Strain energy release rate for a circular-arc edge crack in a bar under tension or bending

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Abstract
A bar of circular cross-section is modelled with two-dimensional plane-stress finite elements. The bar has a crack at its edge, the front of which is a circular arc. The ends of the bar remote from the crack are subjected to either an axial load or a bending moment in the plane of symmetry of the cracked section. The strain energy release rate of the crack is determined from a finite element model as the rate of change of elastic energy in the bar for successive positions of the circular arc crack front. The values of strain energy release rate so determined are found to be comparable with existing results obtained from three-dimensional finite element analyses. The effect of curvature is found to cause a reduction in the strain energy release rate compared to that for a straight fronted crack of the same maximum depth in a bar under the same loading conditions. The results obtained are superimposed to obtain strain energy release rates for the circular are crack edge subjected to a combined tensile load and a bending moment.

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