Structural components are often subjected to cyclic loading and their fluctuations in service conditions. This results in their time-dependent fatigue failure. With the advent of recent research initiatives like the Integrated Computational Materials Engineering (ICME) research in modeling fatigue failure has taken an exciting new dimension. By coupling sophisticated tools of Computational Mechanics and Computational Materials Science, these initiatives are enabling computational models to probe into the origins of cracking at multiple scales due to inhomogeneous plastic flow and follow their evolution to failure. This talk will introduce an approach to the development a multi-scale computational framework for physics-based modeling of fatigue crack nucleation and evolution, in polycrystalline metallic materials. Titanium alloys will be a specific focus in this study.  

The idea of parametric homogenization has been introduced by the Ghosh group as a promising alternative to the conventional homogenization methods. Parametrically Homogenized Constitutive Models or (PHCMs) have been developed for modeling deformation and fatigue crack initiation in Ti alloys. PHCMs are thermodynamically consistent, reduced-order models whose constitutive parameters are explicit functions of Representative Aggregated Microstructural Parameters or (RAMPs), representing statistical distributions of morphological and crystallographic descriptors of the microstructure. The basic forms of the PHCM equations are a-priori selected to reflect the fundamental deformation characteristics of aggregated response of crystal plasticity finite element model (CPFEM) simulations of microstructural statistically equivalent representative volume elements or (SERVEs). Such deformation characteristics include objectivity, anisotropy, tension-compression asymmetry, history/path-dependence, Bauschinger effect, etc. Microstructure-dependent functional forms of the PHCM constitutive parameters are determined in terms of the RAMPs. Machine learning tools are employed to obtain these functional forms using micromechanical time-dependent plastic deformation and fatigue crack nucleation data-sets that are generated from image-based CPFEM simulations of the SERVEs. These constitutive parameters also incorporate state variables representing the up-scaled effect of microstructural deformation mechanisms. The PHCMs are readily incorporated in commercial FE software like ABAQUS through user-defined material modeling interfaces such as UMAT, for microstructure-sensitive structural response predictions. Significantly reduced number of solution variables in the PHCM simulations, compared to DNS of micromechanical models, make them several orders of magnitude more efficient with good accuracy. Parametrically homogenized fatigue crack nucleation models have also been developed from computational homogenization of microstructural fatigue crack nucleation data.

 

The explicit representation of microstructural variables in the PHCM constitutive equations makes them particularly suitable for incorporating the uncertainty quantification (UQ) capabilities. Development of such a comprehensive uncertainty quantification framework for PHCMs is the objective of this paper. Uncertainty in the model output is attributed to the following sources.

1\. Model reduction error (MRE): This is an epistemic uncertainty stemming from the discrepancyn between the machine learning-generated, reduced-order functional forms of PHCM constitutive parameters and the microstructure-dependencies implicit in the micromechanical model;

2\. Data sparsity error (DSE): This is an epistemic uncertainty in the microstructure-dependent constitutive parameters due to the finite size of the micromechanics-based calibration dataset;

3\. Microstructural uncertainty (MSU): This aleatoric uncertainty is due to noisy characterization data or inherent microstructural variability due to processing.

Uncertainties due to MRE and DSE are accounted for by employing a Bayesian framework to calibrate the functional forms of constitutive parameters from CPFEM-generated analysis data

 Macroscopic FE models for Ti-7Al test specimens are created by matching correlation functions of microtexture in EBSD 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 dwell effect in Ti alloys.


Multi-Scale Modeling With Machine Learning and Uncertainty Quantification for Predicting Fatigue Crack Evolution in Titanium Alloys: Part II

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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