Open Access

ARTICLE

A Non-Intrusive Stochastic Phase-Field for Fatigue Fracture in Brittle Materials with Uncertainty in Geometry and Material Properties

by Rajan Aravind^1,2, Sundararajan Natarajan¹, Krishnankutty Jayakumar², Ratna Kumar Annabattula^1,*

1 Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600036, India
2 Vikram Sarabhai Space Centre, Thiruvananthapuram, 695022, India

* Corresponding Author: Ratna Kumar Annabattula. Email:

Computer Modeling in Engineering & Sciences 2024, 141(2), 997-1032. https://doi.org/10.32604/cmes.2024.053047

Received 23 April 2024; Accepted 31 July 2024; Issue published 27 September 2024

Abstract

Understanding the probabilistic nature of brittle materials due to inherent dispersions in their mechanical properties is important to assess their reliability and safety for sensitive engineering applications. This is all the more important when elements composed of brittle materials are exposed to dynamic environments, resulting in catastrophic fatigue failures. The authors propose the application of a non-intrusive polynomial chaos expansion method for probabilistic studies on brittle materials undergoing fatigue fracture when geometrical parameters and material properties are random independent variables. Understanding the probabilistic nature of fatigue fracture in brittle materials is crucial for ensuring the reliability and safety of engineering structures subjected to cyclic loading. Crack growth is modelled using a phase-field approach within a finite element framework. For modelling fatigue, fracture resistance is progressively degraded by modifying the regularised free energy functional using a fatigue degradation function. Number of cycles to failure is treated as the dependent variable of interest and is estimated within acceptable limits due to the randomness in independent properties. Multiple 2D benchmark problems are solved to demonstrate the ability of this approach to predict the dependent variable responses with significantly fewer simulations than the Monte Carlo method. This proposed approach can accurately predict results typically obtained through or more runs in Monte Carlo simulations with a reduction of up to three orders of magnitude in required runs. The independent random variables’ sensitivity to the system response is determined using Sobol’ indices. The proposed approach has low computational overhead and can be useful for computationally intensive problems requiring rapid decision-making in sensitive applications like aerospace, nuclear and biomedical engineering. The technique does not require reformulating existing finite element code and can perform the stochastic study by direct pre/post-processing.

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