Thermodynamic prediction of the eutectoid transformation temperatures of low-alloy steels
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I. INTRODUCTION
QUANTITATIVELY accurate models of the phasetransformation kinetics of low-alloy steels require precise knowledge of the A3 and A1 temperatures encountered under typical heat-treatment conditions. Based on the accumulation of reliable thermodynamic data, many thermodynamic models have been developed for predicting these temperatures.[1– 4] Of these, the orthoequilibrium (OE) model gives predictions for A3 that are very close to those measured experimentally,[4] and these are denoted by Ae3. The OE approach assumes full partitioning of alloying elements, and this is physically reasonable, since the ferrite transformation usually occurs at temperatures at which substitutional and interstitial atoms can quickly diffuse and, thus, become partitioned. In contrast to the predictions of Ae3, the Ae1 temperatures predicted by an OE approach are not satisfactory because substitutional elements are not fully partitioned during the eutectoid transformation. To address this deficiency, investigators have tried to predict experimental A1 temperatures using paraequilibrium (PE) models.[5,6,7] This approach assumes a uniform carbon chemical potential and a continuous substitutional element-to-iron mole-fraction ratio at the transforming interface. The A1 temperatures calculated under this assumption are denoted by Ap1. Hashiguchi et al.[6] calculated Ae1 and Ap1 temperatures for three sets of ternary systems (Fe-C-Cr, Fe-C-Mn, and Fe-C-Ni) and compared them to experimental A1 temperatures. The Ae1 temperatures showed good agreement with the experimental values for the Fe-C-Cr system. In the other systems, however, the Ap1 temperatures were in better accordance with experimental results, although the amount of experimental data was limited. Based on these results, Kirkaldy and Venugopalan[7] YOUNG-KOOK LEE, Research Assistant Professor, and MARK T. LUSK, Associate Professor, are with the Division of Engineering, Colorado School of Mines, Golden, CO 80401-1887. Manuscript submitted February 8, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS A
proposed the following intermediate model to predict the A1 temperatures of low-alloy steels that have arbitrary chemical compositions: Tp1 5 Ap1 1 DT
Cr Ni 1 Cr 1 Mo
DT 5 Ae1 2 Ap1
[1] [2]
Despite the fact that Tp1 offers an improvement in predicting experimental A1 temperatures, deficiencies still exist. Specifically, Eq. [1] implies that only Cr is fully partitioned and does not take into account the partitioning of Mn. In an effort to improve the prediction of A1 as a function of chemistry, the experimental A1 temperatures of 85 lowalloy steels, obtained from the USS Atlas of I-T diagrams,[8] have been analyzed using the thermodynamic model of Eqs. [1] and [2]. A modified equation was then derived that gives more-accurate predictions of A1 temperatures of low-alloy steels. The new model is compared to that of Eqs. [1] and [2]. II. COMPARISON OF Ae1 AND Ap1 TO EXPERIMENTAL A1 TEMPERATURES The A1 temperatures of a set of low-alloy steels, published in the USS Atlas of I-T
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