Deformation of sandwich sheet materials in uniaxial tension
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I. INTRODUCTION T H E deformation of materials used in sheet forming applications is most often limited by the onset of instability rather than fracture. The uniaxlal true stress-true strain curve, (~u = (~u(s is an indispensable tool used to gage stable as well as unstable flow behavior. When loading a ductile sheet in uniaxial tension, stable, uniform elongation is ended when a maximum in applied load is reached. 1,2 This condition is satisfied when: d(~u
d~l
s h e e t t e n s i l e s p e c i m e n . The f o r m a t i o n of the l o c a l i z e d n e c k e s s e n t i a l l y ends the u s e f u l d e f o r m a t i o n of ductile sheet m e t a l s . F o r c o m p o s i t e m a t e r i a l s , flow p r o p e r t i e s a r e often a s s u m e d to be a r e a - w e i g h t e d a v e r a g e s of component p r o p e r t i e s and a r e , t h e r e f o r e , e s t i m a t e d u s i n g the r u l e of m i x t u r e s . F o r e x a m p l e , the s t r e s s - s t r a i n curve of a s y m m e t r i c , two component clad sheet, (rus(el), is taken to be: (rus(el) = A m a u m ( e l ) + A c a u c ( ~ l ) or s i m p l y ,
~u = O.
[1]
A f t e r this load m a x i m u m , u n s t a b l e d e f o r m a t i o n m a y continue u n d e r f a l l i n g load. A neck c h a r a c t e r i z e d by a p r o f i l e r a d i u s o r i e n t e d s y m m e t r i c a l l y about the t e n s i l e axis of the sheet develops at an i r r e g u l a r i t y or i n h o m o geneity in the s p e c i m e n . The extent of this n e c k is a p p r o x i m a t e l y equal to the width of the sheet and, thus, the n e c k is u s u a l l y t e r m e d d i f f u s e . T h e growth of the diffuse n e c k in u n i a x i a l as well as b i a x i a l t e n s i l e s t r e s s s t a t e s has come u n d e r close e x a m i n a t i o n in r e c e n t y e a r s . Ghosh 3'4 has studied how changes in s t r a i n r a t e and s t r e s s state a c t i n g in the diffuse n e c k may r e s u l t in what a m o u n t s to a flow s t a b i l i z i n g effect and i n c r e a s e the o v e r a l l u s e f u l d u c t i l i t y . If f r a c t u r e does not i n t e r vene, a second type of i n s t a b i l i t y , the local i n s t a b i l i t y , m a y then o c c u r at higher s t r a i n l e v e l s P 's T h i s i n s t a b i l i t y leads to a l o c a l i z e d t h r o u g h - t h i c k n e s s t h i n n i n g a l o n g a d i r e c t i o n of z e r o e x t e n s i o n in the plane of a S. L. SEMIATIN,formerly Graduate Student, Department of Metallurgy and Materials Science, Carnegie-MellonUniversity, is now Research Scientist, Metalworking Section, Battelle Columbus Laboratories, Columbus, OH 43201. H. R. PIEHLER is Professor, Department of Metallurgyand Materials Science, Carnegie-MellonUniversity, Pittsburgh, PA 15213. Manuscript submitted June 1, 1978. METALLURGICALTRANSACTIONSA
aUs = A m a u m + Ac(~uc.
The s u b s c r i p t s s, m, and c r e f e r to sandwich, core (middle l a y e r ) , and cladding, r e s p e c t i v e l y . A m and A c a r e the c r o s s - s e
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