Fracture mechanics problems for cracked homogeneous materials under harmonic loading

The present study is devoted to solution of the 3-D elastodynamic problem of a cracked material with the focus on the effect of the cracks’ closure. The detailed procedure for deriving the system of boundary integral equations for displacements and tractions is presented. Full expressions of the integral kernels evaluated by the consecutive differentiation of the Green’s displacement tensor are given in the current work. Due to the contact that takes place between the opposite faces of the crack under the applied harmonic loading, the resulting process is not a harmonic, but a steady-state periodic one. As a result, components of the stress-strain state are expanded into exponential Fourier series. The system of boundary integral equations is solved numerically with the use of an iterative procedure. The solution is refined during the iteration process until the distribution of physical values satisfies the contact constraints. The hyper-singular integrals are treated in the sense of the Hadamard finite part. The distributions of the contact forces and displacement discontinuities at the cracks’ surface are investigated. The stress intensity factors are obtained and analyzed for different values of the wave frequency and crack configuration. Influence of the material properties and numerical parameters on the solution is studied and the possible relations are found. The significance of taking the effect of the cracks’ closure into account was shown. The difference between the results obtained for the case of accounting for cracks’ closure and neglecting it is not only qualitative but also quantitative and can reach more than 100% for two closely located in-plane cracks. Finally, the main results are summarised. It is shown that accounting for the crack closure is vital for the correct assessment of the stress strain state in the vicinity of the crack front. Moreover, a set of recommendations regarding future work are given.EThOS - Electronic Theses Online ServiceGBUnited Kingdo