Simulation of the Cutting Process Basic Instability Using Molecular Dynamics Technique

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1 Simulation of the Cutting Process Basic Instability Using Molecular Dynamics Technique M. BANU, A. BURUIANA, G. FRUMUSANU, A. EPUREANU, S. TOTOLICI, O. MARINESCU Manufacturing Science and Engineering Department Dunarea de Jos University of Galati 111 Domneasca Str., ROMANIA Abstract: - Cutting processes are unstable machining processes. The influence of the instability on the deformation mechanism that leads to the chip formation at the atomic scale is analysed in this paper. Fundamental aspects of the crystalline networks deformation are underlined by using molecular dynamics technique applied to the microscopic level of the deformed material and are defined as basic instability. Thus, the goal of this research is to determine the influence of the basic instability in cutting processes on the crystalline networks belonging to the workmaterial area which participates at the chip formation. The simulation using molecular dynamics technique uses the external conditions of the cutting processes as periodic boundary conditions for a selected crystalline network of the workmaterial. Moreover, the influence of the network integrity is studied as a possible cause of instability at the atomic scale that further, it is added to the global process instability. A measure of the atomic instability is the evolution of the kinetic energy at the atomic level. Three different crystalline networks are considered - with free defects, vacation and interstitial atom to estimate the differences in kinetic energies at the atomic level and the influence on the cutting force time evolution. The fluctuations of the forces at the atomic level are considered one of the causes of the macroscopic perturbation of the cutting process itself named basic instability. Key-Words: - molecular dynamics, micro-cutting process, basic instability, simulation, cutting force, chip formation 1 Introduction The machining process productivity or the generated surface quality may be severely affected by instability. The geometrical or kinematical particularities of the machining process, as well as the ones regarding worked material structure or machining system dynamics, may lead to the appearance of instability in various forms. Because their starting mechanisms are different, the study of each among them requires a separate approach. Let us consider a cutting process whose geometrical and kinematical parameters are kept rigorously unchanged e.g. a slotting process, Fig.1. Fig.1 Cutting process basic instability The cutting speed, v and the chip thickness, a, are maintained constant, while the worked material is supposed to be perfect homogenous. Despite all, more output parameters have an uncontrolled variation. Thus, the cutting force F modulus and direction (angle θ) continuously change. One presumed cause of this fact is the discontinuity of chip forming, proved by chip variable section, although its provenience layer of material has constant section. The material sliding associated to the chip formation, in the direction given through Φ angle, is intermittent and leads to specific chip elements. This is the phenomenon called cutting process primary instability and appears, inevitably, in all observed cases, no matter of the worked material, the cutting regime or the machining system characteristics. We presume that it might be one among the sources of the dynamic instability and it could explain some of the practical observations to whom the current theories concerning cutting were not able to answer until now. Its inmost mechanism was not clearly explicated yet. During the last years, numerous researchers analyzed the instability of chip formation and gave possible explanations. Lipatov observed a connection between the chip saw-tooth profile and the cyclic variation in the shear angle, consequently machining being accompanied ISSN: ISBN:

2 by fluctuations in the cutting force [6]. Yang studied the mechanism of chip formation during high-speed milling process and developed a finite element model; he explained that the saw-tooth chip is caused by double actions of thermoplastic instability and plastic instability [12]. Liu found that the ductile chip formation is the result of a large compressive stress and shear stress in the chip formation zone, which shields the growth of pre-existing flaws by suppressing the stress intensity factor [7]. Biermann studied the influence of cutting edge geometry and cutting edge radius on the stability of micromilling processes [2]. Komandouri made an analysis of the shear-localized chip formation process and the temperature generated in the shear band due to various heat sources in machining [5]. Very recent researches have used the molecular dynamics investigations to study material deformations in nanometric cutting processes [1], [9]. In this paper we tried to explain the basic instability appearance by starting from examining the effects of the cutting process specific stresses on material, at atomic level, by using molecular dynamics investigations techniques. Molecular dynamic simulations are used at the atomic level to study the basic instability characterized by atomic instabilities exhibited through fluctuations of the kinetic and potential energies of the atoms belonging to the crystalline networks. 2 Numerical Simulation To analyze the basically phenomenon that initiate the instability of the chip formation, an elementary area of workmaterial is selected. The stress state in this area corresponds to large plastic deformations due to the shearing on the preferential angle of the deformation correlated with the angle of the cutting tool in contact with workmaterial. The selected area is figured out in figure 2, for three cases of the crystalline network: homogeneous free defect (a), vacant position (b) and interstitial atom (c). For this elementary area the periodic boundary conditions are applied by considering the stresses produced by the cutting forces on the atoms area. 56 atoms are considered and the workmaterial is mild carbon steel. The material characteristics are associated to this material. Molecular dynamics simulation is applied to determine the evolution of the atoms energy when the pressure exerted on the atoms varies based on a harmonic law. By Lemaitre John s potential, the kinetic energy, the temperature during deformation and the potential energy are calculated for a deformation time interval of 7.0 s. a) b) c) Fig. 2 Crystalline network of an elementary area of workmaterial from the chip formation zone: a) homogeneous and free defects crystalline network, b) atomic lattice with a vacant position, c) an interstitial atom (inclusion) The model of the simulation aided by VMD molecular dynamic software is composed of: - 56 de atoms; - cell size 6.9μmx6.9μm; - initial temperature of the atoms 400ºC; - external pressure 1Pa; Initial force value F 0 =2.44 x10-18 N. 3 Results In the case of the free defects crystalline network, the pressure increases near to 1 Pa having some fluctuations that could be associated to the gliding of the atoms of two grain borders. The gliding is not uniform having some fractions of time when the atoms are not in contact. These intervals are small enough to create only some perturbations of the pressure-time evolution. The effect of the pressure on the three different crystalline networks (fig. 3) shows that the slope of the pressure time evolution in the perfect lattice is bigger then in the case of the lattice with imperfections. The fluctuations of the pressure time evolution in the three cases is different but all exhibit some variations in the pressure at almost the same time-step. This interval corresponds to the time that atoms of the neighbor networks are in contact during gliding boundary by boundary. Figures 3 and 4 shows the differences of the energies and temperatures obtained for the three cases of the crystalline networks considered for the molecular dynamics simulations. ISSN: ISBN:

3 Fig. 3 Evolution of the pressure (Pa) during the simulation time (s) obtained at the deformation of three types of crystalline networks Fig. 4 Evolution of the energies (kinetic and potential) during the simulation time (s) obtained at the deformation of three types of crystalline networks ISSN: ISBN:

4 Because the other parameters that influence the cutting processes are avoided for this simulation, it could be assumed that this nonuniformity is a basic instability source of the global cutting process. Moreover, this instability starts from the atomic level and should be checked in the further research if these nonuniformities correspond to the atomic resonance. In the case of the meso- and microscale cutting process, the nonuniformity of the parameters is distinguished more as a perturbation factor then a basic instability factor. h,t, F t [ps] h[e-6m] F[1000*e-18N] T[e-14ºC] Fig. 6 The force variation rate, temperature variation rate and the strain of the considered network for the perfect lattice. It is noticed that all the fluctuations have the same period (frequency) that should be search for in the global perturbation of the cutting force during entire process Fig. 5 Evolution of the temperature during the simulation time (s) obtained at the deformation of three types of crystalline networks 4 Discussions By analyzing the results obtained following the simulations, the three evaluated parameters: deformation force, energy and the temperature have a nonuniform variation in time, even in the case of a perfect atomic lattice. The amount of the nonunformity in time is comparable with the variation itself (Fig. 6). From the three parameters monitored, the force is the most nonunform but the atom distances (the strain) is uniform. 5 Conclusions The molecular simulation of the chip formation through workmaterial deformation during cutting process allowed the following conclusions: - The defects of the crystalline network can be considered as the basis of the nonuniformity variations of the plastic deformation process, but this nonuniformity occurs even for the perfect lattice. Basic instability cannot be avoided at the atomic level. - As the analysing scale decreases until the atomic scale, the nonuniformity of the network behaviors become basic instability cause. - Among the three parameters of which the nonuniformity was studied, the deformation force evidences as the most important source of nonuniformity that is in accordance with the experimental observations. Acknowledgement The authors gratefully acknowledge the financial support of the Romanian Ministry of Education and Research through grant PN II - ID-794/2008. ISSN: ISBN:

5 References: [1] Agraval, P.M. et al., Molecular dynamics investigations on polishing a silicon wafer with a diamond abrasive, Applied Physics, A, [2] Biermann, D. and Baschin, A., Influence of cutting edge geometry and cutting edge radius on the stability of micromilling processes, Production Engineering Resources Development, 3, 2009, pp [3] Cai, J. et al., Novel microstructures from severely deformed Al-Ti alloys created by chip formation in machining, Journal of Materials Science, 43, pp [4] Kiyak, M., Altan, M. & Altan, E., Prediction of chip flow angle in orthogonal turning of mild steel by neural network approach, International Journal of Advanced Manufacturing Technologies, 33, 2007, pp [5] Komanduri, R. and Hou, Z.B., On Thermoplastic Shear Instability in the Machining of a Titanium Alloy (Ti-6Al-4V), Metalurgical and Materials Transactions, 33A, 2002, pp [6] Lipatov, A.A., Instability of Chip Formation and the Wear of a Hard Alloy Tool in Cutting Austenitic Steel, Russian Engineering Research, vol.28, no.9, 2008, pp [7] Liu, K., Li, X.P. & Liang, S.Y., The mechanism of ductile chip formation in cutting of brittle materials, International Journal of Advanced Manufacturing Technologies, 33, 2007, pp [8] Laheurte, R. et al., Behaviour Law for Cutting Processes, International Journal of Advanced Manufacturing Technologies, 29, 2006, pp [9] Pei, Q.X. et al., Study of Material Deformation in Nanometric Cutting by Large-scale Molecular Dynamics Simulations, Nanoscale Res. Lett., 4, 2009, pp [10] Petrushin, S.I. and Proskokov, A.V., Theory of Constrained Motion of Materials: Chip formation with a Single Conditional Shear Surface, Russian Engineering Research, vol.29, no.12, 2009, pp [11] Petrushin, S.I. and Proskokov, A.V., Theory of Constrained Cutting: Chip Formation with a Developed Plastic-Deformation Zone, Russian Engineering Research, vol.30, no.1, 2010, pp [12] Yang, Y. and Li, J.F., Study on mechanism of chip formation during high-speed milling of alloy cast iron, International Journal of Advanced Manufacturing Technologies, 46, 2010, pp ISSN: ISBN: