Slightly curved or kinked cracks

Abstract

A solution is presented for the elastic stress intensity factors at the tip of a slightly curved or kinked two-dimensional crack. The solution is accurate to first order in the deviation of the crack surface from a straight line and is carried out by perturbation procedures analogous to those of Banichuk [1] and Goldstein and Salganik [2,3]. Comparison with exact solutions for circular arc cracks and straight cracks with kinks indicates that the first order solution is numerically accurate for considerable deviations from straightness. The solution is applied to fromulate an equation for the path of crack growth, on the assumption that the path is characterized by pure Mode I conditions (i.e., KH = 0) at the advancing tip. This method confirms the dependence of the stability, under Mode I loading, of a straight crack path on the sign of the non-singular stress term, representing tensile stress T acting parallel to the crack, in the Irwin-Williams expansion of the crack tip field. The straight path is shown to be stable under Mode I loading for T < 0 and unstable for T > 0.

Recent developments in dynamic fracture: some perspectives

“…In 2D and under quasi-static conditions, v c R , it has been shown that the Principle of Local Symmetry [93] offers good approximations for crack paths [94][95][96][97][98][99][100]. This approximation suggests that under quasi-static conditions, and under the assumption that no intrinsic length scales exist near the tip, crack propagation along smooth paths will annihilate any shear (mode II) component of the fields ahead of the tip.…”

Computing stress intensity factors for curvilinear cracks

“…When the crack faces are loaded, a boundary integral over the faces has to be carried out irrespective of the auxiliary fields. For this particular problem it may be appealing to choose a pairing with β DFC such as (35) and (36). Doing so reduces the numerical complexity of the interaction integral as λ greatly simplifies (and vanishes identically in the absence of body forces).…”

“…This proposition is not directly applicable to the discontinuous Galerkin method in §5.1, because in this case it is also necessary to account for the use of an approximation space that does not conform to H 1 . Finally, the two functionals G(u) = I[∇u, β DFC , δγ] in (35) and (36) are not continuous in H 1 (B C ; R 2 ), because of the evaluations of ∇u on the crack faces, so we cannot directly apply the above result.…”

Calculation of dike trajectories from volcanic centers

“…The kink angle is determined by the requirement that the loading of the incremented tip is mode I (equivalently, by the maximum circumferential stress criterion). Moreover, it follows that if the subsequent propagation path curves smoothly (without further kinks), then the tip loading must be such that fracture proceeds in pure mode I [Cotterell and Rice, 1980], and this determines the curvature. Thus smoothly curving dikes propagate along the path for which the only nonzero stress intensity factor is K I .…”