Doctoral thesis

On crack growth under compressive stresses

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Publication Details

Author list: Isaksson, Per

Publisher: Univ.

Place: Luleå

Publication year: 2001

Abstract

This thesis concerns fractures subjected to compressive stresses. In the four papers appended fracture behavior in brittle as well as ductile materials is studied. In the first paper, an expression for the mode II stress intensity factor at a straight extended kink has been calculated under the condition that crack opening is suppressed during crack growth. The expression has been found as a function of the mode II stress intensity factor K2 at 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. Crack growth directions have been suggested based on the result. At a sufficiently high non-isotropic compressive normal stress, so that the crack remains closed, the crack will propagate along a curved path maximizing the mode II stress intensity factor. Only at an isotropic compressive normal stress will the crack continue straight ahead in its original plane without directional change. By analyzing experimental crack growth patterns in paper two, the conclusion is that crack paths experimentally observed indicate that mode II crack growth under compression in some brittle materials follow a propagation path described by a function y=gx^b. In fact, the agreement between the experiments and the propagation path prescribed by the model, in which b=3/2, is astonishingly good since b was found in the interval [1.43-1.58] in all the experiments studied. Further, the investigation of the curvature parameter g has revealed that g also agree with the simplified model, even though not as good as the exponent b. However, the experimentally observed g differs in general less than 15% from the theoretical value predicted by the analytical model discussed in paper I. In paper three, a directional crack growth criterion in a compressed elastic perfectly-plastic material is considered. A slip-line solution is derived for evaluation of the stresses at the crack tip, which considers hydrostatic pressure and friction between the crack surfaces. Based upon the slip-line solution a projection stress based model is discussed for prediction of the direction of initiated crack growth. The opening displacement of an extended kink has been examined in paper four, using a finite element procedure. The conclusion is that an over-critical pressure in the plastic zone surrounding the crack tip suppresses crack opening regardless the direction of crack growth. The only possibility seems to be shear mode crack growth, which occur straight ahead in the crack plane if the crack is assumed to follow the plane of maximum shear stress. At a sub-critical hydrostatic pressure, or lower friction between the crack surfaces, the crack can extend via a kink subjected to local opening mode. An expression for the critical value determining fracture mode has been found as a function of hydrostatic pressure and friction between the crack surfaces assuming the fracture process to be predominantly controlled by local tensile stresses at the crack tip. The crack growth directions predicted by the projection stress based criterion in paper three are comparable with the directions maximizing the opening displacement of an extended kink computed in paper four.

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