Stress relaxation in polypropylene
isobutylene in CCl 4 and benzene the line width approaches a limiting value ( ~ 5 c/s) with decrease in concentration. (2) Chemical shifts of the protons were detected in solid polybutadiene (SKB). A method for determination of the ratio of 1,2 and 1,4 structures in polybutadienes is suggested. Translated by E. O. PHILLIPS REFERENCES 1. 2. 3. 4. 5. 6. 7.
J. G. POWLES, Proc. Phys. Soc. (London), 69B: 281, 1956 F. A. BOVEY, G. V. D. TIERS and G. FILLIPOVITCH, J. Polymer Sci. 38: 73, 1959 N. BLOEMBERGEN, E. M. PURCELL and R. V. POUND, Phys. Rev. 73: 679, 1948 J. G. POWLES, Arch. des. Sci. 10: 253, 1957 A. ODADJIMA, J. Phys. Soc. J a p a n 14: 777, 1959 T. FOX and P. FLORY, J. Phys. Colloid. Chem. 53: 197, 1949 J. A. POPLE, W. G. SCHNEIDER and H. J. BERNSTEIN, Spektry yadernogo n ~ g n i t n o g o rezonansa vysokogo razrusheniya. (High Resolution Nuclear Magnetic Resonance Spectra. ) Foreign Literature Publishing House (Russian translation) 1962 8. H. S. GUTOWSKY, A. SAIKA, M. TAKEDA and D. E. WOESSNER, J. Chem. Phys. 27: 534, 1957 9. V. L. KARPOV, N. M. POMERANTSEV and N. M. SERGEYEV, Vysokomol. soyed. 6: 100, 1964
STRESS RELAXATION IN POLYPROPYLENE* G. L. SLONIMSKII and L. Z. ROGOVINA I n s t i t u t e of E l e m e n t a r y Organic Compounds, U.S.S.R. Academy of Sciences
(Received 29 December 1962)
THE aim of the present work was to study the relaxation processes in a crystalline polymer at different degrees of crystallization, and to find the regularities in stress relaxation in this state. Until now this kind of study has mainly been conducted in the high-elasticity state . METHODS Isotactic polypropylene was used for the study; it contained no amorphous fractions and had a molecular weight of 350,000. Films were produced by compaction at a pressure of 100 kg/em ~ and temperature of 210 °. The cooling rate of the melt was 223°/rain, The specimens were quenched b y p u t t i n g the compaction moulds heated to 210 ° into a mixture of cold ice and toluene. This produced specimens with what is known as a mesomorphic structure , which is typical of the rapidly quenched state of polypropylcne, and which * Vysokomol. soyed. 6: No. 2, 314-320, 1964.
G . I . S L O N m S ~ and L. Z. RoGovr~A
is simply a weak crystallized state. Rectangular specimens were cut out of the Alms and t h e y were stretched rapidly on a Polyani apparatus , after which the time drop in t h e stress was measured. The influence of temperature, and also of the magnitude and rate of strain, were studied as affecting the process of stress relaxation. As we know, the structure and hence the course of the relaxation curves, will v a r y in dependence on very slight changes in t h e conditions under which the film was produced. Fo r this reason each series of measurements was made on specimens t ak en from the same piece of film,
CALCULATIONS I n amorphous polymers stress relaxations follow very closely the equation  a f ~oe-atk + a ~ = E o~e-,tk + E ~ 8 ,
where a is the stress in the specimen at a m o m e n t of time t, a 0 is the m a x i m u m relaxing (variable) part of the stress, a ~ is the equilibrium stress in the specimen when the relaxation process is completed and E 0 is the variable part of the elasticity modulus. E ~ is the equilibrium elasticity modulus, 8 is the strain, a and k are constants which characterize the material of the specimens. Introducing the concept of relaxation time by means of the relation a =
then, in a period of time :, the variable part of the stress a0 will diminish e times as compared with its value in the initial moment. I t is easy to show that r = l/all k •
We used equation (1) for the case of stress relaxation in a crystalline polymer, in order to determine its applicability and the nature of deviation from it. A typical example is shown in Fig. 1.
7Trne , rain
FIG. 1. Relation between the experimental and theoretical stress relaxation curve. Crystalline polylSropylene, 50 °, 8 8 ~ deformation on first stretch. I f we plot the theoretical stress relaxation curve according to this equation, after calculating the constants a o, ~ ,
(the procedure for the calculation will be published separately), it will be seen from the graph t h a t the experimental points lie satisfactorily along this curve. The same results were obtained in a large number of experiments, which shows that it is in principle possible to use this equation to describe stress relaxation in a crystalline polymer.
Stress relaxation in polypropylene
1. Effect of magnitu~le shows t h e m a g n i t u d e o f r e l a x a t i o n . According to same Figure, below 17% o',kg/cm 2 250
of the strain on the process of stress relaxation. F i g u r e 2 the strain in a crystalline p o l y m e r versus t h e stress the s t r e t c h i n g c u r v e o f this p o l y m e r shown in t h e t h e strain is o n l y elastic. A t a p p r o x i m a t e l y 17% the o;,kg/cm z (2
~me , rain
Fio. 2. a-influence of magnitude of strain on the stress relaxation of crystalline polypropylene at, 50 ° (strain indicated in ~/~ on the curve); b--stress versus strain for crystalline polypropylene at 50°. stress reaches a m a x i m u m (recrystallization stress) a n d the falls due to necking. B e t w e e n 70 a n d 5 0 0 % strain t h e necking develops a t c o n s t a n t stress (plateau on t h e curve) a n d f r o m 5 0 0 % t h e entire recrystallized specimen is i n v o l v e d in t h e strain. As usual, in t h e g r a p h t h e stresses are r e l a t e d t o t h e initial cross section. H o w e v e r , as t h e cross section o f the specimen diminishes as t h e strain increases, it would be m o r e correct t o calculate t h e stress per t r u e section. Below we give t h e c o n s t a n t s o f e q u a t i o n (1) where t h e a o a n d values, a n d hence also t h e E o a n d E ~ values, for t h e first section are given as calculated b o t h against the original, a n d t h e t r u e sections. T h e specimen ceases t o be u n i f o r m a f t e r necking begins (there is a t h i c k a n d a t h i n part), a n d two t r u e stresses will coexist. T h e d e p e n d e n c e of the c o n s t a n t s o n t h e m a g n i t u d e o f strain is as follows: e, ~o ao, theor. ao, true E o,
2 69 71 3560
4 99 103 2740
10 149 164 1640
30 108 . .
50 110 . .
88 171 . .
288 175 . .
aco, a~, E=, r,mln
theor. true true
SLONI~Sg2I a n d L . Z. ROG0VINA
134 124 136 129 6800 ' 3080 17"1 28"9
126 139 1390 27"5
95 =-. 7-8
77 . .
56 . .
. . 2"4
As we can see from these figures, in the first part of the stress-strain curve (until necking) the relaxation part of the true stress rises while its equilibrium part ( a ~ ) h a r d l y changes at all. As the strain will be increasing, the corresponding moduli E 0 and E~ diminish while the relaxation time will increase. On further increase in the initial strain, the relaxation time falls, and at stresses corresponding to the beginning of the plateau on the stress-strain curve, it becomes almost constant. At all strains above 70% (including that corresponding to the I I I part of the stress-strain curve) the relaxation and equilibrium parts of the stress remain practically unchanged. 2. Effect of temperature upon the stress relaxation process. As we can see from Fig. 3, with rising temperature the initial stress and its equilibrium part fall while the relaxation part of the stress shows no particular dependence on temperature in our experiments. This is probably due to the fact that the initial stretching of the specimens was too slow.
100~ "x~,, ~o"-..-o 33" ~k~.~"--X--x40, ~.'X,.x ~ ~ 50= 50 r~:L-- -.--.x - - . . . - - - - x ~ × . 70 ° ,ol o ' 30 60 90
50~ 8 5 o f
FIG. 3. E f f e c t o f t e m p e r a t u r e o n s t r e s s r e l a x a t i o n : a - - c r y s t a l l i n e p o l y p r o p y l e n e ; b - - q u e n c h e d p o l y p r o p y l e n e . 50~o s t r a i n o n first s t r e t c h .
I t can be seen from Fig. 4, which gives the temperature dependence of the equilibrium stress, that it is extrapolated to zero at temperatures of approximately 165-170 °, i.e., the melting point of polypropylene. This means that the magnitude of the equilibrium stress shows the crystalline state of the poly-
Stress relaxation in polypropylene
mer, and m a y be directly connected with its melting point. Of course, if the magnitude of the relaxation parts of the stress can be extrapolated to zero, this would be a way of obtaining the glass point of the polymer.
,oo % 6o-
Fir.. 4. E q u i l i b r i u m s t r e s s ' a ~ versus t e m p e r a t u r e of t h e relaxa.tion process. e=50°~o .
I t follows from calculation of the temperature dependencies of the stress relaxation in crystalline and quenched polypropylene (Fig. 3) t h a t the equilibrium elasticity modulus E~ rises with crystallinity, and also E o the variable part of modulus, the appropriate figures for the there temperatures are given below: t, °C a0, crystalline quenched ao0, crystalline quenched V,min crystalline quenched
20 251 86 100 68 6 10.8
50 146 87 57 40 1 2.13
66 120 112 44 30 1 1.48
Analysis of these figures shows t h a t under our experimental conditions relaxation processes become more vigorous with rising crystallinity. 3. Effect of rate of strain on the process of 8tress relaxation. Figure 5a gives stretching curves of up to 715% for a crystalline polymer at three different rates, and stress relaxation curves taken immediately after stretching at these rates. I t can be seen from this graph t h a t the position of the stress-strain curve rises with the rate of stretching, while t h a t of the relaxation curve falls. For a crystalline polymer a0 the relaxation part of the stress will rise with rate of strain and a~ its equilibrium part will fall, while the rate of the relaxation process increases rapidly (i.e. the relaxation time diminishes). For quenched polypropylene the relationship between stress relaxation and strain rate is not so close (Fig. 5b), only at very low rates is there any difference in the relaxation curve.
G.L. SLO~mSK~ and L. Z. ROGOV~A
700 ~. %
60 t, rain
FIG. 5. Effect of strain rate on stress relaxation: a--crystalline polypropylene; I--stress versus strain; //--stress versus time: vz~0.009 mm/sec, vs=O.08 mm/sec, va=0.73 mm/sec; b--quenched polypropylene: vz=0.007 mm/sec, vs=0.066 mm/sec, va=0.59 mm/sec, v 4 = 5 mm/sec. DISCUSSION
From the experimental and theoretical figures shown we can conclude that the nature of the variation in the calculated constants with variation in the first stretching conditions indicate specific features of the stress relaxation process in the crystalline state of the polymer. In the case of high-elasticity polymers we know that E~ the equilibrium elasticity modulus is definitely interrelated with the degree of spacial cross linking of the polymer which, according to the current statistical theory of high elasticity, is equal to the number of sites in the macromolecular space network for 1 cm 3 of the material.When a highelasticity polymer is subject to strain, under conditions where there is no mechanical rupture of the macromolecules, its degree of cross linking is preserved, and therefore the E~ remains constant when the mechanical conditions of strain are varied (the rate, for instance) while a variation in the temperature m a y be accompanied by an increase in the equilibrium modulus in direct proportion to the absolute temperature, as required by the thermodynamics theory of high elasticity. In the case of crystalline polypropylene the E~ value, and hence its corresponding ~ E ~ e value, will be substantially dependent upon the conditions of strain. It will fall monotonically with rising temperature, extrapolated to the zero value of the melting point of the polypropylene, which indicates a reduction in the degree of spacial cross linking with rising temperature. On further increase in the rate of strain E~ will fall as the magnitude of the stress rises, and hence also v the relaxation time.
Stress relaxation in polypropylene
As the extent of strain increases the E~ value also falls, and at the point where the curve enters the plateau it appears to reach minimum values of approximately zero. Of course, this kind of relationship between the equilibrium elasticity modulus (and also the relaxation time) and the condition of strain could be simply due to the fact t h a t the crystalline structure of the material has been destroyed in the process of strain, which means a reduced degree of crosslinking. This disturbed structure is restored in the subsequent process of stress relaxation. This makes it quite understandable t h a t as the magnitude and rate of strain increases the increased stress should lead to .further disturbance of the structure, with further reduction in E ~ . E~ reaches very low values at strains corresponding to the point where the stress-strain curve enters upon the plateau, and this is due to the total rupture of all the structures. I t is interesting t h a t necking should occur at low degrees of strain corresponding precisely to the m a x i m u m stress when, to judge from the E~ value, only part, and not all, of the structure has been ruptured. I t can be seen from Fig. 5 t h a t while E~ and r diminish with rising rate in the crystalline polypropylene, in quenched polypropylene, beginning at a strain rate of 0.066 ram/set, they remain unchanged. I t is natural t h a t the quenched polypropylene should have a less perfect structure, which means t h a t the stresses corresponding to this rate are usually sufficient to destroy all existing structures, while a further increase in stress due to increased rate, will leave them unehanged. A quantitative study of stress relaxations in crystalline polypropylene has thus clearly demonstrated the existence of a spatial structure, and its destruction as a result of strain. The problem of the mechanism of the rupture and the nature of this structure naturally arises. A number of recent structure studies  have shown t h a t in both crystalline and amorphous polymers there is a considerable difference in the secondary structural formations. Bundles of chains forming bands and strips have been found, and from these either spherulites or larger structural elements are formed, or else, under favourable conditions, single crystals. The effect of the differences between these secondary structures upon the mechanical properties of the polymers has been demonstrated . I t is clear from our figures and from published data t h a t in the crystalline state, the mechanism of stress relaxation is different than in the high-elasticity state of the polymer, and it is connected with the destruction and displacement of secondary structural formations. The depth of this mechanical disturbance of the structure probably differs. In  for instance, it was found t h a t stress relaxation leads to the formation of cracks in a crystalline polypropylene at elevated temperatures. This would correspond to the coarsest process of mechanical destruction of the structure. Thus we have shown by two independent methods, structure [6, 7] and phenomenological, t h a t there are certain signs of supermolecular structures in
G.L. SLONDISKIIand L. Z. Roc,ovI.~t
crystalline polymers, and t h a t t h e y vary under strain. Naturally, a combination of the two methods should give an even better idea of the mechanism of the processes which occur during and after the deformation of the polymers. CONCLUSIONS
(1) I t has been found possible to calculate the stress relaxation in stretched specimens of crystalline polypropylene. (2) Analysis of the constants characterizing the relaxation process, as dependent on t e m p e r a t u r e and stress magnitude and rate, and also the depth of crystallization, permits some general conclusions regarding the influence of these factors on the structure of the crystalline polymer, (3) The fracture of the physical structure of a crystalline polymer due to stretching (with the possibility of subsequent recovery) becomes greater with the magn!tude and duration of the stresses. The equilibrium elasticity modulus E~ is the measure of the physical structuration of the crystalline polymer. (4) Current methods of studying supermolecular structures in polymers must be combined with quantitative analysis of the relaxation processes. Translated by V. ALFORD
1. A. B. TOBOLSKY, Properties and structure of polymers, New York-London, John Wiley, 1960; J. B. FERRY, Visco-elastie properties of polymers, New York-London, John Wiley, 1961 2. R. L. MILLER, Polymer 1: 135, 1960 3. G. Sh. IZRAELIT, Mekh. ispyt, reziny i kauehutm. (Mechanical Testing of Rubbers.) Goskhlmizdat, Leningrad-Moscow, 134, 1949 4. G. L. SLONIMSKII, Zh. tekh. fiz. 9: 1791, 1939; F. KOHLRAUSCH,Pogg. Ann. 119: 337, 1863 5. A. KELLER, Phil. mag. 2: 1171, 1957; P. H. TILL, J. Polymer Sci. 24: 301, 1957; V. A. KARGIN, Sovr. probl, nauki o polimerakh. (Current Problems of Polymers.} Izd.-vo. MGU, 1962 6. V. A. KARGIN, T. I. SOGOLOYAand L. L NADAREISHVILI, Vysokomol. soyed. 6: 165, 169, 1964 7. V. A. KARGIN, T. I. SOGOLOYA and N. P. PAVLICHENKO,sb. Karbotsepnye vysokomolekulyarnye soyed. (Carbochain Polymers.) Izd. Akad. Nauk SSSR. 107, 1963; V. A. KARGIN, T. I. SOGOLOVA and N. P. PAVLICHENKO, Dokl. Akad. l~auk SSSR 147: 407, 1962