DISPERSION OF WAVES IN COMPOSITE LAMINATES WITH TRANSVERSE MATRIX CRACKS, FINITE-ELEMENT AND PLATE-THEORY COMPUTATIONS

Dispersion relations for laminated composite plates with transverse ma trix cracks have been computed using two methods. In the first approac h it is assumed that the matrix cracks appear periodically and hence i t is possible to consider a periodic cell of the the structure using B loch-type boundary conditions. This problem was formulated in complex notation and solved in a standard finite element program (ABAQUS) usin g two identical finite element meshes, one for the real part and one f or the imaginary part of the displacements. The two meshes were couple d by the boundary conditions on the cell. The code then computed the e igenfrequencies of the system for a given wave vector. It was then pos sible to compute the phase velocities. The second approach used may be viewed as a two step homogenization. First the cracked layers are hom ogenized and replaced by weaker uncracked layers and then the standard first-order shear-deformation laminate theory is used to compute disp ersion relations. Dispersion relations were computed using both method s for three glass-fiber/epoxy laminates ([0/90](2), [0/90](2) and [0/4 5/-45](s) with cracks in the 90 and +/-45 deg plies). For the lowest f lexural mode the difference in phase velocity between the methods was less then five percent for wavelengths longer than two times the plate thickness. For the extensional merle a wavelength of ten plate thickn esses gave a five percent difference.