thermally-enhanced forming of mg sheets midterm report, dec. 5, 2008 - may 31, 2009
DESCRIPTION
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. One-Year Project Goals (from Research Agreement, signed December 5, 2008). - PowerPoint PPT PresentationTRANSCRIPT
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
Summary
Task I. Constitutive Equation Measurement -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. Test with FEA simulation
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 Test Results:
AUSTEM vs. Posco Mg AZ31B
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 Test Results:
Posco Mg AZ31B
R. H. Wagoner 9
Tensile Tests 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, J. Mater. Proc. Tech. (submitted)
R. H. Wagoner 22
Current Results vs. 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)Current results
• K. Oh and et al., Development of New Formability Test for Sheet Materials using Axiomatic Design, J. Mater. Proc. Tech. (submitted)
R. H. Wagoner 23
C
D
A
B
C
D
A
B
Current Results vs. Oh paper*, Fig. 14
Oh paper*Fig. 14(c)Current results
Minor strain distributionHolding force = 300kNDrawing depth = 60 mm
• K. Oh and et al., Development of New Formability Test for Sheet Materials using Axiomatic Design, J. Mater. Proc. Tech. (submitted)
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
Current Results vs. Oh paper*, Fig. 9
To be compared with Fig. 9 (a)*
• K. Oh and et al., Development of New Formability Test for Sheet Materials using Axiomatic Design, J. Mater. Proc. Tech. (submitted)
R. H. Wagoner 25
A
B
C
D
• K. Oh and et al., Development of New Formability Test for Sheet Materials using Axiomatic Design, J. Mater. Proc. Tech. (submitted)
Current Results and Oh paper*, Fig. 9
To be compared with data for Fig. 9 (c)*
Thickness distributionHolding force = 500kNDrawing depth = 30 mm
R. H. Wagoner 26
Note
R. Wagoner LLC requests the original Oh data* for Figure 9 and possibly other draw depths and variables (thickness strain, von Mises strain) for comparison with current results. Also, as shown on the next slide, punch force vs. draw depths couldbe compared. The paper does not clearly show those results.
• K. Oh and et al., Development of New Formability Test for Sheet Materials using Axiomatic Design, J. Mater. Proc. Tech. (submitted)
R. H. Wagoner 27
Punch Force vs. Draw Depth
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
Conclusions
• Tensile tests of Posco Mg AZ31B have 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 better.
• The Oh formability test has been implemented and tested using Abaqus (material: 340BH).
• Additional data from Oh simulations are requested to permit additional verification.
* K. Oh and et al., “Development of New Formability Test for Sheet Materials using Axiomatic Design”, submitted to J. Mater. Proc. Tech..