Inverse determination of Johnson–Cook model constants of ultra-fine-grained titanium based on chip formation model and iterative gradient search

  • Jinqiang NingEmail author
  • Vinh Nguyen
  • Yong Huang
  • Karl T. Hartwig
  • Steven Y. LiangEmail author


This paper presents an original method to inversely identify the Johnson–Cook model constants (J-C constants) of ultra-fine-grained titanium (UFG Ti) based on a chip formation model and an iterative gradient search method using Kalman filter algorithm. UFG Ti is increasingly finding usefulness in lightweight engineering applications and medical implant filed because of its sufficient mechanical strength, high manufacturability, and high biocompatibility. Johnson–Cook model is one of the constitutive models widely used in analytical modeling of machining force, temperature, and residual stress because it is effective, simple, and easy to use. Currently, the J-C constants of UFG Ti are unavailable and yet an effective identification methodology based upon machining data is not readily available. In this work, multiple cutting tests were conducted under different cutting conditions, in which machining forces were experimentally measured using a piezoelectric dynamometer. The machining forces were also predicted using the chip formation model with inputs of cutting conditions, workpiece material properties, and a set of given model constants. An iterative gradient search method was enforced to find the J-C constants when the difference between predicted forces and experimental forces reached an acceptable low value. To validate the identified J-C constants, machining forces were predicted using the identified J-C constants under different cutting conditions and then compared to the corresponding experimental forces. Close agreements were observed between predicted forces and experimental forces. Considering the simple orthogonal cutting tests, reliable and easily measurable machining forces, and efficient iterative gradient search method, the proposed method has less experimental complexity and high computational efficiency.


Ultra-fine-grained titanium Johnson–Cook model constants Chip formation model Iterative gradient search 


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Funding information

The study received financial support from the US National Science Foundation.


  1. 1.
    Brunette DM, Tengvall P, Textor M, Thomsen P (2001) Titanium in medicine: material science, surface science, engineering, biological responses and medical applications. Springer Verlag Berlin Heidelberg, New YorkCrossRefGoogle Scholar
  2. 2.
    Stolyarov VV, Zhu YT, Alexandrov IV, Lowe TC, Valiev RZ (2001) Influence of ECAP routes on the microstructure and properties of pure Ti. Mater Sci Eng A 299(1–2):59–67CrossRefGoogle Scholar
  3. 3.
    Valiev RZ, Langdon TG (2006) Principles of equal-channel angular pressing as a processing tool for grain refinement. Prog Mater Sci 51(7):881–981CrossRefGoogle Scholar
  4. 4.
    Majzoobi GH, Freshteh-Saniee F, Khosroshahi SFZ, Mohammadloo HB (2010) Determination of materials parameters under dynamic loading. Part I: experiments and simulations. Comput Mater Sci 49(2):192–200CrossRefGoogle Scholar
  5. 5.
    Dorogoy A, Rittel D (2009) Determination of the Johnson–Cook material parameters using the SCS specimen. Exp Mech 49(6):881–885CrossRefGoogle Scholar
  6. 6.
    Khan AS, Suh YS, Kazmi R (2004) Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys. Int J Plast 20(12):2233–2248CrossRefGoogle Scholar
  7. 7.
    Milani AS, Dabboussi W, Nemes JA, Abeyaratne RC (2009) An improved multi-objective identification of Johnson–Cook material parameters. Int J Impact Eng 36(2):294–302CrossRefGoogle Scholar
  8. 8.
    Özel T, Karpat Y (2007) Identification of constitutive material model parameters for high-strain rate metal cutting conditions using evolutionary computational algorithms. Mater Manuf Process 22(5):659–667CrossRefGoogle Scholar
  9. 9.
    Kolsky H (1949) An investigation of the mechanical properties of materials at very high rates of loading. Proc Phys Soc. Section B 62(11):676–700CrossRefGoogle Scholar
  10. 10.
    Shrot A, Bäker M (2012) Determination of Johnson–Cook parameters from machining simulations. Comput Mater Sci 52(1):298–304CrossRefGoogle Scholar
  11. 11.
    Umbrello D, M’saoubi R, Outeiro JC (2007) The influence of Johnson–Cook material constants on finite element simulation of machining of AISI 316L steel. Int J Mach Tools Manuf 47(3):462–470CrossRefGoogle Scholar
  12. 12.
    Agmell M, Ahadi A, Ståhl JE (2014) Identification of plasticity constants from orthogonal cutting and inverse analysis. Mech Mater 77:43–51CrossRefGoogle Scholar
  13. 13.
    Oxley PL, Welsh MJ (1963) Calculating the shear angle in orthogonal metal cutting from fundamental stress-strain-strain rate properties of the work material. In: Proceedings of the fourth international conference on machine tool design and research conference, Manchester, England, pp 73–86Google Scholar
  14. 14.
    Naik P, Naik A (2015) Determination of flow stress constants by Oxley‘s theory. Int J Latest Technol Eng, Manage Appl Sci 4(10):110–116Google Scholar
  15. 15.
    Özel T, Zeren E (2006) A methodology to determine work material flow stress and tool-chip interfacial friction properties by using analysis of machining. J Manuf Sci Eng 128(1):119–129CrossRefGoogle Scholar
  16. 16.
    Tounsi N, Vincenti J, Otho A, Elbestawi MA (2002) From the basic mechanics of orthogonal metal cutting toward the identification of the constitutive equation. Int J Mach Tools Manuf 42(12):1373–1383CrossRefGoogle Scholar
  17. 17.
    Ning J, Liang SY (2018) Model-driven determination of Johnson-Cook material constants using temperature and force measurements. Int J Adv Manuf Technol 97(1–4):1053–1060CrossRefGoogle Scholar
  18. 18.
    Oxley PLB (1989) The mechanics of machining: an analytical approach to assessing machinability. Ellis Horwood Ltd., EnglandGoogle Scholar
  19. 19.
    Adibi-Sedeh AH, Madhavan V, Bahr B (2003) Extension of Oxley’s analysis of machining to use different material models. J Manuf Sci Eng 125(4):656–666CrossRefGoogle Scholar
  20. 20.
    Industrial Administration and Engineering Production Group Applied Mechanics Group, Boothroyd G (1963) Temperatures in orthogonal metal cutting. Proc Inst Mech Eng 177(1):789–810Google Scholar
  21. 21.
    Kalman RE, Bucy RS (1961) New results in linear filtering and prediction theory. J Basic Eng 83(1):95–108MathSciNetCrossRefGoogle Scholar

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© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.George W. Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.Department of Materials Science & EngineeringTexas A&M UniversityCollege StationUSA

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