SIMULATION OF CHIP FORMATION

DURING HIGH-SPEED CUTTING

Authors: Christian Hortig and Bob Svendsen

Jordan Felkner

October 5, 2009

Purpose

Model and simulate shear banding and chip formation during high-speed cutting

Carry out a systematic investigation of size- and orientation-based mesh-dependence of the numerical solutionFinite Element Analysis

A Little VocabShear Band: region where plastic shear has taken

placeAdiabatic Shear Banding: shearing with no heat

transfer○ Mechanical dissipation dominates heat conduction

Mesh: the size and orientation of the element

Why is this Important?

Cutting forcesShear banding represents the main

mechanism of chip formation ○ Results in reduced cutting forces

Tool design Other technological aspects

References[1] M. B¨aker, J. R¨osier, C. Siemers, A finite

element model of high speed metal cutting with adiabatic shearing, Comput. Struct. 80 (2002) 495–513.

[2] M. B¨aker, An investigation of the chip segmentation process using finite elements, Tech. Mech. 23 (2003) 1–9.

[3] M. Baker, Finite element simulation of high speed cutting forces, J. Mater. Process. Technol. 176 (2006) 117–126.

[4] A. Behrens, B. Westhoff, K. Kalisch, Application of the finite element method at the chip forming process under high speed cutting conditions, in: H.K. T¨onshoff, F. Hollmann (Eds.), Hochgeschwindigkeitsspanen,Wileyvch, 2005, ISBN 3-527-31256-0, pp. 112–134.

[5] C. Comi, U. Perego, Criteria for mesh refinement in nonlocal damage finite element analyses, Eur. J. Mech. A/Solids 23 (2004) 615– 632.

[6] E. El-Magd, C. Treppmann, Mechanical behaviour of Materials at high strain rates, in: H. Schulz (Ed.), Scientific Fundamentals of High-Speed Cutting, Hanser, 2001, ISBN 3-446-21799-1, pp. 113–122.

[7] T.I. El-Wardany, M.A. Elbestawi, Effect of material models on the accuracy of highspeed machining simulation, in: H. Schulz (Ed.), Scientific Fundamentals of High-Speed Cutting, Hanser, 2001, ISBN 3-446-21799-1, pp. 77–91.

[8] D.P. Flanagan, T. Belytschko, A Uniform Strain Hexahedron and Quadrilateral with Orthogonal Hourglass Control, Int. J. Numer. Methods Eng. 17 (1981) 679–706.

[9] G.R. Johnson, W.H. Cook, A constitutive model and data for metals subjected to large strain, high strain-rates and high temperatures, in: Proceedings of the 7th International Symposium on Ballistics, The Hague, The

Netherlands, 1983. pp. 541–547.

[10] T. Mabrouki, J.-F. Rigal, A contribution to a qualitative understanding of thermo-mechanical effects during chip formation in hard turning, J. Mater. Process. Technol. 176 (2006) 214–221.

[11] M.E. Merchant, Mechanics of the metal cutting process. I. Orthogonal cutting and a type 2 chip, J. Appl. Phys. 16 (1945) 267–275.

References[1] M. B¨aker, J. R¨osier, C. Siemers, A finite

element model of high speed metal cutting with adiabatic shearing, Comput. Struct. 80 (2002) 495–513.

[2] M. B¨aker, An investigation of the chip segmentation process using finite elements, Tech. Mech. 23 (2003) 1–9.

[3] M. Baker, Finite element simulation of high speed cutting forces, J. Mater. Process. Technol. 176 (2006) 117–126.

[4] A. Behrens, B. Westhoff, K. Kalisch, Application of the finite element method at the chip forming process under high speed cutting conditions, in: H.K. T¨onshoff, F. Hollmann (Eds.), Hochgeschwindigkeitsspanen,Wileyvch, 2005, ISBN 3-527-31256-0, pp. 112–134.

[5] C. Comi, U. Perego, Criteria for mesh refinement in nonlocal damage finite element analyses, Eur. J. Mech. A/Solids 23 (2004) 615– 632.

[6] E. El-Magd, C. Treppmann, Mechanical behaviour of Materials at high strain rates, in: H. Schulz (Ed.), Scientific Fundamentals of High-Speed Cutting, Hanser, 2001, ISBN 3-446-21799-1, pp. 113–122.

[7] T.I. El-Wardany, M.A. Elbestawi, Effect of material models on the accuracy of highspeed machining simulation, in: H. Schulz (Ed.), Scientific Fundamentals of High-Speed Cutting, Hanser, 2001, ISBN 3-446-21799-1, pp. 77–91.

[8] D.P. Flanagan, T. Belytschko, A Uniform Strain Hexahedron and Quadrilateral with Orthogonal Hourglass Control, Int. J. Numer. Methods Eng. 17 (1981) 679–706.

[9] G.R. Johnson, W.H. Cook, A constitutive model and data for metals subjected to large strain, high strain-rates and high temperatures, in: Proceedings of the 7th International Symposium on Ballistics, The Hague, The Netherlands, 1983. pp. 541–547.

[10] T. Mabrouki, J.-F. Rigal, A contribution to a qualitative understanding of thermo-mechanical effects during chip formation in hard turning, J. Mater. Process. Technol. 176 (2006) 214–221.

[11] M.E. Merchant, Mechanics of the metal cutting process. I. Orthogonal cutting and a type 2 chip, J. Appl. Phys. 16 (1945) 267–275.

References[12] E.H. Lee, B.W. Shaffer, The theory of

plasticity applied to a problem of machining, J. Appl. Phys. 18 (1951) 405–413.

[13] T. O¨ zel, T. Altan, Process simulation using finite element method—prediction of cutting forces, tool stresses and temperatures in high speed flat end milling, J. Mach. Tools Manuf. 40 (2000) 713–783.

[14] T. O¨ zel, E. Zeren, Determination of work material flow stress and friction for FEA of machining using orthogonal cutting tests, J. Mater. Process. Technol. 153–154 (2004) 1019–1025.

[15] F. Reusch, B. Svendsen, D. Klingbeil, Local and non local gurson based ductile damage and failure modelling at large deformation, Euro. J. Mech. A/Solid 22 (2003) 779–792.

[16] P. Rosakis, A.J. Rosakis, G. Ravichandran, J. Hodowany,Athermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals, J. Mech. Phys. Solids 48 (2000) 581–607.

[17] R. Sievert, A.-H. Hamann, D. Noack, P. L¨owe, K.N. Singh, G. K¨unecke, R. Clos, U.

Schreppel, P. Veit, E. Uhlmann, R. Zettier, Simulation of chip formation with damage during high-speed cutting, Tech. Mech. 23 (2003) 216–233 (in German).

[18] R. Sievert, A.-H. Hamann, D. Noack, P. L¨owe, K.N. Singh, G. K¨unecke, Simulation of thermal softening, damage and chip segmentation in a nickel super-alloy, in: H.K. T¨onshoff, F. Hollmann (Eds.), Hochgeschwindigkeitsspa-nen,Wiley-vch, 2005, ISBN 3-527-31256-0, pp. 446–469 (in German).

[20] H.K. T¨onshoff, B. Denkena, R. Ben Amor, A. Ostendorf, J. Stein, C. Hollmann, A. Kuhlmann, Chip formation and temperature development at high cutting speeds, in: H.K. T¨onshoff, F. Hollmann (Eds.), Hochgeschwindigkeit-sspanen,Wiley-vch, 2005, ISBN 3-527-31256-0, pp. 1–40 (in German).

[21] Q. Yang, A. Mota, M. Ortiz, A class of variational strain-localization finite elements, Int. J. Numer. Methods in Eng. 62 (2005) 1013–1037.

References[12] E.H. Lee, B.W. Shaffer, The theory of

plasticity applied to a problem of machining, J. Appl. Phys. 18 (1951) 405–413.

[13] T. O¨ zel, T. Altan, Process simulation using finite element method—prediction of cutting forces, tool stresses and temperatures in high speed flat end milling, J. Mach. Tools Manuf. 40 (2000) 713–783.

[14] T. O¨ zel, E. Zeren, Determination of work material flow stress and friction for FEA of machining using orthogonal cutting tests, J. Mater. Process. Technol. 153–154 (2004) 1019–1025.

[15] F. Reusch, B. Svendsen, D. Klingbeil, Local and non local gurson based ductile damage and failure modelling at large deformation, Euro. J. Mech. A/Solid 22 (2003) 779–792.

[16] P. Rosakis, A.J. Rosakis, G. Ravichandran, J. Hodowany,Athermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals, J. Mech. Phys. Solids 48 (2000) 581–607.

[17] R. Sievert, A.-H. Hamann, D. Noack, P. L¨owe, K.N. Singh, G. K¨unecke, R. Clos, U.

Schreppel, P. Veit, E. Uhlmann, R. Zettier, Simulation of chip formation with damage during high-speed cutting, Tech. Mech. 23 (2003) 216–233 (in German).

[18] R. Sievert, A.-H. Hamann, D. Noack, P. L¨owe, K.N. Singh, G. K¨unecke, Simulation of thermal softening, damage and chip segmentation in a nickel super-alloy, in: H.K. T¨onshoff, F. Hollmann (Eds.), Hochgeschwindigkeitsspa-nen,Wiley-vch, 2005, ISBN 3-527-31256-0, pp. 446–469 (in German).

[20] H.K. T¨onshoff, B. Denkena, R. Ben Amor, A. Ostendorf, J. Stein, C. Hollmann, A. Kuhlmann, Chip formation and temperature development at high cutting speeds, in: H.K. T¨onshoff, F. Hollmann (Eds.), Hochgeschwindigkeit-sspanen,Wiley-vch, 2005, ISBN 3-527-31256-0, pp. 1–40 (in German).

[21] Q. Yang, A. Mota, M. Ortiz, A class of variational strain-localization finite elements, Int. J. Numer. Methods in Eng. 62 (2005) 1013–1037.

Material Assumptions Inconel 718

Alloy composed of mostly nickel and chromium Work piece is fundamentally thermoelastic,

viscoplastic in natureThermoelastic

○ Temperature changes induced by stressViscoplastic

○ permanent deformations under a load but continues to creep (equilibrium is impossible)

Isotropic material behavior

Design Principle

Low cutting speedsLow strain-rates“Fast” heat

conduction

High cutting speedsHigh strain-rates“Slow” heat

conduction○ Thermal softening○ Shear banding

Design Principle Johnson-Cook and Hooke Models

Plastic deformation results in a temperature increase○ Temperature increase is a function of strain (left)○ Temperature increase results in softening

At points of maximal mechanical dissipation in the material, softening effects may dominate hardening (right)○ Results in material instability, deformation localization and

shear-band formation

Design Principle

Finite-element simulation of thermal shear-bandingShear angle

○ Φ=40°Cutting tool angle

○ γ=0°Plane strain

deformationVc=1000 m/min

FEA: Parallel Notch represents a geometric inhomogenity

Idealized notched structure discretized with bilinear elements oriented in the predicted shear-band direction. Average element edge-length here is 0.005 mm.

FEA: Parallel

TOP Cutting speed vc=10 m/min Thermal conduction is “fast”

○ No thermal softening○ NO shear-band formation.

BOTTOM Cutting speed vc=1000 m/min Thermal conduction is “slow”

○ Thermal softening○ Shear-band formation○ Chip formation

FEA: Rotated

Restricted to “high” cutting speedAssume adiabatic

Idealized structure with elements oriented at 45◦ to the direction ofshearing. As before, the average element edge length here is 0.005 mm

FEA: Rotated

No shear band formation in the expected direction

Temperature distribution in the mesh from above after shearing at a rate equivalent to a cutting speed of 1000 m/min

FEA: Rotated

Why?Constant strain elements

FEA: Reduced Parallel Different element edge lengths

Temperature distribution in the notched structure discretized parallel to the shear direction using different element edge lengths: 0.005mm (above), 0.0025mm (below).

FEA: Reduced Rotated Different element edge lengths

Temperature distribution in the notched structure discretized at a 45◦ angle to the shear direction using different element edge lengths: 0.005mm (above), 0.0025mm (below).

Results of FEA Shear-band The coarser mesh in both cases, and

the rotated mesh in general, behave more stiffly, resulting in “delayed” shear-band development.

FEA: Chip Formation

δ discretization angle

Finite-element model for the work-piece/tool system used for the cuttingsimulation. Mesh orientation relative to the cutting plane is represented here bythe angle δ.

FEA: Chip Formation

Merchant, Lee and Schaffer Models φ =π/4 - 1/2(arctanμ − γ)

φ Shear angleγ Chip angleμ Coefficient of Friction

FEA: Chip Formation Chip formation becomes increasingly inhibited

and diffuse as δ increases beyond φ.

Chip formation and temperature field development for different mesh orientation angles δ:δ=20◦ (left), δ=40◦ (middle), δ=60◦ (right).

FEA: Chip Formation

Chip formation with γ =−5◦ and δ=30◦ for different discretizations. Left: 60×10 elements; middle: 150×20 elements; right: 250×30 elements. Note the mesh-dependence of segmentation, i.e., an increase in segmentation frequency with mesh refinement.

Conclusion Strong dependence on element size and

orientationAffects chip geometry and cutting forcesUsing the mesh to fit the orientation and

thickness of simulated shear bands to experimental results is somewhat questionable and in any case must be done with great care.

Better understanding of cutting forcesBetter efficiencySave money

Questions?