Fracture modes of a penny-shaped crack in a layer of transversely isotropic solid

Nowadays fracture behavior composites play an important role in geomechanics engineering. Also, it is common knowledge that all existing structural materials contain different inter- and intra-component defect (cracks, delaminations, etc.). On the other hand, analytical techniques can provide a better physical interpretation of problems. In this paper, by using an analytical approach, effects of the fracture modes (opening, shearing and tearing) on a penny-shaped crack in a layer of transversely isotropic solid has been studied. The layer surfaces are fixed from displacement and the system is loaded symmetrically in each mode. In each mode, by substituting the boundary conditions into the governing equations of the medium, the problem reduced to dual integral equations. With the aid some mathematical methods, the dual integral equations are converted to a Fredholm integral equation which is amenable to numerical solution. These Fredholm integral equations are the functions of the thickness of the layer, the radius of crack and the properties of the layer. To evaluate the effect of anisotropic materials on the stress intensity factors(SIFs), several synthetic types of isotropic and transversely isotropic materials are selected. By employing a numerical method the opening, shearing and tearing SIFs for different ratios of layer thickness are obtained. The results for the opening SIF show that by increasing the the SIF decreases substasinaly. On the other hand, an increase in leads to increments in opening SIF. Also, the results demonstrate that the variation in has a negligible effect on the opening SIF. Moreover, an increasing in leads reductions in SIF. For the shearing SIF, has little effect on the results although by decreasing the the shearing SIF increases. Unlike the , the modulus of the young in the plane ( ) of the isotropy has substantial effect on the shearing SIF. An increase in leads increments in the shearing SIF. Also, by increasing the the SIF increases marginally. In the mode III, the tearing SIF is only the functions of (the shear modulus for the plane normal to the plane of isotropy) and . The results show that by reduction in the tearing SIF increases and by increasing the tearing SIF increases. An important point that can be inferred from the results is that by increasing the ratio of layer thickness to the radius of the penny-shaped crack all of the three SIFs increase, this increase for the lower thicknesses is much more in comparison to the greater thicknesses. Additionally, when the layer thickness gets higher, the stress intensity factors for all the materials tend to a constant coefficient. This means that when the layer thickness gets greater and tends to infinity, the SIFs become independent of the material of the layer