Hybrid analysis of Lamb wave reflection by a crack at the fixed edge of a composite plate Original Research Article

A hybrid method has been proposed to solve the problem of reflection of time harmonic plane strain waves normally incident upon a thin planar crack located at the fixed-end of a semi-infinite, uniaxially fibre-reinforced, composite plate of linearly elastic materials. The hybrid method combines a finite element formulation in a bounded interior region of the plate with a wave function expansion representation in an unbounded exterior region. The fixed-end crack is contained in the interior region. The dispersion relation of the plate is solved through an approximate technique to obtain wave functions. The amplitudes of reflected waves are determined by satisfying the continuity conditions at the boundary between the interior and exterior regions. It is shown that the results agree well with known solutions for zero-thickness and through-thickness cracks in a homogeneous isotropic plate. New results are presented for a graphite/epoxy composite plate. The accuracy of the results is verified by checking the satisfaction of the principle of energy conservation and reciprocity relations. The influence of fibre direction elastic stiffness on reflection coefficients has also been studied. The results of the study show potential application in ultrasonic non-destructive evaluation.