Journal article

Prediction of shear crack growth direction under compressive loading

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Author list: Isaksson, Per

Publication year: 2002

Start page: 175

End page: 194

Number of pages: 20

ISSN: 0376-9429

DOI: http://dx.doi.org/10.1023/A:1015581922242


Abstract

A directional crack growth prediction in a compressed homogenous elastic isotropic material under plane strain conditions is considered. The conditions at the parent crack tip are evaluated for a straight stationary crack. Remote load is a combined biaxial compressive normal stress and pure shear. Crack surfaces are assumed to be frictionless and to remain closed during the kink formation wherefore the mode I stress intensity factor KI is vanishing. Hence the mode II stress intensity factor KII remains as the single stress intensity variable for the kinked crack. An expression for the local mode II stress intensity factor k2 at the tip of a straight kink has been calculated numerically with an integral equation using the solution scheme proposed by Lo (1978) and refined by He and Hutchinson (1989). The confidence of the solution is strengthened by verifications with a boundary element method and by particular analytical solutions. The expression has been found as a function of the mode II stress intensity factor KII of the parent crack, the direction and length of the kink, and the difference between the remote compressive normal stresses perpendicular to, and parallel with, the plane of the parent crack. Based on the expression, initial crack growth directions have been suggested. At a sufficiently high non-isotropic compressive normal stress, so that the crack remains closed, the crack is predicted to extend along a curved path that maximizes the mode II stress intensity factor k2. Only at an isotropic remote compressive normal stress the crack will continue straight ahead without change of the direction. Further, an analysis of the shape of the crack path has revealed that the propagation path is, according the model, required to be described by a function y = cx? , where the exponent ? is equal to 3/2. In that case, when ? = 3/2, predicts the analytical model a propagation path that is selfsimilar (i.e. the curvature c is independent of any length of a crack extension), and which can be described by a function of only the mode II stress intensity factor KII at the parent crack tip and the difference between the remote compressive normal stress perpendicular to, and parallel with, the parent crack plane. Comparisons with curved shear cracks in brittle materials reported in literature provide limited support for the model discussed.


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