My wife Tatyana, daughter Mariya, son Alexandr It is well known that the
mixed-mode conditions appear when the direction of the applied loading
does not coincide with the orthogonal K, -Kn-Km space. In general, in
the industrial practice the mixed-mode fracture and the mixed-mode crack
growth are more likely to be considered the rule than the exception.
Miller et al. considers that cracks can grow due to a mixture of
processes (ductile and brittle), mechanisms (static, fatigue, creep) and
loading modes (tension, torsion, biax- ial/multiaxial). Additionally
mixed-mode crack-extension can be affected by many other considerations
such as artifact geometry (thin plates, thick shells, and the size,
shape and orientation of the defect), environmental effects
(temperature, gaseous and liquid surroundings), material state
(crystallographic structure, heat treatment and route of manufacture)
and stress conditions (out-of-phase and ran- dom loading effects). The
main feature of the mixed-mode fracture is that the crack growth would
no longer take place in a self-similar manner and does not follow a
universal trajec- tory that is it will grow on a curvilinear path. There
are various fracture criteria, which predict the behavior of cracks in
brittle and ductile materials loaded in combined modes. Linear elastic
fracture mechanics (LEFM) criteria predict basi- cally the same
direction for crack propagation. Cracks in brittle materials have been
shown to propagate normal to the maximum tangential stress. In ductile
ma- terials yielding occurs at the crack tip and LEFM is no longer
applicable.