A three-dimensional model of anisotropic hardening in metals and its application to the analysis of sheet metal formability

The hardening model proposed by Z. Mróz based on the uniaxial fatigue behavior of many metals is adopted to derive an incremental constitutive equation for general three-dimensional problems. This constitutive law is then employed in the analysis of metal forming problems to assess the influence of loading cycles, of the types involved in standard forming processes, on the ultimate formability of sheet metals. The predicted forming limit curves differ quantitatively from results obtained via an isotropie hardening model and differ qualitatively from those obtained via a kinematic model. Also investigated are the effects of such loading cycles on material response to simple tensile loading, which is often used to characterize a material. Significant differences between the present model and the other two models considered are observed in such characterizers of simple tensile behavior as the stress-strain curve, the anisotropy parameter and the uniform elongation. These differences suggest a rather simple experiment to identify the proper material model to be used in analyses of problems which involve loading cycles. Comparisons with some experimental results reveal that the employment of an anisotropic hardening model, such as the generalized Mróz model derived herein, is indeed crucial in accurately predicting material response to complicated loading histories.