Investigation of shear stress distribution in notch problem under sliding mode case

Abstract

The shear stress distribution for the notch problem of plane elasticity in the sliding mode case is investigated in this paper. Particular features of the shear stress distribution beneath the crown point of notch are analyzed by means of the Muskhelishvili method [1]. It is found that the maximum shear stress σ_{xy, max} is always reached at some point below the surface of the notch. The smaller the radius ρ of the notch, the larger is the maximum shear stress σ_{xy, max}. A relation between σ_{xy, max} and stress intensity factor K _II of the corresponding crack problem is found to be Several specific examples are given to prove the validity of the obtained relation.

% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiaadUeadaWgaaWcbaGaaeysaiaabMeaaeqaaOGaeyypa0ZaaSaa% aeaacaaIZaWaaOaaaeaacaaIZaGaeqiWdahaleqaaaGcbaGaaGOmaa% aadaWfqaqaaiGacYgacaGGPbGaaiyBaaWcbaGaeqyWdiNaeyOKH4Qa% aGimaaqabaGcdaGcaaqaaiabeg8aYjabeo8aZbWcbeaakmaaBaaale% aacaWG4bGaamyEaiaacYcaciGGTbGaaiyyaiaacIhadaahaaadbeqa% amXvP5wqonvsaeHbuLwBLnhiov2DGi1BTfMBG0evGueE0jxyGi0BSr% gaiuaacqWFUaGlaaaaleqaaaaa!6261!\[K_{{\text{II}}} = \frac{{3\sqrt {3\pi } }}{2}\mathop {\lim }\limits_{\rho \to 0} \sqrt {\rho \sigma } _{xy,\max ^. } \]