A Mathematical Model To Predict δ- Ferrite Content In Austenitic Stainless Steel Weld Metals

This paper presents a mathematical model to forecast the level of residual δ ferrite in terms of FN in austenitic stainless steel welds at cooling rates between 10 °C/s up to 103 °C/s. With this aim, two series of austenitic steel specimens were prepared using an electric arc remelt furnace. Whilst the alloying level was kept constant at [Creq+Nieq] = 30 % and [Creq+Nieq] = 40 %, the Creq/Nieq ratio was gradually increased from 1.22 up to 2.00 in each series. For each alloying level, a highly correlated polynomial function (FN vs. Creq /Nieq ), was found, being Creq and Nieq Hammar and Svensson’s equivalents. These experimental results have led to the importance of [Creq +Nieq] and (Creq /Nieq ) variables in the forecast of the residual ferrite content and a general expression including both variables is proposed. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm \bf FN=54.22-126.26(Cr_{eq}+Ni_{eq})+\lbrack-48.11+37.14(Cr_{eq}+Ni_{eq})\rbrack \Big({Cr_{eq}\over Ni_{eq}}\Big)+\lbrack-0.23+61.95(Cr_{eq}+Ni_{eq})\rbrack \Big({Cr_{eq}\over Ni_{eq}}\Big)^2}$$\end{document} The proposed model is able to forecast the level of δ ferrite with a mean error of +1.01 FN within a deviation of +/- 2.12 FN with 95 % probability by just considering the chemical composition of the alloy. This level of error has been proved to be lower than DeLong’s and WRC-1988 diagrams errors. Moreover, the proposed model has also been compared with WRC-1992 diagram and FNN-1999 neural network and it provides a more accurate FN forecast within the range of compositions and cooling rates considered.