Estabelecimento de cotas para os momentos estatísticos do tamanho de trinca, para o modelo de Collipriest via método Fast Crack Bounds

Abstract

In a realistic approach of structures and mechanical components, cracks are admitted. Their presence is usually associated with the fatigue phenomenon. There are several mathematical models that describe the propagation of a crack. In general, the crack propagation models are classified by the type of load, which can have constant stress amplitude (CSA) or variable stress amplitude (VSA). In this work, the CSA type model proposed by Collipriest was used. For many engineering applications, until a certain point, it is not necessary to have great accuracy in predictions of the behavior of statistics, about the evolution of a crack, but a reliable prediction, within certain limits, of this behavior. This work presents theoretical results, which consist of obtaining lower and upper bounds that "envelop" the estimators of the first and second order statistical moments of the crack size function based on the Fast Crack Bounds method. These bounds are polynomials defined in the variable “number of cycles” that consider the Metais - Fadiga uncertainties in the parameters that describe the crack propagation models. The efficiency of the bounds for the statistical moments of crack size is evaluated through the deviation between the bounds and the approximate numerical solutions of the initial value problems (IVP) that describes the Collipriest model. In general, the solution of the IVPs describing crack propagation models is obtained through the use of numerical methods, such as the explicit fourth order Runge-Kutta method (RK4). In this work, the MATLAB software was used to obtain the solutions of the IVP that describes the Collipriest model, to evaluate the computational time of the proposed methodology, besides the deviations of the bounds in relation to the approximated solutions, confirming its efficiency.