Application of modified Dugdale model to two pairs of collinear cracks with coalesced yield zones

In this paper, a modified Dugdale's approach has been presented to arrest four straight collinear quasi-static cracks with coalesced yield zones. An infinite elastic perfectly plastic plate, containing four cracks, is subjected to uniform stresses applied at infinite boundary of the plate. As a result, yield zones develop at each crack tip. On increasing the stresses, yield zones between two pairs of cracks get coalesced and after that at each internal crack tip. In order to detain propagation of cracks, a quadratic yield stress distribution is applied on the rims of the yield zones. This distribution enables to investigate the residual strength of an infinite plate, when the plate fails at a stress which is well below the yield stress of the plate. Muskhelishvili's complex variable technique is use to solve the stated problem. Analytical expressions for stress intensity factor and crack-tip opening displacements are established. The results validate with previously published works.