The plastic flow stability of chip materials in metal cutting process

  • Wei MaEmail author
  • Fei Shuang


This study investigates the chip formation mechanism and relevant plastic flow stability in the orthogonal cutting process (OCP) through high-speed cutting experiments and theoretical modelling for four types of metals. The chip morphology transitions from continuous to serrated and to continuous again are observed with critical speeds depending on the work material properties and cutting conditions. To exam the influence of two-dimensional (2D) effects on plastic flow stability, a complete theoretical framework under plane strain state is established to model the 2D orthogonal cutting process. Based on the new framework, a set of governing equations with three dimensionless parameters are used to analytically derive a universal instability criterion, the approximate velocity fields, and stress fields in the expanding chip formation zone (CFZ). It is shown that the plastic flow of continuous chip may become unstable once the cutting speed reaches a critical value. In contrast to the shear localization deformation in the serrated chip, we found a new instability mechanism occurring in the continuous chip which undergoes the uniform but severe shear deformation due to the plane strain loadings. A new dimensionless parameter therefore is proposed to describe the plastic instability in continuous chip and the shear banding instability in serrated chip. The difference of two instability modes is further investigated in terms of dissipation mechanism of cutting energy, and the plastic instability of continuous chip is shown as the best instability mode regarding tool vibration and surface machining quality. These findings provide practical insights into improving modern cutting technology by controlling the plastic flow instability.


Metal cutting Plastic flow stability Instability criterion Dimensional analysis Transition of chip morphology Cutting energy 


Funding information

This work was supported by the National Nature Science Foundation of China (Grant numbers: 11572337, 11772346, and 51575029).


  1. 1.
    Taylor FW (1906) On the art of cutting metals. Trans Am Soc Mech Eng XXVIII:31–350Google Scholar
  2. 2.
    Finnie I (1956) Review of the metal-cutting analysis of the past hundred years. Mech Eng 78:715–721Google Scholar
  3. 3.
    Shaw MC (1984) Metal cutting principles. Clarendon Press, OxfordGoogle Scholar
  4. 4.
    Arrazola PJ, Özel T, Umbrello D et al (2013) Recent advances in modelling of metal machining processes. CIRP Ann 62:695–718. CrossRefGoogle Scholar
  5. 5.
    Xu J, El Mansori M, Chen M, Ren F (2019) Orthogonal cutting mechanisms of CFRP/Ti6Al4V stacks. Int J Adv Manuf Technol. CrossRefGoogle Scholar
  6. 6.
    Merchant ME (1945) Mechanics of the metal cutting process. I. Orthogonal cutting and a type 2 chip. J Appl Phys 16:267–275. CrossRefGoogle Scholar
  7. 7.
    Burns TJ, Davies MA (1997) Nonlinear Dynamics model for chip segmentation in machining. Phys Rev Lett 79:447–450. CrossRefGoogle Scholar
  8. 8.
    Burns TJ, Davies MA (2002) On repeated adiabatic shear band formation during high-speed machining. Int J Plast 18:487–506. CrossRefzbMATHGoogle Scholar
  9. 9.
    Molinari A, Soldani X, Miguélez MH (2013) Adiabatic shear banding and scaling laws in chip formation with application to cutting of Ti–6Al–4V. J Mech Phys Solids 61:2331–2359. CrossRefGoogle Scholar
  10. 10.
    Li Z, Guo H, Li L et al (2019) Study on surface quality and tool life in ultrasonic vibration countersinking of titanium alloys (Ti6Al4V). Int J Adv Manuf Technol:1119–1137. CrossRefGoogle Scholar
  11. 11.
    Schneider F, Bischof R, Kirsch B et al (2016) Investigation of chip formation and surface integrity when micro-cutting cp-titanium with ultra-fine grain cemented carbide. Proc CIRP 45:115–118. CrossRefGoogle Scholar
  12. 12.
    Atkins AG (2003) Modelling metal cutting using modern ductile fracture mechanics: quantitative explanations for some longstanding problems. Int J Mech Sci 45:373–396. CrossRefGoogle Scholar
  13. 13.
    Liyao G, Minjie W, Chunzheng D (2013) On adiabatic shear localized fracture during serrated chip evolution in high speed machining of hardened AISI 1045 steel. Int J Mech Sci 75:288–298. CrossRefGoogle Scholar
  14. 14.
    Luo XK, Cheng K, Luo XC, Liu XW (2005) A simulated investigation on the machining instability and dynamic surface generation. Int J Adv Manuf Technol 26:718–725. CrossRefGoogle Scholar
  15. 15.
    Mahnama M, Movahhedy MR (2010) Prediction of machining chatter based on FEM simulation of chip formation under dynamic conditions. Int J Mach Tools Manuf 50:611–620. CrossRefGoogle Scholar
  16. 16.
    Moufki A, Devillez A, Segreti M, Dudzinski D (2006) A semi-analytical model of non-linear vibrations in orthogonal cutting and experimental validation. Int J Mach Tools Manuf 46:436–449. CrossRefGoogle Scholar
  17. 17.
    Ye GG, Xue SF, Ma W et al (2012) Cutting AISI 1045 steel at very high speeds. Int J Mach Tools Manuf 56:1–9. CrossRefGoogle Scholar
  18. 18.
    Wan L, Wang D, Gao Y (2016) The investigation of mechanism of serrated chip formation under different cutting speeds. Int J Adv Manuf Technol 82:951–959. CrossRefGoogle Scholar
  19. 19.
    Ma W, Chen X, Shuang F (2017) The chip-flow behaviors and formation mechanisms in the orthogonal cutting process of Ti6Al4V alloy. J Mech Phys Solids. MathSciNetCrossRefGoogle Scholar
  20. 20.
    Wagner V, Baili M, Dessein G (2014) The relationship between the cutting speed, tool wear, and chip formation during Ti-5553 dry cutting. Int J Adv Manuf Technol 76:893–912. CrossRefGoogle Scholar
  21. 21.
    Piispanen V (1948) Theory of formation of metal chips. J Appl Phys 19:876–881. CrossRefGoogle Scholar
  22. 22.
    Palmer WB, Oxley PLB (1959) Mechanics of metal cutting. Proc Inst Mech Eng 173:623–645CrossRefGoogle Scholar
  23. 23.
    Oxley PLB, Welsh MJM (1963) Calculating the shear angle in orthogonal metal cutting from fundamental stress, strain-rate properties of the work material. In: Proceedings 4th International Machine Tool Design and Research Conference. Pergamon, OxfordGoogle Scholar
  24. 24.
    Ma W, Li X, Dai L, Ling Z (2012) Instability criterion of materials in combined stress states and its application to orthogonal cutting process. Int J Plast 30–31:18–40. CrossRefGoogle Scholar
  25. 25.
    Luo J, Li M, Li X, Shi Y (2010) Constitutive model for high temperature deformation of titanium alloys using internal state variables. Mech Mater 42:157–165. CrossRefGoogle Scholar
  26. 26.
    G.T. Gray III, S.R. Chen, W. Wright, M.F. Lopez (1994) Constitutive equations for annealed metals under compression at high strain rates and high temperatures. Los Alamos National Laboratory. LA-12669-MS. UC-000, Issued: JanuaryGoogle Scholar
  27. 27.
    Liu Y, Cai S, Shang X, Dai L (2017) Suppression of Hopf bifurcation in metal cutting by extrusion machining. Nonlinear Dyn 88:433–453. CrossRefGoogle Scholar
  28. 28.
    Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 21:31–48. CrossRefGoogle Scholar
  29. 29.
    Hortig C, Svendsen B (2007) Simulation of chip formation during high-speed cutting. J Mater Process Technol 186:66–76. CrossRefzbMATHGoogle Scholar
  30. 30.
    Shuang F, Chen X, Ma W (2018) Numerical analysis of chip formation mechanisms in orthogonal cutting of Ti6Al4V alloy based on a CEL model. Int J Mater Form. CrossRefGoogle Scholar
  31. 31.
    Fang N (2003) Slip-line modeling of machining with a rounded-edge tool—Part I: new model and theory. J Mech Phys Solids 51:715–742. CrossRefzbMATHGoogle Scholar
  32. 32.
    Bisacre FFP, Bisacre GH (1947) The life of carbide-tipped turning tools. Proc Inst Mech Eng 157:452–469. CrossRefGoogle Scholar
  33. 33.
    Gioia G, Ortiz M (1996) The two-dimensional structure of dynamic boundary layers and shear bands in thermoviscoplastic solids. J Mech Phys Solids 44:251–292. MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Bai YL (1982) Thermo-plastic instability in simple shear. J Mech Phys Solids 30:195–207. CrossRefzbMATHGoogle Scholar
  35. 35.
    Molinari A (1997) Collective behavior and spacing of adiabatic shear bands. J Mech Phys Solids 45:1551–1575. MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Hill R (1950) The mathematical theory of plasticity. Oxford Univ. Press, OxfordzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of MechanicsChinese Academy of SciencesBeijingChina
  2. 2.Department of mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA

Personalised recommendations