Algorithms to Estimate the Ductile to Brittle Transition Temperature, Upper Shelf Energy, and Their Uncertainties for Steel Using Charpy V-Notch Shear Area and Absorbed Energy Data

Abstract

Toughness and the transition from ductile to brittle behavior are long-standing concerns for applications of ferritic steel such as line-pipe. Three algorithms have been developed to fit a hyperbolic tangent curve to any Charpy V-notch dataset and estimate the uncertainty for (1) the 85% shear appearance area transition temperature and (2) the upper shelf absorbed energy. To fit the hyperbolic tangent curve to the data the (I) first algorithm relied on iterative estimation of four-parameters; (II) the second algorithm on two parameters (after simplification based on physical assumptions); and (III) the third algorithm on only one parameter (after further simplification). The algorithms were written using the open-source programing language, R. The minimum input requirements for the algorithm are experimental data for shear appearance area and absorbed energy from at least four temperatures for the four-parameter algorithm, two temperatures for the two-parameter algorithm, and one temperature for the one-parameter algorithm. The test temperatures and quantity of tests at each temperature can vary. The algorithms are described in detail and demonstrated using a data set of 12 Charpy test results (shear area and absorbed energy) from one API-5L grade X52 pipe with 4.5 mm thick Charpy bars. A future paper will test and compare the algorithms using a wide variety of Charpy V-notch data sets to clarify their applicability and possible limitations.