Sheet metal forming processes are an important part of many manufacturing operations today. The numerical simulation of these processes has become an important aspect in the design of the processes and in the understanding of the material forming itself. This thesis document describes the development and formulation of a material model which was used in the numerical simulation of deep drawing problems. The purpose of the material model was to predict the formation of martensite during the plastic straining of metastable austenitic stainless steel and the effect of the martensite formation on the plasticity of the steel. The model was developed from existing work as a modified von Mises isotropic hardening elastic-plastic algorithm. The algorithm was implemented as the subroutine UMAT in the finite element program ABAQUS. Finite element simulations employing the material model were performed on two axisymmetric deep drawing examples. The finite element analysis was performed as a coupled displacement-temperature analysis. The simulations produced results which predicted the distribution of various material state variables such as the volume fraction of martensite, plastic strain, yield stress and temperature in the formed component. The results were consistent with what is intuitively expected from the physics of the problem. They were able to explain phenomena observed in physical tests such as the location of failures in the formed components and the occurrence of delayed cracking. It is concluded that the model was successful in providing qualitative information on the distribution of martensite in components formed by deep drawing. These predictions were for a broad range of stainless steel behaviour. However, extensions to the model are required to be able to make accurate quantitative predictions on the formation of martensite in specific materials
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