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

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 arc crack edge subjected to a combined tensile load and a bending moment.

Stress intensity factors for an edge cracked circular bar in tension and bending

“…For a given crack depth ratio a/D the curvature of the crack front is considerably greater than that modelled in [5], the difference between the two configurations being most marked for shallow cracks. For a given crack depth ratio a/D the curvature of the crack front is considerably greater than that modelled in [5], the difference between the two configurations being most marked for shallow cracks.…”

“…The same technique has been employed [5] to estimate the average strain energy release rate for a circular-arc edge crack in a bar under tension and bending. A crack front with a radius R = (0.5D + a), and a centre of curvature at a distance D from the centre of the bar, was modelled.…”

Experimental and finite element analyses on stress intensity factors of an elliptical surface crack in a circular shaft under tension and bending

“…Early attempts used a straight edge (Daoud et al, 1978;Bush, 1981;Carpinteri, 1992a) or a circular arc to idealize the crack front (Wilhem et al, 1982;Mackay and Alperin, 1985;Daoud and Cartwright, 1985;Forman and Shivakumar, 1986;Raju and Newman, 1986). In some works, the angle of intersection of the crack front with the rod external surface was taken to be 90o to facilitate crack shape definition (Forman and Shivakumar, 1986;Raju and Newman, 1986).…”

“…Available stress intensity solutions from the literatures for surface cracks in cylindrical rods have some limitations. For example, the reported solutions are often limited to the deepest interior point (Daoud et al, 1978;Daoud and Cartwright, 1985;Bush, 1981;Wilhem et al, 1982;Mackay and Alperin, 1985;Forman and Shivakumar, 1986;Murakami and Tsuru, 1987;Couroneau and Royer, 1998) or the deepest interior and the surface interception points on the crack front (Carpinteri, 1992b;Carpinteri and Brighenti, 1996;Astiz, 1986;Athanassiadis, 1981;Shiratori et al, 1986;Caspers et al, 1990). Sometimes, they are available for a limited number of discrete aspect ratios and crack depth ratios.…”

Sickle‐shaped crack in a round bar under complex Mode I loading

“…Several authors have examined the SIF variation along the front of surface defects in round bars under different loading conditions. As has been experimentally observed, such flaws often present an almond shape, 1–20 but sickle‐shaped cracks are also frequent, even if only a few studies have been carried out to derive the SIF values for the latter case 21–24 …”