Parametrically homogenized constitutive models (PHCMs) from micromechanical crystal plasticity FE simulations, part I: Sensitivity analysis and parameter identification for Titanium alloys

Abstract

This is the first of a two part paper that systematically develops a finite deformation elasto-plastic, parametrically homogenized constitutive model (PHCM) for structural-scale macroscopic simulations of Titanium alloy Ti6242S. The PHCMs are thermodynamically consistent, reduced-order continuum models that incorporate functional forms of representative aggregated microstructural parameters (RAMPs) in their constitutive coefficients. These models are designed to represent all characteristics of macroscopic response such as anisotropy, tension-compression asymmetry, strain-rate and temperature dependence, and are consistent with microscopic crystal plasticity relations. An image-based size and rate-dependent crystal plasticity FE (CPFE) model is developed for creating a data-base needed for deriving functional forms of PHCM coefficients using machine learning methods. The first part of this sequence summarizes the generation of microstructure-based statistically equivalent representative volume elements (M-SERVEs) and the image-based CPFE model. Extensive sensitivity analysis is conducted to unravel the effect of specific RAMPs on the overall material response, and hence the PHCM constitutive coefficients. Sobol sensitivity analysis is performed to evaluate the sensitivities of constitutive coefficients in PHCM with respect to RAMPs to examine their suitability for representation. In the second part (Kotha et al., 2019), machine learning will be used with the database to create functional forms of the constitutive coefficients in the PHCMs.