Plasticity around an Axial Surface Crack in a Cylindrical Shell

This paper presents a plasticity model for deep axial surface cracks in pressurised pipes. The model is used in an investigation of the relative merits of fracture criteria based on COD and plastic instability. Recent investigations have shown that the inconsistency of the singular bending stress field in an axially cracked cylindrical shell arising from use of classical eighth order shallow shell theory is removed when use is made of a tenth order shell theory which accounts for transverse shear deformations. Although the membrane stresses are only moderately affected, the influence on the bending stresses is considerable. In the case of surface cracks moments are induced due to the eccentricity of the crack and transverse shear effects should therefore be included. A plasticity model for a rectangular axial surface crack is developed. Like a previous surface crack model by Erdogen and Ratwani,3–5 it generalises Dugdale's assumption of a concentrated yield zone in the plane of the crack but, contrary to that model, transverse shear effects are included and a continuous stress distribution is assumed in the yield zone. The inherent difficulties arising from the use of shell theory to model a three-dimensional problem can be overcome when the crack is sufficiently deep and the material is so ductile that full yield of the section around the crack develops before failure. In that case the calculations confirm the initial assumption of separation of the crack surfaces and the sides of the yield zone. The model is used to analyse published test data on surface cracked pressurised pipes. The analysis consists in COD evaluation and estimate of failure as a consequence of plastic instability. A method is proposed which deals with the problem by simultaneous analysis of a number of cracks with increasing depth. The method avoids iterations and enables, for any load and crack length, calculation of the smallest crack depth which would cause instability.