Numerical study via total Lagrangian smoothed particle hydrodynamics on chip formation in micro cutting

Abstract

Numerical simulation is an effective approach in studying cutting mechanism. The widely used methods for cutting simulation include finite element analysis and molecular dynamics. However, there exist some intrinsic shortcomings when using a mesh-based formulation, and the capable scale of molecular dynamics is extremely small. In contrast, smoothed particle hydrodynamics (SPH) is a candidate to combine the advantages of them. It is a particle method which is suitable for simulating the large deformation process, and is formulated based on continuum mechanics so that large scale problems can be handled in principle. As a result, SPH has also become a main way for the cutting simulation. Since some issues arise while using conventional SPH to handle solid materials, the total Lagrangian smoothed particle hydrodynamics (TLSPH) is developed. But instabilities would still occur during the cutting, which is a critical issue to resolve. This paper studies the effects of TLSPH settings and cutting model parameters on the numerical instability, as well as the chip formation process. Plastic deformation, stress field and cutting forces are analyzed as well. It shows that the hourglass coefficient, critical pairwise deformation and time step are three important parameters to control the stability of the simulation, and a strategy on how to adjust them is provided.

Keywords

Cutting / Total Lagrangian smoothed particle hydrodynamics (TLSPH) / Numerical instability / Chip formation

References

[1.] Fang FZ, Xu FF. Recent advances in micro/nano-cutting: effect of tool edge and material properties. Nanomanuf Metrol, 2018, 1: 4-31.

[2.] Ng EG, El-Wardany TI, Dumitrescu M, et al. Physics-based simulation of high speed machining. Mach Sci Technol, 2002, 6: 301-329.

[3.] Niu W, Mo R, Liu GR, et al. Modeling of orthogonal cutting process of A2024-T351 with an improved SPH method. Int J Adv Manuf Technol, 2018, 95: 905-919.

[4.] Nasr MNA, Ng EG, Elbestawi MA. Modelling the effects of tool-edge radius on residual stresses when orthogonal cutting AISI 316L. Int J Mach Tool Manuf, 2007, 47: 401-411.

[5.] Movahhedy MR, Altintas Y, Gadala MS. Numerical analysis of metal cutting with chamfered and blunt tools. J Manuf Sci Eng, 2002, 124: 178-188.

[6.] Li S, Liu WK. Meshfree and particle methods and their applications. Appl Mech Rev, 2002, 55: 1-34.

[7.] Liu M, Zhang Z. Smoothed particle hydrodynamics (SPH) for modeling fluid-structure interactions. Sci China Phys Mech, 2019, 62: 984701.

[8.] Ikawa N, Shimada S, Tanaka H. Minimum thickness of cut in micromachining. Nanotechnology, 1992, 3: 6.

[9.] Xiao G, To S, Zhang G. Molecular dynamics modelling of brittle–ductile cutting mode transition: case study on silicon carbide. Int J Mach Tool Manuf, 2015, 88: 214-222.

[10.] Pei QX, Lu C, Lee HP, et al. Study of materials deformation in nanometric cutting by large-scale molecular dynamics simulations. Nanoscale Res Lett, 2009, 4: 444-451.

[11.] Lucy LB. A numerical approach to the testing of the fission hypothesis. Astron J, 1977, 82: 1013-1024.

[12.] Liu G, Liu M. Smoothed particle hydrodynamics: a meshfree particle method, 2003, Singapore: World Scientific.

[13.] Swegle JW, Hicks DL, Attaway SW. Smoothed particle hydrodynamics stability analysis. J Comput Phys, 1995, 116: 123-134.

[14.] Bonet J, Kulasegaram S. Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations. Int J Numer Meth Eng, 2000, 47: 1189-1214.

[15.] Niu W, Mo R, Chang Z, et al. Investigating the effect of cutting parameters of Ti-6Al-4 V on surface roughness based on a SPH cutting model. Appl Sci, 2019, 9: 654.

[16.] Liu MB, Zhang ZL, Feng DL. A density-adaptive SPH method with kernel gradient correction for modeling explosive welding. Comput Mech, 2017, 60: 513-529.

[17.] Vignjevic R, Reveles JR, Campbell J. SPH in a total Lagrangian formalism. Comput Model Eng, 2006, 4: 181-198.

[18.] Ganzenmüller GC. An hourglass control algorithm for Lagrangian smooth particle hydrodynamics. Comput Meth Appl Mech Eng, 2015, 286: 87-106.

[19.] Limido J, Espinosa C, Salaun M, et al. Metal cutting modelling SPH approach. Int J Mach Mach Mater, 2011, 9: 177-196.

[20.] Olleak AA, Nasr MNA, El-Hofy HA (2015) The Influence of Johnson–Cook parameters on SPH modeling of orthogonal cutting of AISI 316L. In: 10th European LS-DYNA conference, Würzburg

[21.] Avachat CS, Cherukuri HP (2015) A parametric study of the modeling of orthogonal machining using the smoothed particle hydrodynamics method. In: ASME 2015 international mechanical engineering congress and exposition. American Society of Mechanical Engineers

[22.] Liu Y, Li B, Wu C, et al. Smoothed particle hydrodynamics simulation and experimental analysis of SiC ceramic grinding mechanism. Ceram Int, 2018, 44: 12194-12203.

[23.] Demiral M. SPH modeling of vibro-assisted turning of Ti alloy: influence of vibration parameters. J Vibroeng., 2014, 16: 2685-2694.

[24.] Xi Y, Bermingham M, Wang G, et al. SPH/FE modeling of cutting force and chip formation during thermally assisted machining of Ti6Al4V alloy. Comput Mater Sci, 2014, 84: 188-197.

[25.] Rausch MK, Karniadakis GE, Humphrey JD. Modeling soft tissue damage and failure using a combined particle/continuum approach. Biomech Model Mech, 2017, 16: 249-261.

[26.] Islam MRI, Peng C. A Total Lagrangian SPH method for modelling damage and failure in solids. Int J Mech Sci, 2019, 157: 498-511.

[27.] Leroch S, Varga M, Eder SJ, et al. Smooth particle hydrodynamics simulation of damage induced by a spherical indenter scratching a viscoplastic material. Int J Solids Struct, 2016, 81: 188-202.

[28.] Varga M, Leroch S, Rojacz H, et al. Study of wear mechanisms at high temperature scratch testing. Wear, 2017, 388: 112-118.

[29.] Varga M, Leroch S, Eder SJ, et al. Meshless microscale simulation of wear mechanisms in scratch testing. Wear, 2017, 376: 1122-1129.

[30.] Varga M, Leroch S, Eder SJ, et al. Influence of velocity on high-temperature fundamental abrasive contact: a numerical and experimental approach. Wear, 2019, 426: 370-371.

[31.] Mishra T, Ganzenmüller GC, de Rooij M, et al. Modelling of ploughing in a single-asperity sliding contact using material point method. Wear, 2019, 418: 180-190.

[32.] Bonet J, Kulasegaram S, Rodriguez-Paz MX, et al. Variational formulation for the smooth particle hydrodynamics (SPH) simulation of fluid and solid problems. Comput Meth Appl Mech Eng, 2004, 193: 1245-1256.

[33.] Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comput Phys, 1995, 117: 1-19.

[34.] Desbrun M, Gascuel MP. Ronan B, Gerard H. Smoothed particles: a new paradigm for animating highly deformable bodies. Computer animation and simulation’96, 1996, Vienna: Springer 61-76.

[35.] Prawoto Y, Fanone M, Shahedi S, et al. Computational approach using Johnson-Cook model on dual phase steel. Comput Mater Sci, 2012, 54: 48-55.

Funding

National Natural Science Foundation of China http://dx.doi.org/10.13039/501100001809(61635008); National key Research and Development Program of China(2016YFB1102203); ‘111’ project by the State Administration of Foreign Experts Affairs and the Ministry of Education of China(B07014)