| Abstract: | We suggest a method for the solution of the elastoplastic problem of biaxial tension-compression of a thin cracked plate under the assumption that plastic strains at each tip of the crack are localized along three slip lines. The plastic zone is simulated by three inclined slip strips at the tips of the crack. It is assumed that the material of the plate is absolutely elastoplastic and the yield criterion is satisfied along the slip lines. The strips lying on the continuation of the crack are simulated by segments of discontinuity of normal stresses, while the other strips are simulated by segments of discontinuity of tangential stresses Thus, the elastoplastic problem under consideration is reduced to the boundary-value problem of the linear theory of elasticity for a body weakened by branched cuts with unknown lengths and orientations of side branches. These parameters are determined in the process of numerical solution of the problem by the method of singular integral equations. Numerical results are presented for the semiinfinite plane with edge crack and under the conditions of uniform tension at infinity. We present numerical values of some parameters of nonlinear fracture mechanics, such as crack tip opening displacement and lengths and angles of inclination of plastic strips, for various combinations of the components of external load.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 2, pp. 7–13, March – April, 1995. |
