This thesis is devoted to solution of the two-dimensional elastodynamic problem for a cracked bimaterial loaded by harmonic waves. The system of boundary integral equations for displacements and tractions at the interface is obtained from Somigliana identity with the allowance for the contact interaction of the opposite crack faces. Full expressions of the integral kernels derived by the consecutive differentiation of the Green's displacement tensor are given. Due to the contact that takes place between the faces of the crack under the applied external loading, the resulting process is a steady-state periodic, but not a harmonic one. Thus, components of the stress-strain state are expanded into exponential Fourier series. The collocation method with a piecewise constant approximation on each linear continuous boundary element is used for the numerical solution. The problem is solved using the iterative algorithm. The solution is refined during the iteration process until the distribution of physical values satisfies the imposed constraints. The results are obtained for the interface crack subject to normal tension-compression, normal shear, or oblique tension-compression waves with different values of the angle of the wave incidence and the wide range of the dimensionless wave number. The distributions of the normal and tangential components of the contact forces and displacement discontinuities on the surface of the crack are investigated. The stress intensity factors are computed and analyzed for various values of the wave frequency, the friction coefficient, and material properties. The maximal stress intensity factors at the trailing crack tip differ from the SIF values at the leading crack tip showing non-symmetry of solution with respect the space and time variables. It is concluded that the crack closure and friction effect change the solution both qualitatively and quantitatively, as the difference between comparable results can achieve 30-50%.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:680971 |
| Date | January 2015 |
| Creators | Mikucka, Vita |
| Publisher | University of Aberdeen |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=228606 |
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