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Research Papers

# A Physics-Based Model for Metal Matrix Composites Deformation During Machining: A Modified Constitutive Equation

[+] Author and Article Information
M. N. A. Nasr

Department of Mechanical Engineering,
Faculty of Engineering,
Alexandria University,
Alexandria 21544, Egypt

A. Ghandehariun, H. A. Kishawy

Machining Research Laboratory (MRL),
Faculty of Engineering and Applied Science,
University of Ontario Institute
of Technology (UOIT),

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received April 29, 2016; final manuscript received August 1, 2016; published online October 6, 2016. Assoc. Editor: Marwan K. Khraisheh.

J. Eng. Mater. Technol 139(1), 011003 (Oct 06, 2016) (8 pages) Paper No: MATS-16-1128; doi: 10.1115/1.4034509 History: Received April 29, 2016; Revised August 01, 2016

## Abstract

One of the main challenges encountered in modeling the behavior of metal matrix composites (MMCs) during machining is the availability of a suitable constitutive equation. Currently, the Johnson–Cook (J–C) constitutive equation is being used, even though it was developed for homogeneous materials. In such a case, an equivalent set of homogeneous parameters is used, which is only suitable for a particular combination of particle size and volume fraction. The current work presents a modified form of the J–C constitutive equation that suits MMCs, and explicitly accounts for the effects of particle size and volume fraction, as controlled parameters. Also, an energy-based force model is presented, which considers particle cracking and debonding based on the principles of fracture mechanics. In order to validate the new approach, cutting forces were predicted and compared to experimental results, where a good agreement was found. In addition, the predicted forces were compared to other analytical models available in the literature.

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## References

Lloyd, D. J. , 1994, “ Particle Reinforced Aluminium and Magnesium Matrix Composites,” Int. Mater. Rev., 39(1), pp. 1–23.
Li, Y. , Ramesh, K. T. , and Chin, E. S. C. , 2007, “ Plastic Deformation and Failure in A359 Aluminium and an A359–SiCp MMC Under Quasi-Static and High-Strain-Rate Tension,” J. Compos. Mater., 41(1), pp. 27–40.
Sikder, S. , and Kishawy, H. A. , 2012, “ Analytical Model for Force Prediction When Machining Metal Matrix Composite,” Int. J. Mech. Sci., 59(1), pp. 95–103.
Denkena, B. , Vehmeyer, J. , Niederwestberg, D. , and Maaß, P. , 2014, “ Identification of the Specific Cutting Force for Geometrically Defined Cutting Edges and Varying Cutting Conditions,” Int. J. Mach. Tools Manuf., 82–83, pp. 42–49.
Sonawane, H. A. , and Joshi, S. S. , 2010, “ Analytical Modelling of Chip Geometry and Cutting Forces in Helical Ball End Milling of Superalloy Inconel 718,” CIRP J. Manuf. Sci. Technol., 3(3), pp. 204–217.
Tuysuz, O. , Altintas, Y. , and Feng, H. Y. , 2013, “ Prediction of Cutting Forces in Three and Five-Axis Ballend Milling With Tool Indentation Effect,” Int. J. Mach. Tools Manuf., 66(3), pp. 66–81.
Nasr, M. , Ng, E. G. , and Elbestawi, M. , 2007, “ Modelling the Effects of Tool-Edge Radius on Residual Stresses When Orthogonal Cutting AISI-316L,” Int. J. Mach. Tools Manuf., 47(2), pp. 401–411.
Nasr, M. , and Outeiro, J. , 2015, “ Sensitivity Analysis of Cryogenic Cooling on Machining of Magnesium Alloy AZ31B-O,” Procedia CIRP, 31, pp. 264–269.
Gradisek, J. , Kalveram, M. , and Weinert, K. , 2004, “ Mechanistic Identification of Specific Force Coefficients for a General End Mill,” Int. J. Mach. Tools Manuf., 44(4), pp. 401–414.
Altintas, Y. , Eynian, M. , and Onozuka, H. , 2008, “ Identification of Dynamic Cutting Force Coefficients and Chatter Stability With Process Damping,” CIRP Ann.-Manuf. Technol., 57(1), pp. 371–374.
Chen, L. , El-Wardany, T. I. , Nasr, M. , and Elbestawi, M. , 2006, “ Effects of Edge Preparation and Feed When Hard Turning a Hot Work Die Steel With Polycrystalline Cubic Boron Nitride Tools,” CIRP Ann.-Manuf. Technol., 55(1), pp. 89–92.
Johnson, G. R. , and Cook, W. H. , 1983, “ A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures,” Seventh International Symposium on Ballistics, Hague, The Netherlands, pp. 541–547.
Tomac, N. , Tannessen, K. , and Rasch, F. O. , 1992, “ Machinability of Particulate Aluminium Matrix Composites,” CIRP Ann.-Manuf. Technol., 41(1), pp. 55–58.
Songmene, V. , and Balazinski, M. , 1999, “ Machinability of Graphitic Metal Matrix Composites as a Function of Reinforcing Particles,” CIRP Ann.-Manuf. Technol., 48(1), pp. 77–80.
Weinert, K. , Biermann, D. , and Bergmann, S. , 2007, “ Machining of High Strength Light Weight Alloys for Engine Applications,” CIRP Ann.-Manuf. Technol., 56(1), pp. 105–108.
Kishawy, H. A. , Kannan, S. , and Balazinski, M. , 2004, “ An Energy Based Analytical Force Model for Orthogonal Cutting of Metal Matrix Composites,” CIRP Ann.-Manuf. Technol., 53(1), pp. 91–94.
Pramanik, A. , Zhang, L. C. , and Arsecularatne, J. A. , 2006, “ Prediction of Cutting Forces in Machining of Metal Matrix Composites,” Int. J. Mach. Tools Manuf., 46(14), pp. 1795–1803.
Kishawy, H. A. , Kannan, S. , and Balazinski, M. , 2005, “ Analytical Modelling of Tool Wear Progression During Turning Particulate Reinforced Metal Matrix Composites,” CIRP Ann.-Manuf. Technol., 54(1), pp. 55–58.
Kannan, S. , Kishawy, H. A. , Deiab, I . M. , and Surappa, M. L. , 2005, “ Modelling of Tool Flank Wear Progression During Orthogonal Machining of Metal Matrix Composites,” Trans. North Am. Manuf. Res. Inst. SME NAMRC, 33, pp. 605–612.
Bejjani, R. , 2012, “ Machinability and Modelling of Cutting Mechanism for Titanium Metal Matrix Composites,” Ph.D. thesis, Universite de Montreal, Montreal, QC, Canada.
Ghandehariun, A. , Kishawy, H. , and Balazinski, M. , 2016, “ On Machining Modelling of Metal Matrix Composites: A Novel Comprehensive Constitutive Equation,” Int. J. Mech. Sci., 107(3), pp. 235–241.
Astakhov, V. P. , and Xiao, X. , 2008, “ A Methodology for Practical Cutting Force Evaluation Based on the Energy Spent in the Cutting System,” Mach. Sci. Technol., 12(3), pp. 325–347.
Zhu, Y. , and Kishawy, H. A. , 2005, “ Influence of Alumina Particles on the Mechanics of Machining Metal Matrix Composites,” Int. J. Mach. Tools Manuf., 45(4–5), pp. 389–398.
Li, Y. , and Ramesh, K. T. , 1998, “ Influence of Particle Volume Fraction, Shape, and Aspect Ratio on the Behaviour of Particle-Reinforced Metal–Matrix Composites at High Rates of Strain,” Acta Mater., 46(16), pp. 5633–5646.
Chawla, N. , and Shen, Y. L. , 2001, “ Mechanical Behaviour of Particle Reinforced Metal Matrix Composites,” Adv. Eng. Mater., 3(6), pp. 357–370.
Wallin, K. , Saario, T. , and Torronen, K. , 1987, “ Fracture of Brittle Particles in a Ductile Matrix,” Int. J. Fract., 32(3), pp. 201–209.
Astakhov, V. P. , and Shvets, S. , 2004, “ The Assessment of Plastic Deformation in Metal Cutting,” J. Mater. Process. Technol., 146(2), pp. 193–202.
Oxley, P. L. B. , 1989, The Mechanics of Machining: An Analytical Approach to Assessing Machinability, E. Horwood, New York.
Tay, A. O. , Stevenson, M. G. , de Vahl Davis, G. , and Oxley, P. L. B. , 1976, “ A Numerical Method for Calculating Temperature Distributions in Machining, From Force and Shear Angle Measurements,” Int. J. Mach. Tool Des. Res., 16(4), pp. 335–349.
Hauert, A. , Rossoll, A. , and Mortensen, A. , 2009, “ Particle Fracture in High-Volume-Fraction Ceramic-Reinforced Metals: Governing Parameters and Implications for Composite Failure,” J. Mech. Phys. Solids, 57(11), pp. 1781–1800.
Dabade, U. A. , Dapkekar, D. , and Joshi, S. S. , 2009, “ Modelling of Chip–Tool Interface Friction to Predict Cutting Forces in Machining of Al/SiCp Composites,” Int. J. Mach. Tools Manuf., 49(9), pp. 690–700.
Jiang, J. , Sheng, F. , and Ren, F. , 1998, “ Modelling of Two-Body Abrasive Wear Under Multiple Contact Conditions,” Wear, 217(1), pp. 35–45.
Goddard, J. , and Wilman, H. , 1962, “ A Theory of Friction and Wear During the Abrasion of Metals,” Wear, 5(2), pp. 114–135.
Sin, H. , Saka, N. , and Suh, N. P. , 1979, “ Abrasive Wear Mechanisms and the Grit Size Effect,” Wear, 55(1), pp. 163–190.
Holt, J. M. , Gibson, C. , and Ho, C. Y. , 1999, Structural Alloys Handbook, CINDAS/Purdue University, West Lafayette, IN.
Munro, R. G. , 1997, “ Evaluated Material Properties for a Sintered α-Alumina,” J. Am. Ceram. Soc., 80(8), pp. 1919–1928.
Shackelford, J. F. , and Alexander, W. , 2001, CRC Materials Science and Engineering Handbook, 3rd ed., CRC Press, Boca Raton, FL.
Lesuer, D. R. , Kay, G. J. , and LeBlanc, M. M. , 1999, “ Modelling Large-Strain, High-Rate Deformation in Metals,” Third Biennial Tri-Laboratory Engineering Conference on Modelling and Simulation, Pleasanton, CA.
Fang, N. , 2005, “ A New Quantitative Sensitivity Analysis of the Flow Stress of 18 Engineering Materials in Machining,” ASME J. Eng. Mater. Technol., 127(2), pp. 192–196.
Yadav, S. , Chichili, D. R. , and Ramesh, K. T. , 1995, “ The Mechanical Response of a 6061-T6 Al/Al2O3 Metal Matrix Composite at High Rates of Deformation,” Acta Mater., 43(12), pp. 4453–4464.
Dandekar, C. R. , and Shin, Y. C. , 2009, “ Multi-Step 3-D Finite Element Modelling of Subsurface Damage in Machining Particulate Reinforced Metal Matrix Composites,” Composites, Part A, 40(8), pp. 1231–1239.

## Figures

Fig. 1

A schematic diagram of two-body abrasion parameters

Fig. 4

Effect of particle size on cutting force (Vf = 10%, v = 0.5 m/s, t1 = 0.1 mm, and γ = 0 deg)

Fig. 5

Effect of volume fraction on cutting force (d = 25 μm, v = 0.5 m/s, t1 = 0.1 mm, and γ = 0 deg)

Fig. 2

Effect of feed rate on cutting force (Vf = 10%, d = 17 μm, v = 1 m/s, and γ = 6 deg)

Fig. 3

Effect of cutting speed on cutting force (Vf = 20%, d = 25 μm, t1 = 0.1 mm, and γ = 0 deg)

## Errata

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