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<p>During fatigue life prognosis, a crack is assumed, which will eventually grow and lead to the catastrophic failure of the metallic component. This represents a complex challenge due to uncertainties associated with the material’s mechanical properties, loading conditions, and the surrounding environment. This study presents a novel methodology to quantify the uncertainties of the stochastic process “crack size” in variable amplitude loading, applied to the Generalized Willenborg model. The approach combines random variable modeling, Monte Carlo simulation, and the Fast Crack Bounds (FCB) method to estimate the statistical moments efficiently. The absence of prior studies applying the FCB methodology to variable amplitude crack growth models highlights the originality of the present contribution, which introduces a framework for uncertainty quantification under realistic loading conditions. The proposed framework was evaluated using the classical Example of an edge-cracked plate under tension, based on linear elastic fracture mechanics. The results demonstrate that the method achieves computational gains of at least 516% compared to the fourth-order Runge–Kutta (RK4) approach, with deviations limited to 35.45%. This contribution advances fatigue analysis by enabling probabilistic predictions with reduced computational cost, offering potential benefits for the design and maintenance of mechanical and structural components.</p>

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A novel framework for fatigue crack propagation under variable loading: uncertainty quantification via deterministic bounds

  • 期刊论文

  • 发表日期：

    2025年7月12日

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  • Bruno dos Santos,
  • Cláudio R. Ávila da Silva Jr.,
  • Gracielle Lima de Oliveira,
  • Waldir Machado Mariano Jr.,
  • André Novais Istchuk

摘要

During fatigue life prognosis, a crack is assumed, which will eventually grow and lead to the catastrophic failure of the metallic component. This represents a complex challenge due to uncertainties associated with the material’s mechanical properties, loading conditions, and the surrounding environment. This study presents a novel methodology to quantify the uncertainties of the stochastic process “crack size” in variable amplitude loading, applied to the Generalized Willenborg model. The approach combines random variable modeling, Monte Carlo simulation, and the Fast Crack Bounds (FCB) method to estimate the statistical moments efficiently. The absence of prior studies applying the FCB methodology to variable amplitude crack growth models highlights the originality of the present contribution, which introduces a framework for uncertainty quantification under realistic loading conditions. The proposed framework was evaluated using the classical Example of an edge-cracked plate under tension, based on linear elastic fracture mechanics. The results demonstrate that the method achieves computational gains of at least 516% compared to the fourth-order Runge–Kutta (RK4) approach, with deviations limited to 35.45%. This contribution advances fatigue analysis by enabling probabilistic predictions with reduced computational cost, offering potential benefits for the design and maintenance of mechanical and structural components.