Abstract
The Johnson and Cook (J-C) constitutive model is widely employed in finite element analysis for machining. Currently, inverse approach shows greater superiority on identifying the J-C parameters than the traditional way, like the split Hopkinson pressure bar (SHPB) test. In this paper, a modified parallel-sided shear zone model at primary zone is presented for determining J-C parameters. Based on the assumption of nonequidistant primary zone, the distribution of velocity, strain rate, strain, and temperature is successfully predicted. Finite element simulation (FEM) is subsequently used to verify the theoretical prediction. Based on the proposed shear band model, an inverse approach is developed for determining the J-C parameters. In this method, the parameter determining process is taken as an optimization problem. The J-C parameters are considered as the design variable while the optimization objective is cutting force. In conjugation with the measured cutting forces and chip thickness, the particle swarm optimization (PSO) algorithm was introduced to solve the optimization model. The Johnson-Cook’s model of nickel-base superalloy Inconel 718 is successfully identified from orthogonal cutting test. Finite element models with seven constitutive models from Deform, references and this work are established to predict cutting force. The results showed that the proposed J-C models have higher prediction precision compared with other constitutive models. With the proposed J-C models, the errors between the simulated and measured cutting forces are controlled within 7.3%.
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References
Umbrello D, M’saoubi R, Outeiro J (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):462–470
Arrazola P, Özel T, Umbrello D, Davies M, Jawahir I (2013) Recent advances in modelling of metal machining processes. CIRP Ann-Manuf Technol 62(2):695–718
Zerilli FJ, Armstrong RW (1987) Dislocation-mechanics-based constitutive relations for material dynamics calculations. J Appl Phys 61(5):1816–1825
Johnson GR, Cook WH A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the 7th International Symposium on Ballistics, 1983. The Hague, The Netherlands, pp 541–547
Sartkulvanich P, Altan T, Soehner J (2005) Flow stress data for finite element simulation in metal cutting: a progress report on madams. Mach Sci Technol 9(2):271–288
Shirakashi T, Maekawa K, Usui E (1983) Flow stress of low carbon steel at high temperature and strain rate. I: propriety of incremental strain method in impact compression test with rapid heating and cooling systems. Bull Jpn Soc Precision Eng 17(3):161–166
Maekawa K, Shirakashi T, Usui E (1983) Flow stress of low carbon steel at high temperature and strain rate. II: flow stress under variable temperature and variable strain rate. Bull Jpn Soc Precision Eng 17(3):167–172
Nemat-Nasser S, Guo W-G, Nesterenko VF, Indrakanti S, Gu Y-B (2001) Dynamic response of conventional and hot isostatically pressed Ti–6Al–4V alloys: experiments and modeling. Mech Mater 33(8):425–439
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):659–667
Chen G, Ren C, Yu W, Yang X, Zhang L (2012) Application of genetic algorithms for optimizing the Johnson–Cook constitutive model parameters when simulating the titanium alloy Ti-6Al-4V machining process. Proc Inst Mech Eng B J Eng Manuf 226(8):1287–1297
Lorentzon J, Järvstråt N, Josefson B (2009) Modelling chip formation of alloy 718. J Mater Process Technol 209(10):4645–4653
Jafarian F, Ciaran MI, Umbrello D, Arrazola P, Filice L, Amirabadi H (2014) Finite element simulation of machining Inconel 718 alloy including microstructure changes. Int J Mech Sci 88:110–121
Bäker M, Shrot A (2013) Inverse parameter identification with finite element simulations using knowledge-based descriptors. Comput Mater Sci 69:128–136
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
Shrot A, Bäker M (2012) Determination of Johnson–Cook parameters from machining simulations. Comput Mater Sci 52(1):298–304
Ulutan D, Özel T (2013) Determination of constitutive material model parameters in FE-based machining simulations of Ti-6Al-4V and IN-100 alloys: an inverse methodology. Proceedings of NAMRI/SME 41
Liu R, Melkote S, Pucha R, Morehouse J, Man X, Marusich T (2013) An enhanced constitutive material model for machining of Ti–6Al–4V alloy. J Mater Process Technol 213(12):2238–2246
Lei S, Shin YC, Incropera FP (1999) Material constitutive modeling under high strain rates and temperatures through orthogonal machining tests. J Manuf Sci Eng 121(4):577–585
Oxley PLB, Young H (1989) The mechanics of machining: an analytical approach to assessing machinability. Ellis Horwood Publisher:136–182
Özel T, Zeren E (2004) Determination of work material flow stress and friction for FEA of machining using orthogonal cutting tests. J Mater Process Technol 153:1019–1025
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):119–129
Shatla M, Kerk C, Altan T (2001) Process modeling in machining. Part I: determination of flow stress data. Int J Mach Tools Manuf 41(10):1511–1534
Shatla M, Kerk C, Altan T (2001) Process modeling in machining. Part II: validation and applications of the determined flow stress data. Int J Mach Tools Manuf 41(11):1659–1680
Laakso SVA, Niemi E (2015) Determination of material model parameters from orthogonal cutting experiments. Proc Inst Mech Eng, Part B: J Eng Manuf: 0954405414560620
Li B, Wang X, Hu Y, Li C (2011) Analytical prediction of cutting forces in orthogonal cutting using unequal division shear-zone model. Int J Adv Manuf Technol 54(5–8):431–443
Astakhov VP, Osman M, Hayajneh M (2001) Re-evaluation of the basic mechanics of orthogonal metal cutting: velocity diagram, virtual work equation and upper-bound theorem. Int J Mach Tools Manuf 41(3):393–418
Tounsi N, Vincenti J, Otho A, Elbestawi M (2002) From the basic mechanics of orthogonal metal cutting toward the identification of the constitutive equation. Int J Mach Tools Manuf 42(12):1373–1383
Stevenson M, Oxley P (1969) An experimental investigation of the influence of speed and scale on the strain-rate in a zone of intense plastic deformation. Proc Inst Mech Eng 184(1):561–576
Jawahir I, Van Luttervelt C (1993) Recent developments in chip control research and applications. CIRP Ann-Manuf Technol 42(2):659–693
Lalwani D, Mehta N, Jain P (2009) Extension of Oxley's predictive machining theory for Johnson and Cook flow stress model. J Mater Process Technol 209(12):5305–5312
Shi B, Attia H, Tounsi N (2010) 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(5):051008
Shi B, Attia H, Tounsi N (2010) Identification of material constitutive laws for machining—part II: generation of the constitutive data and validation of the constitutive law. J Manuf Sci Eng 132(5):051009
Pang L (2012) Analytical modeling and simulation of metal cutting forces for engineering alloys. University of Ontario Institute of Technology
Pang L, Kishawy H (2012) Modified primary shear zone analysis for identification of material mechanical behavior during machining process using genetic algorithm. J Manuf Sci Eng 134(4):041003
Boothroyd G (1963) Temperatures in orthogonal metal cutting. Proc Inst Mech Eng 177(1):789–810
Eberhart RC, Kennedy J A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, 1995. New York, NY, pp 39–43
Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. Swarm Intelligence 1(1):33–57
Sima M, Özel T (2010) Modified material constitutive models for serrated chip formation simulations and experimental validation in machining of titanium alloy Ti–6Al–4V. Int J Mach Tools Manuf 50(11):943–960
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Zhou, J., Ren, J., Feng, Y. et al. A modified parallel-sided shear zone model for determining material constitutive law. Int J Adv Manuf Technol 91, 589–603 (2017). https://doi.org/10.1007/s00170-016-9717-7
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DOI: https://doi.org/10.1007/s00170-016-9717-7