The Yield Condition and Flow Rule of a Metal for The Various Pre-Strain Paths

Abstract

An anisotropic yield condition and a flow rule of metal for various complex loadings were investigated in the three dimensional deviatoric vector space. The yield function was derived by considering the distortion and the translation of the yield surface. The configuration of distorted yield surface was represented as a set of points on a series of ellipses whose lengths of the minor axis were changed as a function of the co-ordinate on the symmetrical axis of the yield surface. The subsequent yield surface after the pre-strain path with a corner was assumed to translate in the direction of the stress increment vector. The flow rule was introduced from the normality rule of the plastic strain increment. The yield surfaces and the stress-strain relations along the proportional pre-loading path, the pre-strain paths with a corner and the cyclic loading path were calculated by using the derived yield functions. There was good agreement between the results of calculation and of experiment for brass.