Structure and Fracture of Highly Cross-linked Networks - American

10 Structure and Fracture of Highly Cross-linked Networks J. D. LEMAY, B. J. SWETLIN, and F. N. KELLEY

Downloaded by UNIV LAVAL on July 11, 2016 | http://pubs.acs.org Publication Date: February 16, 1984 | doi: 10.1021/bk-1984-0243.ch010

Institute of Polymer Science, The University of Akron, Akron, OH 44325

Amine cured epoxy networks were investigated t o determine the e f f e c t o f c r o s s - l i n k density on fracture toughness and other properties. Two series of networks were studied: the first having M (the average molecular weight o f a network chain) c o n t r o l l e d by the amine/epoxy reactant ratio; the second c o n t r o l l e d by the average molecular weight of several homologous d i f u n c t i o n a l epoxy prepolymers. Expected t o p o l o g i c a l v a r i a t i o n s o f the first s e r i e s were confirmed by T differences and soluble f r a c t i o n s . The second s e r i e s was presumed to display only M v a r i a t i o n s . Cross-link d e n s i t i e s were characterized above T by equilibrium modulus measurements employing rubber elasticity theory. The r e s u l t s i n d i c a t e that t h i s method y i e l d s s u r p r i s i n g l y reasonable values. Glassy fracture energies of both network s e r i e s showed an M dependence when d u c t i l e y i e l d i n g o f the crack tip preceded crack propagation. Studies on the second s e r i e s suggest that glassy f r a c t u r e energies are c l o s e l y proportional t o M ½. C

g

c

g

C

c

Epoxy thermosets are t y p i c a l densely c r o s s - l i n k e d polymer m a t e r i a l s . They are used i n a wide v a r i e t y of p r a c t i c a l a p p l i c a t i o n s and thus have been s t u d i e d e x t e n s i v e l y . However, t h e q u a n t i t a t i v e dependence of p h y s i c a l p r o p e r t i e s , such as s t r e n g t h , s t i f f n e s s , and f r a c t u r e toughness, on network m i c r o s t r u c t u r e are l a r g e l y undetermined. This can be a t t r i b u t e d , i n p a r t , t o the l a c k o f adequate techniques f o r c h a r a c t e r i z i n g densely c r o s s l i n k e d network s t r u c t u r e . S e v e r a l m i c r o s t r u c t u r e v a r i a b l e s t h a t have been s t u d i e d w i t h some success are ( l ) c r o s s - l i n k d e n s i t y , ( 2 ) s p e c i f i c volume or b u l k d e n s i t y , and (3) nodular o r inhomogeneous morphology. 0097-6156/84/0243-0165S06.00/0 © 1984 American Chemical Society Labana and Dickie; Characterization of Highly Cross-linked Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

166

HIGHLY CROSS-LINKED POLYMERS

T h i s paper presents c h a r a c t e r i z a t i o n studies performed on amine cured epoxy r e s i n s . P a r t i c u l a r emphasis i s placed on the c h a r a c t e r i z a t i o n o f t h e c r o s s - l i n k d e n s i t y , and on i t s i n f l u e n c e on p h y s i c a l p r o p e r t i e s , e s p e c i a l l y the f r a c t u r e toughness.


Cross-link

Density

The e f f e c t i v e c r o s s - l i n k density o r t h e average molecular weight of a network chain, MQ, o f t y p i c a l epoxy thermosetting systems may be modified by a number o f techniques. Most commonly i t has been changed by varying t h e epoxy r e s i n / c u r i n g agent f u n c t i o n a l group r a t i o (l-_8). Unfortunately, t h i s approach introduces v a r i a t i o n s i n the network topology as w e l l as i n c r o s s - l i n k i n g . E l u c i d a t i n g the d i r e c t e f f e c t o f MQ on p h y s i c a l p r o p e r t i e s i s thus complicated by the presence o f other m i c r o s t r u c t u r e v a r i a t i o n s such as dangling chain ends and a s o l u b l e f r a c t i o n . Processing conditions a l s o have been used t o modify t h e c r o s s - l i n k d e n s i t y . They have a d i r e c t e f f e c t on the r e a c t i o n k i n e t i c s which i n t u r n determine the network s t r u c t u r e . F o r example, s e v e r a l s t u d i e s (4,6,9-13) have employed d i f f e r e n t cure and postcure schedules t o modify Mc- As with t h e use o f reactant stoichiometry, t h e use o f processing conditions t o c o n t r o l Mc may y i e l d other changes i n network microstructure . Seemingly, a p r e f e r r e d route t o the c o n t r o l o f MQ would i n v o l v e the use o f d i f f e r e n t molecular weight epoxy r e s i n s cured by simple e n d - l i n k i n g chemistry with a s t o i c h i o m e t r i c q u a n t i t y o f curing agent. Such a s e r i e s o f networks would presumably d i s p l a y v a r i a t i o n s i n only t h e c r o s s - l i n k d e n s i t y . Since the MQ should be d i r e c t l y r e l a t e d t o the r e s i n f u n c t i o n a l i t y and molecular weight, the accuracy o f Mc c h a r a c t e r i z a t i o n techniques could be s t u d i e d , Obviously, the r o l e that Mc might p l a y i n determining p h y s i c a l p r o p e r t i e s would be f a c i l i t a t e d by t h e study o f such networks. Some s t r u c t u r e - p r o p e r t y s t u d i e s using such a s e r i e s o f networks have been reported by Manson e t a l . (β) who u t i l i z e d networks prepared from S h e l l Epon r e s i n s and methylene d i a n i l i n e (MDA). They reported considerable d i f f i c u l t y processing these networks. The c h a r a c t e r i z a t i o n o f Mc f o r epoxy networks has been attempted by t h e o r e t i c a l estimations from the reactant r a t i o and assumed r e a c t i o n k i n e t i c s , estimations by an e m p i r i c a l dependence of M on Tg, s w e l l i n g , and t h e a p p l i c a t i o n o f simple rubber e l a s t i c i t y theory t o experimental e q u i l i b r i u m modulus measurements. The l a t t e r technique appears t o be t h e most promising. B e l l ( 1 4 ) has derived expressions r e l a t i n g Mc t o the amine/epoxy r a t i o using the assumption that the r e a c t i o n proceeds by polymerization o f the epoxy w i t h primary amine followed by c r o s s - l i n k i n g r e a c t i o n s o f epoxy with secondary amine. N i e l s o n (li?) has r e l a t e d the degree of c r o s s - l i n k i n g t o the corresponding s h i f t i n Tg through the e m p i r i c a l equation, Mc = 39,000 ( T g - T g ) , where Tg i s the g l a s s t r a n s i t i o n temperature o f t h e c r o s s - l i n k e d polymer and T g i s that of the uncross-linked polymer. I t i s emphasized t h a t t h i s equation c

Q

Q

Labana and Dickie; Characterization of Highly Cross-linked Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

10.

167

Structure and Fracture of Networks

LEMAY ET AL.

was obtained by averaging data f o r a v a r i e t y o f polymer networks and does not account f o r copolymer e f f e c t s ; i t y i e l d s , at b e s t , rough estimates o f MQ. Reports of s w e l l i n g measurements on epoxy networks are few ( 1 4 , 1 6 ) and the r e s u l t s are g e n e r a l l y i n poor agreement w i t h other techniques. S i g n i f i c a n t d e v i a t i o n s i n MQ may be i n t r o d u c e d by the choice o f the s w e l l i n g equation ( 1 7 1 9 ) , t h e s t a t e o f e q u i l i b r i u m , and the chosen value o f the i n t e r a c t i o n parameter. The most commonly used c h a r a c t e r i z a t i o n method i s the measurement o f the rubbery e q u i l i b r i u m modulus, g e n e r a l l y at temperatures T>Tg+40°C. A number o f i n v e s t i g a t o r s ( 3 , 3 , 2 0 - 2 4 ) have obtained reasonable Mc values by a p p l y i n g the simple rubber e l a s t i c i t y theory t o such modulus measurements. The theory r e l a t e s the e q u i l i b r i u m shear modulus G t o Mc through: Downloaded by UNIV LAVAL on July 11, 2016 | http://pubs.acs.org Publication Date: February 16, 1984 | doi: 10.1021/bk-1984-0243.ch010

e

Mc = pRT/G

(1)

e

where R i s the gas constant, ρ the d e n s i t y a t absolute temperature Τ and φ the f r o n t f a c t o r , the r a t i o o f the mean square end-to-end d i s t a n c e o f a network c h a i n t o t h a t o f a randomly c o i l e d c h a i n . Since t e s t i n g i s done w e l l i n t o the rubbery s t a t e , constant volume deformation assumptions should apply, t h e r e f o r e G can be s u b s t i t u t e d w i t h E /3 where E i s the e q u i l i b r i u m t e n s i l e modulus. A systematic study i n v o l v i n g a s e r i e s of networks o f known MQ's would be extremely u s e f u l f o r determining the a p p l i c a b i l i t y and range o f a p p l i c a t i o n o f t h i s approach t o measuring the c r o s s - l i n k d e n s i t y . Furthermore, such a study would be o f i n t e r e s t from a t h e o r e t i c a l standpoint f o r t e s t i n g some o f the assumptions used i n the simple rubber e l a s t i c i t y theory. e

e

e

Fracture I n t e r e s t i n the f r a c t u r e behavior o f densely c r o s s - l i n k e d polymers i s evidenced b y a l a r g e body o f o r i g i n a l r e s e a r c h ( 2 , 4 , 6 , 7 , 1 0 , 2 5 - 2 9 ) and s e v e r a l reviews o f the s u b j e c t (30,31). Both the energy balance concepts o f G r i f f i t h ( 3 2 ) and l i n e a r e l a s t i c f r a c t u r e mechanics (LEFM) have been employed. I t i s not the o b j e c t i v e o f t h i s work t o extend these concepts, which can be found i n a number o f t e x t s (33,34), but r a t h e r t o d e r i v e from them a m a t e r i a l p r o p e r t y which can be r e l a t e d t o network v a r i a t i o n s . The energy balance approach y i e l d s a c r i t i c a l p o t e n t i a l energy r e l e a s e r a t e , G , which i s r e l a t e d t o the f r a c t u r e energy per u n i t area o f new s u r f a c e γ by the r e l a t i o n G = 2 Y . I n LEFM the f r a c t u r e toughness Κ d e s c r i b e s the s t r e s s f i e l d i n the r e g i o n o f the crack t i p which a t the moment of crack propagation reaches a c r i t i c a l v a l u e , K . For mode I f r a c t u r e (opening mode), the two f r a c t u r e mechanics approaches are r e l a t e d by the expressions ( 2 7 ) : c

C

c

2

K

I C

(2)

= EGj

plane s t r e s s

C

(3) 2

= E G modulus / ( l - v ) and νplane where Ε i s Young's i s P o isstsr oa ni ns r a t i o . T P

1


168


Structure-Property

Relationships

The g e n e r a l i z e d theory o f f r a c t u r e mechanics o f Andrews (35) p r e d i c t s that the cohesive f r a c t u r e energy per u n i t surface area J i s g i v e n by the energy r e q u i r e d t o break the bonds c r o s s i n g the f r a c t u r e plane, J , m u l t i p l i e d by a l o s s f u n c t i o n , θ. 0

(4)

J = J e ( c , T, c ) o

o

Any f a c t o r c o n t r i b u t i n g t o the energy d i s s i p a t i n g c h a r a c t e r i s t i c s of the m a t e r i a l , e.g., as i t may be a f f e c t e d by the a p p l i e d s t r a i n ε , temperature T, and crack v e l o c i t y c, i s r e f l e c t e d i n Θ. I n the absence o f energy l o s s , i . e . , i n a p e r f e c t l y e l a s t i c m a t e r i a l , θ reduces t o u n i t y and J approaches J . Thus, J i s a r a t e and temperature independent lower l i m i t , o r t h r e s h o l d f r a c t u r e energy. Lake and Thomas (36) suggested t h a t c r o s s - l i n k i n g a f f e c t s J , thus r e l a t i n g the m a t e r i a l property J t o a s t r u c t u r a l parameter, MQ. T h e i r d e r i v a t i o n suggests t h a t as network chain lengths are i n c r e a s e d two c o n d i t i o n s e x i s t : ( l ) the number o f bonds capable of supporting s t r e s s are i n c r e a s e d ; and ( 2 ) the number o f chains c r o s s i n g the crack plane are decreased. The net e f f e c t i s a dependence of J on MQ g i v e n by:


0

Q

0

0

Q

Jo = kMc

(5)

where k i s a p r o p o r t i o n a l i t y constant i n c o r p o r a t i n g the polymer d e n s i t y , f l e x i b i l i t y , mass and l e n g t h o f the repeat u n i t and d i s s o c i a t i o n energy o f the weakest chain bond. Thus, under e l a s t i c c o n d i t i o n s , the cohesive f r a c t u r e energy i s p r o p o r t i o n a l t o Mc^. Under normal t e s t i n g c o n d i t i o n s o f rubbery and g l a s s y polymers, however, l o s s c o n d i t i o n s are presumed t o p r e v a i l . The magnitude and s t r u c t u r e dependencies o f Θ, i f any, may mask the simple Mc dependence expressed by Equation 5. Experimental The epoxy networks s t u d i e d were prepared from S h e l l Chemical Co. Epon 828, 1001F, 1002F and 1004F epoxy r e s i n s and the c u r i n g agents 4> 4 -methylene d i a n i l i n e (MDA) and 4,4'-diaminodiphenyl sulfone (DDS). Chemical s t r u c t u r e s and r e l e v a n t p h y s i c a l p r o p e r t i e s are g i v e n i n Table I . The epoxy r e s i n prepolymer equivalent weights were c h a r a c t e r i z e d v i a endgroup t i t r a t i o n per ASTM method D1652. Using the assumption that the r e s i n molecules were d i f u n c t i o n a l , the prepolymer number average molecular weight MQ was estimated as twice the e q u i v a l e n t weight. The amine c u r i n g agents were assumed t o be t e t r a f u n c t i o n a l . Two network systems were prepared: ( l ) Epon 828/MDA n e t works, i n which the r e a c t a n t r a t i o s were v a r i e d ; and (2) s t o i c h i o m e t r i c Epon resin/DDS networks i n c o r p o r a t i n g v a r i a t i o n s i n the prepolymer The more l a t e n t amine DDS was used f o r c u r i n g the 1



Table I .

Experimental M a t e r i a l s

Continued on next page



Shell

Shell

Shell

Shell

Fisher

Aldrich

Epon 1001F

Epon 1002F

Epon 1004F

MDA

DDS

Supplier

Epon 828

Material

248.3

198.3

1720

1342

996

380

g/mole

—

—

4.85

3.52

2.31

0.14

η

175-178

90-93

^100

^ 80

^ 70

< RT

°C

MP

Table I . Experimental M a t e r i a l s ( c o n t i n u e d )


1.38

1.16

1.2

1.2

1.2

1.2

3

23°C g/cm

p

10.

LEMAY ET AL.

171


h i g h e r molecular weight r e s i n s because o f t h e harsher p r o c e s s i n g c o n d i t i o n s r e q u i r e d ; g e l times were long enough (1/2 t o 1 hour) t o permit s u f f i c i e n t mixing and degassing o p e r a t i o n s . The r e a c t a n t r a t i o was designated by an A/E v a l u e , t h e mole r a t i o o f amine hydrogens t o epoxy groups, g i v e n by: A

Ê "

, 4

W A - E E W

W M r

l

b

;

A

where W i s t h e mass and M A i s t h e molecular weight o f t h e amine, and Wj; i s t h e mass and EEW i s t h e e q u i v a l e n t weight o f t h e Epon r e s i n . F o r system 1 three networks o f A/E=0.65> 1.0, and 1.6 were prepared. F o r system 2 a l l networks were prepared w i t h A/E=1.0. System 1 networks were prepared by mixing molten MDA w i t h degassed Epon 828 a t 60°C. The r e s u l t i n g mixture was again degassed and poured i n t o a 60°C preheated Teflon-coated s t e e l mold. The mixture was cured i n a c i r c u l a t i n g a i r oven a c c o r d i n g to t h e schedule i n Table I I . T h i s procedure y i e l d e d v o i d - f r e e sheets from which t e s t samples were machined. A f i n a l postcure o f 5 h r s . a t 180°C under vacuum was a p p l i e d t o a l l samples p r i o r t o testing. System 2 networks were prepared by h e a t i n g and degassing t h e Epon r e s i n s f o r 1-2 h r s . between a minimum temperature o f 50°C and a maximum temperature o f 100°C above t h e i r r e s p e c t i v e m e l t i n g temperatures. Powdered DDS was added and s t i r r e d i n t o t h e r e s i n . The mixture was degassed and poured i n t o preheated molds: T e f l o n coated aluminum molds were used t o prepare sheets, and Dow Corning


A

Table I I .

Time a t Temperature Sequence

Network System Epon 828/MDA

Cure Postcure

Epon 828/DDS

Cure Postcure

Epon 1001F/DDS

Cure Postcure

Epon 1002F/DDS

Epon 1004F/DDS

Cure Schedules

Cure

0.75 h r g 60°C + 0.5 h r g 80°C + 2.5 h r g 150°C 5 h r g 180°C 2 h r g 150°C + 3 h r g 200°C 10 h r g 200°C 2 h r g 150°C + 3 h r g 200°C 10 h r g 200°C 0.5 h r g 180°C + 4.5 h r g 200°C

Postcure

10 h r g 200°C

Cure

5 h r g 200°C

Postcure

10 h r g 200°C


172


S i l a s t i c J s i l i c o n e molds were used t o prepare t e n s i l e microdumbbells. The networks were cured under N according t o the schedules i n Table I I . A f t e r t e s t samples were machined, a f i n a l postcure o f 10 h r s . a t 200°C under vacuum was a p p l i e d . This postcure was found t o give a network w i t h a s t a b l e maximum Tg. 2

S t r u c t u r e C h a r a c t e r i z a t i o n . The m o l e c u l a r weight between c r o s s l i n k s Mc was c h a r a c t e r i z e d by measurement o f t h e e q u i l i b r i u m rubbery t e n s i l e modulus E which was obtained from the slope o f neare q u i l i b r i u m s t r e s s - s t r a i n curves ( F i g u r e s 1 and 2 ) . The two q u a n t i t i e s a r e r e l a t e d i n simple rubber e l a s t i c i t y theory by Equation 1. F o r t h i s work t h e f r o n t f a c t o r φ and d e n s i t y ρ were assumed t o be u n i t y . Dumbbell specimens w i t h a gauge l e n g t h o f 4 cm and a c r o s s - s e c t i o n a l area o f 0.14 cm were t e s t e d a t T=Tg + 40°C i n an I n s t r o n U n i v e r s a l t e s t e r equipped w i t h an e n v i r o n mental chamber continuously purged w i t h N 2 . The specimen was extended i n s m a l l load-increments o f 50 t o 150g a t a r a t e o f 0.05 cm/min t o a t o t a l s t r a i n o f 42), and depends on MQ i n v e r y n e a r l y the same way as the t h r e s h o l d f r a c t u r e energy p r e d i c t i o n s o f Lake and Thomas (36). Obviously t h e g l a s s y s t a t e i s not r e p r e s e n t a t i v e o f t h r e s h o l d c o n d i t i o n s . Why we observe the MQ dependence o f f r a c t u r e energy might be explained by a thermoplastic c r a z i n g theory introduced by Gent (43). He suggests t h a t the d i l a t i o n a l s t r e s s f i e l d induced i n the r e g i o n o f the crack may reach s u f f i c i e n t magnitude t o e f f e c t i v e l y increase the f r a c t i o n a l f r e e volume o f a minute s t r i p o f m a t e r i a l j u s t ahead o f the crack. I f s u f f i c i e n t f r e e volume i s introduced, the e f f e c t i v e Tg may be lowered t o below t h e t e s t i n g temperature making the m a t e r i a l ahead of the crack t i p " r u b b e r - l i k e " . I n thermoplastics t h i s r e g i o n may c a v i t a t e or craze, however i n a densely c r o s s - l i n k e d network c r a z i n g might be i n h i b i t e d by the network s t r u c t u r e . (References on c r a z i n g i n epoxy networks are few and s p e c u l a t i v e (44)·) I f a crack propagated at a s u b c r i t i c a l r a t e through t h i s r u b b e r - l i k e region, then the f r a c t u r e energy could conceivably show s i m i l a r c h a r a c t e r i s t i c s t o rubbery f r a c t u r e , i . e . , a dependence on t h e cross-link density. Conclusions 1.

2.

3.

Based on s t u d i e s o f an homologous, endlinked, epoxy/amine network s e r i e s , t h e simple theory o f rubber e l a s t i c i t y has proved e f f e c t i v e f o r determining reasonable c r o s s - l i n k d e n s i t i e s from e q u i l i b r i u m modulus measurements i n the rubbery s t a t e . C o n t r o l l i n g epoxy network c r o s s - l i n k d e n s i t y by v a r y i n g t h e reactant r a t i o may r e s u l t i n changes i n other s t r u c t u r e v a r i a b l e s as w e l l , which may be observed by t h e i r e f f e c t s on physical properties. As t e s t i n g temperatures approach Tg, t h e f r a c t u r e energy o f g l a s s y epoxy networks i s apparently dependent on the c r o s s l i n k d e n s i t y when crack propagation i s preceded by d u c t i l e y i e l d i n g o f t h e crack t i p . An approximate p r o p o r t i o n a l i t y o f the f r a c t u r e energy t o ( t h e average molecular weight of a network chain) has been observed f o r the homologous network s e r i e s . A theory presuming d e v i t r i f i c a t i o n o f t h e crack t i p i s c o n s i s t e n t with t h i s observation.

Acknowledgment s Support o f t h i s work by t h e A i r Force O f f i c e o f S c i e n t i f i c Research and Hercules Inc. i s g r a t e f u l l y acknowledged.


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Literature Cited 1. B e l l , J . P. J . Appl. Poly. S c i . 1970, 14, 1901. 2. G l e d h i l l , R. A.; Kinloch, A. J . ; Yamini, S.; Young, R. J . Polymer 1978, 19, 574. 3. King, Ν. E.; Andrews, E. H. J . Mat. S c i . 1978, 13, 1291. 4. Yamini, S.; Young, R. J . J . Mat. S c i . 1979, 14, 1609. 5. M i j o v i c , J . S.; Koutsky, J . A. Polymer 1979, 20, 1905. 6. Yamini, S.; Young, R. J . J . Mat. S c i . 1980, 15, 1814. 7. Yamini, S.; Young, R. J . J . Mat. S c i . 1980, 15, 1823. 8. Manson, J . Α.; Sperling, L. H.; Kim, S. L. "Influence of Crosslinking on the Mechanical Properties of High Tg Polymers"; AFML TR-77-109: A. F. Materials Laboratory, WPAFB, Ohio, 1977. 9. Chang, T. D.; Carr, S. H.; Brittain, J . O. Poly. Eng. S c i . 1982, 22, 1205. 10. Chang, T. D.; Carr, S. H.; Brittain, J . O. Poly. Eng. S c i . 1982, 22, 1213. 11. Chang, T. D.; B r i t t a i n , J . O. Poly. Eng. S c i . 1982, 22, 1221. 12. Chang, T. D.; B r i t t a i n , J . O. Poly. Eng. Sci. 1982, 22, 1228. 13. Thomson, K. W.; Broutman, L. J . J . Mat. S c i . 1982, 17, 2700. 14. B e l l , J . P. J . Poly. Sci.-A2 1970, 8, 417. 15. Nielson, L. E. J . Macromol. S c i . 1969, C3, 69. 16. Kelley, F. N.; Swetlin, B. J . ; Trainor, D. in "IUPAC Macromolecules"; Benoit, H.; Rempp, P., Eds.; Pergamon Press: Oxford, 1982; p. 275. 17. Flory, P. J. "Principles of Polymer Chemistry"; Cornell Univ. Press: Ithaca, Ν. Y., 1953; p. 579. 18. Hermans, J . J . J . Poly. S c i . 1962, 59, 191. 19. James, H. M.; Guth, E. J . Chem. Phys. 1953, 21, 1039. 20. Katz, D.; Tobolsky, Α. V. Polymer 1963, 4, 417. 21. Kaelble, D. H. J . Appl. Poly. S c i . 1965, 9, 1213. 22. Murayama, T.; B e l l , J . P. J . Poly. Sci.-A2 1970, 8, 437. 23. Lunak, S.; Dusek, K. J . Poly. S c i . : Sym. No. 53 1975, p. 45. 24. Takahama, T.; G e i l , P. H. J . Poly. S c i . : Poly. Letters 1982, 20, 453. 25. Selby, K.; M i l l e r , L. E. J . Mat. Sci. 1975, 10, 12. 26. P h i l l i p s , D. C.; Scott, J . M.; Jones, M. J . Mat. S c i . 1978, 13, 311. 27. G l e d h i l l , R. Α.; Kinloch, A. J . Poly. Eng. S c i . 1979, 19, 82. 28. Kinloch, A. J . ; Williams, J . G. J . Mat. Sci. 1980, 15, 987. 29. Scott, J . M.; Wells, G. M.; P h i l l i p s , D. C. J . Mat. S c i . 1980, 15, 1436. 30. Pritchard, G.; Rhoades, G. V. Nat. S c i . and Eng. 1976, 21, 1.


10.

31. 32. 33. 34. 35. 36.


37. 38. 39. 40. 41. 42. 43. 44.

LEMAY ET AL.


183

Morgan, R. J . ; O'Neal, J . Poly. Eng. S c i . 1978, 18, 1081. G r i f f i t h , A. A. Philos. Trans. R. Soc. London, Ser. A, 1921, 221, 163. Andrews, E. H. "Fracture i n Polymers"; American Elsevier: New York, 1968. Jayatilaka, A. de S. "Fracture of Engineering B r i t t l e Materials:; Applied Science Publishers Ltd.: London, 1978; Chap. 7. Andrews, E. H. J . Mat. S c i . 1974, 9, 887. Lake, G. J . ; Thomas, A. G. Proc. Roy. Soc. Ser. A. 1967, 300, 108. Bowman, H. Α.; Schoonover, R. M. J . of Resch. of NBS 1967, 71C, 179. Kies, J . Α.; Clark, B. J . i n "Fracture-1969"; Pratt, P. L., Ed.; Chapman H a l l : London, 1969; p. 483. Williams, D. P.; Evans, A. G. J . Testing and Evaluation 1973, 1, 264. Treloar, L. R. G. "The Physics of Rubber E l a s t i c i t y " ; Clarendon Press: Oxford, 1975; Chap. 4. Su, L. Ph.D. Dissertation, The University of Akron, Akron, Ohio, 1983. Plazek, D. J . J . Poly. Sci.-A2 1966, 4, 745. Gent, A. N. J . Mat. S c i . 1970, 5, 925. Kinloch, A. J . ; Williams, J . G. J . Mat. S c i . 1980, 15, 995.

RECEIVED September 14, 1983


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