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.