Quantificação da incerteza dos modelos de Willenborg via metodologia Fast Crack Bounds - Monte Carlo

Abstract

In industrial sectors, the concept of damage tolerance is widely applied, assuming the existence of a crack that will eventually evolve and lead to the catastrophic failure of a component. Hence, it becomes necessary to monitor its evolution under working conditions. Consequently, linear elastic fracture mechanics provides numerous models seeking to describe crack growth. In this study, we explore the application of Willenborg’s variable amplitude stress models, including the original model, the generalized model, and the modified model. Since the crack propagation process is nonlinear and influenced by multiple factors, uncertainties in the model’s defining parameters are acknowledged. Therefore, the objective is to quantify the uncertainty of the crack propagation phenomenon. To achieve this, uncertainty modeling is carried out using random variables. Subsequently, the Monte Carlo simulation and Fast Crack Bounds methods are employed in conjunction to estimate the statistical moments of the stochastic process, namely, the “crack size.” The performance of the proposed approach is evaluated through the combination of Sequential Monte Carlo Simulation methods with fourth-order Runge-Kutta. To validate the proposed solution, four classical examples from fracture mechanics are employed. The results demonstrate the precision and efficiency of the Fast Crack Bounds methodology, with computational gains of at least 10280.95% over the RK4 solution and relative deviations of no more than 29.94%. These findings showcase the applicability and effectiveness of the Fast Crack Bounds method.