Numerical Simulations of Carbon and Nitrogen Composition-Depth Profiles in Nitrocarburized Austenitic Stainless Steels
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with interstitially hardened austenitic stainless steels with enhanced properties. In particular, low-temperature carburization, nitridation, or nitrocarburization results in a steel with a hardened case containing a ‘‘colossal’’ supersaturation of these interstitial solutes, without formation of carbides and nitrides.[1–6] In low-temperature-carburized AISI 316L stainless steels, a non-Erfcian concentration-depth profile of carbon is often observed,[3–5] and our previous work has shown that this non-Erfcian concentrationdepth profile of carbon can be understood by recognizing that the diffusion coefficient of carbon is highly concentration dependent.[7] This type of concentrationdependent diffusion coefficient can be described by an exponential function[8]: X ~ D=D ¼ Exp k ; ½1 Xmax
XIAOTING GU, formerly Doctoral Student with Department of Materials Science and Engineering, Case Western Reserve University, Cleveland, OH, is now Research Scientist with the Atotech USA Inc., Cleveland, OH. Contact e-mail: [email protected]; xiaoting.gu@ atotech.com GARY M. MICHAL, formerly Professor with the Department of Materials Science and Engineering, Case Western Reserve University, Cleveland, OH, is now deceased. FRANK ERNST and ARTHUR H. HEUER, Professor, and HAROLD KAHN, Research Associate Professor, are with the Department of Materials Science and Engineering, Case Western Reserve University. Manuscript submitted April 25, 2014. METALLURGICAL AND MATERIALS TRANSACTIONS A
~ is the concentration-dependent diffusion coefwhere D ficient, D is the diffusion coefficient at infinite dilution, and X and Xmax are the actual concentration and the maximum possible concentration. The parameter k controls the magnitude of the concentration depen~ is ek times D. dence. For example, when X is Xmax, D It is noteworthy that Eq. [1], while empirical, is not unphysical. In fact, there is a substantial literature on the analytical description and physical background of the concentration dependence of the diffusivity of carbon in austenite that supports such an exponential equation. We have performed an extensive literature review on the concentration dependence of carbon diffusivity in austenite; eleven distinct physical models have been published from 1948 to 1997,[9–19] as described elsewhere.[20] The derivations of all eleven physical models are thoroughly discussed in Reference 20, and nine of the eleven have also been discussed in an earlier dissertation.[21] Our critical review of the concentration dependence of carbon diffusivity in austenite[20] clearly showed the physical model proposed by Asimow in 1964,[11] as described by 2 k1 ~ þ DC ¼ DC 1 þ YC Exp½KYC ; ½2 1 Y2C T which provides an excellent description of the concentration dependence of carbon diffusivity,[20] and numerical simulation based upon Asimow’s model fits the experimental carbon concentration-depth profiles in low-temperature-carburized AISI 316L stainless steels very well.[21] In Eq. [2], YC represents the site fraction of carbon in austenite;
k1 is a coefficient in the th
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