Thesis Defense: Deniz Ozturk, “Multi-scale Modeling and Uncertainty Quantification of Deformation and Fatigue Crack Nucleation in Titanium Alloys using Parametrically Homogenized Constitutive Models”

July 17, 2019





Doctoral Candidate

Deniz Ozturk

Friday, July 19, 2019


Latrobe 106

Multi-scale Modeling and Uncertainty Quantification of Deformation and Fatigue Crack Nucleation in Titanium Alloys using Parametrically Homogenized Constitutive Models


This thesis develops novel micromechanical and multi-scale models of deformation and fatigue crack nucleation in Titanium alloys. Image-based rate-, size- and temperature-dependent crystal plasticity finite element (CPFE) models are developed and calibrated from deformation experiments performed on macroscopic and single crystal specimens. Micromechanical analyses are performed on 3D polycrystalline statistically equivalent RVEs (SERVEs) to study the effects of microstructure, crystallography and thermo-mechanical loading conditions on fatigue crack nucleation in Titanium alloys. A probabilistic crack nucleation model is developed and calibrated from in-situ X-ray computed tomography observations of initiating cracks. The crack nucleation model, accounting for both time-dependent and cyclic damage mechanisms successfully reproduce the important characteristics of the experimental crack nucleation lives under both dwell and continuous cyclic loading conditions. Thermo-mechanical simulations of polycrystalline models suggest that an alleviation of the dwell effect at elevated temperatures results from the reduction of the critical resolved shear stress of <c+a> systems. The simulated orientations of initiated cracks are inclined 5°–25° off the crystallographic (0001) planes, in agreement with experimental measurements with micro-tilt fractography.

To predict fatigue crack nucleation in structural components of Titanium alloys, a two-way multi-scale modeling framework is developed next. A parametrically homogenized constitutive model (PHCM) and a parametrically homogenized crack nucleation model (PHCNM) are developed from computational homogenization of CPFE simulation results performed on microstructural SERVEs. A machine learning method is used to derive the microstructure-dependent constitutive parameters of PHCM and PHCNM based on micromechanical analysis data. Macroscopic FE models of test specimens are constructed based on EBSD scans of the material, accounting for microstructural heterogeneity and crystallographic microtexture. Macroscopic simulations of dwell and cyclic loading are performed and nucleation hotspots are identified by PHCNM. Top-down simulations of the local M-SERVEs are performed to probe microstructural fatigue crack nucleation sites and cycles. The computed distributions of nucleation lives and locations follow the experimentally observed characteristics of the dwell effect in Titanium alloys.

Finally, PHCMs are augmented with uncertainty quantification to account for model reduction errors, calibration data sparsity, and microstructural uncertainty. Microstructure-dependent functional forms of stochastic PHCMs are identified by machine learning and Bayesian inference techniques. A novel uncertainty propagation method is developed to propagate the uncertainties in PHCM constitutive parameters and microstructural variables to the model response variables of interest, such as stress, strain or macroscopic fatigue or damage measures, while avoiding expensive Monte Carlo simulations.

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