Abstract
A new analytical approximation to the evaluation of temperature dependence of heat capacity of some alloy steels has been presented in this study. This method is based on the Debye approximation for the heat capacity of solids. The proposed analytical method is general and can be applied to the various alloy steels. As an application of method the calculations have been performed for Fe-18Cr-12Ni-2Mo and Fe-18Cr-16Ni-10Mn stainless steels. It is seen from the comparisons of our results with other studies that our approach is accurate.
Similar content being viewed by others
References
Baddoo, N.R. (2008). “Stainless Steel in Construction: A Review of Research, Applications, Challenges and Opportunities”, Journal of Constructional Steel Research, 64, pp. 1199–1206.
Basak, D., Overfelt, R.A. and Wang, D. (2003). “Measurement of Specific Heat Capacity and Electrical Resistivity of Industrial Alloys Using Pulse Heating Techniques”, International Journal of Thermophysics, 24, pp. 1721.
Barr, W. and Honeyman, A.J.K. (1945). “Steel and Its Practical Applications”, Blackie & Son Limited.
Botvina, L.R., Levin V.P., Tyutin, M.R. and Zharkova, N.A. (2010). “Heat Capacity of Deformed Steels”, Technical Physics, 55, pp. 494.
Cankurtaran, M. and Askerov, B.M. (1996). “Equation of state Isobaric Specific Heat and Thermal Expansion of Solids with Polyatomic Basis in the Einstein-Debye approximation”, Physica Status Solidi B, 194, pp. 499.
Carlson, M.F., Narasimha, B.V. and Thomas, G. (1979). “The Effect of Austenitizing Temperature upon the Microstructure and Mechanical Properties of Experimental Fe/Cr/C Steel”, Metallurgical and Materials Transactions, 10A, pp. 1273–1281.
Crook, W.J. (1927). “Alloy Steels and Their Uses”, Journal of Chemical Education, 5, pp. 583.
Çopuroglu, E. and Mehmetoglu, T. (2015). “Full Analytical Evaluation of the Einstein Relation for Disordered Semiconductors”, IEEE Transactions on Electronic Devices, 62, pp. 1580.
Debye, P. (1912). “Zur Theorie der spezifischen Wärmen”, Annalen der Physik, 39, pp. 789.
Devyatykh, G.G., Gusev, A.V., Zhermenkov, N.V. and Kabanov A.V. and Polozkov S.A. (1986). “Heat-Capacity of Highly-Pure Germanium in the 2-15-K Range” Zhurnal Fizicheskoi Khimi, 60, pp. 1797.
Dugdale, J.S. and MacDonald, D.K.C. (1953). “The Thermal Expansion of Solids” Physics Review, 89, pp. 832.
EUR 20030 EN (2001). “Development of the Use of Stainless Steel in Construction Final Report, Directorategeneral for Research”, European Commission, Technical steel research.
Flubacher, P., Leadbetter, A.J. and Morrison, J.A. (1959). “The Heat Capacity of Pure Silicon and Germanium and Properties of their Vibrational Frequency Spectra” Philosophical Magazine, 4, pp. 273.
Gedge, G. (2008). “Structural Uses of Stainless Steel Buildings and Civil Engineering”, Journal of Constructional Steel Research, 64, pp. 1194–1198.
Gradshteyn, I. S. and Ryzhik, I. M. (1980). “Tables of Integrals, Sums, Series andProducts”, 4th ed., Academic Press, New York
Grigor’ev, I.S. and Meilikov, E.Z. (1991). “Physical Values: A Handbook”, Energoatomizdat, Moscow.
Guseinov, I.I. and Mamedov, B.A. (2004). “Evaluation of incomplete gamma functions using downward recursion and analytical relations”, Journal of Mathematical Chemistry, 36, pp. 341.
Guseinov, I.I. and Mamedov, B.A. (2007). “Calculation of Integer and Noninteger n-Dimensional Debye Functions Using Binomial Coefficients and Incomplete Gamma functions”, International Journal of Thermophysics, 28, pp. 1420.
Guseinov, I.I., Mamedov, B.A. and Ç opuroglu, E. (2009). “Use of integer and noninteger n-dimensional Debye Functions in evaluation of heat capacities of crystals”, Journal of Optoelectronics and Advanced Materials, 1, pp. 289.
Irvine, K.J. (1962). “The Development of High-Strength Steels”, Journal of the Iron and Steel Institute, 12, pp. 620–629.
Kittel C.H. (1976). “Introduction to Solid State Physics”, Wiley, New York.
Kubo, R. (1965). “Statistical Mechanics: An Advanced Course with Problems and Solutions” North-Holland, Amsterdam.
Kut’in, A.M., Markhasin, E.M. and Karyakin, N.V. (2004). “Processing and Approximation of Calorimetric Data by the Generalized Debye Functions” Russian Journal of Physical Chemistry, 78, pp. 571.
Landau, L.D. and Lifshits, E.M. (1980). “Statistical Physics”, Pergamon Press, London.
Landsberg, P.T. (1974). “Problems in Thermodynamics and Statistical Physics”, PION, Mir, Moscow.
Lee, W.S. and Su, T.T. (1999). “Mechanical Properties and Microstructural Features of AISI-4340 High-Strength Alloy Steel under Quenched and Tempered Conditions”, Journal of Materials Processing Technology, 87, pp. 198.
Lee, S., Ham, H.J., Kwon, S.Y., Kim, S.W. and Suh, C.M. (2013). “Thermal Conductivity of Magnesium alloys in the Temperature range from -125C to 400C”, International Journal of Thermophysics, 34, pp.2343.
Miller, P.H. (1937). “Stainless Steel”, H. Milford, London.
Moruzzi, V.L., Janak, J.F. and Williams, A.R. (1978). “Calculated Electronic Properties of Metals”, New York.
Moruzzi, V.L., Janak, J.F. and Schwarz, K. (1988). “Calculated Thermal Properties of Metals”, Physical Review B, 37, pp. 790.
Novikov, I.I. (2000). “Thermodynamics of Spinodals and Phase Transitions”, Nauka, Moscow.
Rajevac, V., Hoelzel, M., Danilkin, S.A., Hoser, A. and Fuess, H. (2004). “Lattice dynamics in austenitic stainless steels Fe-18Cr-12Ni-2Mo and Fe-18Cr-16Ni-10Mn”, Journal of Physics: Condensed Matter, 16, pp. 2609.
Sanstrom, R. and Bergqvist, H. (1977). “Temperature Dependence of Tensile Properties and Strengthening of Nitrogen Alloyed Austenitic Stainless Steels”, Scandinavian Journal of Metallurgy, 6, pp. 156.
Simonson, J.R. (1999). “Engineering Heat Transfer”, New York, Macmillan.
Weng, Y., Dong, H. and Gan, Y. (2011). “Advanced Steels”, Metallurgical Industry Press, Springer.
Touloukian, Y.S., Powell, R.W., Ho, C.Y. and Klemens, P.G. (1970). “Thermopyhsical Properties of Matter”, IFI/Plenum, New York.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Çopuroğlu, E., Sözen, Ş. & Yamçıçıer, A. Analytical evaluation of heat capacities of structural stainless steels by using n-dimensional integer and noninteger Debye functions. Int J Steel Struct 17, 739–742 (2017). https://doi.org/10.1007/s13296-017-6027-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13296-017-6027-3