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The plastic singular field at the tip of a crack growing steadily in a perfectly plastic medium is solved in this paper by use of the basic equations and contiguity conditions given in a previous paper .2 The fifth-order nonlinear differential equation has been integrated to a second-order equation. The five contiguity conditions are given in very simple form. By use of the general solution of the asymptotic equation and the contiguity conditions, the various possible cases of tip-field structures are discussed and the unique reasonable solution is obtained. For the angles of each sector, the numerical solution is given. In this paper, it is found that the strains also possess the singularity of ℓn(A/r) in the sector ahead the crack tip, even if for the case of ν = ½. Finally, a fracture criterion based on the analysis of singularity of strains is given.
elastic-plastic fracture, compatibility equation, contiguity conditions, unloading elastic sector, constant stress region, fan region
Associate professor of mechanics, Harbin Shipbuilding Engineering Institute, Harbin,