On the plastic zone size and crack tip opening displacement of a sub-interface crack in an infinite bi-material plate

• Published in: Philosophical magazine (Abingdon, England) England), 2011-09, Vol.91 (26), p.3456-3472
• Main Authors: Yi, D.K., Xiao, Z.M., Zhuang, J., Sridhar, I.
• Format: Article
• Language: English
• Subjects: Condensed matter: structure, mechanical and thermal properties; crack tip opening displacement; Cracks; Defects and impurities in crystals; microstructure; dislocation; Displacement; dissimilar materials; Elasticity, elastic constants; Exact sciences and technology; Fatigue, brittleness, fracture, and cracks; Instruments for strain, force and torque; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Linear defects: dislocations, disclinations; Mechanical and acoustical properties of condensed matter; Mechanical instruments, equipment and techniques; Mechanical properties of solids; Physics; plastic zone size; Plastic zones; Shear stress; Simulation; Singular integral equations; Small scale; Stresses; Structure of solids and liquids; crystallography; sub-interface crack
• ISSN: 1478-6435; 1478-6443
• DOI: 10.1080/14786435.2011.586374

Elastic-plastic stress analysis has been carried out for the plastic zone size and crack tip opening displacement of a sub-interface crack with small scale yielding. In our study, the shape of plastic zone is assumed as a long, slim strip at both crack tips. In the plastic zone, both normal stress and shear stress exist and are considered due to the bi-material interface. The values of the plastic zone size, normal stress and shear stress are determined by satisfying the conditions where both Modes I and II stress intensity factors vanish and Von Mises yield criterion is met. In the present paper, the sub-interface crack is simulated by continuously distributed dislocations which will result in singular integral equations. Those singular integral equations can be solved by reducing them to a set of linear equations. The values of the plastic zone size and crack tip opening displacement are obtained through an iterative procedure. Finally, the effect of normalized loading, normalized crack depth (distance to the interface) and Dundurs' parameters on the normalized plastic zone size and the normalized crack tip opening displacement is discussed.