Draw-Bend Fracture Prediction
with Dual-Phase Steels
R. H. Wagoner
September 25, 2012
AMPT
Wollongong, Australia
Outline
1. Background – Shear Fracture, 2006
2. DBF Results & Simulations, 2011
Intermediate Conclusions
3. Practical Application, 2012
Ideal DBF Test
Recommended Procedure
4. No Ideal Test?
Results,
Recommended Procedure
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1. Background – Shear Fracture, 2006
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Shear Fracture of AHSS – 2005 Case
Jim Fekete et al, AHSS Workshop, 2006
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Shear Fracture of AHSS - 2011
Forming Technology Forum 2012 Web site: http://www.ivp.ethz.ch/ftf12
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Unpredicted by FEA / FLD
Stoughton, AHSS Workshop, 2006
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Shear Fracture: Related to Microstructure?
Ref: AISI AHSS Guidelines
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Conventional Wisdom, 2006
Shear fracture…
•
•
•
•
is unique to AHSS (maybe only DP steels)
occurs without necking (brittle)
is related to coarse, brittle microstructure
is time/rate independent
Notes:
• All of these based on the A/SP stamping trials, 2005.
• All of these are wrong.
• Most talks assume that these are true, even today.
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NSF Workshop on AHSS (October 2006)
Elongation (%)
70
60
50
40
Mild
30
BH
20
10
0
MART
0
300
600
900
Tensile Strength (MPa)
1200
1600
R. W. Heimbuch: An Overview of the Auto/Steel Partnership and Research Needs [1]
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2. DBF Results & Simulations, 2011
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References: DBF Results & Simulations
J. H. Kim, J. H. Sung, K. Piao, R. H. Wagoner: The Shear Fracture of
Dual-Phase Steel, Int. J. Plasticity, 2011, vol. 27, pp. 1658-1676.
J. H. Sung, J. H. Kim, R. H. Wagoner: A Plastic Constitutive Equation
Incorporating Strain, Strain-Rate, and Temperature, Int. J.
Plasticity, 2010, vol. 26, pp. 1746-1771.
J. H. Sung, J. H. Kim, R. H. Wagoner: The Draw-Bend Fracture Test (DBF)
and Its Application to DP and TRIP Steels, Trans. ASME: J. Eng.
Mater. Technol., (in press)
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DBF Failure Types
V2
Type III
Type II
65o
Type I
65o
V1
Type I: Tensile failure (unbent region)
Type II: Shear failure (not Type I or III)
Type III: Shear failure (fracture at the roller)
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DBF Test: Effect of R/t
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“H/V” Constitutive Eq.: Large-Strain Verification
1000
DP590(B), RD
Hollomon <>=4MPa
-3
Effective Stress (MPa)
Strain Rate=10 /sec
900
o
25 C
H/V <>=1MPa
800
Bulge Test (r=0.84, m=1.83)
Voce <>=1MPa
700
Tensile Test
Fit
Range
600
0.1
Extrapolated, Bulge Test Range
0.2
0.3
0.4
0.5
0.6
0.7
Effective Strain
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FE Simulated Tensile Test: H/V vs. H, V
Engineering Stress (MPa)
700
Experiment(D-B)
600
Voce H/V model Hollomon
500
DP590(B), RD
400
-3
Strain Rate=10 /s
o
100 C, Isothermal
300
0
0.05
0.1
0.15
0.2
0.25
0.3
Engineering Strain
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Predicted ef, H/V vs. H, V: 3 alloys, 3 temperatures
Standard deviation of ef: simulation vs. experiment
Hollomon
Voce
H/V
DP590
0.05 (23%)
0.05 (20%)
0.02 (7%)
DP780
0.03 (18%)
0.04 (22%)
0.01 (6%)
DP980
0.04 (30%)
0.03 (21%)
0.01 (5%)
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FE Draw-Bend Model: Thermo-Mechanical (T-M)
U2, V2
hmetal,air = 20W/m2K
•
•
•
•
Abaqus Standard (V6.7)
3D solid elements (C3D8RT), 5 layers
Von Mises, isotropic hardening
Symmetric model
m = 0.04
hmetal,metal = 5kW/m2K
U1, V1
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Kim et al., IDDRG, 2009
17
Front Stress vs. Front Displacement
1000
Measured
Front Stress, 1
800
T-M
Isothermal
Solid, Shell
600
400
DP780-1.4mm, RD
V1=51mm/s, V2/V1=0
200
R/t=4.5
0
0
20
40
60
80
Front Displacement, U (mm)
1
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Displacement to Maximum Front Load vs. R / t
80
UMax. Load (mm)
Isothermal, Shell
Isothermal, Solid
60
Type I
40
T-M, Solid
Type III
20
Measured
DP780-1.4mm, RD
V =51mm/s, V /V =0
2
1
1
0
0
2
4
6
8
10
12
14
R/t
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Is shear fracture of AHSS
brittle or ductile?
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Fracture Strains: DP 780 (Typical)
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Fracture Strains: TWIP 980 (Exceptional)
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Directional DBF : DP 780 (Typical)
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Directional DBF Formability: DP980 (Exceptional)
Elongation to Fracture (mm)
30
25
20
15
10
5
0
0
RD
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DP980
R/t = 3.3
30
60
Angle to RD (degree)
90
TD
24
Interim Conclusions
• “Shear fracture” occurs by plastic localization.
• Deformation-induced heating dominates the error
in predicting shear failures.
• Brittle cracking can occur. (Poor microstructure or
exceptional tensile ductility, e.g. TWIP).
• T-dependent constitutive equation is essential.
• Shear fracture is predictable plastically.
(Challenges: solid elements, T-M model.)
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3. Practical Application - 2012
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DBF/FE vs. Industrial Practice/FE
Ind.: Plane strain
High rate
~Adiabatic
FE: Shell
Isothermal
Static
DBF: General strain
Moderate rates
Thermo-mech.
FE: Solid element
Thermo-mech.
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Ideal DBF Test: Plane Strain, High Rate
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Ideal Test Results - Stress
Peak Engineering Stress (MPa)
1200
1000
Analytical PS Result
800
(UTS)
600
(R/t)*
400
DP780-1.4mm
0
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2
4
6
8
10 12
Bending Ratio, R / t
14
29
Ideal Test Results - Strain
0.4
Analytical PS Results
DP 780 - 1.4mm
(R/t)*
True Strain
0.3
0.2
Outer Strains
0.1
Center Strains
(Membrane)
FLDo
Inner Strains
0
0
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2
4
6
8
10
Bending Ratio, R / t
12
14
16
30
How to Use Practically: Bend, Unbend Regions
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Practical Application of SF FLD – (1) Direct
For each element in contact
Known: R, t  e*membrane
Predicted Fracture: eFEA > e*membrane
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Practical Application of SF FLD – (2) Indirect
For each element drawn over contact
Known: (R, t)contact  Pmax  *PS tension  e*PS tension
Predicted Fracture: eFEA > e*PS tension
Wu, Zhou, Zhang, Zhou, Du, Shi: SAE 2006-01-0349.
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Calculation: Indirect Method
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Recommended Procedure with Industrial FEA
1. Use adiabatic law in FEA, use rate sensitivity
2. Classify each element based on X-Y position (tooling)
a) Bend (plane-strain)
b) After bend (plane-strain)
c) General (not Bend, not After)
3. Apply 4 criteria:
a) FLD (Bend, After)
b) Direct SF (Bend)
c) Indirect SF (After)
d) Brittle Fracture* (All?)
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4. No Ideal Test?
(What to do?)
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Pmax = f(R/t)
e*membrane = f(R/t)
(PS, high-speed DBF)
(PS, high-speed DBF)
1200
0.4
1000
0.3
Membrane Strain
Peak Load (MPa)
What is Needed?
800
600
0.2
0.1
400
0
0
2
4
6
8
10
Bending Ratio, R / t
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12
14
0
2
4
6
8
10
Bending Ratio, R / t
12
14
16
37
FE Plane Strain DBF Model
m = 0.06
U2, V2 = 0
•
•
•
•
Abaqus Standard (V6.7)
Plane strain solid elements (CPE4R), 5 layers
Von Mises, isotropic hardening
Isothermal, Adiabatic, Thermo-Mechanical
U1, V1
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Adiabatic Constitutive Equation
1600
True Stress (MPa)
-5%
25oC
-12%
75oC
1200
125oC
Adiabatic
800
 adiabatic (e , e )   (e , e , T )
 e
T 
 de

C p 0
DP980(D)-GA-1.45mm
400
-3
de/dt=10 /s
0
0
0.2
0.4
0.6
0.8
1
True Plastic Strain
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Peak Stress, Plane-Strain: DP980
Peak Engineering Stress (MPa)
1400
Analytical Model,
Plane Strain
PS FE Model,
m=0, m=0
1200
UTS
1000
DBF measured
(RD, TD)
800
600
DP980-1.43mm
0
2
4
6
8
10
12
14
R/t
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Membrane Strains at Maximum Load
0.25
Analytical Adiabatic Model
Stopped at Maximum Load
es, True Membrane Strain
DP590
0.2
0.15
DP780
0.1
DP980
0.05
0
0
2
4
6
8
10
12
14
16
Bending Ratio, R / t
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Analytical Model: Model vs. Fit
0.1
es, True Membrane Strain
Analytical Adiabatic Model
Stopped at Maximum Load
DP980
0.08
S = 0.221, e = 0.088
s
o
 t  t
t 
t
  S 

es    eso 
R
R
R
R
max 
 max  
0.06
DP780
0.04
S = 0.198, e
s
o
= 0.101
DP590
0.02
S = 0.167, e
s
o
= 0.138
0
0
0.1
0.2
0.3
0.4
0.5
0.6
1 / Bending Ratio, t / R
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Analytical Model: Model vs. Fit
es, True Membrane Strain
0.25
Analytical Adiabatic Model
Stopped at Maximum Load
0.2
DP590:
S = 0.168, e
o
s
0.15
DP780: S = 0.198, e
s
o
= 0.138
= 0.101
0.1
DP980:
0.05
0
 t  t
t 
t
  S 

es    eso 
R
R
R
R
max 
 max  
0
2
4
6
8
S = 0.221, e
s
10
12
o
= 0.088
14
16
Bending Ratio, R / t
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Conclusions
• Shear fracture is predictable with careful testing or careful
constitutive modeling and FEA.
• “Shear fracture” occurs by plastic localization.
• “Shear fracture” is an inevitable consequence of draw-bending
mechanics. All materials.
• Brittle fracture can occur, but is unusual. (Poor microstructure or
v. high tensile tensile limit, e.g. TWIP).
• T-dependent constitutive equation is essential for AHSS because
of high plastic work. (But probably not Al or many other alloys.)
R. H. Wagoner
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Thank you.
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45
References
•
R. H. Wagoner, J. H. Kim, J. H. Sung: Formability of Advanced High Strength Steels,
Proc. Esaform 2009, U. Twente, Netherlands, 2009 (CD)
•
J. H. Sung, J. H. Kim, R. H. Wagoner: A Plastic Constitutive Equation Incorporating
Strain, Strain-Rate, and Temperature, Int. J. Plasticity, (accepted).
•
A.W. Hudgins, D.K. Matlock, J.G. Speer, and C.J. Van Tyne, "Predicting Instability at Die
Radii in Advanced High Strength Steels," Journal of Materials Processing
Technology, vol. 210, 2010, pp. 741-750.
•
J. H. Kim, J. Sung, R. H. Wagoner: Thermo-Mechanical Modeling of Draw-Bend
Formability Tests, Proc. IDDRG: Mat. Prop. Data for More Effective Num. Anal., eds. B. S.
Levy, D. K. Matlock, C. J. Van Tyne, Colo. School Mines, 2009, pp. 503-512. (ISDN 978-0615-29641-8)
•
R. H. Wagoner and M. Li: Simulation of Springback: Through-Thickness Integration, Int. J.
Plasticity, 2007, Vol. 23, Issue 3, pp. 345-360.
•
M. R. Tharrett, T. B. Stoughton: Stretch-bend forming limits of 1008 AK steel, SAE
technical paper No.2003-01-1157, 2003.
•
M. Yoshida, F. Yoshida, H. Konishi, K. Fukumoto: Fracture Limits of Sheet Metals Under
Stretch Bending, Int. J. Mech. Sci., 2005, 47, pp. 1885-1896.
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Extra Slides
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DP Steels
1200
Engineering Stress(MPa)
DP980(D)-1.45mm
1000
800
DP780(D)-1.4mm
600
DP590(B)-1.4mm
400
Strain Rate: 10-3/sec
Room Temp.
Rolling Direction
200
0
0
5
10
15
20
25
Engineering Strain (%)
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“H/V” Constitutive Framework
   (e , e , T )  f (e , T )  g (e )  h(T )
Special:
f (e , T )   (T ) f Hollo  (1   (T ))  fVoce
 (T )  1   2 (T  TRT )
f Hollo
 Ke n
fVoce  A[1  B exp(Ce )]
Standard:
e 
g (e )   
e 
a [log e ]  b
0
h(T )  (1  D  (T  TRT ))
R. H. Wagoner
Sung et al., Int. J. Plast. 2010
49
Simulated D-B Test: Effect of Draw Speed
1.2
Isothermal
1
F/F
UTS
0.8
Adiabatic
0.6
13mm/s
(0.6/s)
51mm/s
(de/dt=2.5/s)
0.4
-3
(5x10 /s)
2.5mm/s
(0.13/s)
DP980(D)
R/t=4.4, V2/V1=0
0.2
0
0.001mm/s
0
5
10
15
20
25
30
35
Front Displacement (mm)
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DBF Formability: DP980(A), RD vs. TD (Typical)
* Directional Formability: TD=RD
DP980(A)
V =51mm/sec
40
1
V /V =0
2
f
Front Disp. to Failure (U , mm)
50
1
30
20
RD
TD
10
0
2.2
3.4
4.5
5.5
6.6
7.8
10
13.3
R/t
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DBF Formability: DP980(D), RD vs. TD (Exceptional)
* Directional Formability: RD>TD
50
f
Front Disp. to Failure (U , mm)
60
DP980(D)
V1=51mm/sec
V2/V1=0
40
30
20
RD
10
TD
0
2.2
3.3
4.4
5.4
6.6
7.7
9.9
13.1
R/t
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Analytical Model – Curvilinear Derivation
r

r 
e  ln 

e 
2
3
n
ee 
ij
ij
  (r )   
Neutral line

3
t
r

r 
ln 
2
 2 
  dr   (r )
r 
3 
3
rn
R t
2
 2 
 2 
  (r )      dr      dr   (r )
rn 
r 
3 
3 
3
R t
r
2
n
r  rn
r  rn
Materially embedded coordinate  :
dr  r d  
R
T
rn
R  t0
T
rn
d
r
2
 2  r
  d   ( )
3
 3  
  ( )   
  n
n
2
 2  r
 2  r
  ( )      d      d   ( )
n 
 
3  
3  
3
  n

R  t0
T
R t
R  t0
R
R
   dr    
r
d

Fracture Criterion: Fracture occurs at Tmax for given R, to
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DBF Interpretation: Plane-strain vs. Tension
Peak Engineering Stress (MPa)
1200
Simplified FE Model,
m=0, m=0
1000
UTS
800
600
Analytical Model,
Plane Strain
400
DP780-1.4mm
0
2
4
6
8
10
12
14
R/t
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54
Inner and Outer Strains at Maximum Load
0.4
DP590
Analytical Adiabatic Model
Stopped at Maximum Load
DP780
True Strain
0.3
DP980
Outer Strains
0.2
0.1
Inner Strains
0
0
2
4
6
8
10
12
14
16
Bending Ratio, R / t
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Membrane Strains (R/t Affected Only)
0.25
es, True Membrane Strain
Analytical Adiabatic Model
Stopped at Maximum Load
0.2
0.15
DP980
DP780
0.1
0.05
DP590
0
0
2
4
6
8
10
12
14
16
Bending Ratio, R / t
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56
R/t-Affected Membrane Strains vs. t/R
0.25
es, True Membrane Strain
Analytical Adiabatic Model
Stopped at Maximum Load
0.2
0.15
DP980
DP780
0.1
0.05
DP590
0
0
0.1
0.2
0.3
0.4
0.5
0.6
1 / Bending Ratio, t / R
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Forming Limit Diagram
Ref: Hosford & Duncan
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PS T-M Model: Model vs. Fit
es, True Membrane Strain
0.25
Plane Strain Thermo-Mechanical Model
Stopped at Maximum Load
DP590
0.2
 t  t
t 
t
  S 

es    eso 
R
R
R
R
 
max 
 max  
S = 0.753, e
o
s
= 0.149
0.15
DP780
S = 0.330, e
0.1
o
= 0.123
o
= 0.133
s
0.05
DP980
0
S = 0.051, e
s
-0.05
0
0.1
0.2
0.3
0.4
1 / Bending Ratio, t / R
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PS T-M Model: Model vs. Fit
es, True Membrane Strain
0.5
Plane Strain Thermo-Mechanical Model
Stopped at Maximum Load
 t  t
t 
t
  S 

es    eso 
R
R
R
R
 
max 
 max  
0.4
DP590
S = 0.753, e
0.3
o
s
= 0.149
0.2
0.1
DP780: S = 0.330, e
o
= 0.123
DP980: S = 0.051, e
o
= 0.133
s
s
0
0
2
4
6
8
10
12
14
16
Bending Ratio, R / t
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Draw-Bend Fracture Test (DBF): V1, V2 Constant
190.5 mm
Tool radius choices:
2/16, 3/16, 4/16, 5/16, 6/16, 7/16, 9/16, 12/16 inch
3.2, 4.8, 6.4, 7.9, 9.5, 11.1, 14.3, 19 mm
 = V2/V1:
0 and 0.3
444.5 mm(10”)
Specimen width: 25mm
R
190.5 mm
Max. Finish
Start
V2 = V1
444.5 mm (10”)
uf V1
Max. Finish
Start
Wagoner et al., Esaform, 2009
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AHSS vs. HSLA
Ref: AISI AHSS Guidelines
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