Shear waves in fiber-reinforced composites with interfacial cracks

ensemble-average statistical method is used to calculate the overall effective mechanical properties of fiber-reinforced composites with interfacial cracks. The cracks here are specifically the fiber-matrix interfacial cracks which occur during the manufacturing process or are from inherent material defects. The problem starts with the establishment of the Helmholtz equations and boundary conditions followed by a full scale solution of the multiple scattering equations. Then by considering the low frequencies limit and the statistics of randomly spatial distribution of the fibers, a manageable homogeneous linear matrix equation is obtained. In a homogenized point of view the macroscopic mechanical properties of the composite system are derived. The calculated average mechanical properties include the overall effective shear modulus p, the average shear wave phase speed B, and the average specific damping capacity Y of the composite system. The shear modulus corresponds to the elasticity of the static state, while the shear wave phase speed and damping capacity correspond to the viscoelasticity of the dynamic state of the composite. The results show that, among others : 1. the fiber-reinforced composites with interfacial cracks are transversely anisotropic material systems possessing viscoelastic behavior 2. the axially shear modulus of the composite, as the half crack length (6) increases, is in a ‘decreasing steps’ fashion for which Iinite numerical jumps exist between those steps 3. for a fiber-reinforced composite with interfacial cracks, the composite system with 1/2x half crack length is the least attenuated and is nearly transversely isotropic 4. the composite is a non-dispersed material system in low frequency ranges. 0 1998 Elsevier Science Ltd.