Bounds for the Propagation Model of Crack Forman

Abstract

Linear Elastic Fracture Mechanics (LEFM) describes the propagation of a crack exists in a material, and this propagation is proportional to the range of stress intensity factor. In LEFM there are several models that describe the evolution of an initial crack, as the models of Paris-Erdogan and Forman that are formulated and solved by the determination of an Initial Value Problem (IVP). For few practical applications, it is possible to obtain an exact solution of the IVP, and in most applications; approximate numerical solutions are used, which can reflect on aspects such as the time and the computational cost. Therefore, this paper presents a theoretical result establishing upper and lower bounds for the crack size function for Forman model. The bounds are very narrow, hence accurate crack size approximations can be obtained from only two stress intensity factor evaluations. This leads to a huge gain in a computational effort for numerical crack growth computations. Two examples are used within to explore the accuracy and efficiency of the proposed solution for the crack growth initial value problem.