A new framework for the assessment of model probabilities of the different crystal plasticity models for lamellar grains in α+β Titanium alloys

Abstract

This paper presents a novel framework for assessing the relative accuracy of the different slip transfer criterion in modelling the constitutive response of the lamellar morphology grains in α-β Titanium alloys. The main steps involved in the proposed framework include: (i) rigorous statistical evaluation of the salient morphological characteristics of the lamellar grains using image processing techniques, (ii) modelling the effects of dislocation slip transfer as additive penalties to the critical resolved shear strengths of the different slip systems in each phase, (iii) consideration of multiple geometric slip transfer criteria for the numerical evaluation of the different penalty terms, and (iv) the Bayesian calibration of the material parameters in the constitutive descriptions using spherical nanoindentation experimental data on a polycrystalline Ti-6Al-4V sample. Step (iv) described above involves the construction and refinement of a gaussian process (GP) surrogate model for the indentation measurements, which is trained on crystal plasticity finite element (CPFE) simulations incorporating the constitutive descriptions selected in Steps (ii) and (iii). The GP surrogates are then combined with Markov Chain Monte Carlo (MCMC) sampling techniques to calibrate the parameters in the various constitutive models studied in this work. Additionally, we have computed the posterior model probabilities for all the constitutive models considered and identified the most plausible slip transfer criterion. This specific constitutive model is then utilized to present a homogenized crystal plasticity model for the lamellar morphology. The proposed framework presents a robust scale-bridging protocol for incorporating the uncertain information obtained from lower scales.