The goal of this dissertation was to establish the relationship
between a parameter descriptive of the trajectory of a smoothly
curving crack, such as the curvature of the crack path, and the local
stress state in the close vicinity of the crack tip. The behavior of
fast -running cracks propagating along straight and smoothly curving
paths in fracture specimens of various geometries was examined using
dynamic photoelasticity and representations of the running crack
stress field we redeveloped in terms of the coefficients of a set of
infinite series, for both opening and shear mode loading conditions.
Analysis of the isochromatic patterns, using local collocation methods
based on this stress field representation, allowed the stress state in
the neighborhood of the propagating crack-tip to be modelled with a
high degree of accuracy and results were obtained for the variations
with crack tip position of both the singular and leading non- singular
stress field coefficients of interest.
The results obtained for quasi-static and rapid crack propagation
under opening mode conditions in a ring segment revealed the importance of retaining terms of order (at a minimum) r^1/2 even when
only the singular term was to be determined accurately. Furthermore,
it was found that the non-singular stress field coefficients varied
similarly in both static and dynamic situations, with some variations
in magnitude that could be attributed to crack speed.
The results from the curved crack experiments also showed
systematic variation of the non-singular terms, but more importantly,
it was found that the instantaneous curvature of the crack path was
related to the magnitude of the lowest order non-singular stress component (the coefficient of the r^1/2 term) associated with the local
shear mode of deformation in the vicinity of the tip of the running
crack. Furthermore, the results established that the only singularity
associated with a crack propagating along a smoothly curving path in a
brittle, isotropic material was that associated with the opening mode
stress intensity factor, K1, and that the shear mode singularity, KII,
was identically equal to zero
