Three co-planar moving Griffith cracks in an infinite elastic medium

A N Das

doi:10.1007/bf00034561

Abstract

The dynamic in-plane problem of determining the stress and displacement due to three co-planar Griffith cracks moving steadily at a subsonic speed in a fixed direction in an infinite, isotropic, homogeneous medium under normal stress has been treated. The static problem of determining the stress and displacement around three co-planar Griffith cracks in an infinite isotropic elastic medium has also been considered. In both the cases, employing Fourier integral transform, the problems have been reduced to solving a set of four integral equations. These integral equations have been solved using finite Hilbert transform technique and Cook's result [16] to obtain the exact form of crack opening displacement and stress intensity factors which are presented in the form of graphs.

Highlights

IN FRACTURE MECHANICS, the problem of diffraction of elastic waves by cracks of finite dimension in a strip of elastic material has been investigated by several investigators
Using finite Hilbert transform technique developed by SRIVASTAVA and LoWENGRUB [3], LoWENGRUB and SRIVASTAVA [4] solved the statical problem of distribution of stress and displacement in an infinitely long elastic strip containing two coplanar Griffith cracks
Several dynamic problems of determining stress and displacement due to two coplanar moving Griffith cracks have been solved by DAS and GHOSH [5,6,7]

Summary

Introduction

IN FRACTURE MECHANICS, the problem of diffraction of elastic waves by cracks of finite dimension in a strip of elastic material has been investigated by several investigators. Using finite Hilbert transform technique developed by SRIVASTAVA and LoWENGRUB [3], LoWENGRUB and SRIVASTAVA [4] solved the statical problem of distribution of stress and displacement in an infinitely long elastic strip containing two coplanar Griffith cracks. Solved the statical problem of determining the stress distribution in an infinite transversely isotropic medium containing three coplanar Griffith cracks. ·. To the best knowledge of the author, the problem of stress distribution around three coplanar moving Griffith cracks in an infinite elastic strip has not been investigated so far. Employing Fourier integral transform, the problem when the lateral boundaries are subjected to shearing stress, has been reduced to solving a set of four integral equations using finite Hilbert transform technique [3] and CoOK'S result [9] to derive the exact form of stress intensity factors and the crack opening displacement. Numerical results for the stress intensity factors are presented graphically to show their variations with crack speed, crack lengths and the separation distance between the cracks

Statement of the problem

Method of solution

Numerical results and discussions