Fast Crack Bounds in Linear Elastic Fracture Mechanics Establishing Upper Bound function based on the Second Derivative

This paper proposes a new approach to determining the upper bound in fast crack bounds. In linear elastic fracture mechanics (LEFM), there are multiple models for estimating crack propagation, which are often described using ordinary differential equations (ODE) involving initial value problems (IVP). However, analytical solutions are not always possible, necessitating computational methods. The fast crack bounds method (FCB) was created as a faster way to find approximate solutions by creating an envelope with an upper and lower bound. The original upper bound was based on a numerical parameter, but this paper presents a theoretical approach to determine the upper bound without the need for numerical inspections, based on the lower bound’s second derivative. This eliminates the need for the Runge-Kutta numerical method and speeds up the determination of the upper bound.