Asymptotic Analysis of Mode Ⅱ Singular Fields near a Crack Tip in a Hardening Drucker-Prager Elastic-Plastic Material
Taiki SHIMBO and Chikayoshi YATOMI
Abstract:In the geomechanical studies the mechanism of the shear failure for the Mode Ⅱ crack extension is still an open problem. As the basic research, the purpose of this paper is , therefore, to obtain the Mode Ⅱ singular fields near a crack tip . The geomaterials , in general, have a pressure sensitive yield function to yield a dilatant effect. Thus, assuming a proportional loading, we obtain the asymptotic stress and displacement fields for the Mode Ⅱ crack in the linear hardening Drucker-Prager elastic-plastic material. For the Mode Ⅱ crack of the Drucker-Prager material, the boundary conditions can not be given on the extension of the crack surface, since the informations of the boundary are unknown: This is due to the loss of symmetry or asymmetry of the displacements and the stresses because of the existence of a parameter of the dilatant effect. Then the boundary conditions for the Mode Ⅱ crack are given on the crack surfaces; that is, the jumps of the normal displacement, the normal stress, and the shear stress vanish. As a result, a very small normal stress appears on the crack surfaces. We finally examine the angular distribution of the displacement and stress fields which depend on the hardening parameter and the pressure sensitivity parameter. Key Words:Dilatant, Stationary crack, Asymptotic analysis, Plane strain condition, Drucker-Prager elastic-plastic material, Mode Ⅱ