Fast crack bounds in linear elastic fracture mechanics: a new approach to establish the upper bound

Abstract

This work presents a way to improve the fast crack bounds method. There are several crack propagation models in linear elastic fracture mechanics. The fast crack bound (FCB) consists of an upper (UB) and lower bound (LB) to establish the crack size function. The FCB method was validated by comparing the UB and LB functions with the fourth-order Runge–Kutta (RK4) numerical method. The upper bound is based on $$a^*$$ parameter. In previous works, this parameter is established by numeric inspections. This work presents a new approach to determine the upper bound, without mathematical inspections necessity. Therefore, this work shows an alternative to define the upper bound without using the parameter $$a^*$$ , nor the RK4 method, despite the RK4 has been maintained as a study reference. Two numerical examples, involving Paris–Erdogan and Forman model, were used to analyze the performance of the new upper bound proposition.