Dispersion of Waves in Composite Laminates With Transverse Matrix Cracks, Finite Element and Plate Theory Computations

Abstract

Dispersion relations for laminated composite plates with transverse matrix cracks have been computed using two methods. In the first approach it is assumed that the matrix cracks appear periodically and hence it is possible to consider a periodic cell of the structure using Bloch-type boundary conditions. This problem was formulated in complex notation and solved in a standard finite element program (ABAQUS) using two identical finite element meshes, one for the real part and one for the imaginary part of the displacements. The two meshes were coupled by the boundary conditions on the cell. The code then computed the eigenfrequeneies of the system for a given wave vector. It was then possible to compute the phase velocities. The second approach used may be viewed as a two step homogenization. First the cracked layers are homogenized and replaced by weaker uncracked layers and then the standard first-order shear-deformation laminate theory is used to compute dispersion relations. Dispersion relations were computed using both methods for three glass-fiberepoxy laminates ([0/90]2,[0/90]sand[0/45/-45]s with cracks in the 90 and ±45 deg plies). For the lowestflexural 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 mode a wavelength often plate thicknesses gave a five percent difference.