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

  • Deniz Ozturk
  • Shravan Kotha
  • Adam L. Pilchak
  • Somnath GhoshEmail author
Multiscale Computational Strategies for Heterogeneous Materials with Defects: Coupling Modeling with Experiments and Uncertainty Quantification


This paper develops a bottom-up and top-down multi-scale modeling framework for predicting fatigue crack nucleation in structures of titanium alloys, e.g., Ti-7Al. A parametrically homogenized constitutive model (PHCM) and a parametrically homogenized crack nucleation model (PHCNM) are developed from computational homogenization of crystal plasticity finite element simulation results performed on microstructural statistically equivalent RVEs. Bayesian inference and machine-learning methods are employed to derive microstructure-dependent functional forms of PHCM and PHCNM coefficients. The PHCM is augmented with uncertainty quantification to account for model reduction errors and microstructural uncertainty. Macroscopic finite element models for Ti-7Al test specimens are created by matching correlation functions of microtexture in electron back-scatter diffraction scans. Nucleation hot-spots are identified by PHCNM in macroscopic simulations of stress-controlled dwell loading, then top–down microscopic simulations are performed to probe into the crack nucleation process. The computed distributions of nucleation lives and locations follow experimentally observed characteristics of the dwell effect in Ti alloys.



Crystal plasticity finite element


Electron back-scatter diffraction


Extrusion and transverse directions


Micro-textured region


Parametrically homogenized constitutive model


Parametrically homogenized crack nucleation model


Statistically equivalent representative volume elements


Uncertainty quantification/propagation


Wavelet-induced accelerated multi-timescale integration algorithm


Macroscopic yield strength



This work is supported through a subcontract to JHU (sub-recipient) from the Ohio State University (main recipient) through a sub-Award No. 60038238 from an AFRL Grant No. FA8650-13-2-2347 as a part of the AFRL Collaborative Center of Structural Sciences. The program managers of this grant are Dr. B. Smarslok and Dr. R. Chona, and the PI is Prof. J. McNamara. This support to JHU is gratefully acknowledged. Computer use of the Hopkins High Performance Computing facilities is gratefully acknowledged. Adam Pilchak gratefully acknowledges the support of AFOSR Task No. 12RX01COR, with program manager Dr. A. Sayir.


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Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringJohns Hopkins UniversityBaltimoreUSA
  2. 2.Air Force Research Laboratory, Materials and Manufacturing DirectorateWright Patterson Air Force BaseDaytonUSA
  3. 3.Departments of Civil, Mechanical and Material Science EngineeringJohns Hopkins UniversityBaltimoreUSA

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