On the statistical nature of fatigue crack-growth through Monte Carlo simulations and experimental data

Abstract

Understanding factors that contribute to scatter in crack-growth rates data is fundamental to reduce risk of unexpected structural failures. This document discusses the statistical nature of material scattering observed in fatigue crack propagation tests through a comparison between Monte Carlo simulations and experimental test data. The case study consists of constant amplitude tests on central cracked 2024-T3 aluminium alloy plate specimens loaded in pure Mode-I with stress ratio R equals to 0.2. It was found that results of simulations matched the experimental fatigue lives in terms of both mean value and dispersion around it. Based on these outcomes, the crack-growth behaviour can be described in a statistical manner with the expectation to reduce the inaccuracy present in life predictions.

Uncertainty quantification in fatigue crack-growth predictions

“…Out of the main diagonal, it can be observed that the material parameters are mostly uncorrelated, with the exception of Log 10 C and m that demonstrated a clear linear relationship. This linear dependence was well known from literature, as reported in Cortie and Garrett (1988) and Bergner and Zouhar (2000), and was also highlighted for different materials in Giannella (2021a, b), Giannella (2022) and Annis (2004) where Monte Carlo simulations were similarly adopted. The reader is referred to Bergner and Zouhar (2000) and its references for deepenings.…”

“…Here, the validation of each CGR curve with the experimental data allowed them to be considered interconnected, therefore avoiding the issues highlighted in Annis (2004). The current Monte Carlo strategy was already validated in Giannella (2022) against the experimental test data available in Virkler et al (1979), showing that it was able to predict both mean value and standard deviation of experimental life predictions. The reader is referred to Giannella (2021aGiannella ( , b, 2022 for further information about this procedure.…”

Markov chain‐assisted stochastic model of crack growth rate

“…Inhomogeneities in materials, such as microstructural variations and inherent defects, can cause significant scattering in the fatigue crack growth (FCG) behavior [1,2]. When assessing the structural integrity, probabilistic fracture mechanics considers the crack growth rate a random variable [3].…”

“…Assessing the probability of crack extension is critical in practical applications. In the aerospace and railway fields, a probabilistic analysis of fatigue crack extension is required by considering multiple random variables [2,[4][5][6][7].…”

“…In the second type of model, such as the Yang and Manning stochastic models, the FCG rate is calculated by multiplying the random process by a deterministic function [19][20][21], as shown in Equation (2).…”