Machine learning-based multi-objective optimization for efficient identification of crystal plasticity model parameters

Abstract

A set of constitutive model parameters along with crystallography governs the activation of deformation mechanisms in crystal plasticity. The constitutive parameters are typically established by fitting of mechanical data, while microstructural data is used for verification. This paper develops a Pareto-based multi-objective machine learning methodology for efficient identification of crystal plasticity constitutive parameters. Specifically, the methodology relays on a Gaussian processes-based surrogate model to limit the number of calls to a given crystal plasticity model, and, consequently, to increase the computational efficiency. The constitutive parameters pertaining to an Elasto-Plastic Self-Consistent (EPSC) crystal plasticity model including a dislocation density-based hardening law, a backstress law, and a phase transformations law are identified for two materials, a dual phase (DP) steel, DP780, subjected to load reversals and a stainless steel (SS), 316L, subjected to strain rate and temperature sensitive deformation. The latter material undergoes plasticity-induced martensitic phase transformations. The optimization objectives were the quasi static flow stress data for the DP steel case study, while a set of strain-rate and temperature sensitive flow stress and phase volume fraction data for the SS case study. The procedure and results for the two case studies are presented and discussed illustrating advantages and versatility of the developed methodology. In particular, the efficiency of the developed methodology over an existing genetic algorithm methodology is discussed. Additionally, the parameters identified for the SS case study were utilized to simulate three biaxial tensile loading paths using a finite element implementation of EPSC for further verification.