Crack-tip-opening displacement for four symmetrically situated cracks with coalesced interior yield zones

Abstract

Crack-tip opening displacements are obtained for four collinear straight cracks, weakening an unbounded homogeneous and isotropic elastic-perfectly plastic plate. The cracks are so configured that two symmetrically situated and interiorly lying cracks are of equal-lengths. Other two exteriorly lying, collinear straight cracks (surrounding the interiorly lying straight cracks) are of mutually equal-lengths. Thus an exterior and an interior crack-set are symmetrically oriented with respect to the other interior–exterior collinear cracks-set configuration. Uniform constant load prescribed at remote boundary of the plate, opens the crack in self-similar fashion developing a strip-yield zone ahead each tip of the cracks. It is assumed that the strip-yield zone developed at each of interior tips of an exteriorly and interiorly lying crack-set configuration gets coalesced. The developed yield zones are subjected to normal cohesive yield stress to arrest the crack from further opening. The solution of the problem is obtained by superposing the solutions of the two auxiliary problems, appropriately derived from the given problem. Each of the auxiliary problems, in turn, is solved using complex variable technique. Expressions are derived for quantities of interest viz. crack-tip opening displacement (CTOD), length of each developed yield zone. The effect of applied load and closing load on the parameters CTOD and strip yield zone affecting the crack arrest is presented graphically and concluded.