# NATURALLY STRAINED YIELD SURFACE SHAPE ESTIMATED UNDER PRE-DEFORMATION OF TENSION AND TORSION

### YASUYUKI KATO

The purpose of this study is to investigate the shape of yield surfaces formed under large pre-deformations, based on the Natural Strain theory, and to make clear the mechanism of the development of anisotropy of yield surfaces under large deformations. In particular the shape of yield surfaces obtained after applying the pre-deformation of tension and shear with proportional loading states is examined. Using pure-copper test pieces already pre-deformed, proportional loading tests were carried out again changing the ratio of tension and torsion to determine yield stress in each direction of the stress space. The yield stress was estimated by examining the slope of tangent for the principal deviatoric stress-deviatoric strain curve in proportional loading tests. It was revealed that the shape of the yield surface becomes convex at the side of pre-deformation and becomes flat in the opposite direction of the pre-deformation. Moreover, the shape of the estimated yield surface was compared with the shape of conventional proof stress. Consequently, it became clear that the shapes of both yield surfaces almost coincide at the side of pre-deformation, but on the opposite side, the yield surface by proof stress becomes smaller compared with the estimated yield surface.

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