Crack tip opening displacement of a Dugdale crack in a three-phase cylindrical model composite material

• Published in: International journal of engineering science 2011-06, Vol.49 (6), p.523-535
• Main Authors: Hoh, H.J., Xiao, Z.M., Luo, J.
• Format: Article
• Language: English
• Subjects: Composite; Composite materials; Computer simulation; Condensed matter: structure, mechanical and thermal properties; Crack tip opening displacement; Cracks; Defects and impurities in crystals; microstructure; Dislocation; Dislocations; Displacement; Dugdale plastic zone; Exact sciences and technology; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Interaction; Linear defects: dislocations, disclinations; Mathematical analysis; Mathematical models; Physics; Plastic zones; Singular integral equations; Small scale; Solid mechanics; Structural and continuum mechanics; Structure of solids and liquids; crystallography; Three-phase model
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/j.ijengsci.2011.01.004

The analytical investigation of the plastic zone size of a crack in three-phase cylindrical model composite material was carried out. The physical problem is simulated as a crack near a circular inclusion (a single fiber) in the composite matrix, while the three-phase cylindrical composite model is used to represent the composite matrix. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small scale yielding, a thin strip of yielded plastic zone is introduced at each crack tip. Using the solution for a three-phase model with a single dislocation in the matrix phase as the Green’s function, the physical problem is formulated into a set of singular integral equations. By employing Erdogan and Gupta’s method, as well as iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacements.