The Accounting for Geometrical Nonlinearity for Thin-Walled Pressurized Elastic Pipe With Long Axial Surface Crack

Abstract

Consideration of a geometrical nonlinearity is a common practice for thin-walled pressurized structures, especially when their cross section is not a perfectly circular one due to either initial imperfections or distortions caused by the nonsymmetrical loading. The application of inner pressure leads to so-called rerounding effect when decreasing of local flexibilities takes place. The crack can be also treated as the concentrated flexibility, so the goal of this work is the investigation of dependence of stress intensity factor (SIF) on applied pressure. Two cases of SIF calculation for 1D long axial surface crack in a pipe loaded by inner pressure are considered here: (a) cross section of pipe has an ideal circular form and (b) the form has a small distortion and crack is located at the place of maximal additional bending stresses. The theoretical analysis is based on: (a) well-known crack compliance method (CCM) (Cheng, W., and Finnie, I., 1986, “Measurement of Residual Hoop Stresses in Cylinders Using the Compliance Method,” ASME J. Eng. Mater. Technol., 108(2), pp. 87–92) and (b) analytically linearized solution for deformation of the curved beam in the case of action of uniform longitudinal stresses. It is shown that for moderately deep crack (crack depth to the wall thickness ratio of 0.5 and bigger) in thin-walled pipe (radius to thickness ratio of 25–40) and inner pressure which induce hoop stress up to 300 MPa, the effect investigated can be quite noticeable and can lead to 5–15% reduction of calculated SIF as compared with the linear case. The analytical results are supported by the geometrically nonlinear finite element method (FEM) calculations.