Transcript Document

Thermally-Enhanced Forming of Mg Sheets
Midterm Report, Dec. 5, 2008 - May 31, 2009
Robert H. Wagoner
R. Wagoner, LLC
144 Valley Run Place
Powell OH 43065
R. H. Wagoner
1
One-Year Project Goals
(from Research Agreement, signed December 5, 2008)
Task “1. Formulate a simple, approximate, constitutive equation based on simple
testing temperature at a range of temperatures, rates and strains that is suitable
for implementation in commercial sheet-forming softward (LS-Dyna, PamStamp,
etc.). ”
Status: First fitting completed. (For Posco AZ31B material provided.) To be
improved.
Task “2. Develop a thermo-mechanical FE model of a simplified sample part to be
specified by Posco.”
Status: The simplified model has been constructed in Abaqus and preliminary
testing has been done. Will perform simulations using Abaqus for comparison
with Posco simulation using LS-Dyna or PamStamp. Will refine thermal model.
Task “3. Using the constitutive equation of Goal 2 and the FE model of Goal 3,
identify optimal thermally-assisted forming strategies for the sample part.”
Status: Not started yet.
R. H. Wagoner
2
Summary
Task I. Constitutive Equation – Measurement, fitting
-A. Tensile testing – AUSTEM Mg AZ31B
-B. Screening of material (use 118-5)
-C. Tensile testing
150oC 200oC
Posco Mg AZ31B
250oC 300oC
10-1/s
x
x
x
x
10-2.5/s
x
x
x
x
10-4/s
x
x
x
-D. Fitting to 3 laws: H, V, H&V
-E. Verify const. eq. using FEA simulation (tensile to broken)
Task II. Postech/Posco Formability Test Simulation
-A. Put in ABAQUS model
-B. Modify B.C. for convergence
-C. Preliminary simulation using Posco/Postech constitutive eq*
* K. Oh and et al., “Development of New Formability Test for Sheet Materials using Axiomatic Design”,
submitted to J. Mater. Proc. Tech..
R. H. Wagoner
3
Summary of Properties of Mg sheets
Material
material
used
Thickness (mm)
YS (MPa)
UTS (MPa)
Ave.
Standard
Dev.
Ave.
Standard
Dev.
Ave.
Standard
Dev.
108-5
0.996
0.007
197
5
284
3
118-5
0.973
0.009
197
3
284
2
336-3
1.020
0.007
196
2
280
2
R. H. Wagoner
4
Tensile Tests Results:
AUSTEM vs. Posco
R. H. Wagoner
5
Tensile Tests of Mg AZ31B at 150oC & 200oC
300
300
o
o
Mg AZ31B, 150 C
Posco sample, t = 1mm
AUSTEM sample, t = 2mm
-1
10 /s,P
250
Mg AZ31B, 200 C
Posco sample, t = 1mm
AUSTEM sample, t = 2mm
250
-1
10 /s, A
200
10
150
10
-2.5
-2.5
True Stress (MPa)
True Stress (MPa)
200
/s, P
/s, A
100
-1
10 /s, P
-1
150
10 /s, A
100
10
-2.5
/s, A
10
-4
-2.5
/s, P
10 /s, A
-4
10 /s, P
50
50
-4
-4
10 /s, A
10 /s, P
0
0
0
0.2
0.4
True Strain
R. H. Wagoner
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
True Strain
6
Tensile Tests of Mg AZ31B at 250oC & 300oC
300
300
o
o
Mg AZ31B, 200 C
Posco sample, t = 1mm
AUSTEM sample, t = 2mm
250
250
200
-1
10 /s, P
True Stress (MPa)
True Stress (MPa)
200
-1
150
10 /s, A
100
10
-2.5
Mg AZ31B, 300 C
Posco sample, t = 1mm
AUSTEM sample, t = 2mm
150
100
/s, A
10
-2.5
/s, P
-1
-1
10 /s, A
10 /s, P
50
50
10
-4
-4
10 /s, A
10 /s, P
10
-2.5
-2.5
/s, A
/s, P
0
0
0
0.2
0.4
True Strain
R. H. Wagoner
0.6
0.8
1
0
0.2
0.4
0.6
True Strain
0.8
1
7
Tensile Tests Results
of Posco Mg AZ31B Sheets
R. H. Wagoner
8
Tensile Test of Mg AZ31B at 10-1/s & 10-2.5/s
250
250
o
150 C
200
200
o
o
200 C
150
True Stress (MPa)
True Stress (MPa)
150 C
100
150
o
200 C
100
o
250 C
o
250 C
o
300 C
50
50
o
300 C
-1
10 /s, Posco sample Mg AZ31B
10
-2.5
/s, Posco sample Mg AZ31B
0
0
0
0.2
0.4
True Strain
R. H. Wagoner
0.6
0.8
0
0.2
0.4
0.6
0.8
True Strain
9
Tensile Test of Mg AZ31B at 10-4/s
250
-4
10 /s, Posco sample Mg AZ31B
True Stress (MPa)
200
150
o
150 C
100
o
200 C
50
o
250 C
0
0
0.2
0.4
0.6
0.8
True Strain
R. H. Wagoner
10
Constitutive Equation Framework
  f ( , T)g()h(T)
Hollomon:
f H ( , T)  K1 n
  
g   
 0 
m
Voce:
f V ( , T)  K 2 (1  B * exp(C * ))
H / V:
f ( , T)  f H  (1   )f v
Three versions:
# Parameters
(h(T) w/1 parameter)
1) Hollomon:
 1
4
2) Voce:
 0
5
3) H / V:
R. H. Wagoner
h (T) = 3 choices
  0  1T
8
11
Fitting Procedure
Least squares fit to 4, 5, or 8 parameters, using tensile data
from 0.02 –  u
Software: SigmaPlot
Starting parameters were varied in this order:
K1, K2 = 50, 100, …, 1000
n = 0.05, 0.06, …, 0.5
m = 0.05, 0.06, …, 0.2
B = 0.01, 0.05,…, 0.5
C = 5, 10, …, 200
 0= 0.1, 0.2, …,1
1 = 0.1, 0.2, …,1
Least squares fit => K1, n, m, K2, B, C, 0 , 1 (smallest
standard dev.)
R. H. Wagoner
12
Choice of Temperature Function h(T)
h1 (T)  1  k *
T  273
273
h 2 (T)  1  k1 *
T  273
T  273 2
 k2 *(
)
273
273
h 3 (T)  exp( k *
R. H. Wagoner
T  273
)
273
“T-1”
“T-2”
“T-exp”
13
Least-Squares Fits
Para.
H
T-1
H
T-2
H
T-exp
K1 (MPa)
293
440
n
0.1376
0.1313
(Current Best Eq.)
V
T-1
V
T-2
V
T-exp
H&V
T-1
H&V
T-exp
492
2000
435
0.1304
0.6439
0.0943
K2 (MPa)
562
420
495
2000
2000
B
0.7169
0.4302
0.4545
0.8418
0.8648
C
1.5726
6.7328
5.7193
0.1636
0.6974
0.0917
0.0919
0.0916
0.0919
0.0917
0.0914
1.8603
0.7304
1.8512
1.8316
1.8594
-0.0890
0.0103
0.8692
0.9006
9
(MPa)
8
(MPa)
m
0.0916
k
0.7319
0.0916
k1
-0.5699
-0.5629
k2
1.3951
1.3863
0
1
Stand.
Dev.
11
(MPa)
R. H. Wagoner
8
(MPa)
8
(MPa)
11
(MPa)
7
(MPa)
8
(MPa)
14
Fitting of Tensile Test at 150oC & 200oC
250
250
-1
-1
10 /s,H 10 /s,V
o
200 C, Posco Mg AZ31B
Hollomon vs. Voce Law (T-2)
-1
10 /s, Exp
200
200
-2.5
10
True Stress (MPa)
-1
-1
10 /s,V
10 /s,H
/s, Exp
-2.5
/s, H
10
-2.5
-1
10 /s, Exp
/s, V
True Stress (MPa)
10
150
-4
10 /s, Exp
-4
-4
10 /s, H 10 /s, V
100
150
10
10
100
-2.5
-2.5
/s, H 10
-2.5
/s, V
/s, Exp
-4
-4
10 /s, H
10 /s, V
-4
10 /s, Exp
50
50
o
150 C, Posco Mg AZ31B
Hollomon vs. Voce Law (T-2)
0
0
0
0.03
0.06
0.09
True Strain
R. H. Wagoner
0.12
0.15
0
0.03
0.06
0.09
0.12
0.15
True Strain
15
Fitting of Tensile Test at 250oC & 300oC
250
250
o
o
250 C, Posco Mg AZ31B
Hollomon vs. Voce Law (T-2)
300 C, Posco Mg AZ31B
Hollomon vs. Voce Law (T-2)
200
True Stress (MPa)
True Stress (MPa)
200
150
-1
10 /s, Exp
-1
10 /s,H
-1
10 /s,V
100
10
-2.5
/s, Exp
10
-2.5
/s, H
10
150
-1
100
10 /s, Exp
-1
10 /s,H 10-1/s,V
-2.5
/s, V
-4
-4
10 /s, H 10 /s, V
10
50
-2.5
/s, H 10
-2.5
/s, V
50
-2.5
10
-4
10 /s, Exp
0
/s, Exp
0
0
0.03
0.06
0.09
True Strain
R. H. Wagoner
0.12
0.15
0
0.03
0.06
0.09
0.12
0.15
True Strain
16
Test of Best-Fit Constitutive Equations
Tensile test simulations:
• FEM model, using ABAQUS software
• Uniform temperature distribution
• Solid element: C3D8R
• Material property: Voce Law – (T-2)
R. H. Wagoner
17
Tensile test of Mg AZ31B – Voce (T-2)
250
250
o
o
200 C, Posco Mg AZ31B
150 C, Posco Mg AZ31B
FEA / VOCE
Expt.
-1
10 /s
150
-2.5
10
FEA / VOCE
Expt.
200
Eng Stress (MPa)
Eng Stress (MPa)
200
/s
100
150
-1
10 /s
100
10
-2.5
/s
-4
10 /s
50
50
-4
10 /s
0
0
0
0.2
0.4
Eng Strain
R. H. Wagoner
0.6
0.8
0
0.2
0.4
0.6
0.8
Eng Strain
18
Tensile test of Mg AZ31B – Voce (T-2)
250
250
o
o
300 C, Posco Mg AZ31B
250 C, Posco Mg AZ31B
FEA / VOCE
Expt.
FEA / VOCE
Expt.
200
Eng Stress (MPa)
Eng Stress (MPa)
200
150
100
150
100
-1
10 /s
-1
10 /s
50
10
-2.5
50
/s
10
-2.5
/s
-4
10 /s
0
0
0
0.2
0.4
Eng Strain
R. H. Wagoner
0.6
0.8
0
0.2
0.4
0.6
0.8
Eng Strain
19
PosTech / Posco Formability Test
Simulation
R. H. Wagoner
20
Simulation of Stamping Process
ABAQUS/Standard
• Material: 340BH*
Thickness = 0.738 mm
*
  605.85(  0.01016)0.2282
• Contact:
Friction coefficient: 0.15*
• The z-coordinates of the nodes in
blankholder which were not 0 were
changed to 0.
* K. Oh and et al., “Development of New Formability Test
for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech..
R. H. Wagoner
21
Comparison: Current Results and Oh paper*, Fig. 14
D
D
C
A
A
C
B
Current results
B
Oh paper*
Fig. 14(c)
Minor strain distribution
Holding force = 300kN
Drawing depth = 60 mm
* K. Oh and et al., “Development of New Formability Test
for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech..
R. H. Wagoner
22
Comparison: Current Results and Oh paper*, Fig. 14
B
B
C
C
A
D
Current results
A
D
Oh paper*
Fig. 14(c)
Minor strain distribution
Holding force = 300kN
Drawing depth = 60 mm
* K. Oh and et al., “Development of New Formability Test
for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech..
R. H. Wagoner
23
Comparison: Current Results and Oh paper*, Fig. 9
D
D
A
A
C
C
B
To be compared with Fig. 9 (a)*
Thickness distribution
Holding force = 100kN
Drawing depth = 30 mm
B
To be compared with Fig. 9 (a)*
Thickness distribution
Holding force = 300kN
Drawing depth = 30 mm
* K. Oh and et al., “Development of New Formability Test
for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech..
R. H. Wagoner
24
Comparison: Current Results and Oh paper*, Fig. 9
D
A
C
B
To be compared with Fig. 9 (c)*
Thickness distribution
Holding force = 500kN
Drawing depth = 30 mm
* K. Oh and et al., “Development of New Formability Test
for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech..
R. H. Wagoner
25
Note
Need original Oh data* for Figure 9 and possibly other draw depths +
variables for comparison with current results.
* K. Oh and et al., “Development of New Formability Test for Sheet Materials using Axiomatic Design”,
submitted to J. Mater. Proc. Tech..
R. H. Wagoner
26
Simulation of Stamping Process
350
CPU Time
(hour)
Holding force = 500kN
300
100kN 2.8
250
Punch Force (kN)
Holding force = 300kN
300kN 2.7
200
500kN 2.6
150
Holding force = 100kN
100
50
Posco Stamping Process Simulation
Material: BH340
0
0
20
40
60
Distance (mm)
* K. Oh and et al., “Development of New Formability Test
for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech..
R. H. Wagoner
27
Conclusion
• Tensile tests of Posco Mg AZ31B has been carried out, 150oC - 300oC,
10-1/s - 10-4/s.
• A preliminary constitutive model reproduces measured tensile data with
Reasonable accuracy (<> = 7 MPa)
• Further refinement of constitutive model is needed to reproduce
large-strain tensile response.
• The Oh formability test has been implemented and tested using Abaqus
(material: 340BH)
• Additional data from Oh simulations are requested to make additional
Verification.
* K. Oh and et al., “Development of New Formability Test for Sheet Materials using Axiomatic Design”,
submitted to J. Mater. Proc. Tech..
R. H. Wagoner
28