The prediction of precipitation strengthening in microalloyed steels
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I.
INTRODUCTION
THE additions
of strong carbide and nitride forming elements such as niobium, vanadium, and titanium to increase the strength of steels has been widely used. The two most important strengthening contributions from microalloying are from grain size refinement and precipitation, rl,21 Strengthening via grain size refinement appears to be well established and well understood. 13-6J In the case of precipitation strengthening, considerable effort has been directed toward the mechanism of formation of interphase boundary precipitates. I7'8'91 These precipitate particles, formed at the austenite/ferrite interphase boundary during the y ---> c~ + carbide transformation are very small in size ( - 5 nm diameter) and result in large strengthening additions because of their small size and fine distribution. The effectiveness of precipitation strengthening depends on the (temperature dependent) solubility of the precipitating phase in austenite and the austenitizing (or soaking) temperature; particles that do not dissolve in austenite may lead to grain refinement but are too large and widely spaced to contribute to precipitation strengthening. In order to be able to relate the compositions of microalloyed steels and their heat treatments to precipitation strengthening one needs to be able to determine those weight fractions of microalloying element, carbon, and nitrogen that will be in solution at the austenitizing temperature and therefore available for precipitate formation during the y ---> a + carbide transformation. Given the solubility product and the steel's composition, one can determine whether or not the precipitating phase is completely in solution. 12j However, if the solubility limit is exceeded, the composition of the austenite in equilibrium with the carbide or nitride phase cannot he determined exactly unless the tie lines for the y-MC and y-MN fields are known at the temperature considered. Experimental determinations of tie lines for Fe-M-C and Fe-M-N systems are generally lacking. In order to locate tie lines utilizing thermodynamic models, one would first apH.R. LIN is Associate Scientist, Research and Development, China Steel Corporation, Kaohsiung, Taiwan, Republic of China. A.A. HENDRICKSON is Professor, Department of Metallurgical Engineering, Michigan Technological University, Houghton, MI 49931. Manuscript submitted January 6, 1986. METALLURGICALTRANSACTIONS A
proximate the free energy surfaces for both austenite and the carbide (or nitride) phases and then obtain the tie lines from the points of tangency of a plane placed against the convex, free energy surfaces. The zeroeth approximation, regular solution treatment of interstitial solid solutions developed by Hillert and Staffansson tIll has been applied extensively to phase equilibria in Fe-M-C systems by Uhrenius and his co-workers tl2-tSI and application of this thermodynamic model to interstitial solutions has been shown to reproduce experimental information fairly well, e.g., Uhrenius's analysis of the Fe-V-C system. I121Use
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