Skip to main content
SpringerLink
Log in

A modified Zerilli–Armstrong model as the asymmetric visco-plastic part of a multi-mechanism model for cutting simulations

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

The Zerilli–Armstrong (ZA) model is modified to describe asymmetric visco-plastic material properties as part of a multi-mechanism model (MMM) for cutting simulations. This is done as an improvement of an existing modified Johnson–Cook (JC) model. Based on the modification of the ZA model by Samantatray et al.  for elevated-temperature behaviour, we replace the hardening stress by the sum of nonlinear and linear isotropic hardening stresses using internal variables, thus consider history effects. Furthermore, weighting functions related to stress modes are applied taking asymmetric effect of strength into account. For calibrating the modified ZA model, experimental data in a wide range of strain rates and temperatures as well as under different loading types are used. Moreover, a systematic comparative study on the modified JC and ZA model is made regarding their dependence on strain, strain rate, and temperature. Finally, the modified ZA model is validated by comparing temperatures and cutting forces of cutting simulations with those of hard turning experiments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. Abed, F.H., Voyiadjis, G.Z.: A consistent modified Zerilli–Armstrong flow stress model for BCC and FCC metals for elevated temperatures. Acta Mech. 175, 1–18 (2005)

    Article  MATH  Google Scholar 

  2. Ammar, K., Appolaire, B., Cailletaud, G., Feyel, F., Forest, S.: Finite element formulation of a phase field model based on the concept of generalized stresses. Comput. Mater. Sci. 45, 800–805 (2009)

    Article  Google Scholar 

  3. ASM Handbook: Mechanical Testing and Evaluation, Materials Part Ohio, Vol. 8 (2002)

  4. Behrens, A., Westhoff, B., Kalisch, K.: Application of the finite element method at the chip forming process under high speed cutting conditions. In: Tönshoff, H.K., Hollmann, F. (Eds.) Hochgeschwindigkeitsspanen, pp. 112–134. Wiley (2005)

  5. Carroll, J.T., Strenkowski, J.S.: Finite element models of orthogonal cutting with application to single point diamond turning. Int. J. Mech. Sci. 30, 899–920 (1988)

    Article  Google Scholar 

  6. Chaboche, J.L.: A review of some plasticity and viscoplasticity constitutive theories. Int. J. Plast. 24, 1642–1693 (2008)

    Article  MATH  Google Scholar 

  7. Chen, C., Yin, H., Humail, I.S., Wang, Y., Qu, X.: A comparative study of a back propagation artificial neural network and a Zerilli–Armstrong model for pure molybdenum during hot deformation. Int. J. Refract. Met. Hard Mater. 25(5–6), 411–416 (2007)

    Article  Google Scholar 

  8. Cheng, C., Mahnken, R.: A multi-mechanism model for cutting simulations based on the concept of generalized stresses. Comput. Mater. Sci. B 100, 144–158 (2015)

    Article  Google Scholar 

  9. Cheng, C., Mahnken, R.: Extension of a multi-mechanism model: hardness-based flow and transformation induced plasticity for austenitization. Int. J. Solids Struct. 102–103, 127–141 (2016)

    Article  Google Scholar 

  10. Cheng, C., Mahnken, R.: A multi-mechanism model for cutting simulation: a Ginzburg–Landau type phase gradient and numerical implementations. Int. J. Solids Struct. 160, 1–17 (2018)

    Article  Google Scholar 

  11. Chiou, S.T., Cheng, W.C., Lee, W.S.: Strain rate effects on the mechanical properties of a Fe–Mn–Al alloy under dynamic impact deformations. Mater. Sci. Eng. A 392, 156–162 (2005)

    Article  Google Scholar 

  12. Dudzinski, D., Molinari, A.: A modelling of cutting for viscoplastic materials. Int. J. Mech. Sci. 39(4), 369–389 (1997)

    Article  MATH  Google Scholar 

  13. Ehlers, W.: A single-surface yield function for geomaterials. Arch. Appl. Mech. 65, 246–259 (1995)

    Article  MATH  Google Scholar 

  14. Farrokh, B., Khan, A.S.: Grain size, strain rate, and temperature dependence of flow stress in ultra-fine grained and nanocrystalline Cu and Al: synthesis, experiment, and constitutive modeling. Int. J. P. 25, 715–732 (2009)

    Article  MATH  Google Scholar 

  15. Forest, S., Ammar, K., Appolaire, B.: Micromorphic vs phase-field approaches for gradient viscoplasticity and phase transformations. Lect. Notes Appl. Comput. Mech. 59(2011), 69–88 (2011)

    Article  MathSciNet  Google Scholar 

  16. Haddag, B., Atlati, S., Nouari, M., Moufiki, A.: Dry machining aeronautical aluminum alloy AA2024-T351: analysis of cutting forces, chip segmentation and built-up edge formation. Alumin. Alloys 6(9), 197 (2016)

    Google Scholar 

  17. Hallberg, H., Hakansson, P., Ristimaa, M.: A constitutive model for the formation of martensite in austenitic steels under large strain plasticity. Int. J. Plast. 23, 1213–1239 (2007)

    Article  MATH  Google Scholar 

  18. Haupt, P.: Continuum Mechanics and Theory of Materials. Springer, Berlin (2002)

    Book  MATH  Google Scholar 

  19. He, A., Xie, G., Zhang, H., Wang, X.: A modified Zerilli–Armstrong constitutive model to predict hot deformation behavior of 20CrMo alloy steel. Mater. Des. 56, 122–127 (2014)

    Article  Google Scholar 

  20. Hortig, C.: Local and Non-local Thermomechanical Modeling and Finite-element Simulation of High-speed Cutting, Dissertation, University of Dortmund (2010)

  21. Ivanov, I.M.: Simulationsmodell als Basis zur Ableitung von Zerspanstrategien zur Reduzierung von thermischen Bearbeitungseinflssen beim Hartdrehen, Dissertation, TU Berlin, Germany (2017)

  22. Jaspers, S.P.F.C., Dautzenberg, J.H.: Material behaviour in conditions similar to metal cutting: flow stress in the primary shear zone. Int. J. Mater. Process. Technol. 122, 322–330 (2002)

    Article  Google Scholar 

  23. Johnson, G.R.; Cook, W.H.: A constitutive model and data for metals subjected to large strain rates and high temperatures. In: Proceedings of the 7th International Symposium on Ballistics. The Hague, pp. 541–547 (1983)

  24. Khan, A.S., Zhang, H., Takacs, L.: Mechanical response and modeling of fully compacted nanocrystalline iron and copper. Int. J. Plast. 16, 1459–1476 (2000)

    Article  MATH  Google Scholar 

  25. Leblond, J.B.: Mathematical modelling of transformation plasticity in steels II: coupling with strain hardening phenomena. Int. J. Plast. 5, 537–591 (1989)

    Article  Google Scholar 

  26. Levitas, A.V., Idesman, A.V., Olson, G.B.: Continuum modeling of strain-induced martensitic phase transformation at shear-band intersections. Acta Mater. 47(1), 219–233 (1998)

    Article  Google Scholar 

  27. Li, H.Y., Khan, H., Wang, X.F., Wei, D.D., Hu, J.D., Li, Y.H.: A comparative study on modified Zerilli–Armstrong, Arrhenius-type and artificial neural network models to predict high-temperature deformation behavior in T24 steel. Mater. Sci. Eng. A 536, 216–222 (2012)

    Article  Google Scholar 

  28. Liang, R., Khan, A.S.: A critical review of experimental results and constitutive models for BCC and FCC metals over a wide range of strain rates and temperatures. Int. J. Plast. 15, 963–980 (1999)

    Article  MATH  Google Scholar 

  29. Lin, Y., Chen, X.: A combined Johnson–Cook and Zerilli–Armstrong model for hot compressed typical high-strength alloy steel. Comput. Mater. Sci. 49(3), 628–633 (2010)

    Article  Google Scholar 

  30. Mahnken, R.: Theoretical, numerical and identification aspects of a new model class for ductile damage. Int. J. Plast. 18, 801–831 (2002)

    Article  MATH  Google Scholar 

  31. Mahnken, R.: Creep simulation of asymmetric effects by use of stress mode dependent weighting functions. Int. J. Solids Struct. 40, 6189–6209 (2003)

    Article  MATH  Google Scholar 

  32. Mahnken, R.: Void growth in finite deformation elasto-plasticity due to hydrostatic stress states. Comput. Methods Appl. Mech. Eng. 194, 3689–3709 (2005)

    Article  MATH  Google Scholar 

  33. Mahnken, R.: Identification of material parameters for constitutive equations. In: Encyclopedia of Computational Mechanics Second Edition. Wiley (2017)

  34. Mahnken, R., Schneidt, A., Antretter, T.: Macro modelling and homogenization for transformation induced plasticity of a low-alloy steel. Int. J. Plast. 25, 183–204 (2009)

    Article  MATH  Google Scholar 

  35. Mahnken, R., Wolff, M., Schneidt, A., Böhm, M.: Multi-phase transformations at large strains—thermodynamic framework and simulation. Int. J. Plast. 39, 1–26 (2012)

    Article  Google Scholar 

  36. Mahnken, R., Wolff, M., Cheng, C.: A multi-mechanism model for cutting simulations combining visco-plastic asymmetry and phase transformation. Int. J. Solids Struct. 50, 3045–3066 (2013)

    Article  Google Scholar 

  37. Marusich, T., Ortiz, M.: Modelling and simulation of high-speed machining. Int. J. Numer. Methods Eng. 38, 3675–3694 (1995)

    Article  MATH  Google Scholar 

  38. Oxley, P.L.B.: Mechanics of Machining, an Analytical Approach to Assessing Machinability. Ellis Horwood Ltd., Chichester (1989)

    Google Scholar 

  39. Ozel, T., Zeren, E.: Determination of work material flow stress and friction for FEA of machining using orthogonal cutting tests. J. Mater. Process. Technol. 153–154, 1019–1025 (2004)

    Article  Google Scholar 

  40. Preston, D.L., Tonks, D.L., Wallace, D.C.: Model of plastic deformation for extreme loading conditions. J. Appl. Phys. 93, 211–220 (2003)

    Article  Google Scholar 

  41. Samantaray, D., Mandal, S., Borah, U., Bhaduri, A.K., Sivaprasad, P.V.: A thermo-viscoplastic constitutive model to predict elevated-temperature flow behaviour in a titanium-modified austenitic stainless steel. Mater. Sci. Eng. A 526, 1–6 (2009)

    Article  Google Scholar 

  42. Samantaray, D., Mandal, S., Bhaduri, A.K.: A comparative study on Johnson–Cook, modified Zerilli–Armstrong and Arrhenius-type constitutive models to predict elevated temperature flow behaviour in modified 9Cr–1Mo steel. Comput. Mater. Sci. 47(2), 568–576 (2009)

    Article  Google Scholar 

  43. Sartkulvanich, P., Koppka, F., Altan, T.: Determination of flow stress for metal cut-ting simulation A progress report. J. Mater. Process. Technol. 146, 61–71 (2004)

    Article  Google Scholar 

  44. Shi, B., Attia, H., Tounsi, N.: Identification of material constitutive laws for machining part I: an analytical model describing the stress, strain, strain rate, and temperature fields in the primary shear zone in orthogonal metal cutting. J. Manuf. Sci. Eng. 132, 051008-1 (2010)

  45. Simo, J.C., Hughes, T.J.R.: Computational Inelasticity, Interdisciplinary Applied Mathematics, vol. 7. Mechanics and Materials. Springer (1998)

  46. Stouffer, D.C., Dame, L.T.: Inelastic Deformation of Metals. Wiley, New York (1996)

    Google Scholar 

  47. Spencer, A.J.M.: Theory of invariants. In: Eringen, A.C. (ed.) Continuum Physics, vol. 1. Academic press, New York (1971)

    Google Scholar 

  48. Spitzig, W.A., Sober, R.J., Richmond, O.: Pressure dependence of yielding and associated volume expansion in tempered martensite. Acta Metall. 23, 885–893 (1975)

    Article  Google Scholar 

  49. Umbrello, D., Saoubi, R.M., Outeiro, J.C.: The influence of Johnson–Cook material constants on finite element simulation of machining of AISI 316L steel. Int. J. Mach. Tools Manuf. 47, 462–470 (2007)

    Article  Google Scholar 

  50. Voyiadjis, G.Z., Abed, F.H.: Microstructural based models for BCC and FCC metals with temperature and strain rate dependency. Mech. Mater. Mech. Mater. 37(2–3), 355–378 (2005)

    Article  Google Scholar 

  51. Voyiadjis, G.Z., Almasri, A.H.: A physically based constitutive model for FCC metals with applications to dynamic hardness. Mech. Mater. 40, 549–563 (2008)

    Article  Google Scholar 

  52. Zerilli, F.J., Armstrong, R.W.: Dislocation-mechanics-based constitutive relations for material dynamics calculations. J. Appl. Phys. 61(5), 1816 (1987)

    Article  Google Scholar 

  53. Zerilli, F.J.: Dislocation-mechanics-based constitutive equations. Metall. Mater. Trans. A 35, 2547–2555 (2004)

    Article  Google Scholar 

  54. Zhan, H.Y., Wang, G., Kent, D., Dargusch, M.: Constitutive modelling of the flow behaviour of a titanium alloy at high strain rates and elevated temperatures using the Johnson–Cook and modified Zerilli–Armstrong models. Mater. Sci. Eng. A 612, 71–79 (2014)

    Article  Google Scholar 

Download references

Acknowledgements

This paper is an extension of the research work based on investigations of priority point program 1480 (SPP 1480), which is kindly supported by the Deutsche Forschungsgemeinschaft (DFG).

Author information

Authors and Affiliations

  1. College of Mechanical Engineering, Yangzhou University, Yangzhou, 225127, People’s Republic of China

    C. Cheng

  2. Chair of Engineering Mechanics, University of Paderborn, Warburger Str. 100, 33098, Paderborn, Germany

    R. Mahnken

Authors
  1. C. Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Mahnken
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Cheng.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A: Mechanical tests of steel AISI 52100

Appendix A: Mechanical tests of steel AISI 52100

In order to identify the asymmetric visco-plasticity of the studied material steel AISI 52100, we use the existing mechanical data as given in [9], where the thermal-mechanical tests are investigated in a big range of strain rates and temperatures as listed in Table 4.

The experimental results are shown in Fig. 21; the inelastic asymmetry, where the inelastic behaviours are different under tension, compression, and torsion tests, is proved. Otherwise, the material shows significant dependence on temperature and strain rate.

Table 4 Experiments for AISI 52100 at different temperatures and strain rates under tension, compression, and shear
Full size table
Fig. 21
figure 21

Mechanical tests for steel AISI 52100

Full size image

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheng, C., Mahnken, R. A modified Zerilli–Armstrong model as the asymmetric visco-plastic part of a multi-mechanism model for cutting simulations. Arch Appl Mech 91, 3869–3888 (2021). https://doi.org/10.1007/s00419-021-01982-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-021-01982-6

Keywords

Search

Navigation