The equations to generate a J-R curve from a four-point bend test on circumferentially cracked pipe have been known for many years. Given the experimental pipe load-displacement record and crack growth, the only impediment to routinely calculating pipe J-R curves is the requirement to know the non-cracked pipe elastic and plastic displacements. Traditionally, finite element analyses are used to find these displacements. This paper presents a semi-closed-form solution for the total (elastic plus plastic) non-cracked pipe displacements that eliminates the need to perform finite element analyses to calculate a pipe J-R curve.
Using a Ramberg-Osgood nonlinear representation of the stress-strain curve and the assumption that plane sections remain plane, beam bending equations can be written to find nonlinear beam displacements for pipe bend geometries with a base metal crack. Building on this result, the solution is extended to the dissimilar metal weld (DMW) case with five nonlinear materials.
The non-cracked pipe displacement solutions are presented as well as comparisons using these equations between compact tension specimen J-R toughness curves and J-R curves from pipe experiments.
