Equivalent plastic strain for the Hill's yield criterion under general three-dimensional loading

Abstract

In many industrial applications, an accurate model of the initial yield surface of materials with a significant degree of anisotropy is required. Anisotropy due to preferred orientation can occur in sheet metal parts used in automotive applications due to the rolling processes used to form the sheets. Hill's quadratic yield criterion for anisotropic metals can be used to more accurately model these materials, allowing for improved constitutive models for the prediction of plastic failure and ductile fracture. In this thesis, a derivation of the equivalent plastic strain for plane stress in matrix notation is presented using associated plastic flow and work conjugation. A similar method is attempted for the general three-dimensional case; however, a singularity appears as the six components of the strain increment vector are not independent under plastic incompressibility. To remedy this, a reduced-order system was defined in terms of deviatoric stress, with one normal component eliminated, so that the previous method could be applied; the eliminated component was reintroduced in the final expression. This result was also further expanded to introduce the possibility of defining different plastic potentials and yield criteria under non-associated flow. The result is two expressions for equivalent plastic strain for the Hill's yield criterion in both plane stress and three-dimensional cases that have been partially validated analytically through testing limiting cases such as material isotropy.