Elastoplastic finite element analyses of metal deformations using polycrystal constitutive models

A finite element formulation using an elastoplastic polycrystal constitutive theory is presented. The crystal constitutive equations are expressed in an intermediate configuration obtained by unloading the deformed crystal without rotation from the current configuration to a stress-free state through small elastic strains. These constitutive relations and an associated integration procedure are implemented in a pressure-velocity (mixed) finite element formulation. Both small scale (finite element dimensions comparable to crystal dimensions) and large scale (finite element dimensions much larger than the crystal size) problems are solved to illustrate the formulation's application to metal deformations, including the determination of the R-value in a tensile specimen and the prediction of residual stresses in a thick ring deformed in an upsetting operation.