Authors Christian Hortig and Bob Svendsen Jordan Felkner October 5 2009 Purpose Model and simulate shear banding and chip formation during highspeed cutting Carry out a systematic investigation of size and orientationbased meshdependence of the numerical solution ID: 757566
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Slide1
Simulation of chip formation during high-speed cutting
Authors: Christian
Hortig
and Bob
Svendsen
Jordan
Felkner
October 5, 2009Slide2
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 solution
Finite Element AnalysisSlide3
A Little Vocab
Shear Band: region where plastic shear has taken place
Adiabatic Shear Banding: shearing with no heat transfer
Mechanical dissipation dominates heat conduction
Mesh: the size and orientation of the elementSlide4
Why is this Important?
Cutting forces
Shear banding represents the main mechanism of chip formation
Results in reduced cutting forces
Tool design
Other technological aspectsSlide5
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.Slide6
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.Slide7
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.Slide8
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.Slide9
Material Assumptions
Inconel
718
Alloy composed of mostly nickel and chromium
Work piece is fundamentally
thermoelastic, viscoplastic
in nature
Thermoelastic
Temperature changes induced by stress
Viscoplastic
permanent deformations under a load but continues to creep (equilibrium is impossible)
Isotropic material behaviorSlide10
Design Principle
Low cutting speeds
Low strain-rates
“Fast” heat conduction
High cutting speeds
High strain-rates
“Slow” heat conduction
Thermal softening
Shear bandingSlide11
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 formationSlide12
Design Principle
Finite-element simulation of thermal shear-banding
Shear angle
Φ
=40°
Cutting tool angleγ=0°Plane strain
deformation
V
c
=1000 m/minSlide13
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.Slide14
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 softeningShear-band formationChip formationSlide15
FEA: Rotated
Restricted to “high” cutting speed
Assume adiabatic
Idealized structure with elements oriented at 45◦ to the direction of
shearing. As before, the average element edge length here is 0.005 mmSlide16
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/minSlide17
FEA: Rotated
Why?
Constant strain elementsSlide18
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).Slide19
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).Slide20
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.Slide21
FEA: Chip Formation
δ
discretization
angle
Finite-element model for the work-piece/tool system used for the cutting
simulation. Mesh orientation relative to the cutting plane is represented here by
the angle
δ.Slide22
FEA: Chip Formation
Merchant, Lee and Schaffer Models
φ =π
/4 - 1/2
(
arctanμ − γ)φ
Shear angle
γ
Chip angle
μ
Coefficient of FrictionSlide23
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).Slide24
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.Slide25
Conclusion
Strong dependence on element size and orientation
Affects chip geometry and cutting forces
Using 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 forces
Better efficiency
Save moneySlide26
Questions?