A study of three-dimensional cracks
Abstract
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.
Description
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