r. h. wagoner 1 thermally-enhanced forming of mg sheets midterm report, dec. 5, 2008 - may 31, 2009...
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R. H. Wagoner 1
Thermally-Enhanced Forming of Mg Sheets
Midterm Report, Dec. 5, 2008 - May 31, 2009
Robert H. WagonerR. Wagoner, LLC
144 Valley Run PlacePowell OH 43065
R. H. Wagoner 2
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 3
SummaryTask I. Constitutive Equation – Measurement, fitting -A. Tensile testing – AUSTEM Mg AZ31B -B. Screening of material (use 118-5) -C. Tensile testing Posco Mg AZ31B
-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..
150oC 200oC 250oC 300oC
10-1/s x x x x
10-2.5/s x x x x
10-4/s x x x
R. H. Wagoner 4
Summary of Properties of Mg sheets
Material 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
materialused
R. H. Wagoner 5
Tensile Tests Results:
AUSTEM vs. Posco
R. H. Wagoner 6
Tensile Tests of Mg AZ31B at 150oC & 200oC
0
50
100
150
200
250
300
0 0.2 0.4 0.6 0.8 1
Tru
e S
tre
ss
(M
Pa
)
True Strain
Mg AZ31B, 150oCPosco sample, t = 1mmAUSTEM sample, t = 2mm
10-1/s,P
10-1/s, A
10-2.5/s, P
10-2.5/s, A
10-4/s, P10-4/s, A
0
50
100
150
200
250
300
0 0.2 0.4 0.6 0.8 1
Tru
e S
tre
ss
(M
Pa
)
True Strain
Mg AZ31B, 200oCPosco sample, t = 1mmAUSTEM sample, t = 2mm
10-1/s, P
10-1/s, A
10-2.5/s, P10-2.5/s, A
10-4/s, P10-4/s, A
R. H. Wagoner 7
Tensile Tests of Mg AZ31B at 250oC & 300oC
0
50
100
150
200
250
300
0 0.2 0.4 0.6 0.8 1
Tru
e S
tre
ss
(M
Pa
)
True Strain
Mg AZ31B, 200oCPosco sample, t = 1mmAUSTEM sample, t = 2mm
10-1/s, P
10-1/s, A
10-2.5/s, P10-2.5/s, A
10-4/s, P10-4/s, A
0
50
100
150
200
250
300
0 0.2 0.4 0.6 0.8 1
Tru
e S
tre
ss
(M
Pa
)
True Strain
Mg AZ31B, 300oCPosco sample, t = 1mmAUSTEM sample, t = 2mm
10-1/s, P10-1/s, A
10-2.5/s, P
10-2.5/s, A
R. H. Wagoner 8
Tensile Tests Results
of Posco Mg AZ31B Sheets
R. H. Wagoner 9
Tensile Test of Mg AZ31B at 10-1/s & 10-2.5/s
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8
Tru
e S
tre
ss (
MP
a)
True Strain
10-1/s, Posco sample Mg AZ31B
150oC
200oC
250oC
300oC
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8
Tru
e S
tre
ss (
MP
a)
True Strain
10-2.5/s, Posco sample Mg AZ31B
150oC
200oC
250oC
300oC
R. H. Wagoner 10
Tensile Test of Mg AZ31B at 10-4/s
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8
Tru
e S
tre
ss
(M
Pa
)
True Strain
10-4/s, Posco sample Mg AZ31B
150oC
200oC
250oC
R. H. Wagoner 11
Constitutive Equation Framework
)T(h)(g)T,(f m
0g
n1H K)T,(f
))*Cexp(*B1(K)T,(f 2V
vH f)1(f)T,(f
Three versions: # Parameters (h(T) w/1 parameter)
1) Hollomon: 4
2) Voce: 5
3) H / V: 8
1
0
T10
)T(h = 3 choices
Hollomon:
Voce:
H / V:
R. H. Wagoner 12
Fitting Procedure
Least squares fit to 4, 5, or 8 parameters, using tensile data from 0.02 –
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 = 0.1, 0.2, …,1 = 0.1, 0.2, …,1
Least squares fit => K1, n, m, K2, B, C, , (smallest standard dev.)
u
0
0 1
1
R. H. Wagoner 13
Choice of Temperature Function h(T)
)273
273T*kexp()T(h3
273273T
*k1)T(h1
2212 )
273273T
(*k273
273T*k1)T(h
“T-1”
“T-2”
“T-exp”
R. H. Wagoner 14
Least-Squares FitsPara. H
T-1
H
T-2
H
T-exp
V
T-1
V
T-2
V
T-exp
H&V
T-1
H&V
T-exp
K1 (MPa)
293 440 492 2000 435
n 0.1376 0.1313 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
m 0.0916 0.0916 0.0917 0.0919 0.0916 0.0919 0.0917 0.0914
k 0.7319 1.8603 0.7304 1.8512 1.8316 1.8594
k1 -0.5699 -0.5629
k2 1.3951 1.3863
-0.0890 0.0103
0.8692 0.9006
Stand.
Dev.
11
(MPa)
8
(MPa)
8
(MPa)
11
(MPa)
7
(MPa)
8
(MPa)
9
(MPa)
8
(MPa)
0
1
(Current Best Eq.)
R. H. Wagoner 15
Fitting of Tensile Test at 150oC & 200oC
0
50
100
150
200
250
0 0.03 0.06 0.09 0.12 0.15
Tru
e S
tre
ss
(M
Pa
)
True Strain
150oC, Posco Mg AZ31BHollomon vs. Voce Law (T-2)
10-1/s, Exp
10-2.5/s, H
10-1/s,H
10-4/s, Exp
10-2.5/s, Exp
10-4/s, H 10-4/s, V
10-2.5/s, V
10-1/s,V
0
50
100
150
200
250
0 0.03 0.06 0.09 0.12 0.15
Tru
e S
tre
ss
(M
Pa
)
True Strain
200oC, Posco Mg AZ31BHollomon vs. Voce Law (T-2)
10-1/s, Exp
10-2.5/s, H
10-1/s,H
10-4/s, Exp
10-2.5/s, Exp
10-4/s, H 10-4/s, V
10-2.5/s, V
10-1/s,V
R. H. Wagoner 16
Fitting of Tensile Test at 250oC & 300oC
0
50
100
150
200
250
0 0.03 0.06 0.09 0.12 0.15
Tru
e S
tre
ss
(M
Pa
)
True Strain
250oC, Posco Mg AZ31BHollomon vs. Voce Law (T-2)
10-1/s, Exp
10-2.5/s, H
10-1/s,H
10-4/s, Exp
10-2.5/s, Exp
10-4/s, H 10-4/s, V
10-2.5/s, V
10-1/s,V
0
50
100
150
200
250
0 0.03 0.06 0.09 0.12 0.15
Tru
e S
tre
ss
(M
Pa
)
True Strain
300oC, Posco Mg AZ31BHollomon vs. Voce Law (T-2)
10-1/s, Exp
10-2.5/s, H
10-1/s,H
10-2.5/s, Exp
10-2.5/s, V
10-1/s,V
R. H. Wagoner 17
Test of Best-Fit Constitutive Equations
• FEM model, using ABAQUS software• Uniform temperature distribution • Solid element: C3D8R• Material property: Voce Law – (T-2)
Tensile test simulations:
R. H. Wagoner 18
Tensile test of Mg AZ31B – Voce (T-2)
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8
En
g S
tre
ss (
MP
a)
Eng Strain
150oC, Posco Mg AZ31B
10-1/s
10-2.5/s
10-4/s
FEA / VOCEExpt.
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8
En
g S
tre
ss (
MP
a)
Eng Strain
200oC, Posco Mg AZ31B
10-1/s
10-2.5/s
10-4/s
FEA / VOCEExpt.
R. H. Wagoner 19
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8
En
g S
tre
ss (
MP
a)
Eng Strain
250oC, Posco Mg AZ31B
10-1/s
10-2.5/s
10-4/s
FEA / VOCEExpt.
0
50
100
150
200
250
0 0.2 0.4 0.6 0.8
En
g S
tre
ss (
MP
a)
Eng Strain
300oC, Posco Mg AZ31B
10-1/s
10-2.5/s
FEA / VOCEExpt.
Tensile test of Mg AZ31B – Voce (T-2)
R. H. Wagoner 20
PosTech / Posco Formability Test
Simulation
R. H. Wagoner 21
Simulation of Stamping Process
ABAQUS/Standard
• Material: 340BH* Thickness = 0.738 mm*
• Contact:Friction coefficient: 0.15*
• The z-coordinates of the nodes in blankholder which were not 0 were changed to 0.
2282.0)01016.0(85.605
* 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
Minor strain distributionHolding force = 300kNDrawing depth = 60 mm
A
B
C
D
A
B
C
D
Oh paper*Fig. 14(c)
* K. Oh and et al., “Development of New Formability Test for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech..
Current results
R. H. Wagoner 23
C
D
A
B
C
D
A
B
Comparison: Current Results and Oh paper*, Fig. 14
* K. Oh and et al., “Development of New Formability Test for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech..
Oh paper*Fig. 14(c)Current results
Minor strain distributionHolding force = 300kNDrawing depth = 60 mm
R. H. Wagoner 24
Thickness distributionHolding force = 100kNDrawing depth = 30 mm
To be compared with Fig. 9 (a)*
Thickness distributionHolding force = 300kNDrawing depth = 30 mm
A
B
C
D
A
B
C
D
* K. Oh and et al., “Development of New Formability Test for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech..
Comparison: Current Results and Oh paper*, Fig. 9
To be compared with Fig. 9 (a)*
R. H. Wagoner 25
A
B
C
D
* K. Oh and et al., “Development of New Formability Test for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech..
Comparison: Current Results and Oh paper*, Fig. 9
To be compared with Fig. 9 (c)*
Thickness distributionHolding force = 500kNDrawing depth = 30 mm
R. H. Wagoner 26
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 27
Simulation of Stamping Process
0
50
100
150
200
250
300
350
0 20 40 60
Pu
nc
h F
orc
e (k
N)
Distance (mm)
Holding force = 500kN
Holding force = 300kN
Holding force = 100kN
Posco Stamping Process SimulationMaterial: BH340
CPU Time
(hour)
100kN 2.8
300kN 2.7
500kN 2.6
* 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
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 withReasonable 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..