Mg AZ31B Sheet Behavior and Formability at Elevated...

Kun Piao 1

Mg AZ31B Sheet Behavior and Formability at Elevated, Differential Temperature

Kun Piao

Dissertation Overview

Overview committee:Dr. Robert H. Wagoner, AdvisorDr. Glenn S. DaehnDr. Katharine M. Flores

Kun Piao 2

Outline

• Background

• Device Design

8 minutes for 350oC, ΔT (gauge length) < 8oC

• A novel test to determine transition T of twin and slip

• 1D constitutive equations

150oC-300oC; 10-4/s-10-1/s

• Application: temperature-differential forming

Kun Piao 3

Monotonic Tension and Compression of Mg at RT

Lou, X.Y. et al., I. J. of Plast., 2007

Tension Compression

Kun Piao 4

RT Tension / Compression Test Setup

Boger, R.K. et al., I. J. Plast., 2005

Side Pressure

Kun Piao 5

Tension / Compression Test - Corrections

• Biaxial Correction

• Friction Correction

sidefriction F2F μ=

Tension Part on Tension-Compression Curve

( )( )23

21

2312

1 σσσσσ ++−=

0

50

100

150

200

250

0 0.005 0.01 0.015 0.02

True

Str

ess

(MPa

)

True Strain

Raw Data, No Correction

Uniaxial Test(no side force)

Friction CorrectionOnly

Both Friction andBiaxial Corrections

Mg AZ31B, TD, t = 3.2 mmSide Force = 12kN

Biaxial CorrectionOnly

Lou, X.Y. et al., I. J. of Plast., 2007

frictionrawactual FFF −=

Kun Piao 6

Device Design

1) Thermal analysis

2) Mechanical analysis

3) Buckling analysis

Kun Piao 7

Thermal Analysis for Heating System

FEM Model: ABAQUS / Standard, Thermal Transfer Analysis

Heat Plate

Mg Specimen

Insulation Block

GripMechanical Support Plate

25oC

25oC

• Solid Element• Symmetric• Initial T = 25oC• Steady State / Transient

x

y

z

Kun Piao 8

Thermal PropertiesMg Sample:• kMg = 100 W/mK• Cp = 1 J/gK

Al Heat Plate:• kAl = 120 W/mK• Cp = 0.96 J/gK

Wood Block:• kwood = 0.17 W/mK• Cp = 1 J/gK

• Heat transfer coefficient between sample and HP h1 = 400 W/m2K• Heat transfer coefficient between metal and wood h2 = 90 W/m2K• Heat transfer coefficient between grip and sample h3 = 1000 W/m2K

Measured

Measured

Handbook

Measured

Handbook

Handbook

Handbook

By fitting

k : Conductivity

Cp : Capacity

h : Heat transfer coefficient

Kun Piao 9

Transient ProcessHeat Plate Steady State

Tmax (oC) Time to200oC

ΔT (oC) (at 200oC)

Time to300oC

ΔT (oC) (at 300oC)

#1 Al 7075-T6 HP 310 310 s 4.5 1120 s 6.5

#2 D2 Tool Steel HP 335 335 s 9.0 960 s 13.0

#3 Al 7075-T6 HP+ D2 Tool Steel Cover

295

#4 Al 7075-T6 HP+ Wood Insulation + D2 Tool Steel Cover

356 305 s 4.5 755 s 7.0

#5 D2 Tool Steel HP+ Wood Insulation + D2 Tool Steel Cover

386 356 s 9.0 795 s 13.0

A

B

C

Material Selection for Heat Plates (Simulated)

Kun Piao 10

Comparison of Simulation and Measurement

0

100

200

300

-100 -50 0 50 100

Tem

pera

ture

(C)

X (mm)

608 second

300 second

100 second

Measurement:Target Temperature = 250oCU = 105V, I = 1.85A

Simulation:Surface Heat Flux=0.048W/m2

500 second

400 second

200 second

Gage Length

Kun Piao 11

Stress Analysis of Heating System

14MPa (Al 7075-T6)7% of YS at 300oC

217MPa (D2 Tool Steel)36% of YS at RT

Mg

Al

Wood

Steel

FEM Model: ABAQUS / Standard, General Mechanical Analysis

• Solid Element (CPS4R)• Symmetric• Concentrated Force

(Maximum Side Force = 8kN)

x

y

z

Kun Piao 12

Voltage Transformer

TemperatureController

Compressed Air Cylinder

Heat plates

New Setup for High-Temperature T / C Test

Kun Piao 13

Buckling FEA Model

FEM Model: ABAQUS / Standard, General Mechanical Analysis

• Sample: Solid Element (C3D8R)Side plates: Rigid-body Element (R3D4)

• Compression test• Concentrated Force loaded on the RP• Friction coefficient = 0.08• Eccentricity = 0.01mm, 0.1mm, and 0.5mm

BC1: Fixed

BC2: Eccentricity• Contact:

1) Tangential behavior: penalty method

2) Normal behavior: exponential pressure-overclosure

Compression

Kun Piao 14

Buckling Simulation

0

200

400

600

800

1000

1200

0

2

4

6

8

0 0.05 0.1 0.15 0.2

Abs

olut

e Tr

ue S

tres

s (M

Pa)

δp

Absolute True Strain

DP800, RD, Compression, Side force = 3.3kNThickness = 1.40mmStrain rate = 0.001/s, μ = 0.08Experiment vs. simulation

δz=0.01mmδz=0.1mm

δz=0.5mm

Kun Piao 15

Buckling Simulation – Thickness Effect

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 5 10 15 20 25 30 35

Abs

. Buc

klin

g Tr

ue S

trai

n, |ε

b|

Side Force (kN)

DP780, RDThickness = 1.90mm

FEA, δz = 0.01mm

FEA, δz = 0.1mm

FEA, δz = 0.5mm

Experiment

Interference limit

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 5 10 15 20 25 30 35

Abs

. Buc

klin

g Tr

ue S

trai

n, |ε

b|

Side Force (kN)

DP800, RDThickness = 1.40mm

FEA, δz = 0.01mm

FEA, δz = 0.1mm

FEA, δz = 0.5mm

Experiment

Interference limit

Kun Piao 16

Buckling Simulation – YS Effect

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 5 10 15 20

Abs

. Buc

klin

g Tr

ue S

trai

n, |ε

b|

Side Force (kN)

DP590DP800

DP980

FEA

Experiment FEA

DP590DP800DP980

Experiment

Thickness=1.4mm

Kun Piao 17

MaterialThickn

ess(mm)

0.2% YS(MPa)

UTS(MPa) Exp. εb

Simulated εb

Calculatedεb

TWIP steel 1.4 454 1570 -0.13 -0.15

-0.10

-0.12

-0.12

-0.13

-0.14

-0.10

-0.09

-0.10

Trip780 1.5 507 866 -0.09 -0.13

DP980 1.4 552 990 -0.10 -0.12

DP800 1.4 422 800 -0.12 -0.13

DP780 1.9 714 844 -0.10 -0.16

DP590 1.4 369 613 -0.12 -0.15

AA6022-TD 0.93 135 250 -0.10 -0.11

HSLA 0.80 400 455 -0.11 -0.07

Buckling Simulation

Kun Piao 18

Conclusions

• Develop high-temperature T/C device

Temperature range: RT - 350oC

Heating time = 15 minutes for 350oC, ΔT (Gage Length) < 8oC

Device can be safely used with SFmax=8kN

εb vs. material, σ, t; <εb> = 0.015

Kun Piao 19

A NOVEL TEST TO DETERMINE TRANSITION T BETWEEN SLIP AND

TWIN

1) Cyclic T/C test

2) Determine transition T

3) Microstructure verification

4) Strain-rate effect, grain-size effect

Kun Piao 20

0

100

200

300

400

0 0.05 0.1 0.15 0.2 0.25

Abs

olut

e Tr

ue S

tres

s (M

Pa)

Accumulated Absolute True Strain

Mg AZ31B-O, RD

Thickness = 2.0 mm, Strain rate = 10-3/s

RT50oC

75oC

100oC

125oC

150oC

175oC

200oC225oC

250oCTension TensionCompression

T-C-T Tests at Elevated Temperatures

Kun Piao 21

0

100

200

300

400

0 0.05 0.1 0.15 0.2 0.25 0.3

Abs

olut

e Tr

ue S

tres

s (M

Pa)

Accumulated Absoluted True Strain

Mg AZ31B-O, RD

Thickness = 2.0 mmStrain rate = 10-3/s

RT 50oC

75oC

100oC

125oC

150oC

175oC

200oC225oC

250oCCompression CompressionTension

C-T-C Tests at Elevated Temperatures

Kun Piao 22

Optical Microscopy

No deformation, RT

C(-8%)-T(6%)-C(-2%) test, 125oC

C(-8%)-T(6%)-C(-2%) test, 150oC

Kun Piao 23

Cyclic Test for Transition Temperature

-200

-100

0

100

200

300

0 0.2 0.4 0.6 0.8

True

Str

ess

(MPa

)

Accumulated True Strain

Mg AZ31B (AU) T-C cyclic test t=2mm, gs=5.1μm, strain rate=0.001/s

150oC 140oC 130oC 120oC 110oC

Kun Piao 24

Calculation of Transition Temperature: Curvature

120

140

160

180

200

0 0.02 0.04 0.06 0.08 0.1

Abs

olut

e Tr

ue S

tres

s (M

Pa)


110oC (A=4219MPa)

120oC (A=2223MPa)

130oC (A=1078MPa)

140oC (A=-164MPa)

150oC (A=-1956MPa)

Mg AZ31B (AU) compressive cycles,t=2mm, gs = 5.1μm, strain rate = 0.001/s

120

140

160

180

200

0 0.02 0.04 0.06 0.08 0.1

Abs

olut

e Tr

ue S

tres

s (M

Pa)


110oC (A=16465MPa)

120oC (A=10143MPa)

130oC (A=3946MPa)

140oC (A=27MPa)

150oC (A=-2591MPa)

Mg AZ31B (AU), Tensile cycles,t=2mm, gs=5.1μm, strain rate = 0.001/s

Aε2+Bε+C

Kun Piao 25

Calculation of Transition Temperature

-5000

0

5000

1x104

1.5x104

2x104

100 110 120 130 140 150 160

A (M

Pa)

Temperature (oC)

Mg AZ31B (AU) T-C cycle testt=2mm, gs=5.1μm, strain rate = 0.001/s

Tension

Compression

QuadraticCurve fit

Tc

Tt

Kun Piao 26

Transition Temperature vs. Strain Rate

120

140

160

180

200

220

240

0.0001 0.001 0.01 0.1

y = 258.47 + 39.299log(x) R= 0.98132 Tr

ansi

tion

tem

pera

ture

(o C)

Strain rate (/s)

Mg AZ31B (AU), RD,t=2mm, gs=5.1μm

Kun Piao 27

Monotonic C Test for Verification-10-3/s to 10-2/s

100

120

140

160

180

200

0 0.02 0.04 0.06 0.08 0.1 0.12

Abs

olut

e Tr

ue S

tres

s (M

Pa)


Mg AZ31B (AU), Ct=2mm, gs=5.1μm, strain rate = 0.001/s

120oC (A=3967MPa)

130oC (A=1031MPa)

140oC (A=-28MPa)

150oC (A=-1490MPa)

160oC (A=-1971MPa)

100

120

140

160

180

200

0 0.02 0.04 0.06 0.08 0.1 0.12

Abs

olut

e Tr

ue S

tres

s (M

Pa)



150oC (A=2663MPa)

160oC (A=655MPa)

170oC (A=-1027MPa)

180oC (A=-1276MPa)

190oC (A=-1364MPa)

50

75

100

125

150

0 0.02 0.04 0.06 0.08 0.1 0.12

Abs

olut

e Tr

ue S

tres

s (M

Pa)



210oC (A=-235MPa)

220oC (A=-1274MPa)

230oC (A=-1397MPa)

240oC (A=-1630MPa)

250oC (A=-1471MPa)

Kun Piao 28

Microstructure Verification

10-3/s, 130oC, 9.7% 10-3/s, 140oC, 7.1%

10-3/s, 150oC, 1%

Kun Piao 29

Twin Area Fraction vs. Temperature

-10

0

10

20

30

40

150 200 250

Twin

Are

al F

ract

ion

(%)

Temperature (oC)

Mg AZ31B (AU), RD, Ct=2mm, gs= 5.1μm, ε=-0.08

10-3/s10-2/s

10-1/s

Mech. test shapefor limit

Kun Piao 30

Transition Temperature vs. Grain Size

140

160

180

200

220

240

4 5 6 7 8 9 10 11 12

y = 113.65 + 7.1786x R= 0.88079 Tr

ansi

tion

tem

pera

ture

(o C)

Grain size (μm)

Mg AZ31B, RD, 2mm and 1mmStrain rate = 0.001/s

Kun Piao 31

Conclusions

• High Temperature T/C testing of Mg AZ31B sheet:Inflected flow (twinning) disappears between 125oC - 150oC for strain rate of 10-3/s

Transition T determined by novel cyclic test

Microstructure verification: twin fraction of 8% Transition T

Transition T dependents on grain size and strain rate

Kun Piao 32

MG CONSTITUTIVE EQUATIONS

1) Uniaxial tensile tests: 150oC-300oC, 10-1/s-10-4/s

2) Modified Voce law: numerical fitting

3) FEA verification

Kun Piao 33

0

100

200

300

0 0.2 0.4 0.6 0.8

True

Str

ess

(MPa

)

True Strain

Tensile Test of Mg AZ31B, 150oC

10-1/s

10-2.5/s

10-4/s

Tensile Test of Mg AZ31B (150oC - 300oC)

0

100

200

300

0 0.2 0.4 0.6 0.8

True

Str

ess

(MPa

)

True Strain


10-1/s

10-2.5/s

10-4/s

0

100

200

0 0.2 0.4 0.6 0.8

True

Str

ess

(MPa

)

True Strain


10-1/s

10-2.5/s

10-4/s

300

0

100

200

0 0.2 0.4 0.6 0.8

True

Str

ess

(MPa

)

True Strain


10-1/s

10-2.5/s

300

Kun Piao 34

Method:

Constitutive Equation Framework)(g),T,(f εεεσ &&=

m

0001.0g ⎟

⎠⎞

⎜⎝⎛=

ε&

))C*(expB*1(K)εT,,f(ε 2 ε−−=&1) Fit to ε = 0.2:

2) Fit to post-uniform data:

1) ε = 0 – 0.2 2) From Post-Uniform ABAQUS Simulation

0323.0log0152.0m +ε−= &

1227.0T*0377.0C +=0313.1)log(*0632.0T*0014.0B +ε+−= &

6.80)log(*7.16)T/3.859exp(*5.36K2 −+= ε&

Standard Deviation <σ> = 4 MPa (150oC – 300oC)# Data points: 152

Kun Piao 35

0

100

200

300

0 0.2 0.4 0.6 0.8

True

Str

ess

(MPa

)

True Strain

Tensile test of Mg AZ31B200oC, 10-2.5/s

ε))*16.38exp(*0.233(1*130σ −−=

Step 1:

0

0

0

0

0 0.2 0.4 0.6 0.8

Eng Strain

Tensile Test of Mg AZ31B200oC, 10-2.5/s

10-2.5/s_m=0.05

10-2.5/s_m=0.1

FEA / VExpt.

10-2.5/s_m=0.07

10

20

30

Eng

Stre

ss (M

Pa)

0.8UTS

Step 2:

Constitutive Equation Fit – Example

minterplate = 0.06

Kun Piao 36

Results: FEA/Constitutive Equations vs. Experiments (Used for Fit)

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8

Eng

Stre

ss (M

Pa)

Eng Strain

150oC, Posco Mg AZ31BFEA vs. Experiments

10-1/s

10-2.5/s

10-4/s

Expt

Constitutive Eq.

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8

Eng

Stre

ss (M

Pa)

Eng Strain


10-1/s

10-2.5/s

10-4/s

Constitutive Eq.

Expt

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8

Eng

Stre

ss (M

Pa)

Eng Strain


10-1/s

10-2.5/s

10-4/s

Constitutive Eq.

Expt.

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8

Eng

Stre

ss (M

Pa)

Eng Strain


10-1/s

10-2.5/s

Constitutive Eq.

Expt

Kun Piao 37

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8

Eng

Stre

ss (M

Pa)

Eng Strain


10-1/s

10-2.5/s

10-4/s

Constitutive Eq.Expt.

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8

Eng

Stre

ss (M

Pa)

Eng Strain


10-1/s

10-2.5/s

10-4/s

Constitutive Eq.

Expt

Results: Experiments Verification

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8

Eng

Stre

ss (M

Pa)

Eng Strain


10-1/s

10-2.5/s

Constitutive Eq.

Expt

Standard Deviation <σ> = 4 MPaT: 175oC – 275oC# Data points: 64

Kun Piao 38

Conclusions

• 1D Constitutive equations for Mg AZ31B sheet:Experiments, numerical fitting and FEA verification

150oC - 300oC, 0.1-10-4/s, standard deviation = 4MPa

Kun Piao 39

APPLICATION: TEMPERATURE DIFFERENTIALFORMING, 150oC – 300oC

1) FEA Explicit model for deep-drawing problem

2) Temperature differential forming to improve formability

Kun Piao 40

Geometry & Mesh for the Deep Drawing Problem

• ¼ Mg AZ31 sheet, shell element, S4RT• Friction coeffcient = 0.1• Fix the positions of die, load = 1kN at RP of holder• Isothermal, or different temperatures on punch and die +blank holder• Finer Mesh in the corner of punch and die• Velocity of punch = 10, 1, and 0.1 mm/s

Punch, R = 25mmBlank holder

Die

Blank: t = 1 mm, R = 60 mm

R = 5 mm

Kun Piao 41

#1. 150oC #2. 150oC-300oC

Thickness Strain Gradient on Sheet

R=50mm, Punch speed = 1mm/s R=80mm, Punch speed = 1mm/s

Kun Piao 42

Future Work

• Temperature differential deep drawing on Mg with different blank holding force, drawing speeds, and temperature.

• Temperature differential deep drawing on virtual materials with Voce law

• Temperature differential deep drawing on Steel or Al alloys sheets

Kun Piao 43

Conclusions• Develop high-temperature T/C device

Temperature range: RT - 350oC

Heating time = 15 minutes for 350oC, ΔT (Gage Length) < 8oC

• High Temperature T/C testing of Mg AZ31B sheet:Inflected flow (twinning) disappears between 125oC - 150oC for strain rate of 10-3/s

Transition T dependents on grain size and strain rate

• Constitutive equations for Mg AZ31B sheet:Experiments, numerical fitting and FEA verification

150oC - 300oC, 0.1-10-4/s, standard deviation = 4MPa

• T-differential deep drawing:Non-isothermal heating improve the LDR from 1.9 to 3.3

• High Temperature T/C testing of AHSS:Large Bauschinger effect was observed

Kun Piao 44

Thank you!

Mg AZ31B Sheet Behavior and Formability at Elevated...

Documents

Transcript of Mg AZ31B Sheet Behavior and Formability at Elevated...