Instability of plastic flow in the directions of pure shear: II. Experimental
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f o r m a t i o n and c o a l e s c e n c e of p o r e s is r e c o g n i z e d as a b a s i c mode of f r a c t u r e . A second f r a c t u r e mode is f i r m l y e s t a b l i s h e d e x p e r i m e n t a l l y and is des c r i b e d in a p r e v i o u s paper a along with its t h e o r e t i c a l b a s i s . The i n i t i a t i o n event is i n t e r p r e t e d as the a c t i vation of a d i s c o n t i n u i t y in t a n g e n t i a l d e f o r m a t i o n v e locity along a c h a r a c t e r i s t i c as defined in c o n t i n u u m p l a s t i c i t y t h e o r y . A n e c e s s a r y condition is the t r a n s i tion f r o m the s t r a i n h a r d e n i n g state to the d y n a m i c ideal p l a s t i c state, w r i t t e n as: 8a (~)Se
dar= o
+
8a
.
6T = 0
[1]
where (y s d T 7-=0
is the t r u e flow s t r e s s is the t r u e p l a s t i c s t r a i n is the t r u e s t r a i n r a t e is the absolute t e m p e r a t u r e is the g e n e r i c t i m e for the o n s e t of s h e a r i n g instability
Eq. [1] s p e c i f i e s that such a state is achieved at a s t r a i n at which the t r u e flow s t r e s s is a m a x i m u m . The flow s t r e s s should r e m a i n c o n s t a n t or d e c r e a s e ( s t r a i n softening) with f u r t h e r s t r a i n i n g .
do>o
:
I21
The p u r p o s e of this paper is to p r e s e n t e x p e r i m e n t a l evidence that 1) f r a c t u r e by such a mode ( s h e a r i n g i n s t a b i l i t y f r a c t u r e ) o c c u r s along i n s t a b i l i t y bands in the characteristic direction and 2) the condition given by Eq. [2] marks the onset of the instability. AMIYA K. CHAKRABARTI,formerly with Metals and Ceramics Laboratory, Aerospace Research Laboratories, Wright-PattersonAFB, is now with Metals and Ceramics Division,Air Force Materials Laboratory, Wright-PattersonAFB, Ohio 45433. JOSEPH W. SPRETNAK is the Earl M. Tilton Professor of MechanicalMetallurgy, The Ohio State University. Manuscript submitted April 25, 1974. METALLURGICALTRANSACTIONSA
EXPERIMENTAL PROCEDURE The material used in this study was AISI4340 steel (0.41C, 0.73Mn, 0.31Si, 0.012 P, 0.017S, 1.75Ni, 0.83 Cr, 0.23 Mo) which was rough machined, austenitized at 830~ (1103 K) for 3/4 h, oil quenched and then tempered at one of three temperatures followed by air cooling. The tempering temperatures were 616, 755 and 892 K. The corresponding ultimate strength values are 1634.06, 1310.00 and 1006.06 MN/m2. Two types of specimens were used in the present investigation namely I) plane strain tensile specimens after Clausing2 and 2) flat sheet tensile specimens of different width to thickness ratios. The details of the plane strain and sheet tensile specimens are presented in Fig. 1. In thin sheet specimens, the stress in the thickness direction is assumed to be zero (a3 = 0), yielding a plane stress condition. As the geometric constraint to contraction in the transverse direction is increased, a tensile stress % is generated in increasing magnitude. As the ratio e2/al reaches a va
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