Bayesian analysis of parametric uncertainties and model form probabilities for two different crystal plasticity models of lamellar grains in α+β Titanium alloys

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

“…Finally, we utilize the insights gained in the above workflow to propose a new homogenized crystal plasticity model for the lamellar morphology grains that accounts for slip transmission across the phase boundary. We show that this new model exhibits higher model probability compared to the simpler homogenized models considered in our previous study [18]. We note that the overall framework presented in this study represents an objective methodology to refine colony-scale homogenized models by incorporating salient information extracted from lower-scale analyses.…”

“…Previous studies have generally homogenized the lamellar morphology into an equivalent single crystal [13,15,18], by including different combinations of the aforementioned slip families. In our recent study [18], we considered two such models with the goal of evaluating their relative model probabilities; these are also employed in this study. The first model (hereafter referred to as 'H1') was inspired by the experimental results from Mills et al [4,5,27,53].…”

“…In total, the H2 model involved seven adjustable parameters: τ pr CRSS , τ ba CRSS , τ pyr−a CRSS , τ bcc CRSS , κ 0 , k y and A. The mean values of these model parameters were established as (see Venkatraman et al [18] The prior application of the three-step Bayesian framework using the same experimental dataset used in this study revealed that the H2 model was more plausible compared to the H1 model. As already discussed, these homogenized models greatly simplify the effects of plastic strain and stress concentrations at the phase boundary.…”

“…This approach is reasonable, especially when the β-phase volume fractions are low. Several efforts [11,13,[15][16][17][18] have successfully employed this strategy for modeling the effective mechanical response of the colony grains in α − β Ti alloys. One of the main reasons behind the popularity of this approach is its lower computational cost compared to the more refined models that account explicitly for the individual lamellae.…”

“…The central goal of this study is to evaluate objectively the relative accuracy of the different geometric slip transfer criteria proposed in current literature through their ability to explain the recently aggregated collection [47] of spherical indentation-based colony-scale measurements from a polycrystalline sample of Ti-6Al-4V. Towards this goal, we will first estimate the feasible sets of intrinsic properties for each slip transfer model form (implemented in a CPFE model) through a suitable calibration with the available indentation measurements using a three-step Bayesian framework established in our prior work [18]. More specifically, this three-step framework involves (i) the establishment of a high-fidelity low-cost Gaussian process (GP) regression (GPR) surrogate model for the indentation measured properties as a function of the intrinsic model parameters as well as the lattice orientation of the indented grain, (ii) sampling feasible sets of values for the intrinsic properties that best match the surrogate model to the available experimental measurements using Markov Chain Monte Carlo (MCMC) techniques, and (iii) the application of the Bayesian model selection technique to estimate the relative probabilities of the different model forms under consideration.…”