Generally, all existing structural materials contain various inter- and intra-component defects. For instance, cracks and delaminations often occur at the bonding surfaces between two dissimilar materials. The presence of these defects considerably decreases the strength and the lifetime of the structures as well as significantly increases the cost of exploitation. Therefore it is necessary to understand the mechanism of fracture in cracked materials and to ensure that the residual strength of the structure will not fall below an acceptable level over the required service life. The majority of previous studies are limited by the case of cracked homogeneous solids due to the substantial complications in solution of such problems in heterogeneous materials. However the industry requires solutions of much more complex problems involving composite structures with cracks subjected to dynamic loading.

 Layered material with cracks An interface crack between two half-spaces

The current project is devoted to a 2-D problem for interface cracks located between two dissimilar materials under harmonic external loading. The system of boundary integral equations for displacements and tractions is derived from the dynamic Somigliana identity. The distributions of the displacements and tractions at the bonding interface and the surface of the cracks are analysed for the normally incident harmonic waves. The dynamic stress intensity factors are also computed for different values of the frequency of the incident wave and different material properties.

Tangential displacements at the bonding interface

Related publications:

• Mykhailova II, Menshykov OV, Menshykova MV, Guz IA. Boundary integral equations for an interface linear crack under harmonic loading. Journal of Computational and Applied Mathematics, 2009, pp. [in press], DOI: 10.1016/j.cam.2009.08.084.

• Menshykov OV, Menshykov VA, Guz IA. Elastodynamics of a crack on the bimaterial interface. Engineering Analysis with Boundary Elements, 2009, 33(3), pp.294-301.

• Menshykov OV, Guz IA, Menshykov VA. Boundary integral equations in elastodynamics of interface cracks. The Philosophical Transactions of the Royal Society A. 2008, 366(1871), pp.1835-1839.

• Menshikov VA, Menshikov AV, Guz IA. Passages to the limit in the dynamic problem for a crack at the interface between elastic media. International Applied Mechanics. 2008, 44(7), pp.739-746.

• Mykhailova II, Menshykov OV, Guz IA. Elastodynamic problem of an interface linear crack under harmonic loading. PAMM - Proceedings in Applied Mathematics and Mechanics. 2008, 8(1), pp.10229-10230.

• Guz IA, Menshykov AV, Menshykov VA. On the limit transition in dynamic problem of an interphase crack under decreasing load frequency. Proceedings of the National Academy of Sciences of Ukraine,  2008, No.3, pp.50-54.

• Menshykov OV, Menshykov VA, Guz IA. The effect of frequency in the problem of interface crack under harmonic loading. International Journal of Fracture. 2007, 146(3), pp.197-202.

• Menshikov VA, Menshikov AV, Guz IA. Interfacial crack between elastic half-spaces under harmonic loading. International Applied Mechanics, 2007, 43(8), pp.865-873.

• Guz IA, Menshykov O, Menshykov V. Application of boundary integral equations to elastodynamics of an interface crack. International Journal of Fracture. 2006, 140(1-4), pp.277-284.