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A nanotwin-based analytical model to predict dynamics in cryogenic orthogonal machining copper

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Abstract

Cryogenic cooling helps to improve the machining performance and reduce the tool wear. Cryogenic condition could activate these substructures such as deformation twins and dislocation cells. The effects of the substructures are not taken into consideration in the conventional machining models. The conventional models cannot characterize the dynamics in cryogenic machining, i.e., the evolutions of cutting force and temperature with time. Here, considering the effect of the substructures, a new analytical model for metal cutting was proposed to predict the dynamics in cryogenic orthogonal machining. To validate the applicability of the proposed model, the experiments of orthogonal cutting copper at liquid nitrogen temperature and room temperature were conducted. Transmission electron microscope observations show that nanotwins formed in cryogenic cutting copper. The comparisons between experimental cutting forces and the proposed model or the conventional models validate the rationality of the nanotwin-based analytical model. Numerical calculations were further carried out to reveal the underlying mechanism. The periodic oscillation of cutting force in liquid nitrogen condition is a phenomenon of Hopf bifurcation resulting from the formation of nanotwins.

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Abbreviations

t 0 :

precut thickness

t c :

chip thickness

w :

workpiece thickness

ϕ :

shear angle

V :

cutting speed

F c :

cutting force

ρ :

mobile dislocation density

t :

time

d :

mean grain size

τ y :

shear yield strength

R TW :

mean radius of nanotwin

h TW :

thickness of nanotwin

k a :

annihilation constant

ρ 0 :

initial dislocation density

γ SF :

stacking fault energy

b :

modulus of Burgers vector

G :

shear modulus

T :

temperature

τ :

flow shear stress

\( \hat{t} \) :

dimensionless time

\( \hat{d} \) :

dimensionless grain size

a11(T), a12(T), a13, a14, b11, b12, b13 :

dimensionless coefficients

f nt :

volume fraction of nanotwin

N TW :

concentration of active twins

η :

fraction of plastically dissipated energy

ε D :

energy of dislocation line per unit length

Δ:

mean distance of nanotwins

V nt :

speed of nanotwin formation

V D :

dislocation motion velocity

n 0 :

total number of twinning system

ρ anh :

annihilation rate of dislocation

τ g :

shear yield strength of deformed grains

τ nt :

shear yield strength of nanotwinned grains

A 1 :

coefficient 1 for deformed grains

A 2 :

coefficient 2 for deformed grains

B 1 :

coefficient 1 for nanotwinned grains

B 2 :

coefficient 2 for nanotwinned grains

τ 0 :

dislocation gliding frictional stress

α :

dislocation interaction term

k TW :

coefficient of twinning strengthening

\( \hat{\tau} \) :

dimensionless flow shear stress

\( \hat{\rho} \) :

dimensionless dislocation density

\( {\hat{\rho}}^{\ast } \) :

equilibrium dislocation density

\( {f}_{\mathrm{nt}}^{\ast } \) :

equilibrium nanotwin volume fraction

References

  1. Yildiz Y, Nalbant M (2008) A review of cryogenic cooling in machining processes. Int J Mach Tools Manuf 48(9):947–964. https://doi.org/10.1016/j.ijmachtools.2008.01.008

    Article  Google Scholar 

  2. Sharif MN, Pervaiz S, Deiab I (2017) Potential of alternative lubrication strategies for metal cutting processes: a review. Int J Adv Manuf Technol 89(5):2447–2479. https://doi.org/10.1007/s00170-016-9298-5

    Article  Google Scholar 

  3. Hong SY, Ding Y (2001) Cooling approaches and cutting temperatures in cryogenic machining of Ti-6Al-4V. Int J Mach Tools Manuf 41(10):1417–1437. https://doi.org/10.1016/S0890-6955(01)00026-8

    Article  Google Scholar 

  4. Danish M, Ginta TL, Habib K, Carou D, Rani AMA, Saha BB (2017) Thermal analysis during turning of AZ31 magnesium alloy under dry and cryogenic conditions. Int J Adv Manuf Technol 91(5):2855–2868. https://doi.org/10.1007/s00170-016-9893-5

    Article  Google Scholar 

  5. Sharma VS, Dogra M, Suri NM (2009) Cooling techniques for improved productivity in turning. Int J Mach Tools Manuf 49(6):435–453. https://doi.org/10.1016/j.ijmachtools.2008.12.010

    Article  Google Scholar 

  6. Kaynak Y (2014) Evaluation of machining performance in cryogenic machining of Inconel 718 and comparison with dry and MQL machining. Int J Adv Manuf Technol 72(5):919–933. https://doi.org/10.1007/s00170-014-5683-0

    Article  Google Scholar 

  7. Trabelsi S, Morel A, Germain G, Bouaziz Z (2017) Tool wear and cutting forces under cryogenic machining of titanium alloy (Ti17). Int J Adv Manuf Technol 91(5):1493–1505. https://doi.org/10.1007/s00170-016-9841-4

    Article  Google Scholar 

  8. Bertolini R, Lizzul L, Pezzato L, Ghiotti A, Bruschi S (2019) Improving surface integrity and corrosion resistance of additive manufactured Ti6Al4V alloy by cryogenic machining. Int J Adv Manuf Technol 104(5):2839–2850. https://doi.org/10.1007/s00170-019-04180-5

    Article  Google Scholar 

  9. Pereira WH, Delijaicov S (2019) Surface integrity of INCONEL 718 turned under cryogenic conditions at high cutting speeds. Int J Adv Manuf Technol 104(5):2163–2177. https://doi.org/10.1007/s00170-019-03946-1

    Article  Google Scholar 

  10. Gong L, Zhao W, Ren F, He N, Li L, Xu Q, Khan AM (2019) Experimental study on surface integrity in cryogenic milling of 35CrMnSiA high-strength steel. Int J Adv Manuf Technol 103(1):605–615. https://doi.org/10.1007/s00170-019-03577-6

    Article  Google Scholar 

  11. Zhao W, Ren F, Iqbal A, Gong L, He N, Xu Q (2020) Effect of liquid nitrogen cooling on surface integrity in cryogenic milling of Ti-6Al-4V titanium alloy. Int J Adv Manuf Technol 106(3):1497–1508. https://doi.org/10.1007/s00170-019-04721-y

    Article  Google Scholar 

  12. Imbrogno S, Rotella G, Rinaldi S (2020) Surface and subsurface modifications of AA7075-T6 induced by dry and cryogenic high speed machining. Int J Adv Manuf Technol 107(1):905–918. https://doi.org/10.1007/s00170-020-05108-0

    Article  Google Scholar 

  13. Zhang C, Zhang S, Yan X, Zhang Q (2016) Effects of internal cooling channel structures on cutting forces and tool life in side milling of H13 steel under cryogenic minimum quantity lubrication condition. Int J Adv Manuf Technol 83(5):975–984. https://doi.org/10.1007/s00170-015-7644-7

    Article  Google Scholar 

  14. Abdelrazek AH, Choudhury IA, Nukman Y, Kazi SN (2020) Metal cutting lubricants and cutting tools: a review on the performance improvement and sustainability assessment. Int J Adv Manuf Technol 106(9):4221–4245. https://doi.org/10.1007/s00170-019-04890-w

    Article  Google Scholar 

  15. Merchant ME (1945) Mechanics of the metal cutting process. I. Orthogonal cutting and a type 2 chip. J Appl Phys 16(5):267–275

    Article  Google Scholar 

  16. Burns TJ, Davies MA (1997) Nonlinear dynamics model for chip segmentation in machining. Phys Rev Lett 79(3):447–450. https://doi.org/10.1103/PhysRevLett.79.447

    Article  Google Scholar 

  17. Ye GG, Xue SF, Ma W, Jiang MQ, Ling Z, Tong XH, Dai LH (2012) Cutting AISI 1045 steel at very high speeds. Int J Mach Tools Manuf 56(0):1–9. https://doi.org/10.1016/j.ijmachtools.2011.12.009

    Article  Google Scholar 

  18. Molnar TG, Berezvai S, Kiss AK, Bachrathy D, Stepan G (2019) Experimental investigation of dynamic chip formation in orthogonal cutting. Int J Mach Tools Manuf 145:103429. https://doi.org/10.1016/j.ijmachtools.2019.103429

    Article  Google Scholar 

  19. Molinari A, Musquar C, Sutter G (2002) Adiabatic shear banding in high speed machining of Ti–6Al–4V: experiments and modeling. Int J Plast 18(4):443–459. https://doi.org/10.1016/s0749-6419(01)00003-1

    Article  MATH  Google Scholar 

  20. Ye GG, Xue SF, Jiang MQ, Tong XH, Dai LH (2013) Modeling periodic adiabatic shear band evolution during high speed machining Ti-6Al-4V alloy. Int J Plast 40(0):39–55. https://doi.org/10.1016/j.ijplas.2012.07.001

    Article  Google Scholar 

  21. Sutter G, List G (2013) Very high speed cutting of Ti–6Al–4V titanium alloy – change in morphology and mechanism of chip formation. Int J Mach Tools Manuf 66(0):37–43. https://doi.org/10.1016/j.ijmachtools.2012.11.004

    Article  Google Scholar 

  22. Ye GG, Chen Y, Xue SF, Dai LH (2014) Critical cutting speed for onset of serrated chip flow in high speed machining. Int J Mach Tools Manuf 86(0):18–33. https://doi.org/10.1016/j.ijmachtools.2014.06.006

    Article  Google Scholar 

  23. Cai SL, Dai LH (2014) Suppression of repeated adiabatic shear banding by dynamic large strain extrusion machining. J Mech Phys Solids 73(0):84–102. https://doi.org/10.1016/j.jmps.2014.09.004

    Article  Google Scholar 

  24. Liu Y, Cai S, Shang X, Dai L (2017) Suppression of Hopf bifurcation in metal cutting by extrusion machining. Nonlinear Dyn 88(1):433–453. https://doi.org/10.1007/s11071-016-3251-x

    Article  Google Scholar 

  25. Guo Y, Compton WD, Chandrasekar S (2015) In situ analysis of flow dynamics and deformation fields in cutting and sliding of metals. Proc R Soc A Math Phys Eng Sci 471(2178):20150194. https://doi.org/10.1098/rspa.2015.0194

    Article  Google Scholar 

  26. Yeung H, Viswanathan K, Udupa A, Mahato A, Chandrasekar S (2017) Sinuous flow in cutting of metals. Phys Rev Appl 8(5):054044. https://doi.org/10.1103/PhysRevApplied.8.054044

    Article  Google Scholar 

  27. Mohammed WM, Ng E, Elbestawi MA (2011) Modeling the effect of the microstructure of compacted graphite iron on chip formation. Int J Mach Tools Manuf 51(10):753–765. https://doi.org/10.1016/j.ijmachtools.2011.06.005

    Article  Google Scholar 

  28. Lee WB, Wang H, Chan CY, To S (2013) Finite element modelling of shear angle and cutting force variation induced by material anisotropy in ultra-precision diamond turning. Int J Mach Tools Manuf 75:82–86. https://doi.org/10.1016/j.ijmachtools.2013.09.007

    Article  Google Scholar 

  29. Rahman MA, Rahman M, Kumar AS (2017) Modelling of flow stress by correlating the material grain size and chip thickness in ultra-precision machining. Int J Mach Tools Manuf 123:57–75. https://doi.org/10.1016/j.ijmachtools.2017.08.001

    Article  Google Scholar 

  30. Zhang W, Wang X, Hu Y, Wang S (2018) Predictive modelling of microstructure changes, micro-hardness and residual stress in machining of 304 austenitic stainless steel. Int J Mach Tools Manuf 130-131:36–48. https://doi.org/10.1016/j.ijmachtools.2018.03.008

    Article  Google Scholar 

  31. Li C, Li X, Wu Y, Zhang F, Huang H (2019) Deformation mechanism and force modelling of the grinding of YAG single crystals. Int J Mach Tools Manuf 143:23–37. https://doi.org/10.1016/j.ijmachtools.2019.05.003

    Article  Google Scholar 

  32. Ning J, Nguyen V, Huang Y, Hartwig KT, Liang SY (2018) Inverse determination of Johnson–Cook model constants of ultra-fine-grained titanium based on chip formation model and iterative gradient search. Int J Adv Manuf Technol 99(5-8):1131–1140. https://doi.org/10.1007/s00170-018-2508-6

    Article  Google Scholar 

  33. Ning J, Nguyen V, Huang Y, Hartwig KT, Liang SY (2019) Constitutive modeling of ultra-fine-grained titanium flow stress for machining temperature prediction. Bio-Des Manuf 2(3):153–160. https://doi.org/10.1007/s42242-019-00044-9

    Article  Google Scholar 

  34. Ning J, Nguyen V, Liang SY (2019) Analytical modeling of machining forces of ultra-fine-grained titanium. Int J Adv Manuf Technol 101(1):627–636. https://doi.org/10.1007/s00170-018-2889-6

    Article  Google Scholar 

  35. Ning J, Liang SY (2019) A comparative study of analytical thermal models to predict the orthogonal cutting temperature of AISI 1045 steel. Int J Adv Manuf Technol 102(9):3109–3119. https://doi.org/10.1007/s00170-019-03415-9

    Article  Google Scholar 

  36. Li XB, Jiang GM, Di JP, Yang Y, Wang CL (2020) Effect of cryogenic rolling on the microstructural evolution and mechanical properties of pure copper sheet. Mater Sci Eng A 772:138811. https://doi.org/10.1016/j.msea.2019.138811

    Article  Google Scholar 

  37. Nag S, Sardar P, Jain A, Himanshu A, Mondal DK (2014) Correlation between ferrite grain size, microstructure and tensile properties of 0.17 wt% carbon steel with traces of microalloying elements. Mater Sci Eng A 597:253–263. https://doi.org/10.1016/j.msea.2013.12.073

    Article  Google Scholar 

  38. Wan M, Wen D-Y, Ma Y-C, Zhang W-H (2019) On material separation and cutting force prediction in micro milling through involving the effect of dead metal zone. Int J Mach Tools Manuf 146:103452. https://doi.org/10.1016/j.ijmachtools.2019.103452

    Article  Google Scholar 

  39. Campbell CE, Bendersky LA, Boettinger WJ, Ivester R (2006) Microstructural characterization of Al-7075-T651 chips and work pieces produced by high-speed machining. Mater Sci Eng A Struct Mater Prop Microstruct Process 430(1-2):15–26. https://doi.org/10.1016/j.msea.2006.04.122

    Article  Google Scholar 

  40. Geng X, Wang D, Deng J, Fanfan J, Zhufeng Y (2017) Simulation of the orthogonal cutting of OFHC copper based on the smoothed particle hydrodynamics method. Int J Adv Manuf Technol 91(1-4):265–272. https://doi.org/10.1007/s00170-016-9723-9

    Article  Google Scholar 

  41. Hodge AM, Furnish TA, Navid AA, Barbee TW (2011) Shear band formation and ductility in nanotwinned Cu. Scr Mater 65(11):1006–1009. https://doi.org/10.1016/j.scriptamat.2011.09.002

    Article  Google Scholar 

  42. Wang YM, Ma E (2003) Temperature and strain rate effects on the strength and ductility of nanostructured copper. Appl Phys Lett 83(15):3165–3167. https://doi.org/10.1063/1.1618370

    Article  Google Scholar 

  43. Matsushita M, Ohfuji H (2010) Analysis of the recrystallization of cold-rolled copper after isothermal annealing using electron backscattered diffraction patterns. Defect Diffus Forum 297-301:359–364

    Article  Google Scholar 

  44. Lu L, Chen X, Huang X, Lu K (2009) Revealing the maximum strength in nanotwinned copper. Science 323(5914):607–610. https://doi.org/10.1126/science.1167641

    Article  Google Scholar 

  45. Lu L, You ZS, Lu K (2012) Work hardening of polycrystalline Cu with nanoscale twins. Scr Mater 66(11):837–842. https://doi.org/10.1016/j.scriptamat.2011.12.046

    Article  Google Scholar 

  46. Mayer AE, Khishchenko KV, Levashov PR, Mayer PN (2013) Modeling of plasticity and fracture of metals at shock loading. J Appl Phys 113(19):193508. https://doi.org/10.1063/1.4805713

    Article  Google Scholar 

  47. Merchant ME (1945) Mechanics of the metal cutting process. II. Plasticity conditions in orthogonal cutting. J Appl Phys 16(6):318–324

    Article  Google Scholar 

  48. Brown TL, Saldana C, Murthy TG, Mann JB, Guo Y, Allard LF, King AH, Compton WD, Trumble KP, Chandrasekar S (2009) A study of the interactive effects of strain, strain rate and temperature in LSEM of copper. Acta Mater 57(18):5491–5500. https://doi.org/10.1016/j.actamat.2009.07.052

    Article  Google Scholar 

  49. Guo Y, Efe M, Moscoso W, Sagapuram D, Trumble KP, Chandrasekar S (2012) Deformation field in LSEM and implications for deformation processing. Scr Mater 66(5):235–238. https://doi.org/10.1016/j.scriptamat.2011.10.045

    Article  Google Scholar 

  50. Dao M, Lu L, Shen YF, Suresh S (2006) Strength, strain-rate sensitivity and ductility of copper with nanoscale twins. Acta Mater 54(20):5421–5432. https://doi.org/10.1016/j.actamat.2006.06.062

    Article  Google Scholar 

  51. Frost HJ, Ashby MF (1982) Deformation-mechanism maps: the plasticity and creep of metals and ceramics. Pergamon Press, Oxford

    Google Scholar 

  52. Kittel C (2005) Introduction to solid state physics. Wiley, New York

    MATH  Google Scholar 

  53. Liu Y, Cai S, Xu F, Wang Y, Dai L (2019) Enhancing strength without compromising ductility in copper by combining extrusion machining and heat treatment. J Mater Process Technol 267:52–60. https://doi.org/10.1016/j.jmatprotec.2018.12.001

    Article  Google Scholar 

  54. Christian JW, Mahajan S (1995) Deformation twinning. Prog Mater Sci 39(1-2):1–157

    Article  Google Scholar 

  55. Malygin GA (1999) Dislocation self-organization processes and crystal plasticity. Physics-Uspekhi 42(9):887–916. https://doi.org/10.1070/pu1999v042n09abeh000563

    Article  Google Scholar 

  56. Ding R, Guo ZX (2001) Coupled quantitative simulation of microstructural evolution and plastic flow during dynamic recrystallization. Acta Mater 49(16):3163–3175. https://doi.org/10.1016/S1359-6454(01)00233-6

    Article  Google Scholar 

  57. Meyers MA, Chawla KK (2009) Mechanical behavior of materials, 2nd edn. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  58. De Chiffre L (1976) Extrusion-cutting. Int J Mach Tool Des Res 16(2):137–144. https://doi.org/10.1016/0020-7357(76)90032-9

    Article  Google Scholar 

  59. Saldana C, Murthy TG, Shankar MR, Stach EA, Chandrasekar S (2009) Stabilizing nanostructured materials by coherent nanotwins and their grain boundary triple junction drag. Appl Phys Lett 94(2):021910. https://doi.org/10.1063/1.3072595

    Article  Google Scholar 

  60. Swaminathan S, Brown TL, Chandrasekar S, McNelley TR, Compton WD (2007) Severe plastic deformation of copper by machining: microstructure refinement and nanostructure evolution with strain. Scr Mater 56(12):1047–1050. https://doi.org/10.1016/j.scriptamat.2007.02.034

    Article  Google Scholar 

  61. Meyers MA, Mishra A, Benson DJ (2006) Mechanical properties of nanocrystalline materials. Prog Mater Sci 51(4):427–556. https://doi.org/10.1016/j.pmatsci.2005.08.003

    Article  Google Scholar 

  62. Lu L, Schwaiger R, Shan ZW, Dao M, Lu K, Suresh S (2005) Nano-sized twins induce high rate sensitivity of flow stress in pure copper. Acta Mater 53(7):2169–2179. https://doi.org/10.1016/j.actamat.2005.01.031

    Article  Google Scholar 

  63. Lu L, Shen YF, Chen XH, Qian LH, Lu K (2004) Ultrahigh strength and high electrical conductivity in copper. Science 304(5669):422–426. https://doi.org/10.1126/science.1092905

    Article  Google Scholar 

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Funding

This study was funded by the National Key Research and Development Program of China (grant number 2017YFB0702003), the National Natural Science Foundation of China (grant numbers 12072327 and 11802013), Fundamental Research Funds for the Central Universities (grant number FRF-TP-18-020A2), China Scholarship Council (grant number 201909110036), the Strategic Priority Research Program of the Chinese Academy of Sciences (grant numbers XDB22040302 and XDB22040303), and the Key Research Program of Frontier Sciences (grant number QYZDJSSW-JSC011).

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Liu, Y., Cai, S., Chen, Y. et al. A nanotwin-based analytical model to predict dynamics in cryogenic orthogonal machining copper. Int J Adv Manuf Technol 111, 3189–3205 (2020). https://doi.org/10.1007/s00170-020-06303-9

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