Correspondence between Strain Path and Stress Path in Plastic Deformation.

Abstract

This paper deals with the connections between the local geometries of associated paths of stress and strain under plastic deformation. This is a classical topic; nevertheless, some practically important aspects remain to be investigated in depth. The studies of the mutual relations between these paths reported in the literature have been performed in plane deformation, where the shape of stress path on the (σ1, σ2) plane is compared with the strain path shape on the (ε1, ε2) plane. However, even though plane stress deformation is assumed, there exists an ε3 component. Hence, the planar shape of strain path on the (ε1, ε2) plane does not show the real path shape, but is only the projection of the three-dimensional path to this plane. The strain in plastic deformation is always constraint on the deviatoric plane passing through the origin, and its shape correlates with the shape of deviatoric stress path. Therefore, the intrinsic correlation between strain and stress should be discussed on that plane, where Levy-Mises theory gives a very simple correspondence showing that the stress vector changes its angle with a rate equal to the curvature of the strain path. Taking into account the stress rate dependence in the constitutive equations used, the effect of this dependence on the shape correspondence between these paths is discussed.