Elastodynamics of interface cracks in laminated composites

The active industrial application of the achievements of material science such as the new high-tech materials (both, homogeneous and heterogeneous, like micro- and nano-composites) makes it possible to significantly improve the strength and stiffness of designed structures as well as the safety level. On the other hand, modern design and service conditions of exploitable mechanical systems require a continued increase in the magnitude and the frequency of the external loading. The level of safety requirements increases consequently because the cost of unpredictable fracture is always enormously high.

It is a common knowledge that all existing composite materials contain various inter- and intra-component defects, e.g. cracks and delaminations. Such defects appear in real-life materials during the fabrication or in-service (fatigue, consequences of an impact, etc.). As applied to laminated composites, both inter- and intra-laminar cracks can contribute to the initiation of fracture process. The presence of cracks and delaminations considerably decreases the strength and the lifetime of composite structures as well as significantly increases the cost of exploitation. Unfortunately, the micro-defects cannot be fully avoided. Therefore it is necessary to ensure the residual strength of the composite structure will not fall below an acceptable level over the required service life.

Cracks often have a non-zero initial opening or a three-dimensional shape. The appearance of cracks with a non-zero opening can be attributed to the microbuckling in the vicinity of cracks (which are modelled by mathematical sections without any opening) under initial static loading. It is equally true for both, homogeneous and heterogeneous materials. As applied to laminated composites, both inter- and intra-laminar cracks can contribute to the initiation of fracture process.

The present study concerns with application of boundary integral equations to the problem of an interface crack between two elastic half-spaces with different mechanical properties under dynamic loading. The Somigliana dynamic identity is used. The derived system of equations allows evaluation of the displacements at the crack faces, and traction and the displacements at the interface.