Parametrically Homogenized Constitutive Models (PHCMs) for Multi-scale Predictions of Fatigue Crack Nucleation in Titanium Alloys

Ozturk, Deniz; Kotha, Shravan; Pilchak, Adam L.; Ghosh, Somnath

doi:10.1007/s11837-019-03554-0

Cited by 16 publications

(17 citation statements)

References 38 publications

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“…This uncertain error is referred to as the data sparsity error, and is represented by the Bayesian posterior distribution of model coefficients. Within a Bayesian calibration framework, it may be shown that this type of uncertainty depends on both the number and distribution of the calibration data points in the RAMP-space 14 . For a given microstructure, the total deviation of the PHCM-predicted response from the micromechanics-based response is accounted for by the model reduction and data sparsity errors.…”

Section: Uncertainty Quantification (Uq) and Uncertainty Propagation mentioning

confidence: 99%

“…The methods follow a framework that has been introduced in ref. 14 . Assuming the CPFEM simulation-based micromechanical response as the true model, the three main sources of uncertainty discussed above are considered in this framework.…”

Section: Uncertainty Quantification (Uq) and Uncertainty Propagation mentioning

confidence: 99%

“…1a. The anisotropic phases, colony structures and crystallographic orientation mismatch at grain and lath boundaries significantly influence their deformation, creep, and fatigue characteristics [9][10][11][12][13][14] . Under dwell loading conditions, the near-α and α/β alloys undergo time-dependent load shedding at boundaries between grains with moderate to large lattice misorientation, leading to facet formation signaling the nucleation of fatigue cracks [15][16][17] .…”

Section: Introductionmentioning

confidence: 99%

“…Bayesian inference, along with maximum likelihood estimation, has been used in ref. 14 to quantify (i) the uncertainty associated with constitutive parameters in PHCM functional forms obtained from machine learning, and (ii) the uncertainty due to data-sparsity associated with a limited number of microstructures and micromechanical simulations used in calibrating the PHCMs. Furthermore, with evolving deformation, the uncertainty in PHCM constitutive parameters is propagated to response variables like stresses and plastic strains.…”

Section: Introductionmentioning

confidence: 99%

“…A Taylor-series expansion-based uncertainty propagation method, originally developed in ref. 14 , is used to propagate the uncertainty to response variables. The resulting uncertainty-quantified PHCM has a unique advantage of being incorporated in any commercial software through user material windows without having to perform expensive Monte-Carlo simulations.…”

Section: Introductionmentioning

confidence: 99%

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

2020

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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.

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Section: Uncertainty Quantification (Uq) and Uncertainty Propagation mentioning

confidence: 99%

Section: Uncertainty Quantification (Uq) and Uncertainty Propagation mentioning

confidence: 99%