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Anisotropy of mechanical relaxation in monotextured polyethylene specimens
Amsotropy of mechanical relaxation in PE specimens
99 ]:
REFERENCES 1. R. P. KMABOUR, Macromolec. Rev. 7: 1, 1973 2. H. {~. OLF and A. PETERLIN, J. Polymer Sci., Polymer Phys. Ed. 12: 2209, 1974 3. Ye. A. SINEVICH, R. P. OGORODOV and N. F. BAKEYEV, Dokl. AI~ SSSR 212: 1383, 1973 4. A. L. VOLYNSKII and N. F. BAKEYEV, Vysokomol. soyed. A17: 1610, 1975 (Translated' in Polymer Sci. U.S.S.R. 17: 7, 1855, 1975) 5. A. N. TYNNYI, Prochnost' i razrusheniye polimerov pod vozdeistviyem zhldkikh srcd (Strength and I)estructlon of Polymers Exposed to Licluld ]~[edia). Izd. "I~aukova dumka", 1975 6. A. L. VOLYNSKII, A. G. ALESKEROV, T. Ye. GROKHOVSKAYA and N. F. BAKEYEV, Vysokomol. soyed. A18: 2114, 1976 (Translated in Polymer Sci. U.S.S.R. 18: 9, 2419, 1976) 7. T. Ye. GROKHOVSKAYA, Candidate's dissertation, Moscow State Univ. (MGU), 197T 8. A. Y. YEFIMOV, V. Y. BONDAREV, P. V. KOZLOY and N. F. BAKEYEV, Vysokomol. soyed. B1 9: 804, 1977 (Not translated in Polymer Sei. U.S.S.R.) 9. V. I. GERASIMOV and D. Ya. TSVANKIN, Pribory 1 tekhnlka eksperimenta, 1~o. 2, 204, 1968 10. K. RODGER, Constructional Properties of Plastics, p. 193, Izd. "Mir", 1967 11. A. V. KISELE¥ and V. P. DREVING (Eds.), Eksperimental'nye mctody v adserbtsii 1 molekulyarnoi khromatografii (Experimental Techniques in Adsorption and Molecular Chromatography) p. 221, Moscow Univ. Press, 1973 12. C. E. ROGERS, V. STANNET and M. SZWARG, J. Polymer Sci. 29: 61, 1960 13. A. PETERL1N, J. Mac~omolec. Sei. B l l : 57, 1975 14. A. PETERLIN, J. L. WILLIAMS and V. STANNET, J. Polymer Sci. 5, A-2: 957, 1967 15. M. M. DUBININ, In book: Osnovnye problemy teorh fizicheskoi adsorbtsii (Main Problems in Theory of Physical Adsorption). p. 251, Izd. "Nauka", 1970
Polymer Science U.S.S.R. Vol. 23, No. 4, pp. 991-996, 1981 Printed in Poland
0032-3950/81/040991--06$07.50t0, © 1982 Pergamon Press Ltd.
ANISOTROPY OF MECHANICAL RELAXATION IN MONOTEXTURED POLYETHYLENE SPECIMENS* Y u . V. ZEL]~NEV a n d L. A. DEnTUVA Moscow Textde Institute Forestry Technical Institute, Voronezh
(Receivexl 28 January 1980) The anisotropy of mechanical loss m high- and low-density monotextured PE specimens has been investigated with the aid of a torsion pendulum (frequency• 5 Hz) in the temperature range corresponding to ~- and B-relaxation, The result~ * Vysokomol. soyed. AZS: No. 4, 887-891, 1981.
~}92
Yly. V. ZS~NEV and L. A. DELTUV~-
obtained are analyzed from the standpoint of two competing hypotheses normally used for the interpretation of ormntational dependence of m~ ~-peak: hypotheses of mtra- and interlaminar shear. Only the first hypothesis is not at variance with experimental findings; m particular, mechanical losses are maximal when the orientation ofa speoimen being measured is favourable for shear m the plane of bc m the direction of the c-axis. This fact is m accord with the Pechhold hypothesis relatizlg ~-relaxation m PE involving cooperative para-elastie sliding of helical dislocations with Burger's [001] vector. IN THE temperature interval from 120 to --65 ° two energy absorption peaks (--~- and p- [1, 2]) appear on mechanical loss curves of PE. In high density P E (HDPE), in contradistinction to low density P E (LDPE), two components of an ~-peak are normally resolved [1, 2]. Persistent interest has been shown by m a n y authors [3-8] in the nature of these peaks, since their measurements cotlld yield information on the mechanism of nonelastic deformation of PE at low levels .of stress. Various hypotheses [1-3] have been proposed to account for mechanisms v f ~- and fl-relaxatlon processes in PE, but not one of the latter m a y be said to have been finally proved. In particular, two mechanisms for the ~-process have been the subject of much discussion [9]; 1) interlaminar shear--relaxation is caused b y shear stress applied along interlamellar interlayers; 2) intralaminar ~shear--relaxat~on is caused by shear stress of the type of (hk0) [00/], acting within crystals. To refine these mechanisms it is worthwhile investigating relaxation anisotropy, i.e. the peak height in relation to the orientation of a textured specimen in an external stress field. Published information rela~ing to this aspect of relaxation processes [9] is contradictory in character. The methods of orientation used in [4, 10-12] (uniaxial drawing, zone crystallization, tempering) were such as allow only one of the crystallographic axes to be determined in a particular direction, which is not conductive to an unambiguous interpretation of the results. Stachurski [9] has described the anisotropy of the viscoelastic behaviour of L D P E under flexing oscillatings for specimens with a practically unique orientation of three crystallographic axes. Although the texture of these specimens (prepared by rolling previously drawn films) was single at the elementary cell level, it remained dual at the level of supermolecular structure (there were two discrete orientation angles of lamcllae relative to the crystallographic axes). Monocrysta]s would undoubtedly be ideal for investigations of this type. Unfortunately it has not yet proved possible to get sufficiently large PE monocrystals t h a t would be suitable for macroscopic mechanical measurements. We therefore recently proposed [13] a method of preparing P E specimens having a single texture both at the elementary cell level and at the superstrucrural level. These monotextured specimens (which m a y be regarded as macroscopic analogues of monocrystals) are prepared by rolling isotropic tablets, followed by thermal relaxation. The following results were obtained in a comparative analysis of mechanical
Anisotropy of mechanical relaxation in PE specnnens
993
relaxation anisotropy (torsional vibrations) in monotextured LDPE and HDPE specimens in the temperature interval - - 6 5 - 1 2 0 ° . The starting materials, LDPE and H D P E (of Somet manufacture, with degrees of arystallinity N 55 and N70% respectively) were in the form of sheets of thickness 5 ram. Rolling was done on laboratory eqmpment at room temperature. Degrees of deformation were estimated from the relative reduction in the thickness of the sheet. Specimens with rectangular cross sectmn, laterally 1-3 mm and lengthwise 20-50 mm were cut from rolled tablets along and across the rolling direction. Mechanical losses were measured with a return torsional pendulum under conditions of free oscillation at a frequency of ~0.5 Hz. An inertia mass in the form of a rod with ferromagnetic weights at the ends was suspended over the specimen on a steel torsion wire, and was offset with a counterbalance.-An additional longitudinal load intended to ensure stabdity of the oscillatory process was selected and was small enough to ensure that deformation of the specimen ( ~ 10-s) caused by it had lie effect on the measurement data. The oscillation amplitude (using an electromagnetic means of excitation) was recorded visually with the aid of an optical "lever". Maximum deformatmn on the surface of a specimen did not exceed 10-8, m which case no amplitude dependence was detected, tteating of the specimens took place in an electric tubular oven provided with a photoelectric heat regulator; cooling took place in a cryostat with a cooling medium m the form of acetone mixed with sohd carbon dioxide. Mechanmal losses-A = ~ tan $ (¢?bemg the loss angle) were calculated by the formula [1] A ==
2
I
ve'4c-- VTAT
v~(1-A~/4~,)-vg' where Ac and v¢ are the logarithrmc decrement of damping arid the oscillatmn frequency for the combined system (torsmn--spemmen); AT and VT are the logarithmic decrement and the tormon frequency (system without the specimen). The rotsmn stiffness was selected according to the rigidity of the specimen so that the logarithmic damping decrement for the combined system Ac would not exceed 0.1 over the entire temperature interval examined. In this case the relative error m determining zI was N 2%.
F i g u r e l a , b c o m p a r e s t e m p e r a t u r e d e p e n d e n c e s of m e c h a n i c a l losses for v e r t i c a l a n d h o r i z o n t a l H D P E s p e c i m e n s for t w o d e g r e e s o f d e f o r m a t i o n . I n t h e h i g h t e m p e r a t u r e p o r t i o n s o f t h e c u r v e s t h e r e is a n i n t e n s e ~ - p e a k on w h i c h a less i n t e n s e f l - p e a k is s u p e r p o s e d on t h e low t e m p e r a t u r e side. S i m i l a r d a t a f o r L D P E a p p e a r in F i g . lc, d. T h e t w o ~ - p e a k c o m p o n e n t s a r e r e s o l v e d . I t c a n b e seen t h a t m e c h a n i c a l losses in b o t h m a t e r i a l s a r e h i g h e r in t h e h o r i z o n t a l s p e c i m e n s , p a r t i c u l a r l y i n t h e h i g h t e m p e r a t u r e p o r t i o n of t h e s p e c t r u m . A s t h e d e f o r m a t i o n i n c r e a s e s effects of t h e d e v e l o p m e n t o f a n i s o t r o p y a r e i n t e n s i fied. L e t us a n a l y s e t h e r e s u l t s i n t e r m s of t h e a b o v e - m e n t i o n e d h y p o t h e s e s o f i n t e r - a n d i n t r a l a m i n a r shear. T o do so l e t us t a k e as a b a s i s t h e s t r e s s d i s t r i b u t i o n o b s e r v e d on m e a s u r i n g m e c h a n i c a l losses, c o n s i d e r i n g t h e m o l e c u l a r a n d s u p e r m o l e c u l a r t e x t u r e o f a s p e c i m e n , a n d d e t e r m i n e w h i c h of t h e t w o cases o f o r i e n t a t i o n e x a m i n e d for a s p e c i m e n in a n e x t e r n a l s t r e s s field w o u l d be t h e m o s t f a v o u r a b l e for i n t e r - or i n t r a l a m i n a r s h e a r .
994
Yu. V. ZELE~,~V and L. A. DELTUVA
Let us take a rectangular coordinate system with the z-axis perpendicular to the direction of rolling and the y-axis in the rolling plane (see Fig. 2). Let us consider the distribution of stress developing during measurement of mechanical losses when a specimen in the form of a prismatic rod of rectangular cross section is twisted b y a pair of forces applied at one end of the rod, while the other end is held fast. It is clear from the solution of this problem in [14] that if the z-axis is the torsion axis, the maximum tangential stress will act through areas perpendicular to the z-axis in the direction of x and y (vx~ and Vy~)and according to the pairing principle, through areas parallel to the z-axis along z (vzz and vzu). According to the data in [13] based on low angle X-ray scattering the base surface of lamellae in rolled P E that has subsequently been annealed is parallel to the y-axis and sloping at an angle of ~ 36 ° relative to the z-axis (Fig. 3). For the
l.qI
1.2
1.3
a
b
O"
0"6 / 1 2 I Gq
0.5
0.2 -qO
0
40
~ '~1 80 -40 0 40 80 I
a
P
0.o.6qf~i~ 0.2 -20 20 60 100
t
J
i
l
-20 20 60 1007-~
Fro. 1. Anisotropy of mechanical losses in HDPE (a, b) and LDPE (c, d) after rolling with ~ - 9 4 0 (a), 80 (b), 69 (c) and 77% (d) with subsequent annealing for 1 hr at 81 (a, b) and 110° (c, d); /--longitudinal, 2--transverse specimen.
Aniso~ropy of mechanical relaxation in P E specimens
995
orientation in question the maximum tangential stresses along base surfaces of lamellae will develop during torsion about the y-axis, i.e. in transverse specimens. This means that in line with the hypothesis of interlaminar shear one must expect that mechanical losses will be more marked in transverse specimens than in longitudinal ones, which is at variance with experimental findings. x
!
X
z Fro. 2
z FZG. 3
FzG. 2. l~otatlon of mare directions m rolled tablet. FzG. 3. Ormntatlon of crystallographic axes and lamellae in surface zones of the tablet after rolling and anneahng (see scheme): 1--1amelia, 2--rolling plane.
Let us now turn to the intralaminar shear hypothesis. According to the results of wide angle X-ray diffraction analysis [13] the situation of the crystallographic b-axis in the specimens examined is in the rolling plane perpendicular to the rolling direction; the crystallographic a- and c-axes are in the plane of ~z in directions close to the coordinate x- and z-axes respectively (Fig. 3). For a preset single cell orientation during testing of longitudinal specimens (the torsion axis being the z-axis) the highest values will be those of the stress tensor tangential components rzx, zxz, z~y and ~yz; during testing of transverse specimens (the torsion axis being the y-axis) the highest values will be observed for components zuz, ~zu, zzv and zyz. Allowing for the observed anisotropy (mechanical losses are higher in longitudina lspecimens) we conclude that a preferential role in development of the a-relaxation process is played by tangential stresses v= and vxz, which give rise to shear in the plane of bc in the direction of the c-axis and in the plane of ab in the direction of the a-axis respectively. It is significant that this conclusion is valid both for LDPE and, according to [9, 12], for HDPE also, counterbalancing refs. [9, 11] Investigations reported in [9, 12] relate to LDPE specimens with fibre symmetry and with a lower orthorhombic symmetry. Testing o£ these specimens under a regime of flexing oscillations showed that the H D P E a-peak anisotropy is controlled by shear in planes parallel or perpendicular to the c-axis. A subsequent analysis [15] of the experimental data in [12] in terms of an aggregate model showed that taking the sum total of these planes there are four systems that are most favourable for shear, viz.: (ac) [el, (bc) [c], (ab) [a] and (~b) [b]. On
996
Yu. V. ZELENEV and L. A. DEL'ruvA
t h e basis o f our m e a s u r e m e n t s it is now possible to limit t h e choice of feasible slip s y s t e m s to o n l y two o f the foregoing four. A l t h o u g h t h e H D P E a-peak was a t r r i b u t e d in [9-11] to intermolecular shear, t h e results r e p o r t e d in [9-11] m a y be equally well a c c o u n t e d for f r o m a standp o i n t o f i n t r a l a m i n a r shear. T h e a m b i g u i t y o f i n t e r p r e t a t i o n is due to t h e f a c t t h a t specimens used in the investigations in question h a d preferential o r i e n t a t i o n o f o n l y one of the crystallographic axes. P e c h h o l d [16] r e c e n t l y p r e s e n t e d a h y p o t h e s i s w h e r e b y . t h e a-peak in P E involving a cooperative para-elastic slip o f helical dislocations is r e l a t e d t o B u e r g e r ' s [001] vector. I t is k n o w n [17] t h a t the plane o f (be) is the sole p r o b a b l e glide plane for these dislocations. This m e a n s t h a t our conclusion based on a n analysis of anisotropic effects t h a t shear s y s t e m (bc)[c] plays a d o m i n a n t role in exciting a-relaxation is in accord with the P e c h h o l d hypothesis.
Translated by R. J. A. HENDRY REFERENCES
1. I. I. PEREPECHKO, Akusticheskiye metody issledovamya polimerov (Acoustic Techniques for Polymer Research), Izd. "Khimiya", 1973 2. G. P. ANDRIANOVA, FLzikokhimiya poliolefinov (Physmoehemlstry of Polyolefins). Izd. "Khimiya", 1974 3. J. HOFFMAN, G. 'W1T~TIA.~MS and E. PASSAGLIA, Transitions and Relaxation Phenomena in Polymers, p. 1937, Izd. "Mir", 1968 4. G. M. BARTENEV and Yu. V. ZELENEV, Mekhanika polimerov, No. 1, 30, 1969 5. I. I. PEREPECI~KO and L. A. KVACHEVA, Vysokomol. soyed. B12" 484, 1970 (Not translated in Polymer Sci. U.S.S.R.) 6. V. A. AULOV, F. F. SI~HOV, N. A. SLOVOKHOT(IVA and V. A. KARGIN, Vysokomol. soyed. BI~: 757, 1970 (Not translated in Polymer Sci. U.S.S.R.) 7. A. Z. GOLIK, Yu. F.ZABASHTA, M. A. GENINA and A. I. ALEKSEYEV, Ukr. flzich. zh. 20: 280, 1975 8. A.K. YEVSEYEV, Yu. N. PANOV, V. N. KRENEV, V. G. BARANOV and S. Ya. FRENKEL, Vysokomol. soyed. R19: 310, 1977 (Not translated in Polymer Sci. U.S.S.R.) 9. Z. H. STACHURSKI and I. M. WARD, J. Macromolec. Sei. B3: 445, 1969 10. J. C R I S S ~ and E. PASSAGLIA, J. Res. Nat. Bur. Standards AYO: 225, 1966 11. N. G. MeCRUM and E. L. MORRIS, Prec. Roy. Soc. A292" 506, 1966 12. Z. H. STACHURSKI and I. M. WARD, J. Polymer Sci. A2: 1083, 1968 13. J. J. POINT, G. A. HOMES, D. GESOVICH and A.KELLER, J. Mater. Sei. 4: 908, 1969 14. S. P. TIMOSHENKO and J. GOODYEAR, Teoriya uprugosti (Theory of Elasticity). Izd. "Nauka", 1975 15. Z.H. STACHURSKI and I. M. WARD, J. Macromolec. Scl. B3: 427, 1969 16. W. PECHHOLD, J. Polymer Sci. C22: 123, 1971 17. J. M. PETERSON, J. Appl. Phys. 89: 4920, 1968
99 ]:
REFERENCES 1. R. P. KMABOUR, Macromolec. Rev. 7: 1, 1973 2. H. {~. OLF and A. PETERLIN, J. Polymer Sci., Polymer Phys. Ed. 12: 2209, 1974 3. Ye. A. SINEVICH, R. P. OGORODOV and N. F. BAKEYEV, Dokl. AI~ SSSR 212: 1383, 1973 4. A. L. VOLYNSKII and N. F. BAKEYEV, Vysokomol. soyed. A17: 1610, 1975 (Translated' in Polymer Sci. U.S.S.R. 17: 7, 1855, 1975) 5. A. N. TYNNYI, Prochnost' i razrusheniye polimerov pod vozdeistviyem zhldkikh srcd (Strength and I)estructlon of Polymers Exposed to Licluld ]~[edia). Izd. "I~aukova dumka", 1975 6. A. L. VOLYNSKII, A. G. ALESKEROV, T. Ye. GROKHOVSKAYA and N. F. BAKEYEV, Vysokomol. soyed. A18: 2114, 1976 (Translated in Polymer Sci. U.S.S.R. 18: 9, 2419, 1976) 7. T. Ye. GROKHOVSKAYA, Candidate's dissertation, Moscow State Univ. (MGU), 197T 8. A. Y. YEFIMOV, V. Y. BONDAREV, P. V. KOZLOY and N. F. BAKEYEV, Vysokomol. soyed. B1 9: 804, 1977 (Not translated in Polymer Sei. U.S.S.R.) 9. V. I. GERASIMOV and D. Ya. TSVANKIN, Pribory 1 tekhnlka eksperimenta, 1~o. 2, 204, 1968 10. K. RODGER, Constructional Properties of Plastics, p. 193, Izd. "Mir", 1967 11. A. V. KISELE¥ and V. P. DREVING (Eds.), Eksperimental'nye mctody v adserbtsii 1 molekulyarnoi khromatografii (Experimental Techniques in Adsorption and Molecular Chromatography) p. 221, Moscow Univ. Press, 1973 12. C. E. ROGERS, V. STANNET and M. SZWARG, J. Polymer Sci. 29: 61, 1960 13. A. PETERL1N, J. Mac~omolec. Sei. B l l : 57, 1975 14. A. PETERLIN, J. L. WILLIAMS and V. STANNET, J. Polymer Sci. 5, A-2: 957, 1967 15. M. M. DUBININ, In book: Osnovnye problemy teorh fizicheskoi adsorbtsii (Main Problems in Theory of Physical Adsorption). p. 251, Izd. "Nauka", 1970
Polymer Science U.S.S.R. Vol. 23, No. 4, pp. 991-996, 1981 Printed in Poland
0032-3950/81/040991--06$07.50t0, © 1982 Pergamon Press Ltd.
ANISOTROPY OF MECHANICAL RELAXATION IN MONOTEXTURED POLYETHYLENE SPECIMENS* Y u . V. ZEL]~NEV a n d L. A. DEnTUVA Moscow Textde Institute Forestry Technical Institute, Voronezh
(Receivexl 28 January 1980) The anisotropy of mechanical loss m high- and low-density monotextured PE specimens has been investigated with the aid of a torsion pendulum (frequency• 5 Hz) in the temperature range corresponding to ~- and B-relaxation, The result~ * Vysokomol. soyed. AZS: No. 4, 887-891, 1981.
~}92
Yly. V. ZS~NEV and L. A. DELTUV~-
obtained are analyzed from the standpoint of two competing hypotheses normally used for the interpretation of ormntational dependence of m~ ~-peak: hypotheses of mtra- and interlaminar shear. Only the first hypothesis is not at variance with experimental findings; m particular, mechanical losses are maximal when the orientation ofa speoimen being measured is favourable for shear m the plane of bc m the direction of the c-axis. This fact is m accord with the Pechhold hypothesis relatizlg ~-relaxation m PE involving cooperative para-elastie sliding of helical dislocations with Burger's [001] vector. IN THE temperature interval from 120 to --65 ° two energy absorption peaks (--~- and p- [1, 2]) appear on mechanical loss curves of PE. In high density P E (HDPE), in contradistinction to low density P E (LDPE), two components of an ~-peak are normally resolved [1, 2]. Persistent interest has been shown by m a n y authors [3-8] in the nature of these peaks, since their measurements cotlld yield information on the mechanism of nonelastic deformation of PE at low levels .of stress. Various hypotheses [1-3] have been proposed to account for mechanisms v f ~- and fl-relaxatlon processes in PE, but not one of the latter m a y be said to have been finally proved. In particular, two mechanisms for the ~-process have been the subject of much discussion [9]; 1) interlaminar shear--relaxation is caused b y shear stress applied along interlamellar interlayers; 2) intralaminar ~shear--relaxat~on is caused by shear stress of the type of (hk0) [00/], acting within crystals. To refine these mechanisms it is worthwhile investigating relaxation anisotropy, i.e. the peak height in relation to the orientation of a textured specimen in an external stress field. Published information rela~ing to this aspect of relaxation processes [9] is contradictory in character. The methods of orientation used in [4, 10-12] (uniaxial drawing, zone crystallization, tempering) were such as allow only one of the crystallographic axes to be determined in a particular direction, which is not conductive to an unambiguous interpretation of the results. Stachurski [9] has described the anisotropy of the viscoelastic behaviour of L D P E under flexing oscillatings for specimens with a practically unique orientation of three crystallographic axes. Although the texture of these specimens (prepared by rolling previously drawn films) was single at the elementary cell level, it remained dual at the level of supermolecular structure (there were two discrete orientation angles of lamcllae relative to the crystallographic axes). Monocrysta]s would undoubtedly be ideal for investigations of this type. Unfortunately it has not yet proved possible to get sufficiently large PE monocrystals t h a t would be suitable for macroscopic mechanical measurements. We therefore recently proposed [13] a method of preparing P E specimens having a single texture both at the elementary cell level and at the superstrucrural level. These monotextured specimens (which m a y be regarded as macroscopic analogues of monocrystals) are prepared by rolling isotropic tablets, followed by thermal relaxation. The following results were obtained in a comparative analysis of mechanical
Anisotropy of mechanical relaxation in PE specnnens
993
relaxation anisotropy (torsional vibrations) in monotextured LDPE and HDPE specimens in the temperature interval - - 6 5 - 1 2 0 ° . The starting materials, LDPE and H D P E (of Somet manufacture, with degrees of arystallinity N 55 and N70% respectively) were in the form of sheets of thickness 5 ram. Rolling was done on laboratory eqmpment at room temperature. Degrees of deformation were estimated from the relative reduction in the thickness of the sheet. Specimens with rectangular cross sectmn, laterally 1-3 mm and lengthwise 20-50 mm were cut from rolled tablets along and across the rolling direction. Mechanical losses were measured with a return torsional pendulum under conditions of free oscillation at a frequency of ~0.5 Hz. An inertia mass in the form of a rod with ferromagnetic weights at the ends was suspended over the specimen on a steel torsion wire, and was offset with a counterbalance.-An additional longitudinal load intended to ensure stabdity of the oscillatory process was selected and was small enough to ensure that deformation of the specimen ( ~ 10-s) caused by it had lie effect on the measurement data. The oscillation amplitude (using an electromagnetic means of excitation) was recorded visually with the aid of an optical "lever". Maximum deformatmn on the surface of a specimen did not exceed 10-8, m which case no amplitude dependence was detected, tteating of the specimens took place in an electric tubular oven provided with a photoelectric heat regulator; cooling took place in a cryostat with a cooling medium m the form of acetone mixed with sohd carbon dioxide. Mechanmal losses-A = ~ tan $ (¢?bemg the loss angle) were calculated by the formula [1] A ==
2
I
ve'4c-- VTAT
v~(1-A~/4~,)-vg' where Ac and v¢ are the logarithrmc decrement of damping arid the oscillatmn frequency for the combined system (torsmn--spemmen); AT and VT are the logarithmic decrement and the tormon frequency (system without the specimen). The rotsmn stiffness was selected according to the rigidity of the specimen so that the logarithmic damping decrement for the combined system Ac would not exceed 0.1 over the entire temperature interval examined. In this case the relative error m determining zI was N 2%.
F i g u r e l a , b c o m p a r e s t e m p e r a t u r e d e p e n d e n c e s of m e c h a n i c a l losses for v e r t i c a l a n d h o r i z o n t a l H D P E s p e c i m e n s for t w o d e g r e e s o f d e f o r m a t i o n . I n t h e h i g h t e m p e r a t u r e p o r t i o n s o f t h e c u r v e s t h e r e is a n i n t e n s e ~ - p e a k on w h i c h a less i n t e n s e f l - p e a k is s u p e r p o s e d on t h e low t e m p e r a t u r e side. S i m i l a r d a t a f o r L D P E a p p e a r in F i g . lc, d. T h e t w o ~ - p e a k c o m p o n e n t s a r e r e s o l v e d . I t c a n b e seen t h a t m e c h a n i c a l losses in b o t h m a t e r i a l s a r e h i g h e r in t h e h o r i z o n t a l s p e c i m e n s , p a r t i c u l a r l y i n t h e h i g h t e m p e r a t u r e p o r t i o n of t h e s p e c t r u m . A s t h e d e f o r m a t i o n i n c r e a s e s effects of t h e d e v e l o p m e n t o f a n i s o t r o p y a r e i n t e n s i fied. L e t us a n a l y s e t h e r e s u l t s i n t e r m s of t h e a b o v e - m e n t i o n e d h y p o t h e s e s o f i n t e r - a n d i n t r a l a m i n a r shear. T o do so l e t us t a k e as a b a s i s t h e s t r e s s d i s t r i b u t i o n o b s e r v e d on m e a s u r i n g m e c h a n i c a l losses, c o n s i d e r i n g t h e m o l e c u l a r a n d s u p e r m o l e c u l a r t e x t u r e o f a s p e c i m e n , a n d d e t e r m i n e w h i c h of t h e t w o cases o f o r i e n t a t i o n e x a m i n e d for a s p e c i m e n in a n e x t e r n a l s t r e s s field w o u l d be t h e m o s t f a v o u r a b l e for i n t e r - or i n t r a l a m i n a r s h e a r .
994
Yu. V. ZELE~,~V and L. A. DELTUVA
Let us take a rectangular coordinate system with the z-axis perpendicular to the direction of rolling and the y-axis in the rolling plane (see Fig. 2). Let us consider the distribution of stress developing during measurement of mechanical losses when a specimen in the form of a prismatic rod of rectangular cross section is twisted b y a pair of forces applied at one end of the rod, while the other end is held fast. It is clear from the solution of this problem in [14] that if the z-axis is the torsion axis, the maximum tangential stress will act through areas perpendicular to the z-axis in the direction of x and y (vx~ and Vy~)and according to the pairing principle, through areas parallel to the z-axis along z (vzz and vzu). According to the data in [13] based on low angle X-ray scattering the base surface of lamellae in rolled P E that has subsequently been annealed is parallel to the y-axis and sloping at an angle of ~ 36 ° relative to the z-axis (Fig. 3). For the
l.qI
1.2
1.3
a
b
O"
0"6 / 1 2 I Gq
0.5
0.2 -qO
0
40
~ '~1 80 -40 0 40 80 I
a
P
0.o.6qf~i~ 0.2 -20 20 60 100
t
J
i
l
-20 20 60 1007-~
Fro. 1. Anisotropy of mechanical losses in HDPE (a, b) and LDPE (c, d) after rolling with ~ - 9 4 0 (a), 80 (b), 69 (c) and 77% (d) with subsequent annealing for 1 hr at 81 (a, b) and 110° (c, d); /--longitudinal, 2--transverse specimen.
Aniso~ropy of mechanical relaxation in P E specimens
995
orientation in question the maximum tangential stresses along base surfaces of lamellae will develop during torsion about the y-axis, i.e. in transverse specimens. This means that in line with the hypothesis of interlaminar shear one must expect that mechanical losses will be more marked in transverse specimens than in longitudinal ones, which is at variance with experimental findings. x
!
X
z Fro. 2
z FZG. 3
FzG. 2. l~otatlon of mare directions m rolled tablet. FzG. 3. Ormntatlon of crystallographic axes and lamellae in surface zones of the tablet after rolling and anneahng (see scheme): 1--1amelia, 2--rolling plane.
Let us now turn to the intralaminar shear hypothesis. According to the results of wide angle X-ray diffraction analysis [13] the situation of the crystallographic b-axis in the specimens examined is in the rolling plane perpendicular to the rolling direction; the crystallographic a- and c-axes are in the plane of ~z in directions close to the coordinate x- and z-axes respectively (Fig. 3). For a preset single cell orientation during testing of longitudinal specimens (the torsion axis being the z-axis) the highest values will be those of the stress tensor tangential components rzx, zxz, z~y and ~yz; during testing of transverse specimens (the torsion axis being the y-axis) the highest values will be observed for components zuz, ~zu, zzv and zyz. Allowing for the observed anisotropy (mechanical losses are higher in longitudina lspecimens) we conclude that a preferential role in development of the a-relaxation process is played by tangential stresses v= and vxz, which give rise to shear in the plane of bc in the direction of the c-axis and in the plane of ab in the direction of the a-axis respectively. It is significant that this conclusion is valid both for LDPE and, according to [9, 12], for HDPE also, counterbalancing refs. [9, 11] Investigations reported in [9, 12] relate to LDPE specimens with fibre symmetry and with a lower orthorhombic symmetry. Testing o£ these specimens under a regime of flexing oscillations showed that the H D P E a-peak anisotropy is controlled by shear in planes parallel or perpendicular to the c-axis. A subsequent analysis [15] of the experimental data in [12] in terms of an aggregate model showed that taking the sum total of these planes there are four systems that are most favourable for shear, viz.: (ac) [el, (bc) [c], (ab) [a] and (~b) [b]. On
996
Yu. V. ZELENEV and L. A. DEL'ruvA
t h e basis o f our m e a s u r e m e n t s it is now possible to limit t h e choice of feasible slip s y s t e m s to o n l y two o f the foregoing four. A l t h o u g h t h e H D P E a-peak was a t r r i b u t e d in [9-11] to intermolecular shear, t h e results r e p o r t e d in [9-11] m a y be equally well a c c o u n t e d for f r o m a standp o i n t o f i n t r a l a m i n a r shear. T h e a m b i g u i t y o f i n t e r p r e t a t i o n is due to t h e f a c t t h a t specimens used in the investigations in question h a d preferential o r i e n t a t i o n o f o n l y one of the crystallographic axes. P e c h h o l d [16] r e c e n t l y p r e s e n t e d a h y p o t h e s i s w h e r e b y . t h e a-peak in P E involving a cooperative para-elastic slip o f helical dislocations is r e l a t e d t o B u e r g e r ' s [001] vector. I t is k n o w n [17] t h a t the plane o f (be) is the sole p r o b a b l e glide plane for these dislocations. This m e a n s t h a t our conclusion based on a n analysis of anisotropic effects t h a t shear s y s t e m (bc)[c] plays a d o m i n a n t role in exciting a-relaxation is in accord with the P e c h h o l d hypothesis.
Translated by R. J. A. HENDRY REFERENCES
1. I. I. PEREPECHKO, Akusticheskiye metody issledovamya polimerov (Acoustic Techniques for Polymer Research), Izd. "Khimiya", 1973 2. G. P. ANDRIANOVA, FLzikokhimiya poliolefinov (Physmoehemlstry of Polyolefins). Izd. "Khimiya", 1974 3. J. HOFFMAN, G. 'W1T~TIA.~MS and E. PASSAGLIA, Transitions and Relaxation Phenomena in Polymers, p. 1937, Izd. "Mir", 1968 4. G. M. BARTENEV and Yu. V. ZELENEV, Mekhanika polimerov, No. 1, 30, 1969 5. I. I. PEREPECI~KO and L. A. KVACHEVA, Vysokomol. soyed. B12" 484, 1970 (Not translated in Polymer Sci. U.S.S.R.) 6. V. A. AULOV, F. F. SI~HOV, N. A. SLOVOKHOT(IVA and V. A. KARGIN, Vysokomol. soyed. BI~: 757, 1970 (Not translated in Polymer Sci. U.S.S.R.) 7. A. Z. GOLIK, Yu. F.ZABASHTA, M. A. GENINA and A. I. ALEKSEYEV, Ukr. flzich. zh. 20: 280, 1975 8. A.K. YEVSEYEV, Yu. N. PANOV, V. N. KRENEV, V. G. BARANOV and S. Ya. FRENKEL, Vysokomol. soyed. R19: 310, 1977 (Not translated in Polymer Sci. U.S.S.R.) 9. Z. H. STACHURSKI and I. M. WARD, J. Macromolec. Sei. B3: 445, 1969 10. J. C R I S S ~ and E. PASSAGLIA, J. Res. Nat. Bur. Standards AYO: 225, 1966 11. N. G. MeCRUM and E. L. MORRIS, Prec. Roy. Soc. A292" 506, 1966 12. Z. H. STACHURSKI and I. M. WARD, J. Polymer Sci. A2: 1083, 1968 13. J. J. POINT, G. A. HOMES, D. GESOVICH and A.KELLER, J. Mater. Sei. 4: 908, 1969 14. S. P. TIMOSHENKO and J. GOODYEAR, Teoriya uprugosti (Theory of Elasticity). Izd. "Nauka", 1975 15. Z.H. STACHURSKI and I. M. WARD, J. Macromolec. Scl. B3: 427, 1969 16. W. PECHHOLD, J. Polymer Sci. C22: 123, 1971 17. J. M. PETERSON, J. Appl. Phys. 89: 4920, 1968