An isoparametric piecewise representation of the anisotropic strength of polycrystalline solids

A methodology for representing the anisotropic strength of polycrystalline solids using an isoparametric mapping is presented. A four-dimensional hypersphere in five-dimensional (deviatoric) deformation rate space is defined using Lagrange elements for a suite of deformation rate directions with a specified (reference) magnitude. Onto this surface are mapped values of the flow stress required to induce plastic flow for the corresponding values of the reference deformation rate. The flow stress values are evaluated from a combination of experimental data and computational results using polycrystal plasticity. The methodology is demonstrated for three example systems: Ti–6Al–4V plate, AA5182 hot rolled plate, and AL6XN hot rolled plate.