Mechanics

2002, No. 2

L.V. Stepanova

STRESS FIELD NEAR A MODE II CRACK TIP UNDER PLANE STRESS FOR PERFECTLY PLASTIC MATERIAL

An exact asymptotic analysis is presented for the stress fields near the tip of a static plane stress mode II crack in perfectly plastic material. The solution obtained completes the class of the solutions known for static plane strain and plane stress mode I cracks and a plane strain mode II crack in the perfectly plastic material. However, the stress field near a mode II crack tip under plane stress in the perfectly plastic material seems to have not been obtained yet. It is shown that there are three discriminated sectors in the vicinity of the crack tip where the stress field is determined by the different formulae. They are the two sectors which can be described in slip line terminology as "constant stress" and "centered fan" sector of non-constant stress. These three different sector types constitute the complete set of asymptotically admissible solutions near the crack tip. The angles separating the sectors are numerically found from the solution of the system of the two trigonometric equations expressing the stress continuity conditions. The solution can not be considered as the full solution for the elastic - perfectly plastic material since only the equilibrium equations and the von Mises yield criterion are analyzed. The solution will be full if it will be possible to analyze the deformation filed near the crack tip. In the framework of the present study it is possible to establish the strain asymptotic of the type 1/r in the "centered fan" only.