The influence of constitutive behavior on the sheet-metal forming limit strains predicted using an imperfection growth model

Sheet metal forming limit strains for proportional and non-proportional loading histories have been predicted using an imperfection growth model. This model is the generally accepted method for prediction of forming limit strains in sheet materials. The influence of constitutive behavior on the forming limit strains predicted using this model has been studied.; The forming limit strains determined experimentally in sheet metals are found to be dependent on the imposed strain path as a result of the history dependence of non-elastic deformation. The MATMOD-4V-2D constitutive equations have been utilized to predict history dependent constitutive behavior in an imperfection growth model. The use of complex constitutive behavior increased the predictive capability of the imperfection growth model for predicting sheet metal forming limit strains as well as developing insight into the physical processes important in optimizing formability. Forming limit strains were predicted with increased quantitative accuracy. The complex constitutive behavior, including structure variables representing both isotropic and kinematic hardening, allowed for prediction of behavior observed to be associated with "aluminum alloy-like" materials as well as "steel-like" materials when subjected to non-proportional loading histories.; Through the structure evolution predicted for non-proportional loading histories, insight into the material processes which must be considered to optimize sheet metal formability were defined. Substructure dissolution resulting from changes in the strain path was found to adversely effect the predicted forming limit behavior of materials. This was particularly important in "steel-like" materials where substructure formation strongly influences the flow stress. In "aluminum alloy-like" materials, second phase particles can lead to the formation of a polarized dislocation structure resulting in kinematic (direction dependent) hardening. Changes in the strain path require the rearrangement of the backstresses which can lead to high hardening rates in certain material directions immediately following the change in strain path. These high rates of hardening were found to stabilize plastic deformation. Formability enhancements were predicted in materials where kinematic contributions dominated the overall hardening behavior of a material.