Research On Dynamic Near-Tip Fields In Elastic-Plastic Materials

The asymptotic near-tip fields of dynamic steadily propagating Mode-I crack under plane strain condition in elastic-perfectly plastic materials and power-law hardening materials are studied. All the materials are assumed to obey the Von Mises yield criterion and the associated flow rule of plasticity.In order to understand the dynamic strong discontinuity, two different jump models are proposed in this paper. The first one is thin layer jump model which requires all the fundamental field equations are satisfied within the thin layer. The result reveals that any strong discontinuity is not admissible, and the stresses and strains must be continuous. The contiguity conditions of the plastic flow factor λ across three different kinds of boundaries between two near-tip sectors are obtained. The other one is a jump model without transition layer and a jump condition is assumed for it.For the elastic-perfectly plastic incompressible materials, this paper discusses the contiguity condition of plastic flow factor X across the boundary between two plastic sectors, and confirms the validity of fully continuous solution given by Leighton et al. The qualitative analysis of the governing differential field equation shows that it contains an isolated singular point, but no "envelope" of its integration curves exists. A singular asymptotic near-tip field is obtained.For the elastic-perfectly plastic compressible materials, this paper constructs a singular asymptotic near-tip field and a family of fully continuous bounded stress and strain fields. The fully continuous dynamic stress field reduces to the Prandtl stress field in the limit as the crack speed tends to zero.Finally the asymptotic near-tip fields in incompressible and compressible power-law hardening materials are analyzed. The result shows if the stresses and strains are singular, the angular distributions of the stresses and strains in these materials are the same as those in elastic-perfectly plastic materials. Therefore only discontinuous solutions can be obtained. However, if the values of the stresses and strains are bounded, the existence of fully continuous stress and strain fields is possible. The detailed construction of such fully continuous near-tip fields are given in this paper.