S T R E S S R E L A X A T I O N I N T H E R M O S E T T I N G P O L Y M E R S

R . F . E m e l ' y a n o v a n d A . A . K r i t s u k UDC 539.376+532.135

Several studies of the deformat ion mecha_uism of va r ious epoxide p o l y m e r composi t ions at no rma l and e levated t e m p e r a t u r e s and with shor t and long- t ime loading a r e r epor t ed in the l i t e r a tu re [1, 3]. In them it is shown that the total de format ion is made up of two main components : e las t ic and highly e las t ic {rubber-l ike) . A sharp fall in e las t ic i ty , with inc reased deformabi l i ty and ductibi l i ty, i s obse rved at t e m - p e r a t u r e s above the g lass t rans i t ion t e m p e r a t u r e . Almos t all the work on this subjec t has deal t with the behav io r of p o l y m e r s under tensi le fo rces , although the dis t inct behav io r under c o m p r e s s i o n has been noted.

In the p re sen t a r t i c le the r e su l t s of an exper imen ta l invest igat ion on the re laxa t ion of c o m p r e s s i v e s t r e s s at var ious t e m p e r a t u r e s in an epoxide composi t ion a r e p resen ted .

The p o l y m e r inves t iga ted was an e p o x i d e - m a l e i c compos i t i on of the following p ropor t ions [1]: 65% by weight of epoxy r e s i n m a r k ~D-6, and 35% of male ic anhydride as ha rdener . This h a r d e n e r was chosen because i t g ives a homogeneous p o l y m e r without gas inclusion, and g ives m o r e cons is tent r e su l t s in mechanica l tes t s . F r o m the pys icomechan ica l p r o p e r t i e s of this p o l y m e r the behav io r of o ther t h e r m o s e t - ting po lymer s f rom epoxy r e s i n with other h a r d e n e r s can be pred ic ted .

The mos t impor tan t c h a r a c t e r i s t i c of the p o l y m e r f rom the viewpoint of displaying high e las t ic i ty is the g l a s s t rans i t ion t e m p e r a t u r e Tc, which d e t e r m i n e s i t s mechanica l heat capaci ty . The g l a s s t r ans i t ion

E'lO-t, kg/mm2; e,%;

--z..

2O

5

0

o, / r n m 2

Z~ 5O 75 100 7;,~

o, kg/cm 2

a,, t 6

i

'1

2 0 /00 200

,wi

41

i �9 ?0~'1~00 t,h

Fig. 1 Fig. 2

Fig. 1. Var ia t ion in mechanica l p r o p e r t i e s with t e m p e r a t u r e .

Fig. 2. Curves of load re laxat ion aga ins t t e m p e r a t u r e , 20~ - 1) e = 1%; 2) 8 = 1.27o; 3) a = 1.5%; 4) ~ = 1.8%; 5) ~ = 2.1~0; 6} ~ = 2.4%; 7) ~ = 2.7~0; s ) ~ = 3 , 0 % .

Insti tute of Mechanics , Academy of Sciences of the Ukrainian SSR, Kiev. T r a n s l a t e d f r o m P r o b - l emy Prochnos t i , No. 6, pp. 32-35, June, 1970. Original a r t i c le submi t ted January 20, 1970.

�9 1971 Consultants Bureau, a division o[ Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. All rights reserved. This article cannot be reproduced [or any purpose whatsoever without permission o[ the publisher. A copy o[ this article is available [rom the publisher for $15.00.

536

E, kg/mm z

250 0 JO0 600 gO0 /200 t, h

Fig. 3. Dependence of modulus of e l a s t i c i t y on t ime.

E=o, kg I /mm z I ~ . . .

300

250

""~,,~,,,,

200

150 0 45 1.0 1,5 2.0 ' 2,5 ~,%

Fig. 4. L o n g - t e r m modulus of e l a s t i c i t y aga ins t deformat ion , a t 20~

o, kg/mm 2

2 ~ ~ 2"

i ~ _ 3

o I00 200 300 #00 t, h

o, kg/mm z

! 0

15 - - (

~3 2

, {

~,0,0 20/) "fo/~ *00

Fig. 5 Fig. 6

J l

i

L :

~ )

i i

h

Fig. 5. S t r e s s r e l axa t ion cu rves with cons tant se t de fo rmat ion ~ = 1% for: 1) T = 20~ 2) T = 50~ 3) T = 75~ 4) T = 100%

Fig. 6. Curves of s t r e s s r e laxa t ion at 50 ~ for : 1) ~ = 0.6%; 2) e = 0.8%; 3) e = 1.0%; 4) a = 1.2%; 5) ~ = 1 . 4 ~ 6) ~ = 1.6%.

t e m p e r a t u r e , as d e t e r m i n e d by the Mar tens method, for the p r e s e n t compos i t ion was approx ima te ly 80fl3 which is in good a g r e e m e n t with publ i shed r e s u l t s [1, 2].

La rge sca l e s a m p l e s , to GOST 4651-63, were p r e p a r e d for de t e rmin ing the mechanica l p r o p e r t i e s of the p o l y m e r under sho r t t ime c o m p r e s s i o n loading.

The t e s t s were c a r r i e d out on two un ive r sa l t es t ing mach ines , a two- ton RS-2 and a 13-ton RH-30, which p rov ided constant ra te of loading o r de format ion and e l e c t r o n i c / m e c h a n i c a l r eco rd ing of the P - A/ ( l o a d - e x t e n s i o n ) d i a g r a m . The e leva ted t e m p e r a t u r e t e s t s were c a r r i e d out in a hot c h a m b e r which had a t e m p e r a t u r e regula t ion a c c u r a c y of +2~ The s a m p l e s were main ta ined at se t t e m p e r a t u r e s of 20, 50, 75, 100, and 125 ~ fo r 30 min. The ra te of loading was kept constant at 20 kg/mm2"min. The mechan ica l p r o p e r t i e s w e r e d e t e r m i n e d fo r 5 s a m p l e s at each t e m p e r a t u r e , and the a r i t h m e t i c mean taken.

F r o m the r e s u l t s of the s h o r t - t i m e c o m p r e s s i o n t e s t s on the above m a t e r i a l , Fig . 1 was cons t ruc ted , showing the v a r i a t i o n of: e l a s t i c i t y (curve 1); UTS (curve 2); r e l a t i ve de format ion at b r e a k {curve 3); l i m i t of cons t r a ined r u b b e r - l i k e e l a s t i c i t y (curve 5), aga ins t t e m p e r a t u r e .

The shape of the curves shows that n e a r to, and above the g l a s s t r ans i t i on t e m p e r a t u r e ther~ i s a sha rp d e c r e a s e in: e l a s t i c i ty ; l i m i t of cons t r a ined r u b b e r - l i k e e l a s t i c i ty ; and r e l a t ive de fo rmat ion at the onse t of cons t r a ined r u b b e r - l i k e e l a s t i c i t y . However , the r e l a t i ve de format ion at b r e a k r e m a i n s p r a c t i c a l - ly constant . This i s connected with a s igni f icant weakening of the i n t e r m o l e c u l a r bonds, with a sharp in - c r e a s e in the k ine t ic mot ion of the m o l e c u l a r chains of the p o l y m e r , and i t s t r ans i t i on into the r u b b e r - l i k e e l a s t i c condi t ion at T -> T c.

537

Eoo

230

20C

130

I00

/ ram 2

\

\

0 25 50

,> \

Fig. 7. Long- te rm modulus of elast ici ty against t empera tu re for constant set deformation e = l % .

E ~,, kg/mm 2

' ",.- . .~ ~..............

175

Fig. 8. Long- te rm modulus of e l a s - t icity against set deformation for constant t empera tu re T = 50 ~

The analysis of the resul ts of these tes ts on the given polymer shows the different behavior under compress ion as compared to that under tensile loading [1]; the onset of constra ined rubber- l ike e las t i - city and the relative deformation are severa l t imes g r e a t e r than with tensile loading.

The r i se in the constrained rubber- l ike e las t ic i ty under com- press ion of thermoset t ing c ross - l inked po lymers can be explained by a cer tain "loss of res i s tance" in the network s t ructure . With grea t compaction of the molecule, the f r ac tu re of the given composition is bri t t le at both normal and elevated t empera tu res due to the formation of c racks parallel to the direct ion of the applied load.

The investigation on s t r e s s relaxation was ca r r i ed out on an REL-5 relaxation testing machine modi- fied for testing polymers in compress ion , and provided with an opt ica l -e lec t ronic s e r v o - s y s t e m which en- abled the assigned deformation to be maintained with an accuracy of +0.001 mm, and an apparatus for con- troll ing and automatically reducing the load with constant initial deformation. The e r r o r in the load m e a - surement is *1% of the maximum load.

The load relaxation tes ts at elevated t empera tu res were ca r r i ed out in a tubular e lec t r ic furnace sup- plied through an au to t ransformer . The control and maintenance of the t empera tu re and its measurement were ca r r i ed out by means of an I~PV2-06 apparatus and an automat ic r e c o r d e r using a C h r o m e l - e u p e l thermocouple. Calibration tests on the furnace showed that the var ia t ion f rom the set t empera tu re was �9 2~ The specimens were heated at the given t empera tu re for 30 man, including the shor t t ime testing.

During the s t r e s s relaxation investigation the graph of load against t ime (P - t) was drawn automat i - cally. This was then converted into a s t r e s s t ime graph ( ~ - t).

At room tempera tu re the set relat ive deformations were 1% and f rom 1.2% to 3% in steps of 0.3%.

Figure 2 shows the family of curves of s t r e ss relaxation at room tempera tu re for given deformations in ~ - t coordinates.

Using this diagram, a family of i sochronic curves of ~ - e for var ious t ime intervals was con- structed. Analysis of this la t ter showed the p resence of two regions of different types of deformation, a region of l ineari ty and a region of s imilar i ty .

The presence of a l inear region in the i sochronic curves makes it possible to cons t ruc t a curve of modulus of elast ici ty against t ime (for a constant value of deformation} f rom the resul ts of the s t r e s s r e - laxation tests , Fig. 3. As is seen f rom the figure, the modulus of elast ici ty dec reases initially and then tends to a constant value (for the given composition} which is called the long t e rm modulus of elast ici ty, E~o. As t - -0 , the modulus of elast ici ty tends to its limiting value - the instantaneous modulus of e las t i - city E. This resul t fttlly supports the view that the relaxation p roce s s in thermoset t ing c ross - l inked poly- m e r s is of a molecular nature [3].

The influence of e on E~ was established, so fa r as the range of deformation taken is concerned, and is shown in Fig. 4.

538

The value E~ was taken as the rat io of the equilibrium loading, ff~, to the set deformation. It may be seen f rom Fig. 4 that there is a l inear relation between E~ and set deformation (within the range taken}.

The resul t s obtained may be analyzed in the following manner; the p roces s of relaxation for com- p res s ive s t r e s s at normal t empera tu re obeys one and the same law for different values of initially set e last ic deformation.

The investigation on s t r e s s relaxation at higher t empera tu res was ca r r i ed out in two stages: 1) keep- ing the relat ive deformation constant at ~ = 1% and varying the tempera ture as follows: 20, 50, 75, and 100 ~ (Fig. 5); and 2) keeping the t empera tu re constant at 50 ~ and changing the deformation f rom 0.6% to 1.6% in in tervals of 0.2%, Fig. 6.

F r o m the resul ts of these tes ts , graphs of long t e r m modulus of elastici ty against tempera ture for a constant set deformation (Fig. 7), and against set deformation for a constant tempera ture (Fig. 8) were plotted. As seen f rom Figs. 7 and 8, the relat ions E ~(T) with ~ = const and E~o(~) with T = const are l inear.

However, it must be noted that with increased tempera ture and set deformation the t ime required for es tabl ishment of equilibrium conditions grows at higher t empera tu res . At t empera tu res T > T c the com- p ress ive s t r e s s in the sample re laxes right down to zero , and the t ime to reach equilibrium is 150-200 h.

Thus, the resul ts of the investigation show that the p rocess of s t r e s s relaxation in thermoset t ing c ross - l inked po lymers under compress ion at normal and elevated t empera tu res is not connected with a stage of s t ructura l changes in the po lymer and in prac t ice obeys a l inear law and can therefore be descr ibed by Bolzmann 's equation [1, 4], where the constants of proport ional i ty are determined direct ly f rom tes ts in compress ion .

1. 2. 3.

4.

L I T E R A T U R E C I T E D

V.I . Ozerov, Author ' s Abst rac t of Candidates Disser ta t ion, Inst. Mekhan. AN USSR, Kiev (1966). L . I . Golubenkova, High-Molecular Compounds [in Russian], Vysokomolek. Soed., 1, No. 1 (1959). V.A. Kargin and G.L. Slonimskii, A Short Outline of Physica l Chemist ry of Po lymer s [in Russian], MGU , Moscow (1960}. G.M. Bartenev and Yu.V. Zelenev, Mekhan. Pol imerov, No, 1 (1969).

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