UBC Theses and Dissertations
Determination of stress intensity factors for laboratory test specimens using numerical methods Ge, Baolai
Using the Airy stress function, plane bnear elasticity problems reduce to solving a biharmonic problem of the first type. Analytic solutions to the biharmonic problems of the first type in a domain with a re-entrant sharp corner are discussed in this thesis. General solutions to the biharmonic equation in the vicinity of the sharp corner are given in terms of a series of some special eigenfunctions, which are obtained from two auxiliary eigenvalue problems corresponding to symmetric and anti-symmetric stress states. In the case of a line crack, the leading term in each series contains the singularity in stresses near the crack tip, and its coefficient determines the stress intensity factor of Mode I or Mode II loading. In this thesis, stress intensity factors are evaluated with the specimens of two simple geometries - circular disc and rectangle - that are subjected to three types of loadings: uniformly distributed forces, concentrated forces and those yielding pure bending. Stress fields are found using the series stress functions with the boundary collocation method. The least squares approach is applied to the system of linear equations arising from the boundary collocation procedure. Compared to other sophisticated methods, the present approach employing the technique of boundary collocation is straightforward and relatively efficient in numerical computation. Numerical values of stress intensity factors are compared to the results obtained using other less efficient methods. A sound and overall agreement is found in most cases. The approach presented in this thesis along with the results may be used as an auxiliary tool to determine the fracture toughness of laboratory test specimens.
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