Aplicação da metodologia numérica “fast bounds crack” para uma estimativa eficiente da evolução do tamanho de trinca

Abstract

A significant part of the life of a mechanical component occurs, the crack propagation stage in fatigue. Currently, it is had several mathematical models to describe the crack growth behavior. These models are classified into two categories in terms of stress range amplitude: constant and variable. In general, these propagation models are formulated as an initial value problem, and from this, the evolution curve of the crack is obtained by applying a numerical method. This dissertation presented the application of the methodology "Fast Bounds Crack" for the establishment of upper and lower bounds functions for model evolution of crack size. The performance of this methodology was evaluated by the relative deviation and computational times, in relation to approximate numerical solutions obtained by the Runge-Kutta method of 4th explicit order (RK4). Has been reached a maximum relative deviation of 5.92% and the computational time was, for examples solved, 130,000 times more higher than achieved by the method RK4. Was performed yet an Engineering application in order to obtain an approximate numerical solution, from the arithmetic mean of the upper and lower bounds obtained in the methodology applied in this work, when you don’t know the law of evolution. The maximum relative error found in this application was 2.08% which proves the efficiency of the methodology "Fast Bounds Crack".