# Fast crack bounds method applied to crack propagation models under constant amplitude loading

• Rodrigo Villaca Santos
• Waldir Mariano MachadoJr.
• Cláudio R. Ávila da SilvaJr.
Technical Paper

## Abstract

In linear elastic fracture mechanics (LEFM), several models under constant amplitude loading describe the propagation of a crack, and these models are formulated by an initial value problem (IVP). However, for most applications, it is not possible to obtain exact numerical solutions for IVP due to the mathematical formulation of the stress intensity factor. From this, approximate numerical solutions are used for the IVP solution, which may reflect in aspects such as time and high computational cost. Thus, this work presents a new method called Fast Crack Bounds (FCB), to improve the way to obtain the IVP solution. This method was applied to the Paris–Erdogan, Forman, Walker, McEvily and Priddle models by establishing two functions, the upper and lower bounds, for the crack size function. Also, this work presents, for the same models, two new possible solutions through the arithmetic and geometric means of the bounds. For both, bounds and bounds means, the results were compared with the numerical solution obtained by the fourth-order Runge–Kutta method, applied to two numerical examples. As a result, the study presented, for all the models analyzed, an efficient and accurate way to obtain the propagation of an initial crack, reflecting in a considerable computational improvement.

## Keywords

Linear elastic fracture mechanics Crack propagation Initial value problem Bounds Bounds means

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© The Brazilian Society of Mechanical Sciences and Engineering 2018

## Authors and Affiliations

• Rodrigo Villaca Santos
• 1
Email author
• Waldir Mariano MachadoJr.
• 1
• Cláudio R. Ávila da SilvaJr.
• 1
1. 1.NuMAT/PPGEM, Federal University of Technology of ParanaCuritibaBrazil