A statistical framework for generating microstructures of two-phase random materials: application to fatigue analysis

07/04/2019
by   Ustim Khristenko, et al.
0

Random microstructures of heterogeneous materials play a crucial role in the material macroscopic behavior and in predictions of its effective properties. A common approach to modeling random multiphase materials is to develop so-called surrogate models approximating statistical features of the material. However, the surrogate models used in fatigue analysis usually employ simple microstructure, consisting of ideal geometries such as ellipsoidal inclusions, which generally does not capture complex geometries. In this paper, we introduce a simple but flexible surrogate microstructure model for two-phase materials through a level-cut of a Gaussian random field with covariance of Matérn class. Such parametrization of the covariance function allows for the representation of a few key design parameters while representing the geometry of inclusions in a more general setting for a large class of random heterogeneous two-phase media. In addition to the traditional morphology descriptors such as porosity, size and aspect ratio, it provides control of the regularity of the inclusions interface and sphericity. These parameters are estimated from a small number of real material images using Bayesian inversion. An efficient process of evaluating the samples, based on the Fast Fourier Transform, makes possible the use of Monte-Carlo methods to estimate statistical properties for the quantities of interest in a given material class. We demonstrate the overall framework of the use of the surrogate material model in application to the uncertainty quantification in fatigue analysis, its feasibility and efficiency, and its role in the microstructure design.

READ FULL TEXT

page 5

page 8

page 17

10/26/2021

A deep learning driven pseudospectral PCE based FFT homogenization algorithm for complex microstructures

This work is directed to uncertainty quantification of homogenized effec...
04/22/2021

Bayesian inversion for unified ductile phase-field fracture

The prediction of crack initiation and propagation in ductile failure pr...
08/05/2021

Self-supervised optimization of random material microstructures in the small-data regime

While the forward and backward modeling of the process-structure-propert...
04/08/2021

Fast Regression of the Tritium Breeding Ratio in Fusion Reactors

The tritium breeding ratio (TBR) is an essential quantity for the design...
02/14/2022

A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials

In this work we aim to develop a unified mathematical framework and a re...
01/06/2019

Causality and Bayesian network PDEs for multiscale representations of porous media

Microscopic (pore-scale) properties of porous media affect and often det...