Three-dimensional cracks with Dugdale-type plastic zones - Kelly, P; Nowell, D (2000)
A general method for the determination of three-dimensional crack-front plastic zones is presented. The crack-model utilised is of the Dugdale-type, that is a plastic zone is assumed to spread in front of the crack, in the plane of the crack. The solution method relies on the eigenstrain approach to crack-problem solving. Using this approach, the elastic and plastic regions of the crack are first discretised into triangular elements and the stress arising over the crack due to a constant or linear crack-surface displacement in each element is obtained. The stresses are given in terms of hyper-singular integrals, which may be solved numerically. The boundary conditions in the elastic portion (traction-free) and in the plastic zones (Tresca or some other yield condition) are encompassed in an object function in such a way that the boundary conditions are satisfied if and only if the object function is zero. The resulting quadratic programming problem is solved numerically, and hence the crack displacements, and other important quantities, are obtained. Results agree well with some known analytic results regarding the penny shaped crack in tension.