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

  • Multiscale Computational Strategies for Heterogeneous Materials with Defects: Coupling Modeling with Experiments and Uncertainty Quantification
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Abstract

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.

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Abbreviations

CPFE:

Crystal plasticity finite element

EBSD:

Electron back-scatter diffraction

ED/TD:

Extrusion and transverse directions

MTR:

Micro-textured region

PHCM:

Parametrically homogenized constitutive model

PHCNM:

Parametrically homogenized crack nucleation model

SERVE:

Statistically equivalent representative volume elements

UQ/UP:

Uncertainty quantification/propagation

WATMUS:

Wavelet-induced accelerated multi-timescale integration algorithm

Y.S.:

Macroscopic yield strength

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Acknowledgements

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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Authors and Affiliations

  1. Department of Civil Engineering, Johns Hopkins University, Baltimore, USA

    Deniz Ozturk & Shravan Kotha

  2. Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright Patterson Air Force Base, Dayton, OH, 45433, USA

    Adam L. Pilchak

  3. Departments of Civil, Mechanical and Material Science Engineering, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD, 21218, USA

    Somnath Ghosh

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  1. Deniz Ozturk
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  2. Shravan Kotha
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  4. Somnath Ghosh
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Correspondence to Somnath Ghosh.

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Ozturk, D., Kotha, S., Pilchak, A.L. et al. Parametrically Homogenized Constitutive Models (PHCMs) for Multi-scale Predictions of Fatigue Crack Nucleation in Titanium Alloys. JOM 71, 2657–2670 (2019). https://doi.org/10.1007/s11837-019-03554-0

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