The high strain rate compression of 7039 aluminium

Int. J. Mech. Vol. 20, pp. 609-615 © Pergamon Press Ltd., 1978. Printed in Great Britain

0020-7403/7810901-0609/$02.0010

T H E H I G H STRAIN RATE C O M P R E S S I O N OF 7039 A L U M I N I U M G. L. WULF Materials Research Laboratories, Alexandria, NSW, Australia (Received 4 Februa~ 1978)

Summary--Aluminium alloy 7039 was compressed at strain rates between 2 x 103 and 2.5 x 104 s -t using a modified Hopkinson bar. At strain rates between 2 x 103 and 1.2 x 104 s -t there was a linear relationship between the flow stress and strain-rate with a slope corresponding to a macroscopic viscosity of 2.9 kPa s. At strain rates between i.2 and 2.5 x 104 s -I there was a levelling out of the flow stress, but the data was too scattered to give a definite trend. Due to the opposing effects of linear work-hardening and adiabatic heating, at strains above 0.15 the specimens work-softened at a rate inversely proportional to the square root of the strain rate. At the higher strains, specimens cracked along the dominant adiabatic shear band formed during the compression. NOTATION B dislocation damping coefficient b Burgers' vector macroscopic viscosity p,~ mobile dislocation density INTRODUCTION F o r m e t a l s at r o o m t e m p e r a t u r e a n d s t r a i n r a t e s u p to a b o u t 103 s -~, a l i n e a r r e l a t i o n ship h o l d s b e t w e e n flow s t r e s s a n d t h e l o g a r i t h m o f t h e s t r a i n r a t e ) -3 D e f o r m a t i o n at t h e s e s t r a i n r a t e s h a s b e e n w e l l e x p l a i n e d b y the m e c h a n i s m o f t h e r m a l activatio" o f d i s l o c a t i o n s o v e r s h o r t - r a n g e b a r r i e r s . 4 A t s t r a i n r a t e s a b o v e a b o u t 103 s -l t h e r e i a m a r k e d i n c r e a s e in flow s t r e s s , a n d a c h a n g e to a d i r e c t l i n e a r r e l a t i o n s h i p w i t h s t r a t a r a t e ) '3"5-7 A t t h e s e high s t r a i n r a t e s it is t h o u g h t t h a t t h e s t r e s s a c t i n g on t h e d i s l o c a t i o n s is sufficient f o r t h e m to glide p a s t s h o r t - r a n g e b a r r i e r s w i t h o u t w a i t i n g f o r t h e r m a l f l u c t u a t i o n s a n d t h a t t h e d i s l o c a t i o n v e l o c i t y , a n d t h u s s t r a i n r a t e , is l i m i t e d by various damping mechanisms) A t s t r a i n r a t e s a b o v e a b o u t 104 s -~ t h e r a t e o f i n c r e a s e o f flow s t r e s s w i t h s t r a i n r a t e f o r a n n e a l e d a l u m i n i u m , 6"7 c o p p e r 7 a n d b r a s s 7 h a s b e e n o b s e r v e d to d e c r e a s e , b u t f o r a l u m i n i u m 6 to i n c r e a s e d r a m a t i c a l l y a b o v e a b o u t 105 s -~. T h e d r o p in t h e r a t e o f i n c r e a s e o f the flow s t r e s s , o r d i s l o c a t i o n d a m p i n g , h a s b e e n a t t r i b u t e d to a v e l o c i t y d e p e n d e n t r e d u c t i o n in t h e e f f e c t i v e v o l u m e a r o u n d t h e c o r e s o f t h e m o v i n g disl o c a t i o n s t h a t c a n e x c h a n g e e n e r g y w i t h t h e l a t t i c e p h o n o n s . 6 T h e rise in t h e flow s t r e s s at h i g h e r s t r a i n r a t e s m a y b e d u e to " r e l a t i v i s t i c " e f f e c t s as t h e m o v i n g dislocations approach sonic velocities. 6 D u e to e x p e r i m e n t a l difficulties, m o s t w o r k on d e t e r m i n i n g s t r e s s - s t r a i n - s t r a i n r a t e r e l a t i o n s h i p at s t r a i n r a t e s a b o v e 103s -~ h a s b e e n l i m i t e d to s o f t a n n e a l e d m a t e r i a l s Y -7 W h i l e this simplifies e x p e r i m e n t a l p r o b l e m s a n d t h e a n a l y s i s o f t h e r e s u l t s , it c a n o n l y give a p a r t i a l i n s i g h t into t h e b e h a v i o u r o f h a r d e n e d m a t e r i a l s at t h e s e high s t r a i n r a t e s . T h e p r e s e n t w o r k e x a m i n e s the s t r e s s - s t r a i n b e h a v i o u r o f 7039 a l u m i n i u m a r m o u r m a t e r i a l at s t r a i n r a t e s in t h e r a n g e 2 x 103 to 2.5 x 104 s -~ u s i n g a m o d i f i e d H o p k i n s o n bar. T h i s w o r k f o r m s p a r t o f a p r o j e c t s t u d y i n g t h e p e n e t r a t i o n of targets by projectiles, a process that involves strain rates of the order of 104 s -1. EXPERIMENTAL Specimens were prepared from 7039 aluminium (0-24% Fe, 0.09% Cu, 0.12% Si, 2.1% Mg, 4-0% Zn, 0.28% Mn, 0-02% Ti and 0.12% Cr) armour plate. The specimens were first trepaned from a 30 mm thick MSvol. 20, No. 9.--E

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plate and then turned to either 4-8 m m height x 4-8 m m dia, or 6-4 m m height × 6-4 m m dia cylinders. The s p e c i m e n s were used in the as-received (precipitation-hardened) state with a h a r d n e s s of 155 HV10. High strain rate c o m p r e s s i o n tests were performed using a modified H o p k i n s o n bar previously described in detail. 7's The apparatus consists of a split H o p k i n s o n bar in which the input bar has been r e m o v e d and a 12.7 m m dia hardened 4340 steel projectile allowed to impinge on the s p e c i m e n s directly. The load on the s p e c i m e n was m e a s u r e d using two foil strain gauges m o u n t e d on opposite sides of the 12.7 m m dia × 500 m m h a r d e n e d 4340 steel output bar. T h e length of the specimen was m e a s u r e d by the position of the back-end of the projectile in a 25 m m long coaxial capacitor. The s p e c i m e n was held in place by graphite grease which also acted as a lubricant. Since the s p e c i m e n s were relatively small and the impact velocities relatively low, no correction for lateral inertia was made in calculating the stress. For s o m e tests with the 4.8 m m specimens, in order to study the mode of deformation, the impact bar was stopped after a predetermined strain by the use of a hardened 4340 steel restraining ring fitted around the end of the output bar, w h i c h prevented further deformation of the specimen. RESULTS For strain rates b e t w e e n a b o u t 2 x 10~ and 1.2 x 104 s ~ the stress at a given strain increased linearly with strain rate, as s h o w n in Fig. 1. A b o v e 1.2 × 104 s -~ T h e stress appeared to level out, but the results were not reproducible e n o u g h and were too scattered to give a definite trend. All s p e c i m e n s failed by shear. The 4-8 m m s p e c i m e n s failed at a strain of about 0.4, while the 6.4 m m s p e c i m e n s failed at a strain of about 0-3, which corresponded to a c o m p r e s s i o n of 1.6 m m in both cases. 1

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FIG. 1. Stress vs strain rate for 7039 aluminium at a true strain of 0.1. The s t r e s s - s t r a i n m e a s u r e m e n t s indicated work-softening after a strain of about 0.1; this was followed by a s u d d e n drop corresponding to the shear failure of the specimen. Fig. 2 s h o w s schematically the characteristics of s h e a r d e f o r m a t i o n and s u b s e q u e n t cracking in the interior of the c o m p r e s s i o n specimens, and the s t r e s s - s t r a i n curve at a strain rate of 8 x 103 s -t. At str~tins above about 0.2 it was noticed that the rate of work-softening decreased with increasing strain rate. On plotting the rate of the linear worksoftening sgainst strain rate on logarithmic scales a decreasing linear relationship was o b s e r v e d with a slope of 0.5, as s h o w n in Fig. 3. T h e effect of stress, strain and strain rate is s u m m a r i z e d in Fig. 4. For strains up to 0.2 the stress increased linearly with strain rate up to 1.2 x 104 s -~, after which it was constant; work-softening began after a strain of 0'1 and, after a strain of 0.2. the work-softening rate was inversely proportional to the square root of the strain rate, and shear failure occurred at a strain of 0.4. DISCUSSION The linear increase of stress with strain rate above about 103 s -~ is usually interpreted in terms of viscous flow ~. T h e value of the macroscopic viscosity 77 can be obtained from the slope of a plot of shear stress vs s h e a r strain rate. T h e macroscopic viscosity is related to the total dislocation damping coefficient B by the equation rl = B I p , , b 2

where t ~ is the mobile dislocation density and b is the Burgers' vector. T h u s , knowing the value of the macroscopic viscosity and the dislocation d a m p i n g coefficient, usually determined directly by m e a s u r i n g the velocity of individual dislocations as a function of stress, the value of the mobile dislocation density can be calculated. For 7039 aluminium, the m a c r o s c o p i c viscosity was f o u n d to be 2-9 kPa s for strain rates between 2 × 103 and 1.2 x 104 s-~; this c o m p a r e s with the value of 0.8 k P a s for pure aluminium. 7 It is not clear w h e t h e r this increase in the macroscopic viscosity for 7039 a l u m i n i u m c o m p a r e d with pure aluminium is due to an increase in the drag coefficient or a decrease in the density of mobile dislocations, or both. For pure aluminium, the value of the density of mobile dislocations has been calculated to be about 2 × 10 tl m-2. 7 The

The high strain rate compression of 7039 aluminium

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FIG. 3. Graph of the logarithm of the work-softening rate against the logarithm of the strain rate, showing that the work-softening rate is inversely proportional to the square root of the strain rate.

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FIG. 4. Stress-strain-strain rate data for 7039 aluminium at room temperature. The stress drop at a strain of about 0.4 corresponds to the shear failure of the test specimens, presence of precipitates in the 7039 aluminium can be expected to tie-up more dislocations and possibly reduce the mobile dislocation density. Although under viscous flow conditions dislocations nominally do not "see" precipitates, the presence of precipitates must affect the overall lattice properties controlling the drag coefficient. Due to shearing, the specimens after compression were elliptical in cross section. As the specimens shear locally, the two halves of the specimens start to slide across each other. The gross deformation was confined to the tips of the two half sections as the height of the halves was reduced to accommodate the increasing strain; little deformation occurred in the larger cross-sectioned bases. It was noticed that the minor diameter (the diameter of the base of the halves) corresponded to the diameter of a uniformly deformed specimen at a strain of about 0.15. This strain was about the same as the strain at which the specimen was started to work-soften. The specimens deformed at a strain rate of 8 × l0 s s -~ and stopped after a predetermined strain, showed no evidence of concentrated shear for strains less than 0.15. At larger strains intersecting shear deformation bands formed on the diagonals (Fig. 5a) and at strains above about 0.25 shear deformation localized on one of the diagonals (Fig. 5b). Further deformation resulted in the- propagation of cracks from both ends of the predominant shear band (Fig. 5c). The form of the stress-strain curves (Fig. 2) was similar to that calculated by Sulijoadikusumo and Dillon9 assuming adiabatic heating and linear work-hardening. Sulijoadikusumo's calculations were for a Ti-6A1-4V alloy in the temperature range of 1070-1270 K and a strain rate of about 2 s ~ and, under these conditions, the experimental data more closely matched the assumptions of adiabatic heating and asymptotic work-hardening. For 7039 aluminium at high strain rates at room temperature the assumption of linear work-hardening and adiabatic heating are reasonable. At quasi-static rates the work-hardening rate was linear, and at high strain rates the specimen failed by shear along adiabatic-like shear bands. Sulijoadikusumo and Dillon9 used empirical data to solve their equations of state and it is not clear what the relationship was between the slope of the linear work-softening portion of the stress-strain curve and strain rate. For the 7039 aluminium alloy the linear work-softening rate was found to be inversely proportional to the square root of the strain rate. Since the strain rate is an inverse measure of the time available for diffusional processes to occur, the linear work-softening rate is proportional to the square root of time, suggesting that the diffusion of the heat generated is the controlling process which determines the work-softening rate. CONCLUSIONS A l u m i n i u m a l l o y 7039 c o m p r e s s e d

at s t r a i n r a t e s b e t w e e n

2 × 103 a n d 1-2 × 104 s -~

showed a linear relationship between flow stress and strain rate, which has been i n t e r p r e t e d i n t e r m s o f v i s c o u s f l o w a n d g i v e a m a c r o s c o p i c v i s c o s i t y o f 2.9 k P a s. A t s t r a i n r a t e s b e t w e e n 1.2 a n d 2.5 × 104 s -1 t h e f l o w s t r e s s l e v e l s o u t , b u t t h e d a t a is t o o s c a t t e r e d t o g i v e a d e f i n i t e t r e n d . A t s t r a i n s a b o v e 0.15 w o r k - s o f t e n i n g w a s o b s e r v e d

The high strain rate compression of 7039 aluminium

FIG. 5. (a) deformation cross observed at a strain of 0-24 (manification times 20). (b) Shear band formed at a strain of 0-26 (magnification times 20). (c) Cracking along the shear band at a strain of 0-35 (magnification times 20). All at a strain rate of 8 x 10~ s -~.

613

The high strain rate compression of 7039 aluminium

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a n d was a t t r i b u t e d to the o p p o s i n g effects of l i n e a r w o r k - h a r d e n i n g a n d a d i a b a t i c heating. T h e w o r k - s o f t e n i n g rate w a s f o u n d to be i n v e r s e l y p r o p o r t i o n a l to the s q u a r e r o o t of the s t r a i n rate a n d it w a s s u g g e s t e d that the d i f f u s i o n of heat g e n e r a t e d m a y be the c o n t r o l l i n g p r o c e s s . A d i a b a t i c s h e a r b a n d s f o r m e d in the s p e c i m e n s w h i c h s u b s e q u e n t l y failed b y c r a c k p r o p a g a t i o n a l o n g the d o m i n a n t b a n d . W h i l e w o r k s o f t e n i n g o c c u r r e d w h e n a d i a b a t i c s h e a r b a n d s w e r e f o r m e d , the c o n v e r s e w a s n o t n e c e s s a r i l y true.

REFERENCES 1. J. D. CAMPBELL,Mat. Sci. Engng 12, 3 (1973). 2. F. E. HAUSER, J. A. SIMMONSand J. E. DORN, In Response of Metals to High Velocity Deformation (Edited by P. G. SHEWMONand V. F. ZACKAY),p. 93. Interscience, New York (1961). 3. A. R. DOWLING,J. HARDINGand J. D. CAMPBELL,J. Inst. Metals 98, 215 (1970). 4. S. K. MrrRA and J. E. DOaN, Trans. AIME 227, 1015 (1963). 5. W. G. FERGUSON,A. KUMERand J. E. DOI~N,J. Appl. Phys. 38, 1863 (1967). 6. C. K. G. DHARANand F. E. HAUSER,J. Appl. Phys. 44, 1468 (1973). 7. G. L. WULF,Mechanical Properties at High Rates of Strain, Inst. Phys. Con[. Ser. No. 21, p. 105 (1974). 8. G. L. WULFand G. T. RICHARDSON,J. Phys. E: Sci. Instrum. 7, 167 (1974). 9. A. V. SULUOADKUSUMOand O. W. DILLON, JR., In Metallurgical Effects at High Strain Rates (Edited by R. W. ROHDE, B. M. BUTCHER,J. R. HOLLANDand C. H. KARNES),Met. Soc. AIME, p. 501. Plenum Press, New York (1973).