Parameter identification method for a polycrystalline viscoplastic selfconsistent model based on analytical derivatives of the direct model equations

An inverse method for automatic identification of the parameters involved in a polycrystalline viscoplastic selfconsistent (VPSC) model is presented. The parameters of the constitutive viscoplastic law at the single-crystal level, i.e. the critical resolved shear stresses (CRSS) of slip and twinning and the micro-hardening coefficients, can be identified using experimental data at the polycrystal level, i.e. stress-strain curves and deformation-induced textures. The minimization problem is solved by means of a Gauss-Newton scheme and the sensitivity matrix is evaluated by analytical differentiation of the direct model equations. As a particular case, the optimization procedure for the Taylor full constraints (FC) formulation is also presented. The convergence and stability of the identification scheme are analysed using several validation tests for different deformation paths imposed to a polycrystal of hexagonal structure. As an example of application of this inverse method, the relative CRSS of the active deformation systems of a Zircaloy-4 sheet are identified, based on several textures measured for different reductions and rolling directions.