Mathematical model for three equal collinear straight cracks: A modified Dugdale approach

Abstract

The present paper discuss a multiple site damage (MSD) problem of three collinear straight cracks exist in an infinite isotropic elastic perfectly plastic plate. Uniform stress distribution is applied at the infinite boundary of the plate in a direction perpendicular to the faces of the cracks. As a result, yield zones are developed ahead each crack tip. These yield zones are sensitive about the load applied at the boundary of the plate. Since the regions near the crack tips are very week as compared to other parts of the plate, therefore, it is assumed that the behaviour of yield stress of the plate near the yield zones is in linear fashion. Hence, rims of the yield zones are subjected to linearly varying stress distribution to stop further opening of cracks along the real axis. The problem is solved using widely used complex variable technique and closed form expressions are derived for stress intensity factor (SIF), crack tip opening displacement (CTOD) and length of developed yield zones at each crack tip. Under small-scale yielding, numerical results for yield zone length and crack-tip opening displacement as a function of remotely applied stress are obtained and presented graphically.