On iso- and nonisothermal crack problems of a layered anisotropic elastic medium

Abstract

The iso- and non-isothermal crack problems of layered fiber-reinforced composite materials are investigated within the framework of linear anisotropic thermoelasticity and under the state of generalized plane deformation. The crack is assumed to be parallel to the layer bounding surfaces. By employing the Fourier integral transform technique and the flexibility/stiffness matrix formulation, the current mixed boundary value problems are reduced to solving a set of simultaneous singular integral equations with Cauchy-type kernels. The crack·tip stress intensity factors are then defined in terms of the solution of the integral equations. Numerical results are presented addressing the salient and unique features for a class of crack problems involving highly anisotropic fibrous composite materials. Specifically, the cases of a crack embedded i) within a homogeneous and anisotropic slab, ii) between two bonded dissimilar anisotropic half-spaces and iii) within the matrix-rich interlaminar region of a generally laminated anisotropic slab are considered. The effects of relative crack size, crack location and fiber volume fraction on the stress intensity factors are examined as a function of über angle. For the case of layered composites, the matrix-rich interlaminar region is modeled as a separate interlayer. As the interlayer thickness approaches zero, the interlaminar crack model illustrates no smooth transition to the ideal interface crack model of zero interlayer thickness which exhibits oscillatory stress singularities. The mixed-mode crack tip response is shown to involve the simultaneous presence of three fracture modes. It is demonstrated that the corresponding values of stress intensity factors are strongly influenced by the laminate stacking sequence and layer orientation. In addition, the partially insulated crack surface condition is observed to alleviate the severity of thermally-induced stress fields near the crack tip.