The consideration of a geometrical nonlinearity is a common practice for the thin-walled structures. The relevance here are two well-known cases treated in ASME codes. First one is accounting for reduction of the pipe bends flexibility due to the inner pressure. The second one is the retarded increasing (and subsequent saturation) of additional local bending stress with increasing of inner pressure in a pipe with initial cross section form distortion. In both cases the rerounding effect and decreasing of local flexibilities take place. The crack can be treated as the concentrated flexibility and it is quite natural to expect that the stress intensity factor should grow nonlinearly with applied load.
Two cases of SIF calculation for 1-D long axial surface crack in a pipe loaded by inner pressure are considered here: a) cross section has an ideal circular form: b) the form has a small distortion and crack is located in the place of maximal additional bending stresses.
The theoretical analysis is based on: a) the well known crack compliance method  and b) analytical linearized solution obtained for deformation of the curved beam in case of action of fixed circumferential stress due to pressure written in the form convenient for transfer matrix method application.
It was shown that for moderately deep crack (crack depth to the wall thickness ratio is 0.5 and bigger) and typical dimensions of pipes used for oil and gas transportation (radius to thickness ratio is 25–40) and loading which can reach up to 200 to 300 MPa, the effect investigated can be quite noticeable and can lead to 5–15 percent reduction of calculated SIF as compared with linear calculation.
The analytical results are supported by nonlinear FEM calculation.