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Mechanism of increasing the impact strength of plastics using rubber dispersions
Increasing the impact strength of plasties using rubber dispersions 13. 14. 15. 16.
985
N. J. LIV and J. JONAS, J. Magn. Res. 18: 4, 444, 1975 J. A. ANDE]gSON, D. D. DAVIS and W. P. SLI~[TER, Maoromoleoule~ ~: 2, 166, 1 9 6 9 H. SAKARE, J. Polymer Soi., Polymer Phys. Ed. 11: 12, 2413, 1973 I. I. BARA~WIgOVA, A. L. KOVA][~lgIT and A. M. WASSERMAN, Vysokomol. soyed. A24: 1, 91, 1982 (Translated in Polymer SoL U.S.S.R. 24: 1, 105, 1982)
Polymer Science U.S.S.R. Vol. 25, 1~'o. 4, pp. 985--994, 1983 Printed In Poland
0082-3950/83 $10.00 ÷.00 O 1984 Pergamon Press Ltd.
MECHANISM OF INCREASING THE IMPACT STRENGTH OF PLASTICS USING RUBBER DISPERSIONS* G. M. LUKOVKIN, A. L. VOLYNSKII a n d N. F. BAKEYEV M. V. Lomonosov State University, Moscow (Rscelve~/ 22 De~e~nber 1981) Fracture of "brittle" polymers such as PS, PMM_A, PVC is clearly a non-elastic process. The main transformation of the energy of deformation into heat takes plaoe in very small material volumes, which results in thermal decomposition. Calculations show that temperature changes in the zone of plastic deformation of the polymer may reach hundreds of degrees. The addition to the polymer of a rubber dispersion markedly increases the number of places of localized plastic deformation. The real rate of nonelastic transition of the polymer into the oriented state decreases, heat liberation is much lower and the possibility of plastic deformation of the polymer increases and therefore the energy of decomposition is higher. THE effect of increasing t h e i m p a c t s t r e n g t h o f brittle plastics such as PS, PMMA, PVC, etc. b y a d d i t i o n into t h e m o f fine r u b b e r dispersions is well k n o w n a n d w i d e l y u s e d in practice. M a n y studies generalized in a n u m b e r o f reviews a n d m o n o g r a p h s [1-3] are dealing with this effect a n d w i t h establishing its mechanism. Nevertheless, t h e m e c h a n i s m o f this effect so far is n o t clear. M~croscopically, t h e d e f o r m a t i o n o f high-impact plastics differs f r o m deform a t i o n o f h o m o g e n e o u s glassy polymers. T h e m a i n difference is in t h e f a c t t h a t t r a n s i t i o n o f t h e p o l y m e r into t h e oriented s t a t e takes place w i t h o u t n e c k form a t i o n in a n y single place. I t t a k e s place in a n u m b e r o f microscopic zones b y t h e f o r m a t i o n o f specific macrocracks, as observed in d e f o r m a t i o n o f h i g h - i m p a c t P S [41, P M M A [5], ABC plastics [6], or b y multiple f o r m a t i o n o f micro-regions o f shear d e f o r m a t i o n , the same as in d e f o r m a t i o n o f PVC modified b y r u b b e r [7]. * Vysokomol. soyed. A25: No. 4, 848-855, 1983.
G. M. Luxov~n¢ = at.
986
In this respect this deformation has a number ef common features with deformation of glassy polymers in adsorption-active media, where the polymer too changes into the oriented state without neck formation in a number o f microscopic zones--in microeracks. The morphological difference of deformation mechanisms enabled m a n y special features of properties of polymers to be explained, plastic deformation of these polymers taking place in a number of localized zones [8, 9]. An attempt was made in this study to use ideas previously developed [10, 11] in order to explain the mechanism of reinforcing action of rubbers introduced into brittle glassy polymers.
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Fxo. 1. Curves of elongation of PVC (1) and high-impact P¥C (2) obtained at rates of elongation of 1.67 (a) and 450 ram/rain (b). Objects and methods of investigation were described in detail previously [12]. For the correct understanding of the reinforcing action of rubber on glassy polymers, it is necessary to examine briefly main features of this effect. It is known [2] that the main practical consequence of this effect is the sudden increase in the energy of breakdown of glassy polymers when adding to it a rubber dispersion. In view of the practical importance of this problem several theories were developed which explain the effect of rubber inclusions on the mechanical behaviour of plastics. We will not analyse them since they have been dealt with in de~ail in m a n y papers [1-3J, we only note that these theories cannot, to our mind, fully explain the solidification mechanism since they do not allow for specific features of impact loading. The effect of solidification is most clearly apparent precisely in the range of impact rates of loading, while at fairly low rates it is negligible, or disappears completely. Figure 1 shows curves of elongation of pure PVC and PVC containing 15 wt.~o rubbery modifier (ternary eopolymer based on methyl methacrylate-butadiene-styrene). I t is clear t h a t if at high rates of loading the energy of deformation (characterized by the area under the curve of elongation) of pure PVC is, in fact, much lower than t h a t of modified
Increasing the impact strength of plastics using rubber dispersions
987
PVC, at comparatively low rates of deformation on "the other hand the e n e r g y of fracture of pure PVC is higher than that of modified PVC. Therefore, the explanation of the mechanism of increased impact strength of plastics as a result of adding modifying additives should be sought in special features of high-speed deformation of polymers. What are these special features like? It was shown previously [12] that in(.reasing the rate of deformation of PVC results in a marked reduction of breaking elongation. This kind of "embrittlement" is due to a marked increase in heat liberation during plastic deformation of the polymer. Since the heat conductivity of organic polymers is low, heat liberation may result in a very significant temperature change in a localized zone of transition of the polymer into the neck, consequently, it softens and thermal decomposition takes place with low deformation. It is natural that increasing the rate of deformation contributes to transition from isothermal to adiabatic conditions of polymer deformation. Therefore, one of the main differences between conditions of polymer deformation at low rates of loading and conditions of deformation at high rates (particularly under impact) is the adiabatic system, which depends on, difficult, heat removal [12, 13]. Another important feature of deformation of the glassy polymer (this not only shows under conditions of impact loading) is the high three-dimensional localization of the zone of plastic deformation. This deformation is normally restricted to a narrow zone between the unoriented part of the polymer and the neck. I n other words, the entire energy of non-elastic deformation of the polymer is converted into heat in a very small localized volume. It is not surprising therefore, as shown by direct measurements, that the so-called "brittle" rupture of PS and PMMA at room temperature is accompanied by a sudden temperature change in the top part of a rapidly gro~ing crack, reaching 200-300°K [14]. Self-heating of the polymer subjected to deformation at intermediate rates sometimes results in a particular auto-~ibratory mechanism of deformation [15] and there are now attempts being made to use the effect indicated in practice [16]. A further reduction in the rate of deformation contributes to polymer decomposition by the mechanism of "heat explosion" [17], which is evidently of major significance in impact loading of the polymer. To verify this assumption, the temperature change in forced elastic deformation of glassy polymer has to be evaluated. It is therefore necessary to solve the equation of thermal conductivity of the polymer, bearing in mind the real physical pattern of plastic deformation. For simplicity, let us examine elongation at constant rate v of a long and thin polymer rod, during the elongation of which a neck is formed in point x-~0; the edges of this neck extend to the opposite sides along the sample. Of course, the entire energy of plastic deformation of the polymer is transformed into heat in very narrow zones [18] between the neck and the unoriented part of the polymer sample. Therefore, these transitional ranges may be regarded as two point type heat sources. This pattern of cold drawing satisfactorily corresponds to the situation observed in reality during
988
G.M. Luxovx~
s$ a/.
deformation of glassy polymers [19]. This approach enables the problem to be reduced to solving a one~iimensional equation of heat conductivity of the polymer sample. Simulation of heat effects in deformation was carried out as follows. At t = 0 moment of time in point x = 0 two heat sources are f o r m e d with instant heat liberation q, which later separate at a rate of v/2. Temperature distribution along the length of the rod is described for a given case by solving the appropriate equation of heat conductivity
aT
K O2T
+
1 [- /vt
~
+q
/
~ \]
,
(1)
where K is the coefficient of heat conductivity of the material, C is the specific heat, p--linear density of the material. Since we are interested in the case of adiabatic deformation, the term related to heat removal from the surface of the rod is omitted from eqn. (1). To simplify the problem, a point type heat source could be used, however, in this case singularity is observed in the solution of eqn. (1) in points ~:(v[2)t, where the temperature change is infinitely great, which does not correspond to physical reality. To overcome this contradiction, we used the following procedure: having retained the point type nature of sources
to find temperature distribution T(x, t), we carried out convolution Q ± ~ t, with displaced response of the point type source with the following temperature distribution in the source: q
exp[
4a'~-~-bb)]
(3)
T~ (x, ~) = - -
where
=
~. T(~, ~ ) = - -
1
v 0
d~
(4)
--~
as a result of which bearing in mind eqn. (2) temperature distribution is given by the formula
!
,[
fe
. ~/~-~-~+b
0
d~
(5)
Increasing the impact strength of pla~dc~ using rubber dispersions
989
The value of b was found from the condition of constancy of the width o f distribution of source (3) so t h a t on the boundary of the zone of plastic deformation of size d-~ 200 pm temperature was reduced e times, compared with the centre of distribution. This condition results in the ratio
b=d2/16a ~ The approach we adopted enables the time of calculation using a computer to be reduced considerably in determining temperature distribution along the sample. Let us examine the difference between solution (5) and the accurate solution of eqn. (1) with two distributed heat sources in which instant distribution is described b y functions of t y p e (3). I t is easy to see that in points -V(v/2)t=x solution (5) is accurate. In all remaining points it differs from the accurate solution by a lower steepness of decrease of T(x, t), which results in greater delocalization of heat in the sample (compared with the accurate solution). Therefore, the solution of T(x, t) obtained using eqn. (5) results in a reduction of temperature, which is quite admissible, since the calculation is estimated. With elongations (v[2)t>>d solution (5) is accurate in practice. In order to carry out a numerical calculation, we determined the value of q and p. We use results of the experimental study carried out by Andrianova et al. [20], in which a careful calorimetric investigation was carried out of cold drawing of P E T P . I t is very important for us that in this study calorific power values were obtained at several rates of deformation W=dQ/dt. To solve eqn. (1) the dependence of the power of heat source W on the rate of polymer elongation v has to be determined. I n the case of forced elastic deformation of the polymer it m a y be assumed that practically all the mechanical energy used for deformation (A) is converted into heat Q [13, 21], i.e.
S dA~- S dQ The obvious relations follow from here
dA =aSdl=agv~ dQ = Wdt, where a is stress in stationary deformation, 1 is instantaneous length of the polymer sample and S - - i t s cross sectional area. Then,
W=a~v Using the well-known Lazurkin equation for high rates of elongation
\~o/ where R is the universal gas constant and ~ and 3o are constants, we finally
G. M. Luxovxi~ e* a/.
990
obtain
W(v)--~
RT
v vS I n -
(6)
"CO
Equations (5) and (6) enable the temperature change inthe zone of plastic deformation of the polymer to be obtained in impact loading. We evaluate this change using amorphous glassy P E T P which was previously [20] examined in detail and for which all requisite thermal parameters are known. These parameters are as follows: C~=0-3 cal/g-deg [22] p=1.34 g/cm a [20] k-~0.00036 cal/sec.cm.deg [22] To evaluate parameters of eqn. (6), we used direct calorimetric data of the study by Andrianova et al. [20] concerning thermal effects o f deformation of P E T P in a wide range of rates of elongation. TJsing values of heat release at rates of elongation of 1.03 and 10.5 mm/min derived in this study, we determine parameters of the Lazurkin equation In z0------17.97 ram/rain, ~----5150 cal.mm2fkg. Finally, eqn. (6) for P E T P takes the form
W(v) cal/sec-----0.1436v (lnv~-17.97), where heat release refers to the section of a rod 1.25 mrn in diameter [20]. We may now deal with determining the value of q. This is easily done by the following method: let there be a temperature distribution T(x, 1) be in the sample by t = l . Then, the value of Cp ~ T(x, 1) dx denotes heat liberated during this $ime in the sample, i.e. -~
w = Cp I T(x, 1)
(7) q
exp
4a ( l + b - - ~ ) ] + e x p
.
4a2(l~)Jd~
--co
K where a 2- -- -C~ - p' 2a----0.06 cm/sec~, T(x, t) being the function of rate. By norrealization (7) the value of q is directly found and T(x, t) may be determined quantitatively. A typical curve which describes temperature distribution along the sample, plotted using eqn. (5) is shown in Fig. 2. I t can be seen that under adiabatic conditions the temperature of the sample in any section increases evenly as the f~ont of the neck advances along the sample. I t is natural that this situation is typical of the case of low ra~e of elongation, when nonelastic' deformation
Increasing the impact strength of plastics using rubber dispersions
991
takes place trader stationary conditions with neck formation. For the case of impact failure we are interested in the temperature of the polymer at an initial moment of time, when the polymer undergoes plastic deformation. The time when forced elasticity of the polymer is achieved should be accepted as such moment of time, since it is precisely at this point t h a t plastic deformation of 2
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3 1
o.l/
2
1
2
0-025
0.075
a2
:c cm
F,c.. 2. Dependences of the distribution of temperature quoted T(z, 1)=T(z, 1)/(~-~/=-T~~ \~rV
"/
in f,he length of the rod for rates of elongation v----O.01 (1) and 10 cra/aee (2). the polymer takes place and neck formstion occurs. This time t is easily determined exprimentaUy
t=~k" lo/v, where sk is deformation corresponding to maximum forced elasticity of the polymer, l 0 is the initial length of the sample which in our ease is 6 cm [20]. Results obtained for three rates of elongation are: v, cm/sec ~T, K
0.001 10
0.01 60
10 600
Calculation carried out for a comparatively low rate of elongation v~-0.01 em/sec gives a significant value of temperature change AT----60°K which is in satisfactory agreement with results of an earlier paper [13] exceeding Tg of the polymer if elongation is effected at room temperature. It can be seen that with a comparatively low rate of elongation in the polymer extremely high temperature changes
999.
G. M. LlrKovxm t¢ ~ .
are observed which may result in a special auto-vibratory mechanism o f defer. mation [15, 20]. Increasing the rate o f d e f o r m a t i o n naturally approximates to adiabatic conditions and with impact loading heat loss will be minimum. For example, reducing parameters of eqn. (6) to the rate of elongation v-----10 era/see, at which PETP breaks down with low elongation, gives the temperature change value of AT~f00°K. Approximate calculations indicate that at high rates of loading considerable temperature changes occur, so that temperature exceeds considerably the melting point and the temperature of chemical decomposition of corresponding polymers. Breakdown of polymers under these conditions should, in fact, be regarded as "heat explosion". The effect of rubber modifiers on the impact strength of glassy polymers should be regarded by analysing the situation at high rates of loading. It was shown in a number of studies [1-3] that deformation of high-impact compositions takes place without neck formation by transition of the polymer into the oriented state inside specific microcracks or shear bands without disrupting the continuity of the material. There is a lot in common between these two varieties of plastic deformation [23] and they often coexist [24]. l~on-elastie plastic deformation is not carried out in any one place, as is the case with neck formation in the polymer, but simultaneously in a number of places of the sample with the formation of microcracks, or shear bands. Without dwelling on physical causes of initiation of such a number of places of localized deformation* we note that these morphological features of deformation have a lot in common with the deformation mechanism of polymers in adsorption-active media. For example, increasing the rate of elongation of high-impact materials increases the number of mierocracks [25], the same as in deformation of pure polymers in adsorption-active media [10]. As noted previously [11], increasing the number of places of localized deformation reduces the rate of ]ocalized transition into the oriented state at the same macroscopic rate of deformation of the polymer sample, as a whole, and lowers macroscopic stress in stationary deformation. As noted previously, heat flow in plastic deformation of the polymer is proportional to the rate of elongation of the polymer or (what is the same) to the rate of transition into the oriented state. The addition to the glassy polymer of a rubber dispersion is known to result in the formation of many localized places of transition to the oriented state. This is seen for high-impact plastic samples subjected to impact failure in the form of whitening of the operating part of samples (stress whitening) [4, 5]. ~ e try to evaluate the variation of AT in the polymer sample if deformation takes place in many and not just two places, as is the case in high-impact plastics. For this we use direct X-ray [26] or electron-microscope [27, 28] assessments of the number of mierocracks
* Assumptions concerningthe causes of formation of places of localized plastic deformation in high-impact plastics are described in the literature [1~3].
Inereadug the impact strength of plastics using rubber dispersions
993
formed in deformation of high-impact PS. Linear density of microcracks in these materials is 104-105 cm -1. I t is obvious t h a t the formation of such a large number of places of localized deformation considerably reduces the real rate of polymer transition into the oriented state and therefore, heat release (eqn. (16)). I f we assume t h a t the linear density of such places of localized polymer transition to the oriented state is n ~ 1 0 ~ cm -1, the real temperature change according to our estimates decreases 100-fold, which for a rate of elongation of 10 cm/sec increases the temperature of the polymer only by 6°K. I t is natural t h a t this slight heating of the material (evenly distributed in the volume) results in rapid decomposition and considerably eases plastic deformation. I t is therefore not surprising t h a t under these conditions materials such as high-impact PS, or ABC readily undergo plastic deformation, although under experimental conditions the glassy matrix of these materials which is the continuons phase, cannot undergo considerable non-elastic deformation. I t is also e~ident tha~ the work of failure of plastics reinforced with rubber at high (impact) rates of loading increases markedly (Fig. 1), Therefore, the mechanism of reinforcing action of plastics with rubber inclusions involves initiation of a large number of localized places of plastic deformation of the polymer, which reduces the real rate of transition of the polymer to the oriented state, reduces heat release and prevents rapid thermal decomposition of the polymer at impact of loading. The authors are greateful to V. A. Kabanov for the useful discussions held. Translated by E. SEM~.~E REFERENCES 1. R. P. ]~LMBOUR, J. Polymer SoL, Msoz~mo]eo. Rev. 7: 1, 1973
2. 8. G. BRAGAU In: Monogokomponentnyye polimernyye sistemy (Multi-component Polymer Systems). p. 142, Khimiya, Moscow, 1974 3. G. MANSON and L. SplCRLING, Polimernyye smesi i kompozity (Polymer Mixtures and Compositions). p. 76, Khimiya, Moscow, 1979 4. C. R. BUL~IKNALLand R. R. SMITH, Polymer 6: 6, 437, 1965 5. K. TAKAHASHI, J. Polymer Phys. Ed. 12: 10, 1697, 1974 6. R. W. TRUSS and G. A. CHADWICK,J. Mater. Sci. 12: 11, 1383, 1977 7. H. RREUER, F. HAAF and J. 8TABENOV, J. 1Kacromoleo.Sci. 1114: 3, 387, 1977 8. A. G. ALESlffEROV,A. L. VOLYNSKHand N. F. BAKEYEV, Vysokomol. soyed. BIg: 3, 218, 1977 (Not trarislated in Polymer Sci. U.S.S.R.) 9. V. L. VOLYNSKII, N. A. SHITOV and N. F. BAKEYEV, Vysokornol. soyed. A23: 6, 978, 1981 (Translated in Polymer Sci. U.S.S.R. 28: 5, 1089, 1981) 10. L. M. YARYSHEVA, L. Yu. PAZUKHINA, G. M. LUKOV]KIN, A. L. VOLYNSKII, N. F. BAKYEV and P. V. KOZLOV, Vysokomol. soyed. A24: 10, 2149, 1982 (Trans. lated in Polymer Sci. TJ.S.S.R. 24: 10, 2464, 1982) 11. A. L. VOLYNSlgI~.~ G. M. LUKOVKIN, L. M. YARYSHEVA, L. Yu. PAZUKHINA, P. V. KOZL0V and N. F. BAKEYEV, Vysokomol. soyed. A24: 11, 2357, 1982 (Translated in
Polymer Sci. U.S.S.R. 24: 11, 2706, 1982) 12. A. L. VOLYNffglT, A. G. ALESKEROV, A. S. KECHEK'YAN, T. B. ZAVAROVA, A. Ye. SKOROBOGATOVA,8. A. ARZHAKOV and N. F. BAKEYEV, Vysokomol. soyed. BIg: 4, 301, 1977 (Not translated in Polymer Sci. U.S.S.R.)
994
A. P. TYU~EV e~ ~ .
13. J. W. M ~ H E R , R. N. H A W A R D a n d J. N. HAY, J. P o l y m e r Sei., P o l y m e r Phys. E d . 18: 11, 2169, 1980 14. K. N. G. FULLER, P. G. FOX and J. E. H E L D , Prec. Roy. See. A841: 1627, 537, 1975 15. A. S. KECHEK'YAN, G. P. ANDRIANOVA a n d V. A. KARGIN, Vysokomol. soyed. A12: 11, 2424, 1970 (Translated in P o l y m e r Sci. U.S.S.R. 12: 11, 2743, 1970) 16. A. RRUKH, Avtoref. dis. n a soiskaniye ueh. step. kand. tekhn, nauk, M I T K h T im. i~I. V. Lomonosova, Moscow, 1981 17. E. A. EGOROV, V. V. ZIZENKOV, 8. N. BEZLADNOV, I. A. SOKOLOV and E. M. TOMASHEVSKII, A e t a Polymerica 31: 9, 541, 1980 18. A. L. VOLYNSKII, G. M. LIfKOVKIN and N. F. BAKEYEV, Vysokomol. soyed. A I 9 : 4, 785, 1977 (Translated in P o l y m e r Sci. U.S.S.R. 19: 4, 910, 1977) 19. A. CROSS, M. HALL a n d R. N. H A W A R D , Nature 253: 5490, 340, 1975 20. G. P. ANDRIANOVA, Yu. V. POPOV a n d B. A. A R ~ O V , Vysokomol. soyed. AI8: 10, 2311, 1976 (Translated in Polymer Sci. U.S.S.R. 18: 10, 2644, 1976) 21. J. MAGER, J. N. HAY and R. N. H A W A R D , Internat. Symp. Macromolec., Mainz, Prepr. Short. Commun. vol. 2, p. 1433, 1979 22. E. M. EISENSTEIN, In: Entsiklopediya polimerov (Polymer Encyclopaedia) vol. 3, p. ]08, Sovetskaya entsiklopediya, Moscow, 1977 23. G. S. Y. YEH, J. Macromolec. Sci. B7: 4, 729, 1973 24. A. S. ARGON, Pure Appl. Chem. 43: 1-2, 247, 1975 25. R. W. TRUSS and G. A. CHADWICK, J. Mater. Sci. 11: 10, 1385, 1976 26. N. R. ASHUROV, Avtoref. dis. n a soiskaniye ueh. st. kand. fiz.-mat, nauk, IVS A N SSSR, Leningrad, 1978 27. S. B. BUCKN,4LL~ I. C. DRINKWATER and W. E. KEAST, Polymer 18: 1, 115, 1972 28. P. BEHAN, A. THOMAS and M. BEVIS, J. Mater. Sci. 11: 1207, 1976
P o l y m e r Science U.S.S.R. Vol. 25, No. 4, pp. 994-1001, 1983 P r i n t e d in Poland
0032-8950/83 $10.00-[-.00 O 1984 P e r g a m o n Press L t d .
ELECTRICAL EFFECTS BY THE, ACTION OF LOW ENERGY ELECTRONS ON POLYARYLATES* A . P . TYUTNEV, V. S. SAYENKO, P . M. VALETSKII, V. A . Kin, G. P . SA~O~OV, YE. D . POZHIDAYEV, S. V. VINOGRADOVA a n d V. V. KORSHAK I n s t i t u t e of Hetero-organic Compounds, U.S.S.R. Academy of Sciences Moscow I n s t i t u t e o f Electronic Machine Building
(Received 22 Decemb~ 1981) A study was nm~e of the behaviour of polyarylates, (polypltenol phthaleinisottere)-phthalate and polydianeterephthalate), to the action of electron pulses accelerated to an energy of 65 keV in a vacuum of ~ 1.33 × 10 -s P a in a wide range of * Vysokomol. soyed. A$5: No. 4, 856-861, 1983.
985
N. J. LIV and J. JONAS, J. Magn. Res. 18: 4, 444, 1975 J. A. ANDE]gSON, D. D. DAVIS and W. P. SLI~[TER, Maoromoleoule~ ~: 2, 166, 1 9 6 9 H. SAKARE, J. Polymer Soi., Polymer Phys. Ed. 11: 12, 2413, 1973 I. I. BARA~WIgOVA, A. L. KOVA][~lgIT and A. M. WASSERMAN, Vysokomol. soyed. A24: 1, 91, 1982 (Translated in Polymer SoL U.S.S.R. 24: 1, 105, 1982)
Polymer Science U.S.S.R. Vol. 25, 1~'o. 4, pp. 985--994, 1983 Printed In Poland
0082-3950/83 $10.00 ÷.00 O 1984 Pergamon Press Ltd.
MECHANISM OF INCREASING THE IMPACT STRENGTH OF PLASTICS USING RUBBER DISPERSIONS* G. M. LUKOVKIN, A. L. VOLYNSKII a n d N. F. BAKEYEV M. V. Lomonosov State University, Moscow (Rscelve~/ 22 De~e~nber 1981) Fracture of "brittle" polymers such as PS, PMM_A, PVC is clearly a non-elastic process. The main transformation of the energy of deformation into heat takes plaoe in very small material volumes, which results in thermal decomposition. Calculations show that temperature changes in the zone of plastic deformation of the polymer may reach hundreds of degrees. The addition to the polymer of a rubber dispersion markedly increases the number of places of localized plastic deformation. The real rate of nonelastic transition of the polymer into the oriented state decreases, heat liberation is much lower and the possibility of plastic deformation of the polymer increases and therefore the energy of decomposition is higher. THE effect of increasing t h e i m p a c t s t r e n g t h o f brittle plastics such as PS, PMMA, PVC, etc. b y a d d i t i o n into t h e m o f fine r u b b e r dispersions is well k n o w n a n d w i d e l y u s e d in practice. M a n y studies generalized in a n u m b e r o f reviews a n d m o n o g r a p h s [1-3] are dealing with this effect a n d w i t h establishing its mechanism. Nevertheless, t h e m e c h a n i s m o f this effect so far is n o t clear. M~croscopically, t h e d e f o r m a t i o n o f high-impact plastics differs f r o m deform a t i o n o f h o m o g e n e o u s glassy polymers. T h e m a i n difference is in t h e f a c t t h a t t r a n s i t i o n o f t h e p o l y m e r into t h e oriented s t a t e takes place w i t h o u t n e c k form a t i o n in a n y single place. I t t a k e s place in a n u m b e r o f microscopic zones b y t h e f o r m a t i o n o f specific macrocracks, as observed in d e f o r m a t i o n o f h i g h - i m p a c t P S [41, P M M A [5], ABC plastics [6], or b y multiple f o r m a t i o n o f micro-regions o f shear d e f o r m a t i o n , the same as in d e f o r m a t i o n o f PVC modified b y r u b b e r [7]. * Vysokomol. soyed. A25: No. 4, 848-855, 1983.
G. M. Luxov~n¢ = at.
986
In this respect this deformation has a number ef common features with deformation of glassy polymers in adsorption-active media, where the polymer too changes into the oriented state without neck formation in a number o f microscopic zones--in microeracks. The morphological difference of deformation mechanisms enabled m a n y special features of properties of polymers to be explained, plastic deformation of these polymers taking place in a number of localized zones [8, 9]. An attempt was made in this study to use ideas previously developed [10, 11] in order to explain the mechanism of reinforcing action of rubbers introduced into brittle glassy polymers.
70-
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150
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I
15 t1.,%
Fxo. 1. Curves of elongation of PVC (1) and high-impact P¥C (2) obtained at rates of elongation of 1.67 (a) and 450 ram/rain (b). Objects and methods of investigation were described in detail previously [12]. For the correct understanding of the reinforcing action of rubber on glassy polymers, it is necessary to examine briefly main features of this effect. It is known [2] that the main practical consequence of this effect is the sudden increase in the energy of breakdown of glassy polymers when adding to it a rubber dispersion. In view of the practical importance of this problem several theories were developed which explain the effect of rubber inclusions on the mechanical behaviour of plastics. We will not analyse them since they have been dealt with in de~ail in m a n y papers [1-3J, we only note that these theories cannot, to our mind, fully explain the solidification mechanism since they do not allow for specific features of impact loading. The effect of solidification is most clearly apparent precisely in the range of impact rates of loading, while at fairly low rates it is negligible, or disappears completely. Figure 1 shows curves of elongation of pure PVC and PVC containing 15 wt.~o rubbery modifier (ternary eopolymer based on methyl methacrylate-butadiene-styrene). I t is clear t h a t if at high rates of loading the energy of deformation (characterized by the area under the curve of elongation) of pure PVC is, in fact, much lower than t h a t of modified
Increasing the impact strength of plastics using rubber dispersions
987
PVC, at comparatively low rates of deformation on "the other hand the e n e r g y of fracture of pure PVC is higher than that of modified PVC. Therefore, the explanation of the mechanism of increased impact strength of plastics as a result of adding modifying additives should be sought in special features of high-speed deformation of polymers. What are these special features like? It was shown previously [12] that in(.reasing the rate of deformation of PVC results in a marked reduction of breaking elongation. This kind of "embrittlement" is due to a marked increase in heat liberation during plastic deformation of the polymer. Since the heat conductivity of organic polymers is low, heat liberation may result in a very significant temperature change in a localized zone of transition of the polymer into the neck, consequently, it softens and thermal decomposition takes place with low deformation. It is natural that increasing the rate of deformation contributes to transition from isothermal to adiabatic conditions of polymer deformation. Therefore, one of the main differences between conditions of polymer deformation at low rates of loading and conditions of deformation at high rates (particularly under impact) is the adiabatic system, which depends on, difficult, heat removal [12, 13]. Another important feature of deformation of the glassy polymer (this not only shows under conditions of impact loading) is the high three-dimensional localization of the zone of plastic deformation. This deformation is normally restricted to a narrow zone between the unoriented part of the polymer and the neck. I n other words, the entire energy of non-elastic deformation of the polymer is converted into heat in a very small localized volume. It is not surprising therefore, as shown by direct measurements, that the so-called "brittle" rupture of PS and PMMA at room temperature is accompanied by a sudden temperature change in the top part of a rapidly gro~ing crack, reaching 200-300°K [14]. Self-heating of the polymer subjected to deformation at intermediate rates sometimes results in a particular auto-~ibratory mechanism of deformation [15] and there are now attempts being made to use the effect indicated in practice [16]. A further reduction in the rate of deformation contributes to polymer decomposition by the mechanism of "heat explosion" [17], which is evidently of major significance in impact loading of the polymer. To verify this assumption, the temperature change in forced elastic deformation of glassy polymer has to be evaluated. It is therefore necessary to solve the equation of thermal conductivity of the polymer, bearing in mind the real physical pattern of plastic deformation. For simplicity, let us examine elongation at constant rate v of a long and thin polymer rod, during the elongation of which a neck is formed in point x-~0; the edges of this neck extend to the opposite sides along the sample. Of course, the entire energy of plastic deformation of the polymer is transformed into heat in very narrow zones [18] between the neck and the unoriented part of the polymer sample. Therefore, these transitional ranges may be regarded as two point type heat sources. This pattern of cold drawing satisfactorily corresponds to the situation observed in reality during
988
G.M. Luxovx~
s$ a/.
deformation of glassy polymers [19]. This approach enables the problem to be reduced to solving a one~iimensional equation of heat conductivity of the polymer sample. Simulation of heat effects in deformation was carried out as follows. At t = 0 moment of time in point x = 0 two heat sources are f o r m e d with instant heat liberation q, which later separate at a rate of v/2. Temperature distribution along the length of the rod is described for a given case by solving the appropriate equation of heat conductivity
aT
K O2T
+
1 [- /vt
~
+q
/
~ \]
,
(1)
where K is the coefficient of heat conductivity of the material, C is the specific heat, p--linear density of the material. Since we are interested in the case of adiabatic deformation, the term related to heat removal from the surface of the rod is omitted from eqn. (1). To simplify the problem, a point type heat source could be used, however, in this case singularity is observed in the solution of eqn. (1) in points ~:(v[2)t, where the temperature change is infinitely great, which does not correspond to physical reality. To overcome this contradiction, we used the following procedure: having retained the point type nature of sources
to find temperature distribution T(x, t), we carried out convolution Q ± ~ t, with displaced response of the point type source with the following temperature distribution in the source: q
exp[
4a'~-~-bb)]
(3)
T~ (x, ~) = - -
where
=
~. T(~, ~ ) = - -
1
v 0
d~
(4)
--~
as a result of which bearing in mind eqn. (2) temperature distribution is given by the formula
!
,[
fe
. ~/~-~-~+b
0
d~
(5)
Increasing the impact strength of pla~dc~ using rubber dispersions
989
The value of b was found from the condition of constancy of the width o f distribution of source (3) so t h a t on the boundary of the zone of plastic deformation of size d-~ 200 pm temperature was reduced e times, compared with the centre of distribution. This condition results in the ratio
b=d2/16a ~ The approach we adopted enables the time of calculation using a computer to be reduced considerably in determining temperature distribution along the sample. Let us examine the difference between solution (5) and the accurate solution of eqn. (1) with two distributed heat sources in which instant distribution is described b y functions of t y p e (3). I t is easy to see that in points -V(v/2)t=x solution (5) is accurate. In all remaining points it differs from the accurate solution by a lower steepness of decrease of T(x, t), which results in greater delocalization of heat in the sample (compared with the accurate solution). Therefore, the solution of T(x, t) obtained using eqn. (5) results in a reduction of temperature, which is quite admissible, since the calculation is estimated. With elongations (v[2)t>>d solution (5) is accurate in practice. In order to carry out a numerical calculation, we determined the value of q and p. We use results of the experimental study carried out by Andrianova et al. [20], in which a careful calorimetric investigation was carried out of cold drawing of P E T P . I t is very important for us that in this study calorific power values were obtained at several rates of deformation W=dQ/dt. To solve eqn. (1) the dependence of the power of heat source W on the rate of polymer elongation v has to be determined. I n the case of forced elastic deformation of the polymer it m a y be assumed that practically all the mechanical energy used for deformation (A) is converted into heat Q [13, 21], i.e.
S dA~- S dQ The obvious relations follow from here
dA =aSdl=agv~ dQ = Wdt, where a is stress in stationary deformation, 1 is instantaneous length of the polymer sample and S - - i t s cross sectional area. Then,
W=a~v Using the well-known Lazurkin equation for high rates of elongation
\~o/ where R is the universal gas constant and ~ and 3o are constants, we finally
G. M. Luxovxi~ e* a/.
990
obtain
W(v)--~
RT
v vS I n -
(6)
"CO
Equations (5) and (6) enable the temperature change inthe zone of plastic deformation of the polymer to be obtained in impact loading. We evaluate this change using amorphous glassy P E T P which was previously [20] examined in detail and for which all requisite thermal parameters are known. These parameters are as follows: C~=0-3 cal/g-deg [22] p=1.34 g/cm a [20] k-~0.00036 cal/sec.cm.deg [22] To evaluate parameters of eqn. (6), we used direct calorimetric data of the study by Andrianova et al. [20] concerning thermal effects o f deformation of P E T P in a wide range of rates of elongation. TJsing values of heat release at rates of elongation of 1.03 and 10.5 mm/min derived in this study, we determine parameters of the Lazurkin equation In z0------17.97 ram/rain, ~----5150 cal.mm2fkg. Finally, eqn. (6) for P E T P takes the form
W(v) cal/sec-----0.1436v (lnv~-17.97), where heat release refers to the section of a rod 1.25 mrn in diameter [20]. We may now deal with determining the value of q. This is easily done by the following method: let there be a temperature distribution T(x, 1) be in the sample by t = l . Then, the value of Cp ~ T(x, 1) dx denotes heat liberated during this $ime in the sample, i.e. -~
w = Cp I T(x, 1)
(7) q
exp
4a ( l + b - - ~ ) ] + e x p
.
4a2(l~)Jd~
--co
K where a 2- -- -C~ - p' 2a----0.06 cm/sec~, T(x, t) being the function of rate. By norrealization (7) the value of q is directly found and T(x, t) may be determined quantitatively. A typical curve which describes temperature distribution along the sample, plotted using eqn. (5) is shown in Fig. 2. I t can be seen that under adiabatic conditions the temperature of the sample in any section increases evenly as the f~ont of the neck advances along the sample. I t is natural that this situation is typical of the case of low ra~e of elongation, when nonelastic' deformation
Increasing the impact strength of plastics using rubber dispersions
991
takes place trader stationary conditions with neck formation. For the case of impact failure we are interested in the temperature of the polymer at an initial moment of time, when the polymer undergoes plastic deformation. The time when forced elasticity of the polymer is achieved should be accepted as such moment of time, since it is precisely at this point t h a t plastic deformation of 2
I
I
I
I
3 1
o.l/
2
1
2
0-025
0.075
a2
:c cm
F,c.. 2. Dependences of the distribution of temperature quoted T(z, 1)=T(z, 1)/(~-~/=-T~~ \~rV
"/
in f,he length of the rod for rates of elongation v----O.01 (1) and 10 cra/aee (2). the polymer takes place and neck formstion occurs. This time t is easily determined exprimentaUy
t=~k" lo/v, where sk is deformation corresponding to maximum forced elasticity of the polymer, l 0 is the initial length of the sample which in our ease is 6 cm [20]. Results obtained for three rates of elongation are: v, cm/sec ~T, K
0.001 10
0.01 60
10 600
Calculation carried out for a comparatively low rate of elongation v~-0.01 em/sec gives a significant value of temperature change AT----60°K which is in satisfactory agreement with results of an earlier paper [13] exceeding Tg of the polymer if elongation is effected at room temperature. It can be seen that with a comparatively low rate of elongation in the polymer extremely high temperature changes
999.
G. M. LlrKovxm t¢ ~ .
are observed which may result in a special auto-vibratory mechanism o f defer. mation [15, 20]. Increasing the rate o f d e f o r m a t i o n naturally approximates to adiabatic conditions and with impact loading heat loss will be minimum. For example, reducing parameters of eqn. (6) to the rate of elongation v-----10 era/see, at which PETP breaks down with low elongation, gives the temperature change value of AT~f00°K. Approximate calculations indicate that at high rates of loading considerable temperature changes occur, so that temperature exceeds considerably the melting point and the temperature of chemical decomposition of corresponding polymers. Breakdown of polymers under these conditions should, in fact, be regarded as "heat explosion". The effect of rubber modifiers on the impact strength of glassy polymers should be regarded by analysing the situation at high rates of loading. It was shown in a number of studies [1-3] that deformation of high-impact compositions takes place without neck formation by transition of the polymer into the oriented state inside specific microcracks or shear bands without disrupting the continuity of the material. There is a lot in common between these two varieties of plastic deformation [23] and they often coexist [24]. l~on-elastie plastic deformation is not carried out in any one place, as is the case with neck formation in the polymer, but simultaneously in a number of places of the sample with the formation of microcracks, or shear bands. Without dwelling on physical causes of initiation of such a number of places of localized deformation* we note that these morphological features of deformation have a lot in common with the deformation mechanism of polymers in adsorption-active media. For example, increasing the rate of elongation of high-impact materials increases the number of mierocracks [25], the same as in deformation of pure polymers in adsorption-active media [10]. As noted previously [11], increasing the number of places of localized deformation reduces the rate of ]ocalized transition into the oriented state at the same macroscopic rate of deformation of the polymer sample, as a whole, and lowers macroscopic stress in stationary deformation. As noted previously, heat flow in plastic deformation of the polymer is proportional to the rate of elongation of the polymer or (what is the same) to the rate of transition into the oriented state. The addition to the glassy polymer of a rubber dispersion is known to result in the formation of many localized places of transition to the oriented state. This is seen for high-impact plastic samples subjected to impact failure in the form of whitening of the operating part of samples (stress whitening) [4, 5]. ~ e try to evaluate the variation of AT in the polymer sample if deformation takes place in many and not just two places, as is the case in high-impact plastics. For this we use direct X-ray [26] or electron-microscope [27, 28] assessments of the number of mierocracks
* Assumptions concerningthe causes of formation of places of localized plastic deformation in high-impact plastics are described in the literature [1~3].
Inereadug the impact strength of plastics using rubber dispersions
993
formed in deformation of high-impact PS. Linear density of microcracks in these materials is 104-105 cm -1. I t is obvious t h a t the formation of such a large number of places of localized deformation considerably reduces the real rate of polymer transition into the oriented state and therefore, heat release (eqn. (16)). I f we assume t h a t the linear density of such places of localized polymer transition to the oriented state is n ~ 1 0 ~ cm -1, the real temperature change according to our estimates decreases 100-fold, which for a rate of elongation of 10 cm/sec increases the temperature of the polymer only by 6°K. I t is natural t h a t this slight heating of the material (evenly distributed in the volume) results in rapid decomposition and considerably eases plastic deformation. I t is therefore not surprising t h a t under these conditions materials such as high-impact PS, or ABC readily undergo plastic deformation, although under experimental conditions the glassy matrix of these materials which is the continuons phase, cannot undergo considerable non-elastic deformation. I t is also e~ident tha~ the work of failure of plastics reinforced with rubber at high (impact) rates of loading increases markedly (Fig. 1), Therefore, the mechanism of reinforcing action of plastics with rubber inclusions involves initiation of a large number of localized places of plastic deformation of the polymer, which reduces the real rate of transition of the polymer to the oriented state, reduces heat release and prevents rapid thermal decomposition of the polymer at impact of loading. The authors are greateful to V. A. Kabanov for the useful discussions held. Translated by E. SEM~.~E REFERENCES 1. R. P. ]~LMBOUR, J. Polymer SoL, Msoz~mo]eo. Rev. 7: 1, 1973
2. 8. G. BRAGAU In: Monogokomponentnyye polimernyye sistemy (Multi-component Polymer Systems). p. 142, Khimiya, Moscow, 1974 3. G. MANSON and L. SplCRLING, Polimernyye smesi i kompozity (Polymer Mixtures and Compositions). p. 76, Khimiya, Moscow, 1979 4. C. R. BUL~IKNALLand R. R. SMITH, Polymer 6: 6, 437, 1965 5. K. TAKAHASHI, J. Polymer Phys. Ed. 12: 10, 1697, 1974 6. R. W. TRUSS and G. A. CHADWICK,J. Mater. Sci. 12: 11, 1383, 1977 7. H. RREUER, F. HAAF and J. 8TABENOV, J. 1Kacromoleo.Sci. 1114: 3, 387, 1977 8. A. G. ALESlffEROV,A. L. VOLYNSKHand N. F. BAKEYEV, Vysokomol. soyed. BIg: 3, 218, 1977 (Not trarislated in Polymer Sci. U.S.S.R.) 9. V. L. VOLYNSKII, N. A. SHITOV and N. F. BAKEYEV, Vysokornol. soyed. A23: 6, 978, 1981 (Translated in Polymer Sci. U.S.S.R. 28: 5, 1089, 1981) 10. L. M. YARYSHEVA, L. Yu. PAZUKHINA, G. M. LUKOV]KIN, A. L. VOLYNSKII, N. F. BAKYEV and P. V. KOZLOV, Vysokomol. soyed. A24: 10, 2149, 1982 (Trans. lated in Polymer Sci. TJ.S.S.R. 24: 10, 2464, 1982) 11. A. L. VOLYNSlgI~.~ G. M. LUKOVKIN, L. M. YARYSHEVA, L. Yu. PAZUKHINA, P. V. KOZL0V and N. F. BAKEYEV, Vysokomol. soyed. A24: 11, 2357, 1982 (Translated in
Polymer Sci. U.S.S.R. 24: 11, 2706, 1982) 12. A. L. VOLYNffglT, A. G. ALESKEROV, A. S. KECHEK'YAN, T. B. ZAVAROVA, A. Ye. SKOROBOGATOVA,8. A. ARZHAKOV and N. F. BAKEYEV, Vysokomol. soyed. BIg: 4, 301, 1977 (Not translated in Polymer Sci. U.S.S.R.)
994
A. P. TYU~EV e~ ~ .
13. J. W. M ~ H E R , R. N. H A W A R D a n d J. N. HAY, J. P o l y m e r Sei., P o l y m e r Phys. E d . 18: 11, 2169, 1980 14. K. N. G. FULLER, P. G. FOX and J. E. H E L D , Prec. Roy. See. A841: 1627, 537, 1975 15. A. S. KECHEK'YAN, G. P. ANDRIANOVA a n d V. A. KARGIN, Vysokomol. soyed. A12: 11, 2424, 1970 (Translated in P o l y m e r Sci. U.S.S.R. 12: 11, 2743, 1970) 16. A. RRUKH, Avtoref. dis. n a soiskaniye ueh. step. kand. tekhn, nauk, M I T K h T im. i~I. V. Lomonosova, Moscow, 1981 17. E. A. EGOROV, V. V. ZIZENKOV, 8. N. BEZLADNOV, I. A. SOKOLOV and E. M. TOMASHEVSKII, A e t a Polymerica 31: 9, 541, 1980 18. A. L. VOLYNSKII, G. M. LIfKOVKIN and N. F. BAKEYEV, Vysokomol. soyed. A I 9 : 4, 785, 1977 (Translated in P o l y m e r Sci. U.S.S.R. 19: 4, 910, 1977) 19. A. CROSS, M. HALL a n d R. N. H A W A R D , Nature 253: 5490, 340, 1975 20. G. P. ANDRIANOVA, Yu. V. POPOV a n d B. A. A R ~ O V , Vysokomol. soyed. AI8: 10, 2311, 1976 (Translated in Polymer Sci. U.S.S.R. 18: 10, 2644, 1976) 21. J. MAGER, J. N. HAY and R. N. H A W A R D , Internat. Symp. Macromolec., Mainz, Prepr. Short. Commun. vol. 2, p. 1433, 1979 22. E. M. EISENSTEIN, In: Entsiklopediya polimerov (Polymer Encyclopaedia) vol. 3, p. ]08, Sovetskaya entsiklopediya, Moscow, 1977 23. G. S. Y. YEH, J. Macromolec. Sci. B7: 4, 729, 1973 24. A. S. ARGON, Pure Appl. Chem. 43: 1-2, 247, 1975 25. R. W. TRUSS and G. A. CHADWICK, J. Mater. Sci. 11: 10, 1385, 1976 26. N. R. ASHUROV, Avtoref. dis. n a soiskaniye ueh. st. kand. fiz.-mat, nauk, IVS A N SSSR, Leningrad, 1978 27. S. B. BUCKN,4LL~ I. C. DRINKWATER and W. E. KEAST, Polymer 18: 1, 115, 1972 28. P. BEHAN, A. THOMAS and M. BEVIS, J. Mater. Sci. 11: 1207, 1976
P o l y m e r Science U.S.S.R. Vol. 25, No. 4, pp. 994-1001, 1983 P r i n t e d in Poland
0032-8950/83 $10.00-[-.00 O 1984 P e r g a m o n Press L t d .
ELECTRICAL EFFECTS BY THE, ACTION OF LOW ENERGY ELECTRONS ON POLYARYLATES* A . P . TYUTNEV, V. S. SAYENKO, P . M. VALETSKII, V. A . Kin, G. P . SA~O~OV, YE. D . POZHIDAYEV, S. V. VINOGRADOVA a n d V. V. KORSHAK I n s t i t u t e of Hetero-organic Compounds, U.S.S.R. Academy of Sciences Moscow I n s t i t u t e o f Electronic Machine Building
(Received 22 Decemb~ 1981) A study was nm~e of the behaviour of polyarylates, (polypltenol phthaleinisottere)-phthalate and polydianeterephthalate), to the action of electron pulses accelerated to an energy of 65 keV in a vacuum of ~ 1.33 × 10 -s P a in a wide range of * Vysokomol. soyed. A$5: No. 4, 856-861, 1983.