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Plane Strain Extrusion – Slip-line Field Solution vs. FEM Solution
Nanshu LuES 246 Plasticity ProjectJan. 11, 2006
Outline
Metal Forming – Extrusion Slip-line Field Solution Unsymmetrical Extrusion FEM Solution Conclusions
Metal Forming – Extrusion
Extrusion: Metal forming process whereby the workpiece is placed in a chamber with an opening and is forced to escape through the opening, usually being pushed out by a mandrel.
Extrusion (a) and an assortment of extrudates (b)
Metal Forming, Betzalel Avitzur, Lehigh University
Slip-line Field SolutionABC
11 0
22 0 0
12
45 00
p kp k p k
CDE
11 1 1
22 1 1
12
sin 302
15 sin 302
3cos302
kp k p
kp k p
kk
0 1
1
22 1
22
2 24 12
13
12 3 2
12 23 2
p k p k const
p k
kp k
P H k H
11 2
22 2
12
sin 2sin 2
cos 2
p kp kk
Fan CAD
Hill R. (1948)
A
B
CD
EF
Gx 2
x 1H
Unsymmetrical Extrusion
2D dr
D
b cb c
Green A.P. (1955)
Fractional Reduction Eccentricity
Unsymmetrical Extrusion
Rough container walls
Smooth container walls
1 11.33log2 12pk r
1
11r
rr
2
11r
rr
1 2 1 212
p p p r p p
10.13 1 1.33log2 1p r rk r
FEM Solution – Modeling Skills Part:
Billet – 2D deformable shell Ram – 2D analytical rigid body
Property Material – steel
Elastic – 2000GPa, v=0.3 Plastic – Yield Stress = 400MPa, perfectly plastic
Material Orientation – local coordinate system Assembly
Billet – punch contact
Stress- Strai n Curve
0
50
100
150
200
250
300
350
400
450
0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6Strai n ε
Stre
ss σ
(MP
a)
400y MPa
FEM Solution – Modeling Skills Step
“Move ram” after initial step Maximum number of increments = 1000 Initial Increment = 0.0001 Minimum time increment = 1e-6 Nonlinear geometry
Output request History output – reaction force on the ram reference
point DOF monitor – monitor the horizontal displacement of
the ram reference point
FEM Solution – Modeling Skills Interaction
Frictionless surface-to-surface contact between billet and the ram at initial step
Load Boundary Condition
Symmetric boundary condition Displacement constraints Imposed displacement to the ram (=0.05m)
FEM Solution – Modeling Skills Mesh
Structured CPE4R elements Global seed size 0.002m
Job Monitor
FEM Solution – Deformed Shape
FEM Solution – Animation
FEM Solution – Reaction Force History
FEM Solution – P~H RelationH (m) 0 0.2 0.4 0.6 0.8 1
P/k 0.0000 0.6187 1.237
3 1.8560 2.4747 3.0933
Pmax (N) 0 75.6 154.2 217.9 308.4 377.5
Cal-P/k 0.0000 0.6547 1.335
4 1.8871 2.6708 3.2692
Extrusi on Force ~ Bi l l et Wi dth Rel ati on
0. 0000
0. 5000
1. 0000
1. 5000
2. 0000
2. 5000
3. 0000
3. 5000
0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1H (m)
P/k
123 2
H
400y MPa
14 0.13 1 1.33log1
H r rr
r=0.5,
FEM Solution – P~k Relationσy (MPa) 360 380 400 420 440
P/(2H) (MPa) 321.6 339.4 357.3 375.2 393.0 Pmax (N) 68.8 72.2 75.6 78.9 82.2
Cal-P/(2H) 344 361 378 394.5 411
Extrusi on Force ~ Yei l d Stress Rel ati on
320. 0
330. 0
340. 0
350. 0
360. 0
370. 0
380. 0
390. 0
400. 0
410. 0
420. 0
360 370 380 390 400 410 420 430 440Yi el d Stress (MPa)
P/(2
H)(M
Pa)
13 2
k
H=0.2m
FEM Solution – Unsymmetrical Extrusion
ε 0 0.2 0.4 0.6Δp/k 0.0000 0.0300 0.1300 0.2950 P (N) 204.8 206.6 211.3 218.6
Cal- Δp/k 0.0000 0.0390 0.1407 0.2988
I ncrease i n extrusi on pressure due to eccent r i ci ty
0. 0000
0. 0500
0. 1000
0. 1500
0. 2000
0. 2500
0. 3000
0. 3500
0. 4000
0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6Eccent r i ci t y ε
Δp/
k
r=0.8
Conclusion
Slip-line field method gives good solutions for metal-forming process
ABAQUS/CAE v6.5 is able to calculate perfectly-plastic material
Adaptive meshing is needed to simulate metal-forming process accurately
Thermal contact interaction should be included further
Acknowledgement
Joost Vlassak Jennifer Furstenau Xuanhe Zhao