Quantificação da incerteza de modelo de Forman via metodologia "Fast Crack Bounds"

Abstract

The linear elastic fracture mechanics (LEFM) allows quantification of the relationship between the material properties, the stress level, the presence of crack-generating defects and crack propagation mechanisms. There are numerous models seeking to describe the crack growth. These are classified into two main areas, namely: constant amplitude loading (CAL) and variable amplitude loading (VAL). This work presents the use of crack propagation model type constant amplitude loading (CAL) proposed by Forman, assuming the existence of uncertainty in the model definition parameters, aiming at quantification of the uncertainty of the crack propagation phenomenon. For this, the uncertainty modeling will be done through random variables. From this, the Monte Carlo simulation (MCS) and Fast Crack Bounds (FCB) methods will be used together to estimate the statistical moments of the stochastic process ‘crack size’. The performance of the proposal will be evaluated from the combination of MCS and Runge-Kutta fourth order (RK4) methods. Three classic examples of fracture mechanics are used to explore the accuracy and efficiency of the proposed solution to the initial value problem of crack growth. The work identifies computational gains of at least 378.09% more efficient than the RK4 solution and relative deviations of up to 26.28%, demonstrating the applicability and effectiveness of the Fast Crack Bounds methodology