Expression of a Generic Full-Range True Stress-True Strain Model for Pipeline Steels Using the Product-Log (Omega) Function

Steel pipelines are subjected to a variety of complex, and sometimes difficult to predict, loading schemes during the fabrication, installation and operation phases of their lifecycles. Consequently, the mechanical behavior of steel pipelines is not only influenced by the steel grade but also by the loading history of the pipe segments. Due to the resultant intricacies of the nonlinear load-deformation behavior of pipelines, adequate numerical analysis techniques are usually required for simulation of pipelines under different loading schemes. The validity of such numerical simulations is largely influenced by the accuracy of the true stress-true strain characterization of the pipeline steels. However, existing stress-strain mathematical expressions, developed for the characterization of metallic materials over the full-range of the stress-strain relationship, have been observed to either loose predictive accuracy beyond a limited strain range or, for the more accurate full-range models, are cumbersome due to their requirement of a large number of constituent parameters. This paper presents a relatively accurate and simple true stress-true strain model which is capable of accurately predicting the stress-strain behavior of pipeline steels over the full range of strains. The proposed stress-strain model is characteristically unlike existing stress-strain models as it is essentially defined by a Product-Log function using two proposed parameters, and is capable of capturing a reasonable approximation of the yield plateau in the stress-strain curve. To validate the proposed model, curve-fitting techniques are employed for comparison to experimental data of the stress-strain behavior of different pipeline steel grades (X52 – X100). Excellent agreements are observed between the proposed model and the different pipeline steels over the full-range of the true stress-true strain relationship. Furthermore, the applicability of the proposed model is validated by means of a proposed parametric procedure for predicting the ultimate compressive strength of shell elements.