Uncertainty-quantified parametrically homogenized constitutive models (UQ-PHCMs) for dual-phase alpha/beta titanium alloys

This paper develops an uncertainty-quantified parametrically homogenized constitutive model (UQ-PHCM) for dual-phase alpha/beta titanium alloys such as Ti6242S. Their microstructures are characterized by primary alpha-grains consisting ofhcpcrystals and transformed beta-grains consisting of alternating laths of alpha(hcp) and beta(bcc) phases. The PHCMs bridge length-scales through explicit microstructural representation in structure-scale constitutive models. The forms of equations are chosen to reflect fundamental deformation characteristics such as anisotropy, length-scale dependent flow stresses, tension-compression asymmetry, strain-rate dependency, and cyclic hardening under reversed loading conditions. Constitutive coefficients are functions of representative aggregated microstructural parameters or RAMPs that represent distributions of crystallographic orientation and morphology. The functional forms are determined by machine learning tools operating on a data-set generated by crystal plasticity FE analysis. For the dual phase alloys, an equivalent PHCM is developed from a weighted averaging rule to obtain the equivalent material response from individual PHCM responses of primary alpha and transformed beta phases. The PHCMs are readily incorporated in FE codes like ABAQUS through user-defined material modeling windows such as UMAT. Significantly reduced number of solution variables in the PHCM simulations compared to micromechanical models, make them several orders of magnitude more efficient, but with comparable accuracy. Bayesian inference along with a Taylor-expansion based uncertainty propagation method is employed to quantify and propagate different uncertainties in PHCM such asmodel reduction error,data sparsity errorandmicrostructural uncertainty. Numerical examples demonstrate the accuracy of PHCM and the relative importance of different sources of uncertainty.