Generalized griffith problem of shear with regard for the roughness of the crack surfaces

We study the generalized Griffith problem of longitudinal and transverse shear with regard for the roughness of the crack surfaces. The crack lips are modeled in the form of teeth. We study the process of contact of the teeth and its influence on the stress-strain state at the crack tip. The prefracture zone is modeled by cuts whose lips are in the complex stressed state and, hence, suffer the action of average shear and tensile stresses satisfying the Huber-Mises relations. As a result, we obtain expressions for the length of the plastic zone and crack-tip displacements in the cases of both transverse and longitudinal shear. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 36, No. 2, pp. 49–54, March-April, 2000.