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Development and validation of a thermo-mechanical finite element model of the steel quenching process including solid–solid phase changes

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A computational thermo-metallographic and thermoelastoplastic model for the analysis of the quenching process is developed and validated. The diffusive transfor-mations are modeled according to the Johnson–Mehl–Avrami–Kolmogorov model and the Scheil’s additivity rule. Two different models are investigated for the non-diffusive transformation—the Koistinen–Marburger model and the Yu model. A large displacement formulation is assumed for the deformation analysis, modeling the plastic behavior of the material according to the Prandtl–Reuss model. Two different bilinear hardening models—the isotropic and the kinematic hardening model—are used and compared. The model allows to evaluate the transient stress and strain distributions during the quenching process, the final phases and hardness distributions, and to predict the residual stress and the final deformation of the processed part. A good agreement between computational results and reference data is found

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References

  1. A. N. Guz, “On foundations of the ultrasonic nondestructive method for determination of stresses in near-surface layers of solid bodies,” Int. Appl. Mech., 41, 944–955 (2005).

    Article  MathSciNet  ADS  Google Scholar 

  2. A. N. Guz, “On foundations of the nondestructive method of determination of three–axial stresses in solids,” Int. Appl. Mech., 37, 899–905 (2001).

    Article  MathSciNet  Google Scholar 

  3. A. N. Guz, “Elastic waves in bodies with initial (residual) stresses,” Int. Appl. Mech., 38, 23–59 (2002).

    Article  MathSciNet  Google Scholar 

  4. A. N. Guz and F. G. Makhort, “The physical fundamentals of the ultrasonic nondestructive stress analysis of solids,” Int. Appl. Mech., 36, 1119–1149 (2000).

    Article  Google Scholar 

  5. R. E. Green, Jr., “Noncontact acoustical techniques for nondestructive characterization of materials and structures,” Int. Appl. Mech., 38, 253–259 (2002).

    Article  Google Scholar 

  6. C. Cattani, J. J. Rushchitsky, and S. V. Sinchilo, “Comparative analysis of the profile evolutions o fan elastic harmonic wave caused by the second and third harmonics,” Int. Appl. Mech., 40, 183–189 (2004).

    Article  ADS  Google Scholar 

  7. J. J. Rushchitsky, C. Cattani, and S. V. Sinchilo, “Wavelet analysis of the evolution of a solitary wave in a composite material,” Int. Appl. Mech., 40, 311–318 (2004).

    Article  ADS  Google Scholar 

  8. C. Cattani, J. J. Rushchitsky, and S. V. Sinchilo, “Physical constants for one type of nonlinearly elastic fibrous microand nanocomposites with hard and soft nonlinearities,” Int. Appl. Mech., 41, 1368–1377 (2005).

    Article  ADS  Google Scholar 

  9. P. R. Woodard, S. Chandrasekar, and H. T. Y. Yang, “Analysis of temperature and microstructure in the quenching of steel cylinders,” Metallurg. Mater. Trans., B, 30B, 815–822 (1999).

    Article  ADS  Google Scholar 

  10. L. Huiping, Z. Guoqun, N. Shanting, and H. Chuanzhen, “FEM simulation of quenching process and experimental verification of simulation results,” Mater. Sci. Eng., A, 452–453, 705–714 (2007).

    Google Scholar 

  11. S. H. Kang and Y. T. Im, “Finite element investigation of multi–phase transformation within carburized carbon steel,” J. Mater. Process. Technol., 183, 241–248 (2007).

    Article  Google Scholar 

  12. S. H. Kang and Y. T. Im, “Three-dimensional thermo-elastic-plastic finite element modeling of quenching process of plain-carbon steel in couple with phase transformation,” Int. J. Mech. Sci., 49, 423–439 (2007).

    Article  Google Scholar 

  13. D. Hömberg, “A numerical simulation of the Jominy end-quench test,” Acta Mater., 44, 4375–4385 (1996).

    Article  Google Scholar 

  14. S. Hoissan, M. R. Daymond, C. E. Truman, and D. J. Smith, “Prediction and measurement of residual stresses in quenched stainless-steel spheres,” Mater. Sci. Eng., A, 373, 339–349 (2004).

    Article  Google Scholar 

  15. C. H. Gür and A. E. Tekkaya, “Numerical investigation of non-homogeneous plastic deformation in quenching process,” Mater. Sci. Eng., A, 319–321, 164–169 (2001).

    Google Scholar 

  16. C. Heming, H. Xieqing, and W. Honggang, “Calculation of the residual stress of a 45 steel cylinder with a non-linear surface heat-transfer coefficient including phase transformation during quenching,” J. Mater. Process. Technol., 89–90, 339–343 (1999).

    Article  Google Scholar 

  17. I. Tzitzelkov, H. P. Hougardy, and A. Rose, “Mathematische Beschreibung des Zeit-Temperatur-Umwandlungs-Schaubildes für Isotermische und Kontinuierliche Abkühlung,” Arch. Eisenhüttenwesen, 45, 525–532 (1974).

    Google Scholar 

  18. E. Scheil, “Anlaufzeit der Austenitumwandlung,” Arch. Eisenhüttenwesen, 12, 565–567 (1935).

    Google Scholar 

  19. M. Avrami, “Kinetics of phase change I,” J. Chem. Phys., 7, 1103–1112 (1939).

    Article  ADS  Google Scholar 

  20. M. Avrami, “Kinetics of phase change II,” J. Chem. Phys., 8, 212–224 (1940).

    Article  ADS  Google Scholar 

  21. M. Avrami, “Kinetics of phase change III,” J. Chem. Phys., 9, 177–184 (1941).

    Article  ADS  Google Scholar 

  22. J. W. Cahn, “Transformation kinetics during continuous cooling,” Acta Metallurg., 4, 572–575(1956).

    Article  Google Scholar 

  23. M. B. Kuban, R. Jayaraman, E. B. Hawbolt, and J. K. Brimacombe, “An assessment of the additivity principle in predicting continuous-cooling austenite-to-pearlite transformation kinetics using isothermal transformation data,” Metallurg. Mater. Trans., A, 17, 1493–1503 (1986).

    Article  ADS  Google Scholar 

  24. M. Umemoto, K. Horiuchi, and I. Tamura, “Prediction of hardenability effects from isothermal transformation kinetics,” J. Heat Treat., 1, 57–64 (1980).

    Article  Google Scholar 

  25. M. Umemoto, K. Horiuchi, and I. Tamura, “Transformation kinetics of bainite during isothermal holding and continuous cooling,” Trans. Iron and Steel Institute of Japan, 22, 854–861 (1982).

    Article  Google Scholar 

  26. M. Umemoto, K. Horiuchi, and I. Tamura, “Pearlite transformation during continuous cooling and its relation to isothermal transformation,” Trans. Iron and Steel Institute of Japan, 23, 690–695 (1983).

    Article  Google Scholar 

  27. M. Lusk and H. J. Jou, “On the rule of additivity in phase transformation kinetics,” Metallurg. Mater. Trans., A, 28, 287–291 (1997).

    Article  Google Scholar 

  28. Y. T. Zhua, T. C. Lowe, and R. J. Asaro, “Assessment of the theoretical basis of the Rule of Additivity for the nucleation incubation time during continuous cooling,” J. Appl. Phys., 82, 1129–1137 (1997).

    Article  ADS  Google Scholar 

  29. D. P. Koistinen and R. E. Marburger, “A general equation prescribing the extent of the austenite–martensite transformation in pure iron–carbon alloys and carbon steels,” Acta Metallurg., 7, 59–60 (1959).

    Article  Google Scholar 

  30. H. J. Yu and Berechnung von Abkühlungs, Umwandlungs-, Schweiss-, sowie Verformungseigenspannungen mit Hilfe der Methode der finiten Elemente, Ph.D. Thesis, Universität Karlsruhe, Karlsruhe (1977).

  31. V. N. Bastun and A. A. Kaminsky, “Applied problems in the mechanics of strain hardening of structural metallic materials,” Int. Appl. Mech., 41, 1092–1129 (2005).

    Article  ADS  Google Scholar 

  32. Atlas of Isothermal Transformation and Cooling Transformation Diagrams, American Society for Metals, Ohio (1977).

  33. P. Maynier, J. Dollet, and P. Bastien, Hardenability Concepts with Applications to Steels, AIME, New York, 518–544 (1978).

    Google Scholar 

  34. K. F. Wang, S. Chandrasekar, and H. T. Y. Yang, “Experimental and computational study of the quenching of carbon steel,” J. Manufact. Sci. Eng., 119, 257–265 (1997).

    Article  Google Scholar 

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Correspondence to P. Carlone.

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Published in Prikladnaya Mekhanika, Vol. 46, No. 8, pp. 123–144, August 2010

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Carlone, P., Palazzo, G.S. Development and validation of a thermo-mechanical finite element model of the steel quenching process including solid–solid phase changes. Int Appl Mech 46, 955–971 (2011). https://doi.org/10.1007/s10778-011-0386-9

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  • DOI: https://doi.org/10.1007/s10778-011-0386-9

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