Modelling the Effect of Phase Transformations on Cooling Rate During Quenching in Nuclear Forgings Using Effective Heat Capacity

Modelling the Effect of Phase Transformations on Cooling Rate During Quenching in Nuclear Forgings Using Effective Heat Capacity

M.P. Howson1, B.P. Wynne2, P.S. Davies3, J. Talamantes-Silva4

1EPSRC Centre for Doctoral Training in Advanced Metallic Systems, Department of Materials Science and Engineering, The University of Sheffield, Mappin St., Sheffield S1 3JD, UK..

2Department of Materials Science and Engineering, The University of Sheffield, Mappin St., Sheffield S1 3JD, UK..

33 Sheffield Forgemasters RD26 Ltd, 286 Brightside Lane, Sheffield S9 2RW, UK.



A modelling methodology based on experimental heat capacity measurements has been used to predict the effects of latent heat formation on cooling rates in a thick sectioned nuclear forging during quenching. Differential scanning calorimetry was used to measure specific heat capacity as a function of temperature (100 – 1000°C) and cooling rate (5 – 70°C/min) that also incorporates the heat energy release during transformations, which is termed the effective specific heat. A user defined routine then incorporated this data into a finite element model of a full scale heat treatment trial forging that had section thicknesses of 200 and 330mm approximately. Excellent agreement with thermocouple data, taken from key test locations, was obtained, particularly at 0.25 and 0.5 thickness. However, some deviations from thermocouple data were seen that has been attributed to the model assumptions, particularly the method used to represent boundary conditions.

Cite as:

Howson, M., Wynne, B., Davies, P., Talamantes-Silva, J. (2017). Modelling the Effect of Phase Transformations on Cooling Rate During Quenching in Nuclear Forgings Using Effective Heat Capacity. Computer Methods in Materials Science, 17(3), 137 – 144.

Article (PDF):


Quenching, Reactor Pressure Vessel, Finite Element Modelling, Differential Scanning Colorimetry, Latent Heat


Al-Bermani, S. S., Davies, P. S., Chesman, C., Wynne, B. P., &Talamantes-Silva, J., 2015, Use of controlled heattreatment to predict mechanical properties in steelcomponents, Ironmaking & Steelmaking, 43, 351-357.

American Society of Mecnahical Engineers (ASME)., 2013a,ASME Boiler and Pressure Vessel Code, Section II -Part A, 915-925.

American Society of Mecnahical Engineers (ASME)., 2013b,ASME Boiler and Pressure Vessel Code, Section II -Part D, 771-772.

Caballero, F. G., Capdevila, C., Andrés, C. G. D. E., 2003, AnAttempt to Establish the Variables That Most DirectlyInfluence the Austenite Formation Process in Steels, 43,726-735.

Carlone, P., Palazzo, G. S., & Pasquino, R., 2010, Finite elementanalysis of the steel quenching process: Temperaturefield and solid–solid phase change, Computers &Mathematics with Applications, 59, 585-594.

Fernandes, F. M. B., Denis, S., Simon, A., 1985, Mathematicalmodel coupling phase transformation and temperatureevolution during quenching of steels, Materials Scienceand Technology, 1, 838-844.

Haverkamp, K. D., Forch, K., Piehl, K.-H., Witte, W., 1984,Effect of heat treatment and precipitation state ontoughness of heavy section Mn-Mo-Ni-steel for nuclearpower plants components, Nuclear Engineering andDesign, 81, 207-217.

Howson, M. P., Wynne, B. P., Davies, P. S., Al-Bermani, S. S.,Talamantes-Silva, J., 2016, A Comparison of Input DataUsed to Represent Phase Transformations during theQuenching of a Large Nuclear Forging, Key EngineeringMaterials, 716, 555-565.

Jhajj, K. S., Slezak, S. R., Daun, K. J., 2015, Inferring thespecific heat of an ultra high strength steel during theheating stage of hot forming die quenching, throughinverse analysis, Applied Thermal Engineering, 83, 98-107.

Kim, J. T., Kwon, H. K., Chang, H. S., & Park, Y. W., 1997a,Improvement of impact toughness of the SA 508 class 3steel for nuclear pressure vessel through steel-makingand heat-treatment practices, Nuclear Engineering andDesign, 174, 51-58.

Kim, J.-T., Kwon, H.-K., Kim, K.-C., Kim, J.-M., 1997b,Improved mechanical properties of the A 508 class 3steel for nuclear pressure vessel through steelmaking,Steel Forgings, 2, 18-32.

Krielaart, G. P., Brakman, C. M., Van Der Zwaag, S., 1996,Analysis of phase transformation in Fe-C alloys usingdifferential scanning calorimetry, Journal of MaterialsScience, 31, 1501-1508.

Liu, C. C., Xu, X. J., Liu, Z., 2003, A FEM modeling ofquenching and tempering and its application in industrialengineering, Finite Elements in Analysis and Design, 39,1053-1070.

Pan, J., Li, Y., Li, D., 2002, The application of computersimulation in the heat-treatment process of a large-scalebearing roller, Journal of Materials ProcessingTechnology, 122, 241-248.

Pola, A., Gelfi, M., La Vecchia, G. M., 2013, Simulation andvalidation of spray quenching applied to heavy forgings,Journal of Materials Processing Technology, 213, 2247-2253.

Pous-Romero, H., Bhadeshia, H. K. D. H., 2014, ContinuousCooling Transformations in Nuclear Pressure VesselSteels, Metallurgical and Materials Transactions A, 45,4897-4906.

Pous-Romero, H., Lonardelli, I., Cogswell, D., Bhadeshia, H. K.D. H., 2013, Austenite grain growth in a nuclearpressure vessel steel, Materials Science andEngineering: A, 567, 72-79.

Rammerstorfer, F. G., Fischer, D. F., Mitter, W., Bathe, K. J.,Snyder, M. D., 1981, On thermo-elastic-plastic analysisof heat-treatment processes including creep and phasechanges, Computers & Structures, 13, 771-779.

Song, D. L., Gu, J. F., Zhang, W. M., LIU, Y., Pan, J., 2004,Numerical simulation on temperature and microstructureduring quenching process of large-sized AISI P20 steeldie blocks, Trans. Mater. Heat Treatment, 25, 740-745.

Suzuki, K., Kurihara, I., Sasaki, T., Koyoma, Y., Tanaka, Y.,2001, Application of high strength MnMoNi steel topressure vessels for nuclear power plant, NuclearEngineering and Design, 206, 261-277.

Tewkesbury, H., Stapley, A. G. F., Fryer, P. J., 2000, Modellingtemperature distributions in cooling chocolate moulds,Chemical Engineering Science, 55, 3123–3132.

Woodard, P. R., Chandrasekar, S., Yang, H. T. Y., 1999,Analysis of temperature and microstructure in thequenching of steel cylinders, Metallurgical andMaterials Transactions B, 30, 815-822.