r y o f an Epon 828-methylene d i a n i l i n e system. Related s t u d i e s of morphology, other p r o p e r t i e s , and creep as a f u n c t i o n of molecular weight and d i s t r i b u t i o n of the prepolymer are described elsewhere (9-13).


Experimental The m a t e r i a l s used were Epon 828 epoxy r e s i n and methylene d i a n i l i n e (Tonox), both from the S h e l l Chemical Co. The r e s i n and c u r i n g agent were melted together, mixed, degassed, and cast between g l a s s p l a t e s . The cure c y c l e was as f o l l o w s : 45 min at 60°C, 30 min at 80°C, and 2.5 hr at 150°C; then slow c o o l i n g to room temperature. The amine to epoxy r a t i o (A/E) was v a r i e d from 0.7 to 2.0 ( i n terms o f e q u i v a l e n t s ) . Compositions are given i n Table I . Table I .

Composition of Epoxy Specimens

Sample

Amine/Epoxy Ratio

A-7 A-8 A-10 A-12 A--20

0.7 0.8 1.0 1.2 2.0

f o r Creep Study M

a

c

721 457 303 420 1381

d

M i s c a l c u l a t e d based on the rubbery moduli from dynamic mechanical measurements (10), and used as a r e l a t i v e and e f f e c t i v e M^ throughout t h i s study. Creep was measured u s i n g a Gehman t o r s i o n a l t e s t e r (14). [In f a c t , the shear compliance J ( t ) was measured e x p l i c i t l y ; the data are presented as moduli by taking E ( t ) - 3 / J ( t ) . ] Master curves were obtained i n the usual manner ( 3 ) . R e s u l t s and D i s c u s s i o n T y p i c a l creep-modulus behavior i s shown i n F i g u r e 1; v i s c o e l a s t i c parameters deduced from the master curve are given i n Table I I , and d i s c u s s e d below. G l a s s - t r a n s i t i o n temperature ( T ) . The modulus-temperature curves tor a l l trie specimens were composed by p l o t t i n g the 10-sec modulus a t each temperature, as shown i n F i g u r e 2. The g l a s s t r a n s i t i o n temperatures (corresponding to a modulus of 0.2 GPa) are given i n Table I . C a l c u l a t i o n s show that Tg i s i n v e r s e l y p r o p o r t i o n a l to the average molecular weight between c r o s s l i n k s g



KIM ET AL.

Amine-Cured Epoxy Networks

185

X

Log t,

seconds

Figure 1. Typical curves of creep modulus vs. log t at different temperatures (epoxy specimen A-10). Master curve at 169°C shown as solid curve.


186



Temperature.

Figure 2.

°C

Dependence of creep modulus (10-sec) on temperature for series of epoxy resins: (Ο) Α·7; (A) A-8; (Π) A-IO; (·) A-12; (A) A-20


13.

187


κίΜ ET AL.

(M ); as proposed c

by N i e l s o n (15): ( D

M

where T = 350°K, the e x t r a p o l a t e d value o f T f o r M ^ «, d k = 2.9 χ 1 0 . Results are i n e x c e l l e n t agreement with those from other t e s t s (Table II) such as dynamic mechanical s p e c t r o scopy and d i f f e r e n t i a l scanning c a l o r i m e t r y (10). g

c

a

n

4

TABLE I I . No.

Τ

a

r° g '


C

A-7 A-8 A-10 A-12 A-20

132 162 198 185 119

τ

Creep C h a r a c t e r i s t i c s o f Epoxy Resins b

°C 9

g

T

C

101 127 164 146 93

c

g '°

c

Ε ,MPa r'

log x

30 33 50 44 10

-9.7 -2.5 4.0 0.3 -13.0

114 140 168 151 100

d η

c

-0.36 -0.38 -0.42 -0.38 -0.63

B y dynamic mechanical spectroscopy a t 110 Hz ( 9 ) . B y d i f f e r e n t i a l scanning c a l o r i m e t r y (9). ^From the temperature dependence o f creep modulus ( F i g u r e 2) From slope of t r a n s i t i o n r e g i o n i n creep curves; η = d[ln 3 / J ( t ) ] / d(£n t) b

c

S h i f t f a c t o r ( a ) . Experimental s h i f t f a c t o r s were d e t e r mined by composing smooth master curves from the data a t v a r i o u s temperatures, taking Tg as the r e f e r e n c e temperature i n each case. Temperature c o r r e c t i o n s were made o n l y f o r the data above Tg; the c o r r e c t i o n s were found to be small (^10%). A smooth composite curve was obtained by p l o t t i n g l o g a ^ v s . (T-T ) f o r a l l the specimens, as shown i n F i g u r e 3. The composite curve f o l l o w i n g the p r e d i c t i o n o f WLF equation (3) o n l y i n the l i m i t e d range between ( T - 10°C) to ( T + 20°C). While one does not expect the WLF p r e d i c t i o n s to hold below Tg, the p r e d i c t i o n s a r e u s u a l l y good to temperatures as h i g h as (T +100°C). In f a c t , the data could be represented over the e n t i r e temperature range by p l o t t i n g the s h i f t f a c t o r s a g a i n s t 1/T ( i . e . , i n an A r r h e n i u s - p l o t f a s h i o n ) , as shown i n F i g u r e 4. When the data were p l o t t e d a g a i n s t (1/T - 1 / T ) , two s t r a i g h t l i n e s f o r a l l the specimens were obtained as shown i n F i g u r e 5, c o n s i s t e n t w i t h an Arrhenius-type r e l a t i o n s h i p : T

g

g

g

-E l o g a„

2.303 RT

(2)

where R i s the gas constant, Τ i s the a b s o l u t e temperature, and E i s the apparent a c t i v a t i o n energy. From the slopes o f the s t r a i g h t l i n e s , the a c t i v a t i o n energies were found to be 950 k j / mole (227 kcal/mole) above T and 356 kj/mole (85 kcal/mole) a

g



188


Figure 3. Composite curve of experimental shift factors as a function of (Ύ — T ) (symbols are as in Figure 2). The curve predicted by the WLF equation (3) is indicated by the solid line. g



13. κίΜ ET AL.

189


Figure 4. Plots of experimental shift factors for epoxy specimens vs. inverse tem perature (symbols are as in Figure 2)

-30

-20

-10

0

10

(l/T-l/Tg) xlO , 2

(OK)"

20

30

1

Figure 5. Composite plot of experimental shift factors for all epoxy specimens as a function of (1/T — 1/T ) (symbols are as in Figure 2) g


190


below Tg. As shown i n Table I I I , these v a l u e s are i n e x c e l l e n t agreement with the values observed by K i t o h and Suzuki (8) i n a bisphenol-A-type epoxy cured w i t h phenylene diamine: 962 kJ/mole (230 kcal/mole) above T and 381 kJ/mole (91 kcal/mole) below T . Values a l s o agree reasonably w e l l w i t h the apparent a c t i v a t i o n energies that were determined i n our p a r a l l e l study i n which M was v a r i e d by changing prepolymer molecular weight (13) . In com p a r i s o n , apparent energies of a c t i v a t i o n [at Tg, assuming a v i s c o s i t y of 1 0 ^ N.s.nT" (16, p. ) ] , are c a l c u l a t e d to range between 900 kJ/mole (215 kcal/mole) f o r T = 100°C and 1259 kJ/ mole (301 kcal/mole) f o r T = 168°C. Further, the WLF equation p r e d i c t s a continuous decrease i n E as Τ i n c r e a s e s above T . g

g

c

2

2

g

g


a

g

Table I I I . Comparison of Apparent Energies of A c t i v a t i o n f o r R e l a x a t i o n i n Epoxies Ε^, kJ/mole

Range of Τ Τ Τ

a

>
) T . Interestingly, other authors (5,14) have reported v a l i d i t y of the WLF treatment f o r l e s s - d e n s e l y - c r o s s l i n k e d epoxy systems. A l s o , we f i n d that a p l o t of data by Murayama e t . a l . (]7) shows that an Arrhenius-type treatment of dynamic mechanical s h i f t f a c t o r s i s p r e f e r r e d f o r oriented poly(ethylene terephthalate). a

g

g

g

C h a r a c t e r i s t i c creep time. A l l master curves were e m p i r i c a l l y s h i f t e d to the most convenient common temperature, 150°C, as shown i n F i g u r e 6. For convenience, only t r a n s i t i o n regions are shown. An i n c r e a s e i n c r o s s l i n k d e n s i t y (nearing to equiva l e n t s t o i c h i o m e t r y ) s h i f t s the curves to longer times as expected. The c h r a c t e r i s t i c creep time, T , was taken as the time to creep to a modulus v a l u e of l o g E ( t ) = ( l o g E + l o g Er)/2, where Eg and E are the g l a s s y and rubbery modulus, r e s p e c t i v e l y . [While T i s analogous to a r e t a r d a t i o n time, the l a t t e r d e s i g n a t i o n i s not used, because our T i s determined from p l o t s of 3 / J ( t ) , not J / ( t ) , and i s hence not n u m e r i c a l l y equal to the corresponding c

g

r

c

c



KIM ET AL.


191

log t, second Figure 6. Creep-modulus master curves for all epoxy specimens as a function of log tat a reference temperature of 150° C


192

EPOXY

RESIN

CHEMISTRY

r e t a r d a t i o n time. x i s , s t r i c t l y speaking, a r e l a x a t i o n time.] C h a r a c t e r i s t i c creep time i s shown as a f u n c t i o n of the A/E r a t i o and a l s o as a f u n c t i o n of 1/M ( F i g u r e 7 ) . The good s t r a i g h t l i n e r e l a t i o n s h i p between l o g T and 1/M again shows c o n s i s t e n c y i n the behavior of these specimens: c

C

c

T Ί

log

c —

C

=

7.7 —

χ

10

3

(3) C

Coo

where l o g T i s found by e x t r a p o l a t i o n to equal -18, which i s the c h a r a c t e r i s t i c creep time at about 150°C f o r a network having an i n f i n i t e value of M . Since both x and Tg are i n v e r s e l y r e l a t e d to M and the a c t i v a t i o n energies of the s h i f t f a c t o r s are independent of M , a common segmental motion must be i n v o l v e d i n the creep behavior o f a l l these s p e c i m e n s v a r y i n g the c r o s s l i n k d e n s i t y merely s h i f t s the curves along the time a x i s . C o o


c

c

Q

c

D i s t r i b u t i o n of r e l a x a t i o n times, Η ( τ ) . In t h i s d i s c u s s i o n , u s i n g p l o t s of 3 / J ( t ) , we s h a l l d i s c u s s the d i s t r i b u t i o n of c h a r a c t e r i s t i c response times i n terms of r e l a x a t i o n times. The r e l a x a t i o n - t i m e spectrum, Η(τ), can be determined as a f i r s t approximation (18) by the f o l l o w i n g r e l a t i o n s h i p : Η(τ)

=

-

.

_

d[E(t)] / d (log t ) L (4) E ( t )

f

d

nos

L

E

(t>il

J _

M U d ( l o g t) P l o t s of Η(τ) vs l o g t f o r a l l specimens are given i n F i g u r e 8. When data are r e p l o t t e d at the T of each specimen, the d i s t r i b u t i o n of r e l a x a t i o n times f o r the 5 d i f f e r e n t specimens n e a r l y c o i n c i d e with each other u n t i l the rubbery r e g i o n , where some s c a t t e r i s seen ( F i g u r e 9 ) . This confirms that the same mechan ism f o r r e l a x a t i o n i s i n v o l v e d f o r a l l 5 specimens. The slope of Η(τ) ( i . e . , d [ l o g H ( i ) ] / d ( l o g t ) ] a t the g l a s s t r a n s i t i o n r e g i o n (the right-hand p a r t of F i g u r e 9) i s about -0.42, which compares f a i r l y w e l l with the value of -0.33 obtained by K i t o h and Suzuki (8) f o r a bisphenol-A epoxy r e s i n cured with m-phenylene diamine, c o n s i d e r i n g the d i f f e r e n c e s i n the epoxy system and i n the t e s t i n g modes. C l e a r l y the data f o r our p a r a l l e l study (13) i n which M i s v a r i e d by changing prepolymer molecular weight are i n d i s t i n g u i s h a b l e from those of t h i s study (note t r i a n g l e s i n F i g u r e 9 ) . g

c

Conclusions In c o n c l u s i o n , the temperature dependence of s h i f t f a c t o r s f o r the networks s t u d i e d here do not f o l l o w the WLF equation, but r a t h e r an Arrhenius-type r e l a t i o n s h i p . The apparent a c t i v a t i o n energies are independent of s t o i c h i o m e t r i c v a r i a t i o n [as they are when M i s v a r i e d by changing prepolymer molecular weight (13)] . c



13.

193


KIM ET AL.

1.0 1.5

2.0

10

A/E

20

30

l/Mc XIO^

Figure 7. Characteristic creep time for all epoxy specimens as a function of stoichiometry and M : (%) epoxy-rich; (O) amine-rich; (Δ) different series with M varied by changing prepolymer molecular weight (IS) c

c

log t.

second

Figure 8. Distribution of relaxation times for all epoxy specimens as a function of log t (symbols as in Figure 7)




-5

0 log

t,

5

10

second

Figure 9.


13.

κ ί Μ ET AL.


195

Nearing to s t o i c h i o m e t r y (decrease i n M ) merely s h i f t s the creep curves to a longer time s c a l e . Although the c r o s s l i n k den s i t y was lowered ( i n c r e a s e i n M ) more than f o u r - f o l d by v a r y i n g the A/Ε r a t i o , apparently the aromatic r i n g s i n the bisphenol-A and diamine group must be c o n t r o l l i n g ( s t i f f e n i n g ) the segmental motions i n the networks. Thus, c o n s i d e r i n g the r e s u l t s of t h i s work and those o f K i t o h and Suzuki (8) and Murayama e t . a l , (17), we might expect an Arrhenius-type r e l a t i o n s h i p i n the temperature dependence o f s h i f t f a c t o r s f o r r e l a t i v e l y r i g i d networks. c

c


Acknowledgement The authors g r a t e f u l l y acknowledge f i n a n c i a l support from the A i r Force M a t e r i a l s Laboratory through Contract No. F3361575-C-5167.

Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9.

Kosuga, N. and Tsugawa, S. Kobunshi Ronbunshu, 1975, 32, 252. Delmonte, J . Plastics Technol., 1958, 4, 913. Ferry, J . D. "Viscoelastic Properties of Polymers," 2nd Ed., John Wiley & Sons, Inc., New York, NY, 1970, Chap. 11. Theocaris, P. Rheol. Acta, 1962, 2, 92. Kaelble, D. H., J . Appl. Polym. Sci., 1965, 9, 1213. Shito, N. and Sato, M. J . Polym. Sci.-C., 1967, 16, 1069. McCrum, N. G. and Pogany, G. A. J . Macromol. Sci.-Phys., 1970, B4(1), 109. Kitoh, M. and Suzuki, K. Kobunshi Ronbunshu, 1976, 33, 19. Manson, J . Α.; Sperling, L. H. and Kim, S. L. "Influence of Crosslinking on the Mechanical Properties of High-T Polymers," Technical Report AFML-TR-77-109, July 1977. Kim, S. L. and Manson, J . A. "Dynamic Mechanical Behavior of Amine-Cured Epoxy," 19th Canadian High Polymer Forum, Ottawa, Canada, August 1977, to be published. Kim, S. L . ; Skibo, M.; Manson, J . Α.; Hertzberg, R. W. and Janiszewski, J . Polym. Eng.-Sci., 1977. Misra, S. C. Ph.D. Thesis, Lehigh University, 1978. Misra, S. C.; Manson, J . A. and Sperling, L . H. This publication, 1979. ASTM D-1043, American Society of Testing Materials, Philadelphia, PA. Nielson, L . E. J . Macromol. Sci.-Rev. Macromol. Chem., 1969, C3(1), 69. Nielsen, L . E. "Mechanical Properties of Polymers," Van Nostrand Reinhold, New York, 1962. Murayama, T.; Dumbleton, J . H. and Williams, M. L. J . Polym. Sci., 1968, part A-2, 6, 787. Tobolsky, Α. V. "Properties and Structure of Polymers," John Wiley & Sons, Inc., New York, NY, 1960, Chap. 3. g

10. 11. 12. 13. 14. 15. 16. 17. 18.

RECEIVED May 21, 1979.


Creep Behavior of Amine-Cured Epoxy Networks - ACS Publications

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