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Some problems of brittle and non-brittle break of polymeric materials
Some problems of brittle and non-brittle break of polymeric matemals
1285
13. W. O. STATTON, Azm. N.Y. Acad. Sci. 83: 27, 1959; C. R. BOHN, J. R. SCHAEFGEN and W. O. STATTON, J. Polymer Sci. 55: 531, 1961; B. K. WEINSTEIN, X - r a y Diffraction b y Chain Molecules, 304, 1963 14. R. G. SCOTT and A. W. FERGUSON, Text. Res. J. 26: 284, 1956 15. S. N. ZHURKOV, Vestnik AN SSSR, No. 3, 46, 1968 16. M. S. MEZHIROVA and E. A. PAKSHVER, Khimieh. volokna, Iqo. 3, 13, 1968 17. I. I. NOVAK and V. I. VETTEGREN, Vysokomol. soyed. 6: 706, 1964; S. N. ZHURKOV, I. I. NOVAK, B. Ya. LEVIN, A. V. SAVITSKII a n d V. I. BETTEGREN, Vysokomol. soyed. 7: 1203, 1965 (Translated in Polymer Sei. U.S.S.R. 7: 7, 1331,. 1965) 18. L. A. LAIUS and Ye. V. KUVSHINSKII, Vysokomol. soyed. 6: 52, 1964 (Translated in Polymer Sci. U.S.S.R. 6: 1, 60, 1964); G. N. AFANASEVA, IVL I. BESSONOV, L. A. VOLF, A. I. ME()S and S. Ya. FRENKEL', Zh. prikl, kb_imii 37: 1349, 1964 19. S. L. DOBRETSOV, N. V. LOMONOSOVA and V. P. STELMflKH~ Vysokomol. soyed. B l l : 782, 1969 (Not translated in Polymer Sei. U.S.S.R.) 20. L. S. GERASIMOVA, R. A. PALATOVSKAYA, A. B. PAKSHVER and V. A. PANTAYEV, Mekhanika polimerov, 943, 1968; N. V. KOSHELEVA, I. S. OKHRIMENKO and A. D. YAKOVLEV, Vysokomol. soyed. B9: 257, 1967 (Not translated in Polymer Sci. U.S.S.R.) 21. L. A. LAIUS and Ye. V. KUVSHINSKII, Fizika tverdogo tela 5: 3113, 1963 22. R. HOSEMANN, J. Appl. Phys. 34: 25, 1963
SOME PROBLEMS OF BRITTLE AND NON-BRITTLE BREAK OF POLYMERIC MATERIALS* G. L. SLONIMSKII, J~.. A. _A_SKADSKIIa n d V. V. KAZANTSEV• Heteroorganic Compounds Institute, U.S.R.R. Academy of Sciences (Received 11 October 1970) I:N THIS i n v e s t i g a t i o n o u r a i m Was t o s t u d y p r o c e s s e s o f b r i t t l e a n d n o n - b r i t t l e break occurring with solid polymeric materials. Brittle break. According to Alexandrov and Lazurkin [1, 2] polymers become brittle whenever a point is reached, during the lowering of the temperature down to the brittle point Tb, where the forced high-elasticity limit ah.e. exceeds the m a x i m u m brittle strength, a,~ax. I n this case when T ~ T b the material will break rather than soften, as the deterioration in durability proceeds more rapidly than the onset of forced high-elasticity. Let us now consider Tb in relation to the degree of crystallinity of the polymer, a. I n papers [3-5] it was shown t h a t the amorphous regions in crystalline polymers are responsible for their strength (or to be more precise, their "weakness"). A t temperatures above the glass transition temperature (Tg) the polymer is in the high-elastic state. Therefore when T > T g a change in temperature will not lead to any marked difference in the strength of completely amorphous or partially crystalline polymers with identical chemical structures. * Vysokomol. soyed. AI4: No. 5, 1149-1155, 1972.
G . L . SLONIMSKII et al.
1286
Under these conditions (at relatively high temperatures) the maximum strength in either case will greatly exceed the forced high-elasticity limit and the type of break will be brittle break. However, when T
~hg/mm z
:
8tl 8
7 ,8 _ _ / g
/f 13 f~
I
5g
J
IOOE,%
FIG. 1. Tensile curves of crystalline samples of lavsan at --80 (•); --70 (2); --50 (3); --40 (4); --10 (5); 20 (6); 60 (7); 70 (8); 80 (9); 90 (•0); 100 (••); 120 (•2); 140 (13) and 180°. Rate of stretching 0.0675 ram/see. Because of this it was i m p o r t a n t to determine the effect of a v e r y different degrees o f crystallinity on the brittle p o i n t of an amorphous-crystalline polymer. W e accordingly investigated lavsan films with different ~-values p r e p a r e d b y h e a t i n g the a m o r p h o u s film at 120 ° for 30 rain a n d 2 hr, and a t 215 ° for 15 min a n d 5 hr. The degree of crystallinity was d e t e r m i n e d f r o m t h e density of t h e sam-
Some problems of brittle and non-brittle break of polymeric materials
1287
ples, and was found by means of the usual formula
4nv--dam de, dcr --dam
dinv
where dam, dcr and dinv are respectively the densities of the completely amorphous polymer, the crystalline sample, and the sample under investigation. Following the data in [9] it was assumed t h a t dcr= 1"455; ~ for the samples was equal to 0.318, 0.403, 0.506, and 0.591 respectively. ~,,kg/cm z o2 =3 x# o5
o\%j
+7
\#"~-~
, -100
0
T,°C
v
lO0
10
2O0
FIG. 2. Temperature dependence of #h.e. and # m a x for lavsan with ==0.062 (1, 2); 0.318 (3-5); 0.403 (6-8); 0-506 (9-11): 1, 3, 6, 9--brittle break; 4, 7, 10--intermediate break; 2, 5, 8,//--break with necking. T b was determined by the method described in [2], whereby the films were tested for uniaxial extension right up to breaking point, using a Polyani dynamometer in the temperature interval --90 to 180 ° . The usual tensile curves as exemplified in Fig. 1 for one of the samples were then plotted. The test results for all the samples are shown in Fig. 2 giving the temperature dependences of amax and ah.e. T b was determined as the temperature at which the sample showed no forced high-elasticity and failed under only slight extensions. As is seen from Fig. 2, T b is a function of a. (T b is higher for a sample with higher a). The brittleness of the sample with a~0.586 was such t h a t it was unfit for testing on the dynamometer, and so no tensile curve was obtainable in this case. I t was nevertheless found t h a t T b for this sample was much higher than Tg of lavsan. I t is therefore incorrect to say t h a t with the partially crystalline polymer brittleness invariably appears at Tg of the amorphous fraction. The development of brittlehess depends on the a-values of the samples. T b for a the partially crystalhne polymer is largely dependent on a, and m a y be either above or below Tg of the amorphous polymer (see Fig. 3).
1288
G . L . S L O N I M S K I I e~ a~.
Let us now turn to another interesting regularity. As is seen from Fig. 2, the temperature dependences of trmax and ah.e. for the crystalline samples are positioned above the corresponding curves for the completely amorphous sample. However, at T b of the latter the curves in question merge. Thus at temperatures below the brittle point of the amorphous polymer the strength of the samples is not a function of a. When T > T b of the amorphous polymer forced high-
•b•°C 8g
2g 0
l
g'Sa~
-88 FIG. 3. Tb o f l a v s a n vs. a. H.
elasticity apparently exists even in the amorphous regions of the crystalline polymer. It is forced elasticity of a local character, and m a y be fairly high. This results in local orientation, the strength is increased, and the curve of the brittle strength of the crystalline sample is positioned above the corresponding curve of the amorphous sample (Fig. 2). When the temperature falls and the onset of brittleness appears the local orientation is inhibited, or becomes impossible, and identical values of amax are obtained for the polymer samples with their different a-values. This once again confirms that the amorphous regions that are invariably present in crystalline polymers are responsible for the strength of the latter. Our next aim was to verify the above results in respect to the effect of crystallinity upon brittle break and forced high-elastic break, using some other polymer for the purpose. Polycarbonate was accordingly selected; appreciable degrees of deformation are obtainable with this polymer [10] at temperatures below Tg. As the rigidity of the macromolecules greatly impedes the crystallization of polycarbonate, the films used in the experiments had relatively low a-values. The crystalline films were prepared from a solution of the polymer in chloroform, evaporating the latter for 58 and 192 hr on a smooth cellophane substrate. The amorphous film was obtained by press-moulding at 310° followed by rapid cooling. The film densities were 1.199; 1.214 and 1.255 g/cm3; the a-values were 0.0412, 0.194 and 0.303 respectively. The procedm'e in the dynamometric tests was the same as for the lavsan.
Some problems of brittle and non-brittle break of polymeric materials
1289
The test results are shown in Fig. 4. I t is seen that the polycarbonate exhibits brittleness at a temperature considerably lower than Tg of the amorphous polymer (Tg of the latter is 149°). It is interesting to find that a has the same effect upon the position of T b as in the case of lavsan, i.e. T b rises with rising g. This once again confirms the validity of the previously-mentioned conclusion that T b of amorphous-crystalline polymers is greatly influenced b y a. Our experiments show, therefore, that the onset of brittleness in regard to different amorphous-crystalline polymers depends on the amount of amorphous fraction in the latter. The forced elastic deformation capacity of the amorphous regions largely determines the properties of the polymers, i.e. Tb, ah.e. and amax. Non-brittle break,. Let us now analyse and compare the processes of nonbrittle break (softening) in polymers under different conditions of mechanical testing; the term "mechanical softening" used in this connection 11 we are taking to mean the rapid development of deformation in a sample accompanied by the development of a neck ("necking"). Necking is the result of intermittent reorganization of the primary structure of a polymeric material. In the case of crystalline polymers this is called recrystallization, or forced high-elasticity in the case of amorphous polymers. I t has been shown in [12-15] that necking takes place during the extension of polymers at a constant rate (under conditions of constantly rising stress) and also under static loads (when a strictly constant is applied). In the latter case the durability of the form of the polymeric material (the time elapsing from the moment the load is applied up to the moment of necking) will be determined b y the applied stress and b y the temperature. The necking process is therefore not of a critical character (i.e. it does not take place when a certain critical stress arecrys. or ah.e. has been reached), b u t it is a kinetic process, representing the accumulation with time of the elementary acts of reorganization of the primary structure without disruption of the macroscopic wholeness of the polymer sample. In this connection we would observe that the well-known process of brittle break is likewise a thermofluctuating kinetic process and represents the accumulation of elementary acts of break whereby a polymer sample, after the loss of durability, breaks down completely. There appears to be a great deal of similarity between the mechanism of brittle break on the one hand and the phenomenon of recrystallization or forced high-elasticity on the other hand. It is quite obvious that irrespective of the mode of mechanical action deep-seated structural changes will take place at the moment of necking. These changes are preceded by the accumulation of elementary acts of the softening process with time. It was important to determine whether these acts are identical under constant or variable stresses. In other words we had to discover how far the structural changes in the samples would be identical in the case of ordinary dynamometric tests (a ¢ const) and under conditions of strictly maintained constant stress ( a : c o n s t ) . In cases of brittle break involving solid polymers this problem is solved b y introducing the concept of an "accumulation of breaks" in the material (the theory
G . L . SLONIMSKIIet
1290
al.
of superposition) which is expressed mathematically as follows:
dt
tp
J" =1, 0 = [a (t)" T (t)" S (t)]
(1)
where tp is the time prior to the failure of the sample, T (a (t). S (t)] is the durability of the sample when the stress and temperature are constant and equal to the instantaneous values of a (t) and T (t).
~'
~i,
08
- 1000
%
• 11
&
%
~
o
600
l
-lOg
#
x5
o 8
•
,3
\e
\1
i
]
O
2go
IgO
T,oc FIG. 4
loS FIG. 5
Fro. 4. Temperature dependence of ah.e. and amax for polycarbonate with a~0"0412 (1-3); 0.194 (4-6); 0-303 (7-9): 1, 4, 7--brittle break; 2, 5, 8--intermediate break; 3, 6, 9 - - b r e a k with necking. FIG. 5. Log ~ vs. log a at - - 3 0 (1); - - 1 0 (2) and 20 ° (3).
Equation (1) also includes the structural parameter S (t). In a special case, when T (t)=const and S (t)----const (the structure of the material does not vary with time) is rewritten in the form of the well-known Baily criterion [16] tp
dt
-=1. (t)]
0 •
(2)
Several authors have shown [17-20] that with moderate rates of stress the Baily criterion is satisfactorily fulfilled in the case of brittle break. Under conditions involving the development of recrystallization or forced elasticity the Baily criterion has yet to be investigated. We will endeavour to determine its validity in cases of necking. Starting with the Baily criterion one may readily find the dependence of arecrys" or a~.e. on temperature and rate of stress. In the case under consideration under conditions of uniaxial stress and when T = c o n s t the Baily criterion is expressed as t~
_[
dt
(t)----]= 1,
(3)
Some problems of brittle a n d non-brittle b r e a k of polymeric m a t e r i a l s
1291
where z~[a (t)] is the time prior to necking in the case of constant stress equal to the instantaneous value of a (t), t~ is the durability of the form of the polymeric material (adopting the terminology used in [11]). An analysis of the tensile curves shows that in the initial "portions of the latter the stress changes approximately in accordance with the law a=vt, where v is the rate of increase in the stress with time. *
l°S ~recp~s, k,q/cmz
I"/-/
~ I"
os-
.~ J
t
I
I
3"5
i
I
3"8
L
I
2"2
0.3
2.6
~/O-a
3.0 i ~lO-3
3.l/
FIG. 6. ffrecrys. VS. reverse t e m p e r a t u r e f o r l a v s a n (a) and p o l y p r o p y l e n e (b): l - - p o l y p r o p y l e n e ÷1~/o indigo; 2 - - p o l y p r o p y l e u e ~ - 0 . 5 ~ b i s m u t h salicilate and 3 - - i n i t i a l polypropylene. Continuous l i n e - - t h e o r e t i c a l , d a s h e d - - e x p e r i m e n t a l data.
It was shown in [12] that the induction period z~ for necking under conditions where a = c o n s t and T = c o n s t is described b y the equation T~,:-%a-b evmT, (4) where v0 is the pro-exponential factor, b and U are constants for the material, and R is the universal gas constant. Using the above relationship and substituting it in equation (3), we obtain t, 0
dt TOO'-beU/RT--
1.
Taking into account that a=vt, we have t,
dt
~ Zo (Vt)- beUIR~i'= 1 ,
(5)
* H e r e we are referring to stress recalculated for the true cross section o f t h e sample: a ==as(1 ~-c), where a~ is t h e stress calculated for t h e initial cross section, a n d e is t h e b r e a k i n g elongation.
1292
G . L . SLOl~rIMSXII e~ a/.
Integrating and completing a series of conversions, and also taking into a c c o u n t t h a t vt~tTrecrys: o r Vt~tTh.e. w e o b t a i n
logv log ( b + l ) l°g arecrys" (h'e')= b - ~ - ~ b-4-1
log~0
U
~-b~--l+2"3RT(b+l)"
(6)
Equation (6) gives the dependence of arecrys, or ah.e. on temperature and on the rate of stress v. To verify the feasibility of this equation a number of experiments were carried out to find the induction period v, for the amorphous lavsan when a = c o n s t a n t and under conditions of continuous extension. Figure 5 shows the experimental results in the form of curves of log r, vs. log a. It is seen that the curves of log v, vs. log a are straight lines and are satisfactorily described b y equation (4). On evaluating the data in Fig. 5 the following values are obtained for the parameters in equation (6): log ~0= --6; U = 5 5 kcal/mole; b = 33-5. Substituting the found values of all the quantities in (6) we obtain ah.e. for all the investigated temperatures. Figure 6a shows the calculated and the experimental curves of ah.e. VS. temperature. This Figure shows that the calculated values are invariably higher than the experimental ones. Similar results are obtained on comparing the calculated and the experimental values of arec~ys, for polypropylene, i.e. the initial polypropylene and that modified with artificial centres [12] (see Fig. 6b). * Thus in the light of the experiments and the calculations we find that the values of areerys, or ah.e. based on equation (6) are always higher than the experimental values, This in turn shows that the structural transitions taking place under conditions of constant stress (a=const) and of continually increasing stress are non-equivalent. At present we have no data based on direct structural investigations such as would allow us to reach an unambiguous conclusion as to these transitions, b u t investigations with this in view will be undertaken later on. However, it is already possible to say that the structural transitions taking place under conditions of continually rising stress are more pronounced than those oec .urring under constant stress. This would account for the non-equivalence of the calculated and the experimental values of arecr~, and ah.e., though they are qualitatively in agreement. Thus the difference (aezp
Some problems of brittle and non-brittle break of polymeric materials
1293
continually being brought out of the equilibrium state. Taking this into account it is obvious t h a t the application of the theory of the superposition of breaks to the necking process in polymers would be invalid if no account were taken of the structural transitions in the material in view of the non-equivalence of these transitions under dissimilar conditions of mechanical action. In view of these results and the calculations referred to above it is now possible to make a critical approach to the results of ordinary dynamometric testing of polymers. Under the conditions of these tests the polymeric material "forcibly" undergoes continuous deformation right up to the softening point, with the result t h a t the most pronounced structural changes take place in the material. On the other hand under "milder" conditions of mechanical testing the polymeric material is exposed for a longer period of time to the same amount of stress. Consequently lower values of arecrys, or an.e. are obtained by means of dynamometric testing. CONCLUSIONS
(1) The effect of the degree of crystallinity oll the brittle point of of polymers has been investigated. I t is shown t h a t the brittle point of the samples increases with their crystallinity, rising regularly from T b of the amorphous polymer, and approaching the melting point of the crystalhne polymer. (2) Processes of non-brittle break (softening) have been investigated for polymers under different loading conditions. I t is shown t h a t if the Baily criterion is used to describe these processes, it is essential to take account of the structural changes float will have occurred in the material up to the moment of necking. Transla2~ by R. J. A. HE~ri)~Y REFERENCES
1. A. P. ALEKSANDROV and S. N. ZHURKOV, Yavlenio khrupkogo razryva (The Brittle Break Phenomenon). ONTI, 1933 2. Yu. S. LAZURKIN, Thesis, 1954 3. S. N. ZHURKOV, A. I. SLUTSKER and A. A. YASTRERINSKII,Fizika tvordogo tela 6: 360, 1964 4. S.N. ZHURKOV, I. I. NOVAK, B. Ya. LEVIN, A. V. SAVITSKIIand V. I. VETTEGREN, Vysokomol. soyod. 7: i203, 1965 (Translated in Polymer Sei. U.S.S.R. 7: 7, 1331, !965) 5. A. I. 8LUTSKER, A. Ye. GROMOV and V. S. PSHEZHETSKII, Fizika tverdogo tela 6: 456, 1964 6. V. A. KARGIN, V. A.: KABANOV and I. Yu. MARCHENKO, Vysokomol. soyed. 1: 94, 1959 (Translated in Polymer Sei. U.S.S.R. 1: 1, 41, 1959) 7. P. V. KOZLOV, V. A. KABANOVand A. A. FROLOVA, Vysokomol. soyod. 1: 324, 1959 (Not translated in Polymer Sci. U.S.S.R.) 8. G. L. SLONIMSKII, A" A. ASKADSKII and V. V. KAZANTSEVA, Dokl. AN SSSR 185: 371, 1969 9. L. G. KAZARYAN and D. Ya. TSVANKIN, Vysokomol. soyed. 2: 377, 1967 (l~ot translated in Polymer Sci. U.S.S.R.) 10. Transitions and Relaxation Effects in Polymers, ed. by Boyor, p. 290, 1968
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K. A. A _ ~ D ~ O V et al.
11. G. L. SLONIMSKII, A. A. ASKADSKII and A. I. MZHELSKII, Vysokomol. soyed. A12: 1161, 1970 (Translated in Polymer Sci. U.S.S.R. 12: 5, 1317, 1970) 12. V. A. KARGIN, T. I. SOGOLOVA and V. M. RUBSHTEIN, Vysokomol. soyed. Ag: 288, 1967 (Translated in Polymer Sci. U.S.S.R. 9: 2, 315, 1967) 13. S. B. RATNER and Yu. I. BROKHIN, Dokl. A N SSSR 188: 807, 1969 14. I. S. LYAKHOVICH, I. N. MUSAELYAN and N. M. CHIRKOV, Vysokomol. soyed. AIO: 715, 1968 (Translated in Polymer Sci. U.S.S.R. 1O: 4, 829, 1968) 15. D. F. KAGAN and L. A. KANTOR, Plast. massy, No. 4, 9, 1968 16. J. BAILY, Glass. Ind., 20: 21, 59, 95, 143, 1939 17. S. N. ZHURKOV and E. Ye. TOMASHEVSKII, Nekotorye problemy prochnosti tve'rdogo tela (Some Problems of the Strength of Solid Substances). p. 68, Izd. AN SSSR, 1959 18. G. M. BARTENEV, B. I. PANSHIN, I. V. RAZUMOVSKAYA and G. N. FINOGENOV, Izv. A N SSSR, Engng. sect., No. 6, 176, 1960 19. B. I. PANSHIN, G. M. BARTENEV and G. N. FINOGENOV, Plast. massy, No. 11, 47, 1960 20. A. A. ASKADSKII a n d G. L. SLONIMSKII, Fizika tverdogo tela 6: 1430, 1964
ANIONIC COPOLYMERIZATION OF OCTAMETHYL AND 0CTAPHENYLCYCLOTETRASILOXANES * K. A. A~DRIA~COV, B. G. ZAVII~ and G. F. SABLI:N'A Heteroorganic Compounds Institute, U.S.S.R. Academy of Sciences (Received 11 October 1970) INCREASING interest is currently being shown in the synthesis of linear polyorganosiloxane copolymers containing diphenylsfloxane units in the main chain [1, 2]. The principle method of synthesizing these polymers is b y the anionic copolymerization of the appropriate organocyclosfloxanes with diphenylcyclosiloxanes, and in particular b y the copolymerization of octaphenylcyclotetrasfloxane (OPCTS) and octamethylcyclotetrasiloxane (OMCTS). Howver, the anionic copolymerization of OPCTS and OMCTS has been investigated only to a very limited extent: with the exception of paper [2], where the dilatometric method was used to investigate the copolymexization of these monomers with low molar ratios of OPCTS : : OMCTS (the amount of OPCTS in the initial mixture was not more than 20 mole ~o) no o t h e r papers dealing with the kinetics of this reaction have appeared. I t was nevertheless desired for a large number of reasons t h a t the reaction in question should be investigated over a wider range of OPCTS/OMCTS ratios, and a particular objective was to investigate the mechanisms of the anionic eopolymerization of OMCTS and OPCTS with a view~to facilitating t h e synthesis of polymers of the dimethyl(diphenyl)siloxaae series of predetermined composition a n d molecular weight. Moreover a kinetic s t u d y of the reaction together with d a t a on the composition of the products obtained at. different degrees of conversion should enable us to determine the relative reactivity of each of the monomers, and to estimate * Vysokomol. soyed. A14: No. 5, 1156-1162, 1972.
1285
13. W. O. STATTON, Azm. N.Y. Acad. Sci. 83: 27, 1959; C. R. BOHN, J. R. SCHAEFGEN and W. O. STATTON, J. Polymer Sci. 55: 531, 1961; B. K. WEINSTEIN, X - r a y Diffraction b y Chain Molecules, 304, 1963 14. R. G. SCOTT and A. W. FERGUSON, Text. Res. J. 26: 284, 1956 15. S. N. ZHURKOV, Vestnik AN SSSR, No. 3, 46, 1968 16. M. S. MEZHIROVA and E. A. PAKSHVER, Khimieh. volokna, Iqo. 3, 13, 1968 17. I. I. NOVAK and V. I. VETTEGREN, Vysokomol. soyed. 6: 706, 1964; S. N. ZHURKOV, I. I. NOVAK, B. Ya. LEVIN, A. V. SAVITSKII a n d V. I. BETTEGREN, Vysokomol. soyed. 7: 1203, 1965 (Translated in Polymer Sei. U.S.S.R. 7: 7, 1331,. 1965) 18. L. A. LAIUS and Ye. V. KUVSHINSKII, Vysokomol. soyed. 6: 52, 1964 (Translated in Polymer Sci. U.S.S.R. 6: 1, 60, 1964); G. N. AFANASEVA, IVL I. BESSONOV, L. A. VOLF, A. I. ME()S and S. Ya. FRENKEL', Zh. prikl, kb_imii 37: 1349, 1964 19. S. L. DOBRETSOV, N. V. LOMONOSOVA and V. P. STELMflKH~ Vysokomol. soyed. B l l : 782, 1969 (Not translated in Polymer Sei. U.S.S.R.) 20. L. S. GERASIMOVA, R. A. PALATOVSKAYA, A. B. PAKSHVER and V. A. PANTAYEV, Mekhanika polimerov, 943, 1968; N. V. KOSHELEVA, I. S. OKHRIMENKO and A. D. YAKOVLEV, Vysokomol. soyed. B9: 257, 1967 (Not translated in Polymer Sci. U.S.S.R.) 21. L. A. LAIUS and Ye. V. KUVSHINSKII, Fizika tverdogo tela 5: 3113, 1963 22. R. HOSEMANN, J. Appl. Phys. 34: 25, 1963
SOME PROBLEMS OF BRITTLE AND NON-BRITTLE BREAK OF POLYMERIC MATERIALS* G. L. SLONIMSKII, J~.. A. _A_SKADSKIIa n d V. V. KAZANTSEV• Heteroorganic Compounds Institute, U.S.R.R. Academy of Sciences (Received 11 October 1970) I:N THIS i n v e s t i g a t i o n o u r a i m Was t o s t u d y p r o c e s s e s o f b r i t t l e a n d n o n - b r i t t l e break occurring with solid polymeric materials. Brittle break. According to Alexandrov and Lazurkin [1, 2] polymers become brittle whenever a point is reached, during the lowering of the temperature down to the brittle point Tb, where the forced high-elasticity limit ah.e. exceeds the m a x i m u m brittle strength, a,~ax. I n this case when T ~ T b the material will break rather than soften, as the deterioration in durability proceeds more rapidly than the onset of forced high-elasticity. Let us now consider Tb in relation to the degree of crystallinity of the polymer, a. I n papers [3-5] it was shown t h a t the amorphous regions in crystalline polymers are responsible for their strength (or to be more precise, their "weakness"). A t temperatures above the glass transition temperature (Tg) the polymer is in the high-elastic state. Therefore when T > T g a change in temperature will not lead to any marked difference in the strength of completely amorphous or partially crystalline polymers with identical chemical structures. * Vysokomol. soyed. AI4: No. 5, 1149-1155, 1972.
G . L . SLONIMSKII et al.
1286
Under these conditions (at relatively high temperatures) the maximum strength in either case will greatly exceed the forced high-elasticity limit and the type of break will be brittle break. However, when T
~hg/mm z
:
8tl 8
7 ,8 _ _ / g
/f 13 f~
I
5g
J
IOOE,%
FIG. 1. Tensile curves of crystalline samples of lavsan at --80 (•); --70 (2); --50 (3); --40 (4); --10 (5); 20 (6); 60 (7); 70 (8); 80 (9); 90 (•0); 100 (••); 120 (•2); 140 (13) and 180°. Rate of stretching 0.0675 ram/see. Because of this it was i m p o r t a n t to determine the effect of a v e r y different degrees o f crystallinity on the brittle p o i n t of an amorphous-crystalline polymer. W e accordingly investigated lavsan films with different ~-values p r e p a r e d b y h e a t i n g the a m o r p h o u s film at 120 ° for 30 rain a n d 2 hr, and a t 215 ° for 15 min a n d 5 hr. The degree of crystallinity was d e t e r m i n e d f r o m t h e density of t h e sam-
Some problems of brittle and non-brittle break of polymeric materials
1287
ples, and was found by means of the usual formula
4nv--dam de, dcr --dam
dinv
where dam, dcr and dinv are respectively the densities of the completely amorphous polymer, the crystalline sample, and the sample under investigation. Following the data in [9] it was assumed t h a t dcr= 1"455; ~ for the samples was equal to 0.318, 0.403, 0.506, and 0.591 respectively. ~,,kg/cm z o2 =3 x# o5
o\%j
+7
\#"~-~
, -100
0
T,°C
v
lO0
10
2O0
FIG. 2. Temperature dependence of #h.e. and # m a x for lavsan with ==0.062 (1, 2); 0.318 (3-5); 0.403 (6-8); 0-506 (9-11): 1, 3, 6, 9--brittle break; 4, 7, 10--intermediate break; 2, 5, 8,//--break with necking. T b was determined by the method described in [2], whereby the films were tested for uniaxial extension right up to breaking point, using a Polyani dynamometer in the temperature interval --90 to 180 ° . The usual tensile curves as exemplified in Fig. 1 for one of the samples were then plotted. The test results for all the samples are shown in Fig. 2 giving the temperature dependences of amax and ah.e. T b was determined as the temperature at which the sample showed no forced high-elasticity and failed under only slight extensions. As is seen from Fig. 2, T b is a function of a. (T b is higher for a sample with higher a). The brittleness of the sample with a~0.586 was such t h a t it was unfit for testing on the dynamometer, and so no tensile curve was obtainable in this case. I t was nevertheless found t h a t T b for this sample was much higher than Tg of lavsan. I t is therefore incorrect to say t h a t with the partially crystalline polymer brittleness invariably appears at Tg of the amorphous fraction. The development of brittlehess depends on the a-values of the samples. T b for a the partially crystalhne polymer is largely dependent on a, and m a y be either above or below Tg of the amorphous polymer (see Fig. 3).
1288
G . L . S L O N I M S K I I e~ a~.
Let us now turn to another interesting regularity. As is seen from Fig. 2, the temperature dependences of trmax and ah.e. for the crystalline samples are positioned above the corresponding curves for the completely amorphous sample. However, at T b of the latter the curves in question merge. Thus at temperatures below the brittle point of the amorphous polymer the strength of the samples is not a function of a. When T > T b of the amorphous polymer forced high-
•b•°C 8g
2g 0
l
g'Sa~
-88 FIG. 3. Tb o f l a v s a n vs. a. H.
elasticity apparently exists even in the amorphous regions of the crystalline polymer. It is forced elasticity of a local character, and m a y be fairly high. This results in local orientation, the strength is increased, and the curve of the brittle strength of the crystalline sample is positioned above the corresponding curve of the amorphous sample (Fig. 2). When the temperature falls and the onset of brittleness appears the local orientation is inhibited, or becomes impossible, and identical values of amax are obtained for the polymer samples with their different a-values. This once again confirms that the amorphous regions that are invariably present in crystalline polymers are responsible for the strength of the latter. Our next aim was to verify the above results in respect to the effect of crystallinity upon brittle break and forced high-elastic break, using some other polymer for the purpose. Polycarbonate was accordingly selected; appreciable degrees of deformation are obtainable with this polymer [10] at temperatures below Tg. As the rigidity of the macromolecules greatly impedes the crystallization of polycarbonate, the films used in the experiments had relatively low a-values. The crystalline films were prepared from a solution of the polymer in chloroform, evaporating the latter for 58 and 192 hr on a smooth cellophane substrate. The amorphous film was obtained by press-moulding at 310° followed by rapid cooling. The film densities were 1.199; 1.214 and 1.255 g/cm3; the a-values were 0.0412, 0.194 and 0.303 respectively. The procedm'e in the dynamometric tests was the same as for the lavsan.
Some problems of brittle and non-brittle break of polymeric materials
1289
The test results are shown in Fig. 4. I t is seen that the polycarbonate exhibits brittleness at a temperature considerably lower than Tg of the amorphous polymer (Tg of the latter is 149°). It is interesting to find that a has the same effect upon the position of T b as in the case of lavsan, i.e. T b rises with rising g. This once again confirms the validity of the previously-mentioned conclusion that T b of amorphous-crystalline polymers is greatly influenced b y a. Our experiments show, therefore, that the onset of brittleness in regard to different amorphous-crystalline polymers depends on the amount of amorphous fraction in the latter. The forced elastic deformation capacity of the amorphous regions largely determines the properties of the polymers, i.e. Tb, ah.e. and amax. Non-brittle break,. Let us now analyse and compare the processes of nonbrittle break (softening) in polymers under different conditions of mechanical testing; the term "mechanical softening" used in this connection 11 we are taking to mean the rapid development of deformation in a sample accompanied by the development of a neck ("necking"). Necking is the result of intermittent reorganization of the primary structure of a polymeric material. In the case of crystalline polymers this is called recrystallization, or forced high-elasticity in the case of amorphous polymers. I t has been shown in [12-15] that necking takes place during the extension of polymers at a constant rate (under conditions of constantly rising stress) and also under static loads (when a strictly constant is applied). In the latter case the durability of the form of the polymeric material (the time elapsing from the moment the load is applied up to the moment of necking) will be determined b y the applied stress and b y the temperature. The necking process is therefore not of a critical character (i.e. it does not take place when a certain critical stress arecrys. or ah.e. has been reached), b u t it is a kinetic process, representing the accumulation with time of the elementary acts of reorganization of the primary structure without disruption of the macroscopic wholeness of the polymer sample. In this connection we would observe that the well-known process of brittle break is likewise a thermofluctuating kinetic process and represents the accumulation of elementary acts of break whereby a polymer sample, after the loss of durability, breaks down completely. There appears to be a great deal of similarity between the mechanism of brittle break on the one hand and the phenomenon of recrystallization or forced high-elasticity on the other hand. It is quite obvious that irrespective of the mode of mechanical action deep-seated structural changes will take place at the moment of necking. These changes are preceded by the accumulation of elementary acts of the softening process with time. It was important to determine whether these acts are identical under constant or variable stresses. In other words we had to discover how far the structural changes in the samples would be identical in the case of ordinary dynamometric tests (a ¢ const) and under conditions of strictly maintained constant stress ( a : c o n s t ) . In cases of brittle break involving solid polymers this problem is solved b y introducing the concept of an "accumulation of breaks" in the material (the theory
G . L . SLONIMSKIIet
1290
al.
of superposition) which is expressed mathematically as follows:
dt
tp
J" =1, 0 = [a (t)" T (t)" S (t)]
(1)
where tp is the time prior to the failure of the sample, T (a (t). S (t)] is the durability of the sample when the stress and temperature are constant and equal to the instantaneous values of a (t) and T (t).
~'
~i,
08
- 1000
%
• 11
&
%
~
o
600
l
-lOg
#
x5
o 8
•
,3
\e
\1
i
]
O
2go
IgO
T,oc FIG. 4
loS FIG. 5
Fro. 4. Temperature dependence of ah.e. and amax for polycarbonate with a~0"0412 (1-3); 0.194 (4-6); 0-303 (7-9): 1, 4, 7--brittle break; 2, 5, 8--intermediate break; 3, 6, 9 - - b r e a k with necking. FIG. 5. Log ~ vs. log a at - - 3 0 (1); - - 1 0 (2) and 20 ° (3).
Equation (1) also includes the structural parameter S (t). In a special case, when T (t)=const and S (t)----const (the structure of the material does not vary with time) is rewritten in the form of the well-known Baily criterion [16] tp
dt
-=1. (t)]
0 •
(2)
Several authors have shown [17-20] that with moderate rates of stress the Baily criterion is satisfactorily fulfilled in the case of brittle break. Under conditions involving the development of recrystallization or forced elasticity the Baily criterion has yet to be investigated. We will endeavour to determine its validity in cases of necking. Starting with the Baily criterion one may readily find the dependence of arecrys" or a~.e. on temperature and rate of stress. In the case under consideration under conditions of uniaxial stress and when T = c o n s t the Baily criterion is expressed as t~
_[
dt
(t)----]= 1,
(3)
Some problems of brittle a n d non-brittle b r e a k of polymeric m a t e r i a l s
1291
where z~[a (t)] is the time prior to necking in the case of constant stress equal to the instantaneous value of a (t), t~ is the durability of the form of the polymeric material (adopting the terminology used in [11]). An analysis of the tensile curves shows that in the initial "portions of the latter the stress changes approximately in accordance with the law a=vt, where v is the rate of increase in the stress with time. *
l°S ~recp~s, k,q/cmz
I"/-/
~ I"
os-
.~ J
t
I
I
3"5
i
I
3"8
L
I
2"2
0.3
2.6
~/O-a
3.0 i ~lO-3
3.l/
FIG. 6. ffrecrys. VS. reverse t e m p e r a t u r e f o r l a v s a n (a) and p o l y p r o p y l e n e (b): l - - p o l y p r o p y l e n e ÷1~/o indigo; 2 - - p o l y p r o p y l e u e ~ - 0 . 5 ~ b i s m u t h salicilate and 3 - - i n i t i a l polypropylene. Continuous l i n e - - t h e o r e t i c a l , d a s h e d - - e x p e r i m e n t a l data.
It was shown in [12] that the induction period z~ for necking under conditions where a = c o n s t and T = c o n s t is described b y the equation T~,:-%a-b evmT, (4) where v0 is the pro-exponential factor, b and U are constants for the material, and R is the universal gas constant. Using the above relationship and substituting it in equation (3), we obtain t, 0
dt TOO'-beU/RT--
1.
Taking into account that a=vt, we have t,
dt
~ Zo (Vt)- beUIR~i'= 1 ,
(5)
* H e r e we are referring to stress recalculated for the true cross section o f t h e sample: a ==as(1 ~-c), where a~ is t h e stress calculated for t h e initial cross section, a n d e is t h e b r e a k i n g elongation.
1292
G . L . SLOl~rIMSXII e~ a/.
Integrating and completing a series of conversions, and also taking into a c c o u n t t h a t vt~tTrecrys: o r Vt~tTh.e. w e o b t a i n
logv log ( b + l ) l°g arecrys" (h'e')= b - ~ - ~ b-4-1
log~0
U
~-b~--l+2"3RT(b+l)"
(6)
Equation (6) gives the dependence of arecrys, or ah.e. on temperature and on the rate of stress v. To verify the feasibility of this equation a number of experiments were carried out to find the induction period v, for the amorphous lavsan when a = c o n s t a n t and under conditions of continuous extension. Figure 5 shows the experimental results in the form of curves of log r, vs. log a. It is seen that the curves of log v, vs. log a are straight lines and are satisfactorily described b y equation (4). On evaluating the data in Fig. 5 the following values are obtained for the parameters in equation (6): log ~0= --6; U = 5 5 kcal/mole; b = 33-5. Substituting the found values of all the quantities in (6) we obtain ah.e. for all the investigated temperatures. Figure 6a shows the calculated and the experimental curves of ah.e. VS. temperature. This Figure shows that the calculated values are invariably higher than the experimental ones. Similar results are obtained on comparing the calculated and the experimental values of arec~ys, for polypropylene, i.e. the initial polypropylene and that modified with artificial centres [12] (see Fig. 6b). * Thus in the light of the experiments and the calculations we find that the values of areerys, or ah.e. based on equation (6) are always higher than the experimental values, This in turn shows that the structural transitions taking place under conditions of constant stress (a=const) and of continually increasing stress are non-equivalent. At present we have no data based on direct structural investigations such as would allow us to reach an unambiguous conclusion as to these transitions, b u t investigations with this in view will be undertaken later on. However, it is already possible to say that the structural transitions taking place under conditions of continually rising stress are more pronounced than those oec .urring under constant stress. This would account for the non-equivalence of the calculated and the experimental values of arecr~, and ah.e., though they are qualitatively in agreement. Thus the difference (aezp
Some problems of brittle and non-brittle break of polymeric materials
1293
continually being brought out of the equilibrium state. Taking this into account it is obvious t h a t the application of the theory of the superposition of breaks to the necking process in polymers would be invalid if no account were taken of the structural transitions in the material in view of the non-equivalence of these transitions under dissimilar conditions of mechanical action. In view of these results and the calculations referred to above it is now possible to make a critical approach to the results of ordinary dynamometric testing of polymers. Under the conditions of these tests the polymeric material "forcibly" undergoes continuous deformation right up to the softening point, with the result t h a t the most pronounced structural changes take place in the material. On the other hand under "milder" conditions of mechanical testing the polymeric material is exposed for a longer period of time to the same amount of stress. Consequently lower values of arecrys, or an.e. are obtained by means of dynamometric testing. CONCLUSIONS
(1) The effect of the degree of crystallinity oll the brittle point of of polymers has been investigated. I t is shown t h a t the brittle point of the samples increases with their crystallinity, rising regularly from T b of the amorphous polymer, and approaching the melting point of the crystalhne polymer. (2) Processes of non-brittle break (softening) have been investigated for polymers under different loading conditions. I t is shown t h a t if the Baily criterion is used to describe these processes, it is essential to take account of the structural changes float will have occurred in the material up to the moment of necking. Transla2~ by R. J. A. HE~ri)~Y REFERENCES
1. A. P. ALEKSANDROV and S. N. ZHURKOV, Yavlenio khrupkogo razryva (The Brittle Break Phenomenon). ONTI, 1933 2. Yu. S. LAZURKIN, Thesis, 1954 3. S. N. ZHURKOV, A. I. SLUTSKER and A. A. YASTRERINSKII,Fizika tvordogo tela 6: 360, 1964 4. S.N. ZHURKOV, I. I. NOVAK, B. Ya. LEVIN, A. V. SAVITSKIIand V. I. VETTEGREN, Vysokomol. soyod. 7: i203, 1965 (Translated in Polymer Sei. U.S.S.R. 7: 7, 1331, !965) 5. A. I. 8LUTSKER, A. Ye. GROMOV and V. S. PSHEZHETSKII, Fizika tverdogo tela 6: 456, 1964 6. V. A. KARGIN, V. A.: KABANOV and I. Yu. MARCHENKO, Vysokomol. soyed. 1: 94, 1959 (Translated in Polymer Sei. U.S.S.R. 1: 1, 41, 1959) 7. P. V. KOZLOV, V. A. KABANOVand A. A. FROLOVA, Vysokomol. soyod. 1: 324, 1959 (Not translated in Polymer Sci. U.S.S.R.) 8. G. L. SLONIMSKII, A" A. ASKADSKII and V. V. KAZANTSEVA, Dokl. AN SSSR 185: 371, 1969 9. L. G. KAZARYAN and D. Ya. TSVANKIN, Vysokomol. soyed. 2: 377, 1967 (l~ot translated in Polymer Sci. U.S.S.R.) 10. Transitions and Relaxation Effects in Polymers, ed. by Boyor, p. 290, 1968
1294
K. A. A _ ~ D ~ O V et al.
11. G. L. SLONIMSKII, A. A. ASKADSKII and A. I. MZHELSKII, Vysokomol. soyed. A12: 1161, 1970 (Translated in Polymer Sci. U.S.S.R. 12: 5, 1317, 1970) 12. V. A. KARGIN, T. I. SOGOLOVA and V. M. RUBSHTEIN, Vysokomol. soyed. Ag: 288, 1967 (Translated in Polymer Sci. U.S.S.R. 9: 2, 315, 1967) 13. S. B. RATNER and Yu. I. BROKHIN, Dokl. A N SSSR 188: 807, 1969 14. I. S. LYAKHOVICH, I. N. MUSAELYAN and N. M. CHIRKOV, Vysokomol. soyed. AIO: 715, 1968 (Translated in Polymer Sci. U.S.S.R. 1O: 4, 829, 1968) 15. D. F. KAGAN and L. A. KANTOR, Plast. massy, No. 4, 9, 1968 16. J. BAILY, Glass. Ind., 20: 21, 59, 95, 143, 1939 17. S. N. ZHURKOV and E. Ye. TOMASHEVSKII, Nekotorye problemy prochnosti tve'rdogo tela (Some Problems of the Strength of Solid Substances). p. 68, Izd. AN SSSR, 1959 18. G. M. BARTENEV, B. I. PANSHIN, I. V. RAZUMOVSKAYA and G. N. FINOGENOV, Izv. A N SSSR, Engng. sect., No. 6, 176, 1960 19. B. I. PANSHIN, G. M. BARTENEV and G. N. FINOGENOV, Plast. massy, No. 11, 47, 1960 20. A. A. ASKADSKII a n d G. L. SLONIMSKII, Fizika tverdogo tela 6: 1430, 1964
ANIONIC COPOLYMERIZATION OF OCTAMETHYL AND 0CTAPHENYLCYCLOTETRASILOXANES * K. A. A~DRIA~COV, B. G. ZAVII~ and G. F. SABLI:N'A Heteroorganic Compounds Institute, U.S.S.R. Academy of Sciences (Received 11 October 1970) INCREASING interest is currently being shown in the synthesis of linear polyorganosiloxane copolymers containing diphenylsfloxane units in the main chain [1, 2]. The principle method of synthesizing these polymers is b y the anionic copolymerization of the appropriate organocyclosfloxanes with diphenylcyclosiloxanes, and in particular b y the copolymerization of octaphenylcyclotetrasfloxane (OPCTS) and octamethylcyclotetrasiloxane (OMCTS). Howver, the anionic copolymerization of OPCTS and OMCTS has been investigated only to a very limited extent: with the exception of paper [2], where the dilatometric method was used to investigate the copolymexization of these monomers with low molar ratios of OPCTS : : OMCTS (the amount of OPCTS in the initial mixture was not more than 20 mole ~o) no o t h e r papers dealing with the kinetics of this reaction have appeared. I t was nevertheless desired for a large number of reasons t h a t the reaction in question should be investigated over a wider range of OPCTS/OMCTS ratios, and a particular objective was to investigate the mechanisms of the anionic eopolymerization of OMCTS and OPCTS with a view~to facilitating t h e synthesis of polymers of the dimethyl(diphenyl)siloxaae series of predetermined composition a n d molecular weight. Moreover a kinetic s t u d y of the reaction together with d a t a on the composition of the products obtained at. different degrees of conversion should enable us to determine the relative reactivity of each of the monomers, and to estimate * Vysokomol. soyed. A14: No. 5, 1156-1162, 1972.