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w w w . a – s p . o r g 2012 DOE Merit Review
www.a-sp.org
Non Linear Strain Paths A-SP 061
Thomas B. Stoughton
General Motors Company May 18, 2012
Project ID LM064
This presentation does not contain any proprietary, confidential, or otherwise restricted information
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• Start – Oct. 1, 2009 • Finish - Sept. 30, 2011 • 100% Complete
• Predictive modeling tools • Tooling and prototyping • Performance
Total project funding - DOE: $712K - Cost Share: $712K
• Funding received in FY11:
-DOE: $512K
• Funding for FY12: – DOE: $ 13K
Timeline
Budget
Barriers
• Project Leads: – Chrysler Group LLC – Ford Motor Company – General Motors Company
• Interactions/ collaborations: – ArcelorMittal / US Steel – Livermore Software Technology Co. – SuperiorCam – NIST – Oakland Univ. / Wayne State Univ. / MIT /
Tokyo Univ. of A&T
Partners
OVERVIEW
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OBJECTIVES
• Deliver a comprehensive set of experimental data and associated predictive models for the deformation of Advanced High-Strength Steels (AHSS) under nonlinear strain paths.
• The models include constitutive behavior, necking limit and fracture criteria for simulations of stamping, hydroforming, and vehicle crashworthiness.
• The project will – Enable efficient vehicle design to take advantage of the rapid hardening
behavior of AHSS for more weight reduction opportunities – Enable the acceleration of AHSS usage by reducing the cost and time
for reliable validation of AHSS manufacturing processes and vehicle performance
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MILESTONES
Month/Year Milestone or Go/No-Go Decision
June-2011
Milestone #1: A database of biaxial transient hardening and forming limit behavior under continuous strain path change conditions using steel tube hydroforming technology and verification of constitutive models.
July-2011
Milestone #2: A comprehensive database of biaxial transient hardening and forming limit behavior under uniaxial tension after prestrain in uniaxial and equal-biaxial tension, sufficient to develop and validate advanced models.
July-2011 Milestone #3: Validation of forming limit behavior under continuous strain path change conditions in a manufacturing environment.
Sept-2011
Milestone #4: Fracture model for trim edge condition; experiments for different trim conditions, model development and validation.
Sept-2011
Go/No Go Decision: Based on state of the science in modeling metal deformation under nonlinear strain paths, should industry continue to collaborate research in this area using alternate funding sources?
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APPROACH/STRATEGY FOR TASK 1 Transient hardening and forming limits under general
biaxial strain path changes for deep draw quality (DDQ) steel. Adaptive control of axial loading vs. pressure to achieve
desired linear and bilinear strain paths involving combinations of Uniaxial (U), Plane-Strain (P), and Equal-Biaxial (B) Tensions
Apply bilinear paths with and without unloading between stages (prior works suggest this is a factor)
Calculate stresses from mechanical relations of applied loads and geometry to describe the shape of yield surface and evaluate normality rule
Document the effect of strain path change on the forming limits and constitutive model
Courtesy of Yoshida & Kuwabara
Tokyo University of Agriculture and Technology
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APPROACH/STRATEGY FOR TASK 2 Transient hardening and bake-hardening effects under uniaxial tension
after prestrain in uniaxial or equi-biaxial tension. Use DIC to extract strain data beyond uniform elongation Challenge: extraction of useful stress data beyond uniform elongation
Hardening Necking Fracture
Uniaxial (R/T/D) and Biaxial Pre-strain
Uniaxial Tensile to Fracture Bake-Hardening
(for BH & DP Steels)
ε1
ε2
Bake Oven
(1700C, 20min)
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50 mm
10 mm
APPROACH/STRATEGY FOR TASK 2
Transient Hardening & Bake-Hardening (A total of 882 tests):
• 6 Steel Grades: DDQ, BH210, DP600, DP780, TRIP780, DP980
• 3 Pre-strain Orientations: Rolling, Transverse, Diagonal directions
• 7 Pre-strain Levels: Uniaxial 0%, 5%, 10%, 15%, 20%; Equibiaxial: 5%, 10%
• 7 Subsequent Tensile Orientation (relative to pre-straining orientation): 00, 150, 300, 450, 600, 750, 900.
• Digital Image Correlation for strain measurement inside the Diffuse Neck
Uniaxial
280m
m (1
1”)
Rolling Direction; 610mm (24”)
R-0
R-15
R-30 R-45
R-60
R-75
0ε
R-90
RD
TDD45
D135
280m
m (1
1”)
Rolling Direction; 610mm (24”)
R-0
R-15
R-30 R-45
R-60
R-75
0ε
R-90
RD
TDD45
D135RD
TDD45
D135
DIC Point Locations 99 Point Grid in Diffuse Neck
4 Point Virtual Extensometer
Equi-biaxial
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AAPPPPRROOAACCHH//SSTTRRAATTEEGGYY FFOORR TTAASSKK 33
Prediction of Necking Under Nonlinear Strain Path
A nonlinear strain path is created by late contact between the biaxially stretching sheet
and a non-axisymmetric inner punch
Tests on deep draw quality (DDQ) and TRIP 780 steels
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APPROACH/STRATEGY FOR TASK 4: FRACTURE MODELING
Using shear fracture butterfly tests and reverse engineering methods to describe fracture conditions over a range of tests that have been used to develop advanced fracture models at MIT, conduct tests of edge fracture in hole expansion and, evaluate, make improvements, and validate the MIT model for edge fracture.
Experimental study on DP780 for 3 different trim edge conditions (punched (3 clearances), milled, water jet cut) and two types of test.
Develop models to predict damage due to trimming based on simulation using solid element analysis and subsequent formability of trimmed edges based on simulation using shell elements.
Challenge
Central Hole Specimen Tension Test
Hole Expansion Test
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TECHNICAL ACCOMPLISHMENTS FOR TASK 1
FY11 Accomplishments:
• Measured Yield Surface Shape (Plastic Work Contours) and Plastic Strain Directions for Deep Draw Quality steel tubes;
• Verified Yld-2000-2d Model with M=6 for linear strain path
• Obtained continuous stress-strain data for biaxial stress histories up to necking for nonlinear model development and validation
Results for 16% strain
shown here
Example of Strain and Stress Paths for Tests of Plane-Strain Followed by Biaxial Strain without
Unloading
Example of Stress-Strain-Tensor History of one of the above tests
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TECHNICAL ACCOMPLISHMENTS FOR TASK 2
FY11 Accomplishments:
• Developed and Verified Analytical Tool for Automated Data Processing of up to 300 time recordings of strain and position of 103 DIC point data
• Applied to 882 Tensile Test Conditions
• Initiated Compilation of Effects of Strain Path Change on Material Properties
Input Raw Data Sheet (Copy & Paste)
causes automatic update of calculations and figures
Standard Elastic and
Plastic Properties
True Stress vs. True Plastic Strain
Relation
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0
50
100
150
200
250
300
350
400
0.000 0.050 0.100 0.150 0.200
Engineering Strain
Engineering Stress
Engineering StressProportional Limit0.2% Offset YieldUniform Elongation LimitOnset of Max Axial StressCompletion of Max Axial StressLast Recorded Load
TECHNICAL ACCOMPLISHMENTS FOR TASK 2
FY11 Accomplishments:
• Documented unusual behaviors that arise in nonlinear strain paths
Along Rolling after 15% strain along Rolling Direction
0
50
100
150
200
250
300
350
400
0.000 0.005 0.010
Engineering Strain
Engineering Stress
Engineering StressProportional Limit0.2% Offset Yield
DDQ along Rolling (R) Direction
0
50
100
150
200
250
300
0.000 0.100 0.200 0.300 0.400 0.500
Engineering Strain
Engineering Stress
Engineering StressProportional Limit0.2% Offset YieldUniform Elongation LimitOnset of Max Axial StressCompletion of Max Axial StressLast Recorded Load
Along Transverse after 15% strain along Rolling Direction
Problems with 0.2% Offset Yield
Excessively Low Uniform Elongation
15 % strain
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0
50
100
150
200
250
300
350
400
0.000 0.050 0.100 0.150 0.200
Engineering Strain
Engineering Stress
Engineering StressProportional Limit0.2% Offset YieldUniform Elongation LimitOnset of Max Axial StressCompletion of Max Axial StressLast Recorded Load
TECHNICAL ACCOMPLISHMENTS FOR TASK 2
FY11 Accomplishments:
• Documented unusual behaviors that arise in nonlinear strain paths
• Developed algorithm to extend stress-strain relation to high strain
Along R after 15% strain along Rolling Direction
DDQ along Rolling (R) Direction
0
50
100
150
200
250
300
0.000 0.100 0.200 0.300 0.400 0.500
Engineering Strain
Engineering Stress
Engineering StressProportional Limit0.2% Offset YieldUniform Elongation LimitOnset of Max Axial StressCompletion of Max Axial StressLast Recorded Load
Along T after 15% strain along Rolling Direction
15 % strain
0
100
200
300
400
500
600
0.0 0.2 0.4 0.6 0.8 1.0
Stre
ss [M
Pa]
True Plastic X Strain
True Stress
Critical PointTrue StressProportional Limit0.2% Offset YieldOnset of Max Axial StressCompletion of Max Axial LoadEstimated Final State
0
100
200
300
400
500
600
0.0 0.2 0.4 0.6 0.8 1.0
Stre
ss [M
Pa]
True Plastic X Strain
True Stress
Critical PointTrue StressProportional Limit0.2% Offset YieldOnset of Max Axial StressCompletion of Max Axial LoadEstimated Final State
0
100
200
300
400
500
600
0.0 0.2 0.4 0.6 0.8 1.0St
ress
[MPa
]True Plastic X Strain
True Stress
Critical PointTrue StressProportional Limit0.2% Offset YieldOnset of Max Axial StressCompletion of Max Axial LoadEstimated Final State
Monotonic Uniaxial Tension
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TECHNICAL ACCOMPLISHMENTS FOR TASK 2
FY11 Accomplishments:
• Discovered Uniaxial Tension Extends Beyond the End of Uniform Elongation for Linear Loading (to at least twice as high)
• Discovered evidence of microscale (0.5 mm X 0.5 mm gauge area) oscillations in local strain field for nonlinear loading… averaging uniaxial but imply jumping stress states between shearequal-biaxial
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
-0.80 -0.70 -0.60 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10
E11
E22
Strain History At 9 Points Across the Width at the Center of the Diffuse Neck
94
83
72
61
50
39
28
17
6
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
-0.80 -0.70 -0.60 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10
E11
E22
Strain History At 9 Points Across the Width at the Center of the Diffuse Neck
94
83
72
61
50
39
28
17
6
Along R after 15% strain along Rolling Direction
DDQ along Rolling (R) Direction Along T after 15% strain along Rolling Direction
Dashed Line is result if under Unixial Tension with a
constant R Value
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
-0.80 -0.70 -0.60 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10
E11
E22
Strain History At 9 Points Across the Width at the Center of the Diffuse Neck
94
83
72
61
50
39
28
17
6
SU P
B
Implied Stress To Produce A Strain Increment
End of Linear Behavior
End of Uniform Elongation
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TECHNICAL ACCOMPLISHMENTS FOR TASK 3
FY11 Accomplishments:
• Developed and Verified Analytical DIC Method to Identify Onset of Necking
• Verified Dynamic Effect of Nonlinear Strain Path on Necking
• Dynamic Formability Index Allows Prediction of Necking in Nonlinear Paths
DIC Image of Major Engineering Strain Distribution of a Fractured Sample
Live Image of a Fractured Sample
Average Strain is taken from the Strains of the points within a 2mm diameter circle
Method to Extract Necking/Fracture Data
Algorithm to Define Necking Condition
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
0 200 400 600 800 1000 1200
Strain
Incre
amen
t per
step
Punch Loading Steps
Slope.ave
-0.002
-0.001
0
0.001
0.002
0.003
0.004
0.005
0.006
0 200 400 600 800 1000 1200
Chan
ging o
f Stra
in Inc
reame
nt/ste
p
Punch Loading Steps
Curvature
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0 200 400 600 800 1000 1200
True P
rincip
al Str
ain 1
Punch Loading Steps
moving-Ave.
Fracture Starts at Step 1050
5 point rolling average of strain to smooth data
1st Derivative (strain rate)
2nd Derivative: A neck is defined to occur when value permanently exceeds noise.
0
20
40
60
-60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60
Maj
or S
train
(%)
Minor Strain (%)
Fracture Strains by DIC
FLC –Linear Strain Path
Necking Strains by DIC
DDQ Steel
Fracture Strains by DIC
FLC –Linear Strain Path
Trip 780
Necking Strains by DIC
Dynamic FLC Effect
Predicted NECK by
Formability Index
Appears SAFE by Strain FLC
Prediction
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TECHNICAL ACCOMPLISHMENTS FOR TASK 4
FY11 Accomplishments:
• Completed series of edge fracture experiments for DP 780
• Applied DIC method to minimize variation of fracture measurements
• Abacus implementations of fracture model for solid and shell elements
• Description of experiments and calibration method for fracture model
HER Test
CHST Test
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Target Date for
Completion FY11 Milestone Status
June-2011
Milestone #1: A database of biaxial transient hardening and forming limit behavior under continuous strain path change conditions using steel tube hydroforming technology and verification of constitutive models.
Completed
July-2011
Milestone #2: A comprehensive database of biaxial transient hardening and forming limit behavior under uniaxial tension after prestrain in uniaxial and equal-biaxial tension, sufficient to develop and validate advanced models.
Completed
July-2011
Milestone #3: Validation of forming limit behavior under continuous strain path change conditions in a manufacturing environment.
Completed
Sept-2011
Milestone #4: Fracture model for trim edge condition; experiments for different trim conditions, model development and validation
Completed
Sept-2011
Go/No Go Decision: Based on state of the science in modeling metal deformation under nonlinear strain paths, should industry continue to collaborate research in this area using alternate funding sources?
Decision to continue funding through
the Auto-Steel Partnership
FY11 Progress against Milestones:
TECHNICAL ACCOMPLISHMENTS / PROGRESS
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COLLABORATIONS
Partners: • ArcelorMittal (Industry – Prime; within VT): provide sheet steels for testing; uni-axial pre-
straining; expertise on metallurgy and behavior.
• US Steel (Industry – Prime; within VT): provide sheet steels for testing; bake-hardening; expertise on metallurgy and behavior.
• Livermore Software Technology Co (Industry – Prime; outside VT): develop and implement simulation models in the commercial software LS-DYNA; conduct simulations for tooling design.
• SuperiorCam (Industry – Sub; outside VT): tooling design and fabrication.
• Oakland University (Academic – Sub ; outside VT): DIC tests and analysis.
• Wayne State University (Academic – Sub ; outside VT): temperature-dependent tests and analysis; perform tests using SuperiorCam tools.
• MIT (Academic – Sub; outside VT): fracture modeling
• Tokyo University of A & T (Academic – Sub ; outside VT): transient hardening tests under biaxial continuous strain changes.
• NIST Center for Metal Forming (Federal laboratory – Sub ; outside VT): expertise and guidance on materials and test standards.
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FUTURE WORK
FY12: • Project was completed on Sept 30, 2011; Final Report on Dec 18, 2011
• Technology is undergoing evaluation and implementation at the automotive OEMs (Chrysler, Ford and GM) and at the AISI companies (ArcelorMittal, US Steel, etc.)
• ASP-061 activities in 2012 are limited to residual reporting obligations
Beyond FY12: • Auto-Steel Partnership is continuing work in this area using non-government funding
in 2012 and beyond
• Work includes additional biaxial testing to better understand local vs. macro scale effects on modeling
• Development of improved constitutive models for combining nonlinear forming with and without heat treatment effects
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Technical-Backup Slides
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TECHNICAL ACCOMPLISHMENTS FOR TASK 1
FY11 Accomplishments: Example of Results with and without unloading
• Equal Biaxial to 4% strain, followed by Unloading, then Plane Strain to fracture
• Equal Biaxial to 4% strain, then Plane Strain to fracture without unloading
Almost no difference with and without unloading
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AAPPPPRROOAACCHH//SSTTRRAATTEEGGYY FFOORR TTAASSKKSS 22 && 33
Digital Image Correlation (DIC) and Tracking System:
!! Enables the real-time measurement of 3D non-uniform full-field deformation such as displacements and strains from digital images.
!! Offers a sufficient spatial resolution to measure deformations locally at the region of interest, including beyond uniform elongation and hopefully including post localized necking and fracture;
!! Allows real-time measurement and characterization of transient behavior of material responses without resorting to a numerical or analytical model.
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