Transient response of laminated composites with subsurface cracks.

Abstract

The dynamic response of subsurface cracks in fiber reinforced composites is analytically studied. The response of layered half-space and three-layered plate with two interface cracks excited by a plane SH-wave and line load respectively are studied by formulating the problem as integral equations in the frequency domain. The governing equations along with boundary, regularity and continuity conditions across the interface are reduced to a coupled set of singular integral equations by using Betti's reciprocal theorem along with the Green's functions. In addition, the transient response of an orthotropic half-space with a subsurface crack subjected to inplane line load at an arbitrary angle is analyzed. Two new Green's functions for the uncracked medium are developed and used along with the representation theorem to derive the scattered field. Satisfaction of the traction free condition at the crack surfaces gives rise to a system of singular integral equations. Singular integrals involved in the analysis are computed numerically by removing the poles. Part of the integrals containing the poles are then obtained analytically by using residue theorem. The solution of singular integral equations are obtained by expanding the unknown crack opening displacements (COD) in terms of a complete set of Chebychev polynomials. The problem is first solved in the frequency domain, the time histories are then obtained numerically by inverting the spectra via Fast Fourier Transform (FFT) routine. Numerical results are presented for isotropic and anisotropic materials for several different crack geometries. The results show significant influence of crack geometries and material properties on the COD and surface response of composites.