Using Bayesian framework to calibrate a physically based model describing strain-stress behavior of TRIP steels

Abstract

Often times, the development of physical models of materials behavior is hindered not only by the incompleteness of the theoretical approach, but also by uncertainties that arise from limitations in the experimental observations used to validate and calibrate these models. In this work, we present a Bayesian framework for both the calibration of physical models as well as the quantification of likely uncertainty in experimental observations and apply it to a model for the plastic response of multi-phase Transformation Induced Plasticity (TRIP) steels. The model is based on a formulation of irreversible thermodynamics of plastic deformation and accounts for the presence of multiple phases through homogenization theories based on the iso-work approximation. Bayesian calibration through Metropolis-Hastings Markov Chain Monte Carlo has been used to calibrate a subset of the model parameters against experimental data sequentially and simultaneously. The calibrated parameters obtained from sequential training were in turn used to assess the uncertainty in a subset of experimental data—i.e. phase volume fractions—used as input to the models themselves. The viability of the calibration approach has also been examined using synthetic data generated from simultaneous calibrated model.