Pipeline steel stress-strain curves obtained from tension and compression testing of longitudinally and circumferentially oriented specimens of the pipe wall can be significantly different e.g., the pipe material is anisotropic. The anisotropic behavior can result from the manufacturing process (e.g., due to cold expansion of UOE pipe) and can also be influenced by strain aging effects (e.g., due to heated application of pipe coating materials). As described in previous work, the Mroz multilinear kinematic hardening plasticity theory has the ability to accurately model different types of anisotropic pipe material behavior including relatively “sharp” uniaxial circumferential tension response and relatively well-rounded uniaxial longitudinal tension and compression response. The stress-strain curve fitting is accomplished by essentially selecting the sizes and initial positions of elliptical von Mises yield functions in stress-space.
A previously developed and published 8-parameter model is well-suited for fitting a matched pair of longitudinal tension (LT) and hoop tension (HT) stress-strain curves as might typically be available from a strain-based pipeline design project. Fitting a pair of “target” LT-HT stress-strain curves is accomplished using a “2-root” fitting procedure where the roots correspond to locations where the yield functions intercept the stress axes in two-dimensional (longitudinal-hoop) stress space. In this paper, the previously described 8-parameter/2-root fitting procedure is extended to a 10-parameter/3-root fitting procedure for situations where a matched “triple” of pipe steel stress-strain curves are available (e.g., LT, HT and longitudinal compression or LC). This extension allows for analysis of strain-based design conditions using an analytical pipe steel, which provides an accurate representation of the uniaxial longitudinal and circumferential stress-strain response of the pipeline material. This paper reviews the 8-parameter/2-root fitting procedure and outlines the extension to the 10-parameter/3-root fitting approach including example application.