Elastic-plastic analysis of frictionless contact at interfacial crack tips

✍ Scribed by E. Zywicz; D. M. Parks

• Publisher: Springer Netherlands
• Year: 1990
• Tongue: English
• Weight: 891 KB
• Volume: 42
• Category: Article
• ISSN: 1573-2673
• DOI: 10.1007/bf00018382

✦ Synopsis

The asymptotic elastic behavior of an interfacial crack occurring between two dissimilar isotropic media is reviewed. Distinct solutions, based on differing assumptions regarding crack-face boundary conditions, can be generated. The assumption of traction-free faces generally leads to oscillatory singular asymptotic fields which mathematically cause crack-face interpenetration, an inconsistency which can be alleviated by alternatively assuming asymptotic frictionless contact. For predominant tensile loading, the elastically-calculated ratio of contact length to crack size is typically very small, but may become appreciable when shear loading is applied. In either case, the singular crack-tip stresses cannot be sustained in materials capable of limited plastic flow, and small scale yielding (SSY) should be considered. In an extension of previous work [11], we identify conditions for SSY within surrounding dominant elastic regions of both traction-free and frictionless contact types. For the latter case, approximate closed form expressions for the plastic zone size and shape are obtained as the locus of points where the elastically-calculated Mises stress equals the tensile yield strength, or. The maximum extent of this plastic zone is approximately 3Kh2/2a~, where K~i is the closed crack-tip bimaterial stress intensity factor. Precise SSY numerical calculations for an elastic/perfectly-plastic material atop a rigid substrate indicate that the asymptotic stress field in the plastically-deforming material is composed of two fan regions and two constant state regions. Within the plastic zone, the interfacial and crack-face tractions asymptotically reach constant values. Compressive crack-face tractions persist even when contained inelastic crack-tip deformation is included.