Analytical Bounds for Efficient Crack Growth Computation
Claudio Roberto Avila Silva Junior1; Waldir Mariano Machado Junior2; Lucas Gimenis Moura1; Rodrigo Villaca Santos1
1 UTFPR; 2 SENAI-PR
doi:10.20906/CPS/CILAMCE2015-0404
Resumo
In linear elastic fracture mechanics, the rate of crack propagation is proportional to the range of stress intensity factors. The most popular model relating these quantities is the Forman law. Crack growth computation is an initial value problem whose solution cannot be obtained in closed form, as stress intensity factors, hence crack growth rates, depend on the accumulated growth. For complex geometries, stress intensity factors are evaluated numerically, and crack growth computations can become computationally intensive. This paper presentes a theoretical result establishing upper and lower bounds for the crack size function for any number of cycles. The bounds are very narrow, hence accurate crack size approximations can de obtained from only two stress intensity fator evaluations. This leads to a huge gain in computational effort for numerical crack growth computations. Two examples are used herein to explore the accuracy and efficiency of the proposed solution for the crack growth initial problem.
Palavras-chave: Fracture mechanics; Crack size; Forman law; Initial value problem