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In Wang et al. (2002), the mode I crack problem has been analyzed for a functionally graded material strip with arbitrarily distributed properties. For the completeness of the research, this paper provides an analysis method for the mode II in plane and mode III anti-plane elastic crack problems for a functionally graded material (FGM) strip containing a crack along the gradient direction. In the analysis, the gradient region is treated as a number of homogeneous layers stacked along the gradient direction. The analytical models developed in this paper for the modes II and III problems, together with the model developed in Wang et al. (2002) for the mode I crack problem complete the analysis of the mixed-mode crack problem for functionally graded materials with a crack parallel the gradient direction. Those analytical models allow the material properties be any continuous functions along the thickness direction of the strip. [ABSTRACT FROM AUTHOR]

This research is concerned with the fracture mechanics of a laminated composite medium, which contains a central layer sandwiched by two outer layers. There is a periodic array of cracks in the central layer along the central axis of the medium. Fourier transform is used to reduce the problem to the solution of a system of dual integral equations, which are solved by the singular integral equation technique. Rigorous fracture mechanics analysis, which exactly satisfies all boundary conditions of the problem, is conducted. Numerical solutions for the crack tip field and the stress in the medium are obtained for various values such as crack length, crack spacing and layer thickness. Results are also given for the reduction of the equivalent Young’s modulus of the laminate due to multiple cracking. The cases of axial extension and residual temperature change of the composite medium are accounted for. [ABSTRACT FROM AUTHOR]

A two-level fracture model of composites with cracks under compression is proposed. Fiber-reinforced laminated panels with a hole are considered. The panels are compressed along the fibers so that two cracks propagate from the hole boundary at a right angle to the loading direction. The fracture mechanism is analyzed at two levels. The first level is the compression-induced stress concentration at the tip of a finite-thickness crack filled with a fractured material. At this level, the theory of elasticity of linear orthotropic body is used. The second level is compression fracture at the crack tip. The analysis performed at this level involves the three-dimensional linearized theory of stability of solids, considering microcracks in the interface between the fractured and intact materials, and the exact solution describing the compression-induced instability of the cracked interface. The second level is where results obtained by the author are used. Thus, the approach proposed employs the theory of elasticity of linear orthotropic body and the three-dimensional linearized theory of stability of solids to analyze a specific mechanism of fracture [ABSTRACT FROM AUTHOR]