Quantificação da incerteza do modelo randômico de Collipriest via metodologia Monte Carlo e "fast crack bounds"

Abstract

Mechanical structures are subjected to the cicles loads and collapse in fatigue conditions. There are many mathematical models describing the crack propagation. Generally, crack propagation models are classified by the load type, wich can be constant stress amplitude or variable stress amplitude. In this work the Collipriest constant stress amplitude model will be studied. For many engineering applications a reliable estimation of crack propagation are required. Therefore this work presents the theorical results, wich provides in the uncertainty quantification parameters of the used model and considering the lower and upper bounds envelonping the statistical estimators of the first and second terms of the crack size function, on the basis of Fast Crack Bounds method. These bounds are polymonials and defined in the variable cicle number, wich consider the incertanties in parameters of the crack propagation model. The Monte Carlo simulation method was used to obtain the crack size funcion from randomic samples set and based on the Collipriest parameters model. These statistical realization are used to give the estimators and moments of the crack size function. The bounds efficiency of the statistical estimators moments is evaluated throught relative deviations functions between bounds and approximate numerical solutions of the Collipriest model initial value problem. Generally, the initial value problem, wich describes the crack propagtions models, uses numerical methods such as the explicit fourth order Runge-Kutta method. In this work Matlab software will be used to obtain the solutions that describe the Collipriest crack propagation model.