Inverse material modeling and optimization of free-cutting steel with graphite inclusions

  • Mansur AkbariEmail author
  • Darko Smolenicki
  • Hans Roelofs
  • Konrad Wegener


Graphite inclusions in steel are easing chip breakage and act as in situ lubricants. Therefore, graphitized steels are claimed to perform excellent in machining processes. They are considered as environmentally friendly alternatives to widely used Pb-alloyed steels. However, the effectiveness of graphite inclusions in different machining processes is not well understood. With the support of computer simulation techniques, a deeper understanding about chip formation and the role of internal friction (or lubrication) can be obtained. To enter into numerical analysis of material flow and chip formation, the quality of the applied constitutive law is crucial for close-to-reality simulation. In the present work, a most accurate determination of the Johnson-Cook constitutive law of partially graphitized steel 50SiB8 (hardness 214 HB) is aimed for. Johnson-Cook parameters are identified from dynamical compression tests, performed at strain rates up to 20s−1 and temperatures up to 800 °C. The material parameters are derived from two different numerical methods. The first standard method is based on minimizing the sum of squares of the differences between calculation and measurement. The parameters identified from this method are used as initial values for the second method, an inverse material modeling. The second method is based on a multi-case polynomial metamodel optimization in combination with finite element techniques. By applying inverse material modeling, the maximum discrepancy between measurement and calculation is reduced from 12% (regression with standard method) to 1%. A reliable parameter set for the Johnson-Cook model for graphitic steel 50SiB5 as input for future modeling of the chip formation is now available.


Constitutive material law Graphitic steel Johnson-cook parameters Flow curves Material parameters identification 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


Funding information

This study received financial support from the Swiss National Science Foundation under the number 200021-117847 and Swiss Commission for Technology and Innovation (KTI) in the frame of project KTI 13983.2 PFIW-IW. We also acknowledge the support from Dr. Bernd Hochholdinger, Dr. Bekim Berisha, and Dr. Ehsan Hosseini.


  1. 1.
    Essel I (2006) Machinability enhancement of non-leaded free cutting steels. RWTH, AachenGoogle Scholar
  2. 2.
    Luo X (2007) Study on infrastructure materials using neutron radiography and diffraction. University of Tennessee, KnoxvilleGoogle Scholar
  3. 3.
    Iwamoto TMT (2004) Bar and wire steels for gears and valves of automobiles eco-friendly free cutting steel without lead addition. JFE TECHNICAL REPORT no 4 (Nov 2004).
  4. 4.
    Luiz NE, Machado ÁR (2008) Development trends and review of free-machining steels. Proc Inst Mech Eng Pt B: J Eng Manuf 222(2):347–360. CrossRefGoogle Scholar
  5. 5.
    DIN German Institute for Standardization (1998) DIN EN 10087, free-cutting steels - technical delivery conditions for semi-finished products, Hot-rolled bars and rodsGoogle Scholar
  6. 6.
    Amtsblatt der Europäischen Union (2011) Richtlinie 2011/37/EU Der Kommission, 30.3.2011. L.85Google Scholar
  7. 7.
    Brown JR (1967) Sulphur potentials in Iron and in iron-manganese alloys. IRON STEEL INST J 205:154–157Google Scholar
  8. 8.
    Wang Y-N, Yang J, Bao Y-P (2014) Effects of non-metallic inclusions on machinability of free-cutting steels investigated by nano-indentation measurements. MMTA 46(1):281–292. CrossRefGoogle Scholar
  9. 9.
    Johnson GR, Cook WH (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high strain rates and high temperatures. In: The 7th International Symposium on Ballistics, The Hague, The Netherlands, pp 541–547Google Scholar
  10. 10.
    Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. EnFM 21(1):31–48. Google 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(3–4):462–470. CrossRefGoogle Scholar
  12. 12.
    Bosetti P, Maximiliano Giorgio Bort C, Bruschi S (2013) Identification of Johnson–Cook and Tresca’s parameters for numerical modeling of AISI-304 machining processes. J MANUF SCI E-T ASME 135(5):051021–051021. CrossRefGoogle Scholar
  13. 13.
    Hochholdinger B, Grass H, Lipp A (2009) Hora P Determination of flow curves by stack compression tests and inverse analysis for the simulation of hot forming. In: 7th European LS-DYNA conferenceGoogle Scholar
  14. 14.
    Özel T, Altan T (2000) Determination of workpiece flow stress and friction at the chip–tool contact for high-speed cutting. Int J Mach Tools Manuf 40(1):133–152. CrossRefGoogle Scholar
  15. 15.
    Forni D, Chiaia B, Cadoni E (2016) High strain rate response of S355 at high temperatures. Mater Des 94:467–478. CrossRefGoogle Scholar
  16. 16.
    Roth CC, Mohr D (2014) Effect of strain rate on ductile fracture initiation in advanced high strength steel sheets: experiments and modeling. IJP 56:19–44. Google Scholar
  17. 17.
    Kleemola HJ, Nieminen MA (1974) On the strain-hardening parameters of metals. Metall Trans 5(8):1863–1866. CrossRefGoogle Scholar
  18. 18.
    Hochholdinger B (2012) Simulation des Presshärteprozesses und Vorhersage der mechanischen Bauteileigenschaften nach dem Härten. ETH, ZürichGoogle Scholar
  19. 19.
    Hochholdinger B, Hora P, Grass H, Lipp A (2011) Simulation of the Press Hardening Process and Prediction of the Final Mechanical Material Properties. AIP Conf Proc 1383(1):618–625. CrossRefGoogle Scholar
  20. 20.
    Denkena B, Grove T, Dittrich MA, Niederwestberg D, Lahres M (2015) Inverse determination of constitutive equations and cutting force modelling for complex tools using Oxley’s predictive machining theory. Procedia CIRP 31:405–410. CrossRefGoogle Scholar
  21. 21.
    Altintas Y (2000) Manufacturing automation, vol 286 S. Cambridge University Press, CambridgeGoogle Scholar
  22. 22.
    Arrazola PJ, Ugarte D, Domínguez X (2008) A new approach for the friction identification during machining through the use of finite element modeling. Int J Mach Tools Manuf 48(2):173–183. CrossRefGoogle Scholar
  23. 23.
    Katayamaa S (1996) MT (1996) machinability of medium carbon graphitic steel. J Mater Process Technol 62:358–362CrossRefGoogle Scholar
  24. 24.
    Hosseini E, Holdsworth SR, Kuehn I, Mazza E (2015) Modelling heat-to-heat variability in high temperature cyclic deformation behaviour. Mater High Temp 32(3):347–354. CrossRefGoogle Scholar
  25. 25.
    Waltz RA, Morales JL, Nocedal J, Orban D (2006) An interior algorithm for nonlinear optimization that combines line search and trust region steps. Math Program 107(3):391–408. MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Byrd RH, Gilbert JC, Nocedal J (2000) A trust region method based on interior point techniques for nonlinear programming. Math Program 89(1):149–185. MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Byrd RH, Hribar ME, Nocedal J (1999) An interior point algorithm for large-scale nonlinear programming. SIAM J Optim 9(4):877–900. MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Forsgren A, Gill PE, Wright MH (2002) Interior methods for nonlinear optimization. SIAMR 44(4):525–597. MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    The MathWorks Inc (2015) Matlab documentation. In: Constrained nonlinear optimization algorithmsGoogle Scholar
  30. 30.
    Stander N, Craig KJ (2002) On the robustness of a simple domain reduction scheme for simulation-based optimization. EngCo 19(4):431–450.
  31. 31.
    Livermore Software Technology Corporation (2014) LS-OPT manual. Version 5.1. CAGoogle Scholar
  32. 32.
    International Conference on Monte C, Quasi-Monte Carlo Methods in Scientific C (2016) Monte Carlo and Quasi-Monte Carlo Methods : MCQMC, Leuven, Belgium, April 2014, vol volume 163. Springer proceedings in mathematics & Statistics. Springer International Publishing, SwitzerlandGoogle Scholar
  33. 33.
    Nehme GN (2017) Tribological behavior and wear prediction of molybdenum disulfide grease lubricated rolling bearings under variable loads and speeds via experimental and statistical approach. Wear 376–377(Part A):876–884. CrossRefGoogle Scholar
  34. 34.
    Li YP, Onodera E, Chiba A (2010) Friction coefficient in hot compression of cylindrical sample. Mater Trans 51(7):1210–1215. CrossRefGoogle Scholar
  35. 35.
    ALT H, GODAU M (1995) Computing the Fréchet distance between two polygonal curves. Int J Comput Geom Appl 05(01n02):75–91. CrossRefzbMATHGoogle Scholar
  36. 36.
    I. M. SOBOL (1993) Sensitivity estimates for nonlinear mathematical models. MMCE (mathematical modeling and computer experiments), John Wiley and Sons, Inc Hoboken 1 (4):407–414Google Scholar
  37. 37.
    Chan K, Saltelli A, Tarantola S (1997) Sensitivity analysis of model output: variance-based methods make the difference. In: Proceedings of the 29th conference on Winter simulation. IEEE Computer Society, pp 261–268Google Scholar
  38. 38.
    Saltelli A, Sobol' IM (1995) Sensitivity analysis for nonlinear mathematical models: numerical experience. Matematicheskoe Modelirovanie 7(11):16–28MathSciNetzbMATHGoogle Scholar
  39. 39.
    Sivanandam SN, Deepa SN (2007) Introduction to Genetic Algorithms. Springer, Berlin, HeidelbergzbMATHGoogle Scholar
  40. 40.
    Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. In: Addison Wesley series in artificial intelligence. Reading. Addison-Wesley, Massachusetts [etc.]Google Scholar
  41. 41.
    Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21(6):1087–1092. CrossRefGoogle Scholar
  42. 42.
    Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. JSTOR 220(4598):671–680 MathSciNetzbMATHGoogle Scholar
  43. 43.
    Jaspers S, Dautzenberg J (2002) Material behaviour in conditions similar to metal cutting: flow stress in the primary shear zone. J Mater Process Technol 122(2):322–330. CrossRefGoogle Scholar
  44. 44.
    Warlimont H, Spittel M, Spittel T (2009) Metal forming data, vol subvol. C. Numerical data and functional relationships in science and technology / Landolt Börnstein. New series. Group 8, advanced materials and technologies. Vol. 2, materials. Springer, BerlinGoogle Scholar
  45. 45.
    Weber M, Hochrainer T, Gumbsch P, Autenrieth H, Delonnoy L, Schulze V, Löhe D, Kotschenreuther J, Fleischer J (2007) Investigation of size-effects in machining with geometrically defined cutting edges. Mach Sci Technol 11(4):447–473. CrossRefGoogle Scholar
  46. 46.
    N.N (2016) Scientific forming technologies corporation. Documentation of Deform 3D Version 11:1Google Scholar
  47. 47.
    DEFORM (2016) Manual v.11 - Inter-object Data Definition 6–15Google Scholar
  48. 48.
    Smolenicki D (2017) Chip formation analysis of innovative graphitic steel in drilling processes. ETH, ZürichGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Institute of Machine Tools and Manufacturing, ETH ZurichZurichSwitzerland
  2. 2.R&D, Swiss Steel AGEmmenbrückeSwitzerland

Personalised recommendations