Uncertainty-quantified parametrically homogenized constitutive models (UQ-PHCMs) for dual-phase α/β titanium alloys

Abstract

This paper develops an uncertainty-quantified parametrically homogenized constitutive model (UQ-PHCM) for dual-phase α/β titanium alloys such as Ti6242S. Their microstructures are characterized by primary α-grains consisting of hcp crystals and transformed β-grains consisting of alternating laths of α (hcp) and β (bcc) phases. The PHCMs bridge length-scales through explicit microstructural representation in structure-scale constitutive models. The forms of equations are chosen to reflect fundamental deformation characteristics such as anisotropy, length-scale dependent flow stresses, tension-compression asymmetry, strain-rate dependency, and cyclic hardening under reversed loading conditions. Constitutive coefficients are functions of representative aggregated microstructural parameters or RAMPs that represent distributions of crystallographic orientation and morphology. The functional forms are determined by machine learning tools operating on a data-set generated by crystal plasticity FE analysis. For the dual phase alloys, an equivalent PHCM is developed from a weighted averaging rule to obtain the equivalent material response from individual PHCM responses of primary α and transformed β phases. The PHCMs are readily incorporated in FE codes like ABAQUS through user-defined material modeling windows such as UMAT. Significantly reduced number of solution variables in the PHCM simulations compared to micromechanical models, make them several orders of magnitude more efficient, but with comparable accuracy. Bayesian inference along with a Taylor-expansion based uncertainty propagation method is employed to quantify and propagate different uncertainties in PHCM such as model reduction error, data sparsity error and microstructural uncertainty. Numerical examples demonstrate the accuracy of PHCM and the relative importance of different sources of uncertainty.

Uncertainty Quantification of a High-Throughput Profilometry-Based Indentation Plasticity Test of Al 7075 T6 Alloy

“…Top-down approaches are limited by the identifiability problem; i.e., the model parameters cannot always be given unique values by fitting predictions to data (Arendt et al, 2012). Bottom-up approaches can produce distributions or intervals that are unreasonably wide (Salehghaffari et al, 2012), unless the analysis is very selective about the uncertainty being considered (Bandyopadhyay et al, 2019;Kotha et al, 2020;Tan et al, 2021). The combination of topdown and bottom-up has been proposed as a way to make use of more sources of information at once while also finding compromise between the limitations of either pathway (Panchal et al, 2013;Arróyave and McDowell, 2019;Tallman et al, 2017Tallman et al, , 2020.…”

Uncertainty Quantified Parametrically Homogenized Constitutive Models for Microstructure-Integrated Structural Simulations

“…The parametrically homogenized constitutive model, employed in the present paper, has been developed for near-Titanium alloys like Ti6Al-2Sn-4Zr-2Mo-0.1Si or Ti6242S in [20][21][22]. A summary of PHCM is given in this section.…”

PRISMS-Fatigue computational framework for fatigue analysis in polycrystalline metals and alloys

“…Consequently, fatigue crack formation and early growth has typically been investigated using crystal plasticity and homogenized continuum plasticity simulations [1][2][3]6,7 . A parametrically homogenized constitutive model (PHCM) crystal plasticity framework with uncertainty quantification 8 and two-way multiscale coupling was developed by Ozturk, Kotha, and colleagues 9 . This framework has been extensively used to investigate fatigue crack nucleation in titanium alloys 9 .…”