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Analysis of the plastic zones of cracks in an elastic-perfectly plastic half-space under contact loading.pdf

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Analysis of the plastic zones of cracks in an elastic-perfectly plastic half-space under contact loading.pdf

International Journal of Mechanical Sciences 121 (2017) 143–150 Contents lists available at ScienceDirect International Journal of Mechanical Sciences journal homepage: /locate/ijmecsci Analysis of the plastic zones of cracks in an elastic-perfectly plastic halfspace under contact loading Jing Yang, Kun Zhou? School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore MARK ARTICLE INFO Keywords: Crack tip plastic zone Distributed dislocation technique Elastic-perfectly plastic half-space Dugdale model Contact loading ABSTRACT In this paper, a semi-analytic solution is proposed to solve the subsurface stress distribution and plastic zones of an elastic-perfectly plastic half-space with cracks under contact loading. The cracks can be treated as a distribution of edge dislocations with unknown densities based on the distributed dislocation technique. These unknown dislocation densities, contact area and surface pressure distribution can be obtained iteratively when the surface displacement due to the substrate cracks and contact loading is converged by a numerical algorithm according to the conjugate gradient method. The plastic zones at crack tips can be determined by canceling the stress intensity factor (SIF) due to the closure stress and that due to the external applied load based on the Dugdale model of small scale yielding. It is noticed that the plastic zone sizes are a?ected by the original crack length and depth, yield strength of substrate and loading conditions. This solution might provide guidance for the fracture mechanics analysis of materials with cracks in a half-space. 1. Introduction Micro-defects, such as cracks and inclusions, commonly exist in engineering materials and structures. These defects are often formed in materials during their manufacturing or utilization process. The presence of these defects can signi?cantly in?uence the mechanical properties of materials and may event