Bounds for Crack Growth
Cláudio Roberto Ávila da Silva Júnior1; Rodrigo Villaca Santos1; Lucas Gimenis de Moura1; Waldir Mariano Machado Júnior1
1 UTFPR
doi:10.20906/CPS/COB-2015-2658
Resumo
Linear Elastic Fracture Mechanics (LEFM) describes the propagation of a crack exists in a material, and this propagation is proportional to the range of the stress intensity factor. In the 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). To 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, the objective of this work is to propose upper and lower bounds for the crack size function for Paris-Erdogan and Forman models. These bounds were determined by the second-order Taylor expansion with Lagrange's rest. Verification of the potentiality of the proposal of this work was accomplished through two numerical examples, and it was observed that for both models was obtained precision and efficiency in the results obtained.
Palavras-chave: Linear elastic fracture mechanics; Crack; Initial value problem; Bounds