Expanded Lever Rule for Phase Volume Fraction Calculation of High-Strength Low-Alloy Steel in Thermal Simulation
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INTRODUCTION
THE transformed phase volume fractions in continuous cooling processes using thermal simulations are important parameters in materials research.[1–4] There are two methods commonly used for phase volume fraction calculation: metallography analysis and the lever rule. Metallography analysis is a basic method for microstructure-type identification and phase volume fraction calculation. The steps usually include grinding, polishing, chemical etching, and observation. In order to obtain more distinguishable metallographs on the microstructural morphologies or grayscales, different polishing processes and chemical etching reagents are used.[3,5,6] The unique morphology of each phase is often viewed as the most important factor, while the production process and the chemical compositions of the samples are subordinate factors in microstructure-type identification and phase volume fraction calculation. The lever rule is carried out on the dilatation curves, which are drawn with the data recorded by thermal simulators.[3,4] The lever rule complies with mathematical principles that ensure the reliability of the calculation results. The positions of tangent points, tangent lines, and lever lines on the dilatation curve are main factors that affect the calculation accuracy. Accurate operation on and observation of the characteristics of the dilatation curve are the basic skills required to reduce the calculation error. Though metallography analysis often calculates a larger error value than does XUANWEI LEI, Ph.D. Student, JIHUA HUANG, Professor, SHUHAI CHEN and XINGKE ZHAO, Associate Professors, are with the School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, P.R. China. Contact email: [email protected] Manuscript submitted October 15, 2015. Article published online March 24, 2016 METALLURGICAL AND MATERIALS TRANSACTIONS A
the lever rule, both methods can calculate reliable results. But, when two phases show some similarities in their morphologies and an overlap between the transformation process, the metallography analysis and the lever rule can hardly calculate accurate results. Therefore, in some cases, an attempt is made to achieve the phase volume fractions using metallography analysis through special processing methods, such as the special etching method and the corresponding image taking modes. Seldom researchers have focused on the improvement of the lever rule. In the present work, the lever rule is expanded in an overlapped two-phase process. The principle of the expanded lever rule is introduced, and it is applied to high-strength low-alloy (HSLA) steels. The reliability of this method is also exhibited.
II.
EXPANDED LEVER RULE
The metal with a certain length L0 at initial temperature T0 will thermally expand to LT at temperature T when no phase transformation occurs. The length LT can be calculated as[7] h i LT ¼ L0 1 þ aðT T0 Þ þ bðT T0 Þ2 þ ½1 where a and b are expansion coefficients of metal. Generally, the coefficient b, the third item
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