thomas stoughton feb 8-9, 2012 ahss workshop
TRANSCRIPT
MSR Lab Meeting 2012, Jan 31• TBS • 1
Plasticity
Thomas Stoughton
Feb 8-9, 2012
AHSS Workshop
MSR Lab Meeting 2012, Jan 31• TBS • 2
Objective
Presentation on the current state of knowledge of plasticity, constitutive behavior, and forming
limits with a focus on opportunities, roadblocks, threats and requirements for use of AHSS in
automotive applications.
MSR Lab Meeting 2012, Jan 31• TBS • 3
Outline
Microstructure/Polycrystalline vs. ContinuumApplication Needs; Texture & High Exponent Yield Functions; Forming Limits of AHSS; Lessons from Metallic Glass
Elasto-plasticityYoung’s Modulus variation, quasiplastic strain
Distortional Hardening BehaviorIsotropic, kinematic, distortional hardening
Forming LimitsNonlinear Strain Path Effects, Curvature Effects, Necking vs. Fracture, Heightened importance for AHSS
Challenges
MSR Lab Meeting 2012, Jan 31• TBS • 4
Microstructure vs. Continuum Approach
Phenomenon suggesting use of Micro-level ModelTripping and/or Twinning mechanismsDual and Complex phasesHighly textured alloys
Limited Slip Systems (FCC & HCP)Elongated Grain ShapesLarge Grains and/or Ultra-thin sheet
Unusual Hardening or Failure Behaviors
MSR Lab Meeting 2012, Jan 31• TBS • 5
Perceived Characteristics of the Two Approaches to Modeling
Continuum Approach
Low Accuracy High
Cost
High
Low
Microstructure Approach
MSR Lab Meeting 2012, Jan 31• TBS • 6
Reliability is the Primary Driver For Alloy Development
Continuum Approach
Low Accuracy High
Cost
High
LowCost is not so important as an
understanding and opportunity for optimization using a
mechanism-based approach.
Alloy Development
Microstructure Approach
MSR Lab Meeting 2012, Jan 31• TBS • 7
Microstructure Approach is Ideal For Alloy Development
Continuum Approach
Low Accuracy High
Cost
High
Low
Microstructure Approach
Alloy Development
MSR Lab Meeting 2012, Jan 31• TBS • 8
Cost is the Primary Driver For Virtual Die Tryout
Microstructure Approach
Continuum Approach
Low Accuracy High
Virtual Die Tryout
Cost
High
Low
Alloy DevelopmentTwo reasons… Still have Physical Tryout as a backup to oversights
missed by Virtual Tryout… and…
MSR Lab Meeting 2012, Jan 31• TBS • 9
Why COST is so Important in Virtual Tryout
Strain FLC
Finite Element Simulation of the Forming Process
Approve for Die Build
Finding the right forming conditions for a given panel requires SCORES of iterations on blank size, restraining forces, and tool/product shape to get it right…
Multiply this by the 100’s of dies necessary to form the panels of a
vehicle… the need for minimizing cost per analysis is clear.
MSR Lab Meeting 2012, Jan 31• TBS • 10
Can the Micro Approach become more efficient to handle Virtual Die Tryout?
Microstructure Approach
Continuum Approach
Low Accuracy High
Virtual Die Tryout
Cost
High
Low
No Texture Evolution
Weaken Grain Coupling
Ignore Grain Boundaries
Reduce Grain Orientations
These and other modifications can be applied individually or in
combination…
MSR Lab Meeting 2012, Jan 31• TBS • 11
Can the Macro Approach become sufficiently reliable to satisfy the needs?
Microstructure Approach
Continuum Approach
Low Accuracy High
Virtual Die Tryout
Cost
High
LowVon Mises Yield
Hill Yield
ChaboucheHardening Yoshida
Hardening
Non-Associated Flow Barlat Yield
Anisotropic Hardening
These and other modifications can be applied individually or for many cases, in combination…
Multi-phase Hardening
MSR Lab Meeting 2012, Jan 31• TBS • 12
Synergy Between Approaches
Microstructure Approach
Continuum Approach
Low Accuracy High
Virtual Die Tryout
Cost
High
Low
Advanced Material Model
Numerical Experiments
Model Calibration
MSR Lab Meeting 2012, Jan 31• TBS • 13
Alloy Development
Synergy Between Approaches
Microstructure Approach
Continuum Approach
Low Accuracy High
Virtual Die Tryout
Cost
High
Low
Numerical Experiments
Model Calibration
Advanced Model Development
MSR Lab Meeting 2012, Jan 31• TBS • 14
Simplified View of Application Areas
Alloy Development Virtual Die Tryout
Advanced Continuum Model
Development
Microstructure Approach
Continuum Approach
Advanced Continuum Model
Calibration
MSR Lab Meeting 2012, Jan 31• TBS • 15
Outline
Microstructure/Polycrystalline vs. ContinuumApplication Needs; Texture & High Exponent Yield Functions; Forming Limits of AHSS; Lessons from Metallic Glass
Elasto-plasticity HysterisisYoung’s Modulus variation, quasiplastic strain
Distortional HardeningIsotropic, kinematic, distortional hardening
Forming LimitsNonlinear Strain Path Effects, Curvature Effects, Necking vs. Fracture, Heightened importance for AHSS
Challenges
MSR Lab Meeting 2012, Jan 31• TBS • 16
Hysterisis of loading/unloading
1
Complex Unloading Model for Springback Prediction
Dissertation CommitteeDr. Robert H. Wagoner, Advisor
Dr. June Key LeeDr. Stephen Eric BechtelDr. Rebecca B. Dupaix
Dept. of Mechanical EngineeringThe Ohio State University
Oral Examination for the Degree of Doctor PhilosophyFeb 23, 2011
Li Sun
Uniaxial Loading-Unloading Test
8
0
200
400
600
800
1000
1200
0 0.02 0.04 0.06 0.08 0.1
True
Str
ess
(MPa
)
True Strain
DP780-1.4
0
200
400
600
800
1000
1200
0 0.025 0.05 0.075 0.1
True
Str
ess
(MPa
)
True Strain
DP980 -1.43
See Close-Up
DP 780 DP 980
MSR Lab Meeting 2012, Jan 31• TBS • 17
Three ways to model the behaviorExpanded View of Loading-Unloading Test
9
0
200
400
600
800
1000
1200
0.069 0.072 0.075 0.078
True
str
ess
(MPa
)
True strain
DP980 -1.43
Measuredunload-load loop
208 GPa
208 GPa
145 GPa
QPE ep
recov
c1c2
1) Ignore hysterisis and treat it as a change in Elastic Modulus (GREEN Line)
2) Define yield stress near to the proportional limit and treat the nonlinear post-yield behavior as a micro-plasticity domain of conventional plasticity,
3) Leave elasticity and plasticity the same, but include a new type of quasi-plastic strain, QPE.
MSR Lab Meeting 2012, Jan 31• TBS • 18
2 Surface Framework of QPE Model
Elastic state
:d d0 eC
QPE state
0 : :
/ /
e
e
e e
d d dd d d
d d d dQPE
QPE QPE
C
Plastic state0 : : ( )
/ /
e
e
e e
d d d dd d d d
d d d d
p
QPE p
QPE QPE
C CApparent Young’s Modulus
-30
-20
-10
0
10
20
30
1
2
*
nn*
f1
f2
0 1 1 exp pE E E b d d
Elastic + QPE State
Elastic + QPE +Plastic State
Elastic State
MSR Lab Meeting 2012, Jan 31• TBS • 19
Advantages of QPE Model
Unfinished Cycles of Loading-Unloading Test
18
0
200
400
600
800
1000
1200
0.03 0.04 0.05 0.06
True
Str
ess
(MPa
)
True Strain
DP980-1.43
QPE model
Measured (loading)
Measured(unloading)
Partial Unloading of Forming Stresses is Common in Curved Areas of the Product
MSR Lab Meeting 2012, Jan 31• TBS • 20
Outline
Microstructure/Polycrystalline vs. ContinuumApplication Needs; Texture & High Exponent Yield Functions; Forming Limits of AHSS; Lessons from Metallic Glass
Elasto-plasticity HysterisisYoung’s Modulus variation, quasiplastic strain
Distortional HardeningIsotropic, kinematic, distortional hardening
Forming LimitsNonlinear Strain Path Effects, Curvature Effects, Necking vs. Fracture, Heightened importance for AHSS
Challenges
MSR Lab Meeting 2012, Jan 31• TBS • 21
Nature of Distortional Hardening
Deformation Behavior Under Conditions of
Combined Stress
- Prof. Y. Tozawa
1977 GMR Symposium
Experimental Probing of the Yield Surface Evolution
70/30 Brass
-250
-200
-150
-100
-50
0
50
100
150
200
250
-250 -200 -150 -100 -50 0 50 100 150 200 250
Yield Work Contour0.002 0.0050.010 0.0200.030 0.0500.070 0.100
MSR Lab Meeting 2012, Jan 31• TBS • 22
Proportional Loading Tests Suggest Isotropic Hardening
70/30 Brass
Sigma-Z
Sigma-Y
Sigma-X
-200
-150
-100
-50
0
50
100
150
200
-200 -150 -100 -50 0 50 100 150 200
Yield Work0.002 0.0050.010 0.0200.030 0.0500.070 0.100
Pi-plane view shows a von Mises behavior for brass
MSR Lab Meeting 2012, Jan 31• TBS • 23
Complete Non-Proportional Loading Tests Show Complex Hardening Behavior
70/30 Brass
Sigma-Z
Sigma-Y
Sigma-X
-200
-150
-100
-50
0
50
100
150
200
-200 -150 -100 -50 0 50 100 150 200
Yield Work0.002 0.0050.010 0.0200.030 0.0500.070 0.100
70/30 Brass30% Uniaxial
Sigma-Y Sigma-Z
Sigma-X
-600
-400
-200
0
200
400
600
-600 -400 -200 0 200 400 600
Yield Work0.302 0.3100.350 0.400
30% Strain
MSR Lab Meeting 2012, Jan 31• TBS • 24
Complete Non-Proportional Loading Tests Show Complex Hardening Behavior
70/30 Brass30% Uniaxial
Sigma-Y Sigma-Z
Sigma-X
-600
-400
-200
0
200
400
600
-600 -400 -200 0 200 400 600
Yield Work0.302 0.3100.350 0.400
1
1) Distortion of the Yield Surface
MSR Lab Meeting 2012, Jan 31• TBS • 25
Complete Non-Proportional Loading Tests Show Complex Hardening Behavior
70/30 Brass30% Uniaxial
Sigma-Y Sigma-Z
Sigma-X
-600
-400
-200
0
200
400
600
-600 -400 -200 0 200 400 600
Yield Work0.302 0.3100.350 0.400
2
2
1) Distortion of the Yield Surface
2) Anisotropic hardening
MSR Lab Meeting 2012, Jan 31• TBS • 26
Complete Non-Proportional Loading Tests Show Complex Hardening Behavior
70/30 Brass30% Uniaxial
Sigma-Y Sigma-Z
Sigma-X
-600
-400
-200
0
200
400
600
-600 -400 -200 0 200 400 600
Yield Work0.302 0.3100.350 0.400
31) Distortion of the Yield Surface
2) Anisotropic hardening
3) Shape stabilizes after 1% and before 5% strain
1%5%
10%
MSR Lab Meeting 2012, Jan 31• TBS • 27
Complete Non-Proportional Loading Tests Show Complex Hardening Behavior
70/30 Brass30% Uniaxial
Sigma-Y Sigma-Z
Sigma-X
-600
-400
-200
0
200
400
600
-600 -400 -200 0 200 400 600
Yield Work0.302 0.3100.350 0.400
41) Distortion of the Yield Surface
2) Anisotropic hardening
3) Shape stabilizes after 1% and before 5% strain
4) Stabilized shape is different from the Initial Yield Surface
initial“final”
MSR Lab Meeting 2012, Jan 31• TBS • 28
Normalized Yield Behavior to Unit Circle
70/30 Brass30% Uniaxial
Sigma-Y
Sigma-Z
Sigma-X
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Yield Work0.302 0.3100.350 0.400
Initial Yield (0.2%)
Yield (0.2%)After 30% Strain In Uniaxial Tension
Recovery After 1% Strain
Recovery After 5% Strain
Recovery After 10% Strain
Interesting Question: Can one model this with kinematic hardening?
MSR Lab Meeting 2012, Jan 31• TBS • 29
Similar Distortion Observed In Steel
Proportional Loading Tests
Suggest Isotropic Hardening
Uniaxial Prestrain to 5%, 10%, and 20%
Show Distortion of the Subsequent Yield
Anisotropic Hardening After 20% Strain
MSR Lab Meeting 2012, Jan 31• TBS • 30
Advanced Kinematic Hardening Models
Proportional Loading Tests
Suggest Isotropic Hardening
Uniaxial Prestrain to 5%, 10%, and 20%
Show Distortion of the Subsequent Yield
Anisotropic Hardening After 20% Strain
MSR Lab Meeting 2012, Jan 31• TBS • 31
Advanced Kinematic Hardening Models
Initial Yield
Mixed Kinematic Model(Errors up to 15%)
Actual Yield After 20% Uniaxial Prestrain
Prestrain Loading
Direction
Questions:
How do we accurately model this behavior?
What happens under non-linear loading?
MSR Lab Meeting 2012, Jan 31• TBS • 32
Continuum Approach
Characterizing Distortional Hardening is a prime example to benefit from this plan
Advanced Continuum Model
Development
Microstructure Approach
MSR Lab Meeting 2012, Jan 31• TBS • 33
Outline
Microstructure/Polycrystalline vs. ContinuumApplication Needs; Texture & High Exponent Yield Functions; Forming Limits of AHSS; Lessons from Metallic Glass
Elasto-plasticity HysterisisYoung’s Modulus variation, quasiplastic strain
Distortional HardeningIsotropic, kinematic, distortional hardening
Forming LimitsNonlinear Strain Path Effects, Curvature Effects, Necking vs. Fracture, Heightened importance for AHSS
Challenges
MSR Lab Meeting 2012, Jan 31• TBS • 34
Effect of Bending On Forming Limits
Punch Tip Radius, R
Lock Bead Radius6.35 mm
PunchTravel
Die Profile Radius 6.88 mm
Specimen
Punch
38.10 mm
MaterialThickness
63.50 mm
95.25 mm
When does necking occur if the sheet metal is curved?
OK for Necking
Causes Neck to Form
MSR Lab Meeting 2012, Jan 31• TBS • 35
Suppression of Necking Can Lead to Fracture Without Necking
Fracture is not considered in traditional manufacturing
… now recognized as a problem with AHSS
Fracture Limit ?
Necking Limit
0.00
0.10
0.20
0.30
0.40
0.50
0.60
-0.25 -0.15 -0.05 0.05 0.15 0.25
Necking Limit
Fracture Limit
Safe
Neck before
Fracture
Fracture without Necking
MSR Lab Meeting 2012, Jan 31• TBS • 36
Why Fracture is More Important for AHSS
0.00
0.10
0.20
0.30
0.40
0.50
0.60
-0.25 -0.15 -0.05 0.05 0.15 0.25
Necking Limit
Fracture Limit
Fracture without Necking
The possibility of Fracture Without Necking
depends only on geometry, which defines the strain difference through the curved
sheet {=ln(1+t/R) } ,and its relation to the strain gap
between the Necking and Fracture Limits.
MSR Lab Meeting 2012, Jan 31• TBS • 37
The Challenge of Nonlinear Paths
What is SAFE?
2
1
MSR Lab Meeting 2012, Jan 31• TBS • 38
What does this data mean for Linear Paths?
MSR Lab Meeting 2012, Jan 31• TBS • 39
Uniaxial Tension Strain History
0% Strain
MSR Lab Meeting 2012, Jan 31• TBS • 40
Uniaxial Tension Strain History
5% Strain
MSR Lab Meeting 2012, Jan 31• TBS • 41
Uniaxial Tension Strain History
12% Strain
MSR Lab Meeting 2012, Jan 31• TBS • 42
Uniaxial Tension Strain History
17% Strain
MSR Lab Meeting 2012, Jan 31• TBS • 43
The Strain-Based FLC is DYNAMIC
MSR Lab Meeting 2012, Jan 31• TBS • 44
How can we reliably assess formability?
MSR Lab Meeting 2012, Jan 31• TBS • 45
Strain FLC
Strain Analysis +8.7% Margin of Safety
Ignoring the DYNAMIC nature of the FLC has costly consequences
Tryout Result:Splits at “Zone 4”
in an area with 17% thinning
Splits In Zone 4Complex parts & processes designed
base solely on net strain and the strain FLC, even with what seems to be high
margin of safety…
…may still fail in tryout and require additional changes to product and tooling shape or
processing conditions.
MSR Lab Meeting 2012, Jan 31• TBS • 46
Paradigm Change: a new perspective
No assumptions, just a simple question…
Are these experimental results LESS complex in stress-space?
MSR Lab Meeting 2012, Jan 31• TBS • 47
Transformation equations for an arbitrary time record of plastic strain
tr
rt
tKt
np
121 2
01
ttt 12
Normal Anisotropic Hill Model
tt
2
1 t
p ttr
rtttdr
rt0 21
22
21 1
221
1
ttt
1
2
trrtrrtt
1
tt
2
1
Arrieux, et al., 1982
First Proposed By Arrieux in 1982 Based On Forming Limit
Behavior of Steel
MSR Lab Meeting 2012, Jan 31• TBS • 48
Strain FLC to Stress FLC For Linear Strain Paths
2
1
2897.0p
MPa 5.3721
MPa 2.102
02730.0
0994.02
2896.01
Numerical Example
2
1
MSR Lab Meeting 2012, Jan 31• TBS • 49
Strain FLC to Stress FLC For Bi-Linear Strain Paths
2905.0p
MPa 4.3761
MPa 1.212
05578.0
Numerical Example
1244.0pA
070.0070.0
1
2
A
A
2358.00173.0
1
2
1661.0pB1658.00527.0
2
1
B
B
Input
2
1
Does this FLC Curve Look Familiar?
MSR Lab Meeting 2012, Jan 31• TBS • 50
Observation Leads to New Solution
Stress-Based FLC’s do not appear to be sensitive to changes in strain path
MSR Lab Meeting 2012, Jan 31• TBS • 51
Stress Based FLC’s are not Sensitive to Path
MSR Lab Meeting 2012, Jan 31• TBS • 52
Same FEA
Body Side Component
Stress FLC
Stress Analysis-20.1% Margin of Safety
Strain FLC
Strain Analysis Expected +8.7% Margin of Safety
Tryout ResultSplits at “Zone
4”
Splits In Zone 4
Used to Approve Die Build
Stress Map of Critical Areas
Same FE Simulation
MSR Lab Meeting 2012, Jan 31• TBS • 53
Other Stress-Equivalent Solutions
tr
rt
tKt
np
121 2
01
ttt 12
Normal Anisotropic Hill Model
tt
2
1
ttt
1
2
trrtrrtt
1
2
11-to-1p p 1-to-1
t
p ttr
rtttdr
rt0 21
22
21 1
221
1
Arrieux, et al., 1982
Proposed FLC metrics insensitive to path change:
Zeng, et al., 2008
Yoshida, et al., 2007
1-to-1
Stoughton & Yoon, 2011
1tanp
MSR Lab Meeting 2012, Jan 31• TBS • 54
Polar Diagram of the EPS
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30
Long
itudi
nalT
rue
Stra
in
TransverseTrue Strain
Experimental FLC's in Conventional Strain Diagram
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30EP
S*C
OS(
)
EPS*SIN( )
Experimental FLC's in Polar EPS Diagram
MSR Lab Meeting 2012, Jan 31• TBS • 55
Illustration of Similarity & Differences
Path Sensitive Strain FLD Polar EPS Diagram
ttv p cos2
ttv p sin1
A
1
ttp
21, AA
A
eefEPS21, AA ee
A
1
tt
2
1 ttt 1211 ,tantan
MSR Lab Meeting 2012, Jan 31• TBS • 56
Illustration of Similarity & Differences
Path Sensitive Strain FLD Polar EPS Diagram
2 2
3
21, BB ee
2211 , BBBB eeee
B
B
Bo
Bo
21, BBBB eefEPSEPSo
3
21, BB
B
eef
EPSo
MSR Lab Meeting 2012, Jan 31• TBS • 57
The Reason
Path Sensitive Strain FLD Polar EPS Diagram
A
1
2 2
3
A
B
B
Bo
Bo
3
1
Apriori Unknown Evolution of the Strain Limit Static EPS Limit
MSR Lab Meeting 2012, Jan 31• TBS • 58
Importance of Nonlinear Path for AHSS
In the past, anomalous failures caused by ignoring the effect of nonlinear paths on formability… i.e., treating strain limits as static limits… have led industry to limit strains in future applications to even lower limits…Industry cannot afford this solution using AHHS with lower ductility than low carbon steel… not when a solution is available to maximize the use of the available ductility.
MSR Lab Meeting 2012, Jan 31• TBS • 59
Thank you for your attention.
Questions?