A study of three-dimensional cracks
This dissertation presents three studies of three-dimensional cracks. The first study is concerned with a fast boundary element method, which allows one to solve problems involving hundreds and thousands of cracks of arbitrary three-dimensional cracks. The new boundary element method is constructed as a merger between a conventional boundary element method and a fast iterative method in which matrix-vector products are computed with the fast multipole method. The accuracy and efficiency of the new method is confirmed by numerical examples involving closely spaced cracks, large arrays of cracks imbedded in an infinite solid, and periodic arrays of cracks. The second study is concerned with regular and singular asymptotic solutions for non-planar quasi-circular cracks. The regular first-order asymptotic solution complements an existing asymptotic solution for planar quasi-circular cracks, and thus, these two solutions constitute a complete first-order regular asymptotic solution for quasi-circular cracks. The singular first-order asymptotic solution is limited to axisymmetric problems only. The range of validity of the regular and singular asymptotic solutions is evaluated upon comparing them with detailed numerical and closed-form solutions. Also, the asymptotic solutions are applied to stability analysis of growing cracks and crack-like cavities. The third study is concerned with experimental characterization of mixedmode cracks in PMMA. The objective of this study is to identify a criterion for crack growth initiation under truly three-dimensional mixed-mode conditions. Based on macroscopic measurements and microscopic observations, it is proposed that the Mode III loading component would affect the fracture toughness KIC, but does not lead to crack growth initiation in the absence of the Mode I loading component. This implies that one can develop three dimensional crack growth initiation criteria using existing two-dimensional criteria as the basis – the key difference is that in three dimensions KIC must be treated as a function of the Mode III stress intensity factor rather than a constant.