Pressure with friction of a perfectly rigid die upon an elastic half space with cracks

• Published in: Materials science (New York, N.Y.) Vol. 46; no. 3; pp. 283 - 296
• Main Authors: Savruk, M. P., Tomczyk, A.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.12.2010; Springer; Springer Nature B.V
• Subjects: Characterization and Evaluation of Materials; Chemistry and Materials Science; Contact; Cracks; Elastic half spaces; Friction; Half spaces; Materials Science; Orientation; Singular integral equations; Solid Mechanics; Stress concentration; Structural Materials; elastic half space; crack; contact problem; stress intensity factor; friction
• ISSN: 1068-820X; 1573-885X
• DOI: 10.1007/s11003-010-9289-x

We study the interaction of a rigid die with a base of any shape and the surface of an elastic half space containing cracks in the presence of friction in the contact zone. The solution of the plane contact problem of the theory of elasticity is obtained by the method of singular integral equations. The detailed analysis of the problem is performed for the case where the base of the die is parabolic and a crack is rectilinear and appears on the surface of half space. We also investigate the effects of the friction coefficient, crack length, its orientation, and location on stress intensity factors K I and K II at the crack tip and the distribution of contact stresses under the die.