finite element modeling and simulation of ...

FINITE ELEMENT MODELING AND SIMULATION OF MICROMACHINING RANDOM MULTIPHASE MATERIALS

Y.B. Guo, S. Anurag Department of Mechanical Engineering The University of Alabama Tuscaloosa, AL 35487

recovers the shearing-plowing transition and increased specific energy in micromachining.

KEYWORDS Microstructure, micromachining, finite element analysis.

INTRODUCTION Second phase particles distributed in the bulk matrix forms an integral part of microstructure of the general engineering materials. Compared with lithographic techniques, mechanical micromachining is defined as mechanical cutting of features with a large aspect ratio of cutting edge radius to depth-ofcut [Dornfeld et al., 06]. Micromachining is a cluster of competitive processes in automotive, aerospace, biomedical, optical, tooling industries such as fabricating 3-dimensional micro/meso devices or macro or macro components with micro geometric features. Micromachining inherited many characteristics of conventional machining. At the same time, micromachining has distinct process physics mainly due to the comparable sizes of microstructure, cutting edge radius, and depth-of-cut. The downsizing scale of machining results in size effect which may fundamentally changes whole aspect of machining. There are two different aspects of size effects of concern, e.g. when the depth of cut is on the same order as the tool edge radius, and where the microstructure of work material has significant influence on the cutting

ABSTRACT Compared with lithographic techniques, mechanical micromachining is a potential competitive process for fabricating 3D micro/meso components or macro parts with micro-features from diverse materials at high accuracy, efficiency, and low costs, but the size effect induced by the comparable size of microstructures, cutting edge radius, and depthof-cut results in a plowing dominated process. A methodology to incorporate model random microstructure in finite element analysis (FEA) of micromachining multiphase materials has been developed to understand the plowing, tribological, and heat transfer mechanisms. An internal state variable plasticity model has been developed to model the dynamic mechanical behavior including the effect of randomly distributed microstructure, materials damage and evolution. The simulated process variables including chip morphology, forces, and temperatures agree well with the observed experimental phenomena. The simulation

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mechanisms and the resulting surface integrity of the machined components. The bulk literature of micromachining is limited to experimental study, but very few computational approaches to incorporate microstructure effects have been developed to understand the basic mechanism of micromachining. At present, how to model heterogeneous multiphase material in micromachining is a key research issue. Since the phase particles play in a different manner than the matrix material in plastic deformations, the multiphase materials not only affect cutting mechanisms but also surface integrity of the machined devices or components. It has been confirmed by repeated experiments on multiphase engineering materials, that when the second phase is brittle as compared to the matrix material, these particles do not behave as an integral part of the matrix during plastic deformation [Gall et al., 00; Dighe et al., 02; Agarwal et al., 02; Balasundram, 03]. The experiments have proved that inside the ductile matrix, there is high stress concentration at these brittle phase particles. Because they can withstand very little strain, they tend to break easily rather than to flow or deform along with the parent ductile phase. Another issue is that matrix material has different thermal conductivity and melting temperature than second phase particles. So, when the matrix material is in semi-molten state, these particles still remain at a lower temperature and thus tend to break thereby cause internal cracks and voids at the micro level. These concerns play a big role in defining the surface integrity of the machined components. The second phase particles thus affected, serve as preferred site for void nucleation and damage progression in service. Therefore these sites may reduce material strength and aids in damage progression in different materials testing [Balasundram et al., 02; Clarke et al., 03]. However, the particle behavior received little attention in micromachining due to the lack of microstructure modeling techniques. In summary, in order to understand the role of phase particles in micromachining, the development of microstructure modeling and incorporation with finite element analysis (FEA) is highly needed.

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BACKGROUND Micromachining and Process Characteristics The key difference between micromachining and conventional machining resides in the cutting mechanism. In general, shearing is the main cutting mechanism for conventional machining, while a transition of material removal mechanism from shearing to plowing occurs in micromachining [Moriwaki and Okuda, 89]. The transition was manifested by the increased ratio of thrust force to the cutting force. The ratio of edge radius to depth-of-cut predominantly defines the active material removal mechanism such as shearing or plowing, and thus surface integrity. The concept of minimum chip thickness, below which no chip will form, or a minimum depth of cut below which no material removal will occur, has been investigated to ensure proper cutting and avoiding plowing and sliding of the tool [Ikawa et al., 92]. The increased specific energy is closely related to the minimum depth of cut, effective rake angle, and elastic recovery of the work material under the tool flank face. The brittle-ductile transition characterized by continuous chips has been utilized to machine brittle materials such as glasses, ceramic, etc. in the ductile regime under the critical depth of cut, tool geometry, and cutting speed [Bifano et al., 91]. When the tool dimension or a feature is on the same order as that of microstructures of work material, the material cannot be treated as isotropic and homogeneous. Therefore, the cutting mechanism differs significantly from conventional homogeneous and isotropic machining. The different strengths of microstructures may induce force variation, tool vibration and chipping, and degraded surface integrity. Several researchers [To et al., 97] conducted various machining experiments to verify that effect of crystallographic orientations on the cutting forces in micromachining. FEA Modeling The critical issue of micromachining simulation is the microscopic level of the phenomena. Hence it is challenging to make in-process observations and measurements. Moreover, the cutting process itself is very complicated involving elastic/plastic deformation and fracture with high strain rates and temperature and for

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which material properties vary during the process. Thus, analytical modeling is generally considered very difficult at the current level of understanding of dynamic material behavior. The continuum mechanics based FEA simulation provides a suitable tool for many researchers since it is a good compliment to the experimental methods. A FEA simulation can offer a reasonable insight into certain verifiable process variables and mechanism. The major limitation of FEA is that material properties are defined as homogeneous and isotropic whereas, in reality, the material behaves discontinuously in micromachining. Several FEA simulation models [Ueda et al., 91; Ueda and Manabe, 92; Moriwaki et al., 93] have been developed for micromachining. However, these FEA modeling is primarily for isotropic micromachining where no multiphase materials were considered. Chuzhoy et al. [Chuzhoy et al., 02] developed a FE model for machining heterogeneous cast irons (grain size 50 μm and 100 μm) using the depth of cut 150 μm. Their model was capable of describing the microstructure of multiphase materials. However, the aspect ratios, defined as depth-of-cut to grain diameter, are 1.5 to 3. The aspect ratio is for micromachining with aspect ratio usually larger than 5. Park et al [Park et al., 04] tried to calibrate the mechanistic cutting force through FEA simulation for ferrous materials including ductile and gray irons and carbon steels. Their model is primarily based on analysis of the microstructure of the work materials in their various phase, such as graphite, ferrite, and pearlite grains seen in ductile iron, gray iron, and carbon steel microstructures. Their model was mainly used to calibrate a cutting force model. The above literature review reveals several remaining unsolved issues. For characterizing phase randomness, modeling technique of randomness for phase size, location as well as orientation has to be developed. The large aspect ratio of depth-of-cut to particle diameter makes meshing microstructures very difficult since a large number of small phase particles and the workpiece of relative large size has to be meshed. A meshing technique for relative size of edge radius, microstructure features, and workpiece needs to be addressed.

MICROSTRUCTURE MODELING SEM Microstructure Analysis AISI 52100 hardened steel of two phase microstructure was selected as a case material since it has been widely used in hard machining. The work material was initially hardened to 62 HRc. For this purpose, the sample was austenized at 1500 F and held for 2 hours, followed by quenching at 150 F for 15 minutes, and then tempered at 350 F and slow cooled. The SEM image of the microstructure is shown in Fig.1 [Anurag and Guo, 07]. The picture reveals that the microstructure consists of two phases. The white phase particles of cementite are randomly distributed in the grey matrix phase. The volume fraction of the cementite particles was estimated using SEM analysis. Most of the cementite particles display oval and oblong geometries, hence, they were modeled as ellipses for modeling. The distribution of second phase particles is random in three respects. First, the location is random, i.e., the particles don’t have any regular pattern of distribution. At some areas they are concentrated and at others they are sparse. Second, the size is random, the particles are as small as 0.5μm and as big as 5μm in effective diameter. Third, the orientation is random. As it can be seen that they do not have any preferred direction, thus it is apparent that the cementite particles have random orientations.

cementite

FIG 1. TWO PHASE MICROSTRUCTURE OF AISI 52100 HARDENED STEEL (62 HRC).

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Fig. 2 shows the matrix was meshed using 4node plane strain element and the phase particles were modeled using 3-node plane strain elements for orthogonal cutting simulations. The particles and the matrix shares nodes on the interface. The microstructure meshing includes huge amount of elements which leads to high simulation cost. To reduce computation time while ensuring sufficient cutting distance, a cutting region of 175 μm × 60 μm was used for microstructure meshing and the remaining area was meshed with relatively coarse mesh. The overall mesh size is 350 µm × 120 µm.

Mesh Generation of Random Phases Three size levels of the representative particles (2μm, 3μm, and 4μm) were selected to cover the full range of cementite particles. For simplicity, extremely small and large particles were not considered. Ten orientation covering 180 degrees were used in order to introduce randomness in orientation. Thus, the combination of size and orientation makes 30 unique types of particles. For the random location of these particles, a square block was taken as a reference frame having 100 rectangular blocks. One block was allocated for one particle. Every column of 10 blocks fills either 8 or 9 particles that were randomly assigned. The location of the particles was randomly made offset from the block centre. In order to incorporate the true randomness, the standard random function “rand” in Matlab [Matlab, 06] was used to make decisions on random selections. As the code for particle size and its distribution in the matrix was written in Matlab, the distribution was generated using Matlab. Thereafter the distribution was imported to AutoCAD [AutoCad, 04] with a suitable interface. Then the design was loaded to Abaqus [HKS, 06] for meshing. Apart from creating a realistic random geometry in the microstructure, it is more important and challenging to impart different material properties to the phase particles and to the matrix material. To assign the phases and matrix with different material properties, the phase and the matrix were meshed with different elements and thus they can be assigned different material properties.

FEA SIMULATION PROCEDURE Material Properties for Phase Particles and Matrix The stress-strain curves in Fig. 3 of the cementite particles at different strains and temperatures were obtained from uniaxial compression tests [Terashima et al., 06; Umemoto, 04]. For the material properties characterizing matrix mechanical behavior, the internal state variable plasticity model [Bammann et al., 96] was used. The material constants were obtained from a series of material tests and curve fitting [Guo et al., 06] on 52100 steel over a wide range of temperatures. The material constants were incorporated into Abaqus via the user subroutine VUMAT [Guo et al., 06] where all the constitutive equations of the model were coded. Table 1 lists the material constants used for matrix.

3.5

Stress (MPa)

3 2.5 2 1.5 1 0.5 0 0

0.05

0.1

0.15

0.2

0.25

0.3

Strain 573K

873K

973K

1173k

300K

FIG 3. STRESS-STRAIN CURVE OF THE CEMENTITE BY UNIAXIAL COMPRESSION TESTING [Terashima et al., 06; Umemoto, 04].

FIG 2. MESH OF TWO-PHASE MICROSTRUCTURE OF THE AISI 52100 HARDENED STEEL.

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The orthogonal cutting model was used where the workpiece initial temperature is room temperature 22 °C. The tool was assumed to be rigid and only moves horizontally. The workpiece bottom was modeled using semi-infinite elements and the left edge and right lower edge were constrained.

TABLE 1. AISI 52100 MATERIAL CONSTANTS OF THE MATRIX MATERIAL FOR USER SUBROUTINE. Material constants Shear Modulus G (Pa) a Bulk Modulus K (Pa) b Melting point(K) C1 (MPa) C2 (K) C3 (MPa) C4 (K) C5 (1/s) C6 (K) C7 (1/MPa) C8 (K) C9 (MPa) C10 (MPa/K) C11 (s/MPa) C12 (K) C13 (1/MPa) C14 (K) C15 (MPa) C16 (MPa/K) C17 (s/MPa) C18 (K) C19 C20 (K) C21 Initial temperature (K) 3 Heat Coefficient (m K/J) Initial damage Damage exponent

Values 7.85E+10 1.23E+00 1.52E+11 -1.85E+10 1.64E+03 1.00E+00 1.00E+00 1.07E+03 1.00E+00 1.00E+00 -1.20E+04 4.00E-02 0.00E+00 5.60E+03 2.00E+01 2.385E-03 4.00E+02 5.50E-01 3.00E+02 6.00E+05 5.36E+02 3.50E-04 4.00E+03 1.00E-01 6.73E+02 0.00E+00 2.93E+02 2.43E-07 0.01E+00 3.00E+00

RESULTS AND DISCUSSIONS Shearing-Plowing Transition Fig. 4 shows the evolutions of chip morphology, von Mises stress, and cutting temperature when the DOC reduces from 40 µm to 10 µm. Saw-tooth chips were successfully simulated at each DOC level. However, the chip morphology is more serrated at the larger DOC 40µm, while chip is more difficult to produce at the smaller DOC 10µm which is same as the edge radius. It seems the material experiences more shearing at larger DOCs than those at smaller ones. It should be pointed out that experimental study has shown that chips will not form for DOC under a critical value. Though the simulation may not determine the critical DOC, but this observation seems to support the established fact that chips are difficult to generate as DOC reduces.

DOC: 40 µm V: 2.5 m/s Rake: -8° Radius: 10 µm

Simulation Conditions and Cutting Edge Geometry

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The cutting tool edge for micromachining is characterized by a negative rake angle. The depth of cut is on the same order of cutting edge radius. Table 2 shows the tool edge geometry where the edge radius is 10µm. Four levels of depth-of-cut (DOC) (40 µm, 30µm, 20µm, and 10µm) were selected so that the ratio of edge radius to DOC varies from 4 to 1. The cutting conditions enable the simulation to reveal the shearing-plowing transition in micromachining.

DOC: 40 µm V: 2.5 m/s Rake: -8° Radius: 10 µm

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FIG 4(A). CHIP MORPHOLOGY FOR DOC 40 ΜM AND -8° RAKE ANGLE.

DOC: 30 µm V: 2.5 m/s Rake: -8° Radius: 10 µm

DOC: 30 µm V: 2.5 m/s Rake: -8° Radius: 10 µm

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TABLE 2. CUTTING CONDITIONS. Rake Angle α (o) -8 8

DoC (μm) 40, 30, 20, 10 40, 30, 20, 10

R (μm) 10 10

V (m/s) 2.5 2.5

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Relief angle θ (o) 3 6

FIG 4(B). CHIP MORPHOLOGY FOR DOC 30 ΜM AND -8° RAKE ANGLE.

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DOC: 20 µm V: 2.5 m/s Rake: -8° Radius: 10 µm

Deformation Behavior of Phase Particles

DOC: 20 µm V: 2.5 m/s Rake: -8° Radius: 10 µm

Fig. 4 shows that the randomly distributed phase particles can be successfully modeled by the FEA simulation where separate properties were assigned to the phase and matrix material. The different properties assigned to the phase and matrix allows the examination of deformation characteristics in the matrix material. As expected the brittle phase materials experience much higher stress than the matrix material, which can be clearly verified by the stress contours in Fig. 4 for each simulation cases. The matrix materials generate much higher temperatures than the particles. Therefore, it indicates that the particles experience higher stress and less temperature, and therefore, tend to fail/break at their locations when deforming along the matrix.

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FIG 4(C). CHIP MORPHOLOGY FOR DOC 20 ΜM AND -8° RAKE ANGLE.

DOC: 10 µm V: 2.5 m/s Rake: -8° Radius: 10 µm

DOC: 10 µm V: 2.5 m/s Rake: -8° Radius: 10 µm

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20 µm

FIG 4(D). CHIP MORPHOLOGY FOR DOC 10 ΜM AND -8° RAKE ANGLE.

Rake Angle Effect

The material behavior is largely governed by the ratio of DOC to the edge radius. When this ratio is large the material behaves in homogeneous fashion. However, when this ratio approaches 1 or less than 1, the deformation scale reduces down to individual particles. Thus, the particle deformation becomes significant in defining material behavior and surface integrity. Fig. 5 shows the increased ratio of thrust force to the cutting force when DOC decreases. It seems a ratio transition occurs around the DOC 20 µm, which implies that the developed simulation does recover the size effect in micromachining. The force ratio transition is aligned with the transition of shearing-plowing.

To understand the effect of tool rake angle on micromachining, another four simulation cases with a positive rake angle 8 °C were performed. Compared with the stress and temperature contours in Fig. 4, the simulations with the positive rake angle show the different chip morphology, smaller von Mises stress, and lower cutting temperatures in Fig. 6 with the positive rake angle. Compared with the simulation cases with the negative rake angle, chip formation is more difficult in case positive rake angle and the simulation is hard to go through. In reality, it means that cutting edge chipping may occur. However, the edge chipping phenomenon may not be recovered in the simulations since the cutting tool was modeled as rigid.

1.2 1.1

Ploughing

Shearing

Ft/Fc

1 0.9

DOC: 40 µm V: 2.5 m/s Rake: 8° Radius: 10 µm

DOC: 40 µm V: 2.5 m/s Rake: 8° Radius: 10 µm

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20 µm

0.8 0.7 0.6 10

20

30

40

FIG 6(A). CHIP MORPHOLOGY FOR DOC 40 ΜM AND 8° RAKE ANGLE.

Doc (μm)

FIG 5. SHEARING-PLOUGHING TRANSITION IN MICROMACHINING.

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DOC: 30 µm V: 2.5 m/s Rake: 8° Radius: 10 µm

DOC: 30 µm V: 2.5 m/s Rake: 8° Radius: 10 µm

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•

•

FIG 6(B). CHIP MORPHOLOGY FOR DOC 30 ΜM AND 8° RAKE ANGLE.

DOC: 20 µm V: 2.5 m/s Rake: 8° Radius: 10 µm

20 µm

•

DOC: 20 µm V: 2.5 m/s Rake: 8° Radius: 10 µm

The developed microstructure modeling can simulate the randomness of location, size, and orientation of the second phase particles; The different material properties of the phase particles and matrix material can be modeled via the direct material input method and the internal state variable plasticity model respectively; The shearing-plowing transition and increased ratio of thrust-cutting force can be recovered in the micromachining simulations.

ACKNOWLEDGEMENT

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The research is based upon the work supported by the National Science Foundation under Grant No. CMMI-0447452.

FIG 6(C). CHIP MORPHOLOGY FOR DOC 20 ΜM AND 8° RAKE ANGLE.

REFERENCES DOC: 10 µm V: 2.5 m/s Rake: 8° Radius: 10 µm

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Dornfeld, D.A., S. Min, and Y. Takeuchi (2006). “Recent advances in mechanical micromachining.” CIRP Annals, Vol. 55/2, pp. 124.

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Gall, K., M.F. Horstemeyer, D.L. McDowell, and J.H. Fan (2000). “Finite element analysis of the stress distributions near damaged Si particle clusters in cast Al-Si alloys.” Mechanics of Materials, Vol. 32, pp. 277-301.

FIG 6(D). CHIP MORPHOLOGY FOR DOC 10 ΜM AND 8° RAKE ANGLE.

This work is focused on the development of methodology of incorporating random microstructure in simulating micromachining. Therefore no actual experiments were included for a one-to-one comparison. Future work will be extended to the particle behaviors and compare with the pertinent experimental observations. The particle debonding or cracking will be modeled when they reach the critical stress limit via a suitable fracture model.

Dighe, M.D., A.M. Gokhale, and M.F. Horstemeyer (2002). “Effect of loading condition and stress state on damage evolution of silicon particles in an Al-Si-Mg-base cast alloy.” Metallurgical and Materials Transactions, Vol. 33A, pp. 555-565.

CONCLUSIONS

Agrawal, H., A.M. Gokhale, S. Graham, M.F. Horstemeyer, and D.J. Bamman (2002). “Rotations of brittle particles during plastic deformation of ductile alloys.” Materials Science & Engineering, Vol. A328, pp. 310-316.

A FEA simulation methodology to incorporate model random microstructure in micromachining multiphase materials has been developed to understand the plowing, tribological, and heat transfer mechanisms. Several points can be made based on the simulation results.

Balasundaram, A., A.M. Gokhale, S. Graham, and M.F. Horstemeyer (2003). “Three dimensional particle cracking damage development in an Al-Mg-base wrought alloy.” Materials Science & Engineering, Vol. A355, pp. 368-383.

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model.” Journal of Manufacturing Science and Engineering, Vol. 126/ 4, pp. 706-709.

Balasundaram, A., Z. Shan, A.M. Gokhale, S. Graham, and M.F. Horstemeyer (2002). “Particle rotations during plastic deformation of 5086 aluminum alloy.” Materials Characterization, Vol. 48, pp. 363-369.

Anurag, S. and Y.B. Guo (2007). “Particle rotations during plastic deformation in hard turning and grinding.” Transactions of NAMRI/SME, Vol. 35, pp. 65-72.

Clarke, A.P., F.J. Humphreys, and P.S. Bate (2003). “Lattice rotations at large second-phase particles in polycrystalline Aluminum.” Conference: Thermec, Processing and Manufacturing of Advanced Materials, Madrid, Spain, Vol. 426-432, pp. 399-404.

Matlab, (2006, http://www.mathworks.com. AutoCAD, (2004). Http://www.autodesk.com. HKS Inc., (2006 ABAQUS/Explicit Manual, version 6.6, Providence, RI.

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User’s

Terashima T., Y. Tomota, M. Isaka, T. Suzuki, M. Umemoto, and Y. Todaka (2006). “Strength and deformation behavior of bulky cementite synthesized by mechanical milling and plasmasintering.” Scripta Materialia, Vol. 54/11, pp. 1925-1929

Ikawa, N., S. Shimada, and H. Tanaka (1992). “Minimum thickness of cut in micromachining.” Nanotechnology, Vol. 3/1, pp. 6-9. Bifano, T.G., T.A. Dow, and Scattergood (1991). “Ductile-regime grinding. A new technology for machining brittle materials.” Journal of Engineering for Industry, Vol. 113/2, pp. 184189.

Umemoto M., Y. Todaka, T. Takahashi, P. Li, R. Tokumiya, and Tsuchiya (2004). “High temperature deformation behavior of bulk cementite produced by mechanical alloying and spark plasma sintering” , Materials Science and Engineering A, Vol. 375-377, pp. 894-898.

To, S., W.B. Lee, and C.Y. Chan (1997). “Ultraprecision Diamond Turning of Aluminum Single Crystals.” Journal of Material Processing Technology, Vol. 63, pp. 157–162.

Bammann, D.J., M.L. Chiesa, and G.C. Johnson (1996). “Modeling Large Deformation and Failure in Manufacturing Processes.” Theor. and Appl. Mech., pp. 359–376.

Ueda, K., T. Sugita, and Hiraga (1991). “Jintegral approach to material removal mechanisms in micro cutting of ceramics.” CIRP Annals, Vol. 40/1, pp. 61-64.

Guo Y.B., Q. Wen, and K.A. Woodbury (2006). “Dynamic Material Behavior Modeling Using Internal State Variable Plasticity and Its Application in Hard Machining Simulations.” Journal of Manufacturing Science and Engineering, Vol. 128/3, pp. 749-759.

Ueda, K. and K. Manabe (1992). “Chip formation mechanism in micro cutting of an amorphous metal.” CIRP Annals, Vol. 41/1, pp. 129-132. Moriwaki, T., N. Sugimura, and S. Luan (1993). “Combined stress, material flow and heat analysis of orthogonal micromachining of copper.” CIRP Annals, Vol. 42/ 1, pp. 75-78. Chuzhoy, L., R.E. DeVor, S.G. Kapoor, and D.J. Bammann (2002). “Microstructure-Level Modeling of Ductile Iron Machining.” Journal of Manufacturing Science and Engineering,Vol. 124/2, pp. 162-169. Park, S., S.G. Kapoor, and R.E. DeVor (2004). “Mechanistic cutting process calibration via microstructure-level finite element simulation

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