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Measurements and calculations on yield
surfaces in tension–simple shear experiments
Ton van den Boogaard and Maarten van Riel
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Contents
• Vegter yield criterion
• Biaxial experiments
• Non-proportional deformation paths
• Discussion of results
• Comparison experiments / simulations
• Conclusion
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3
The Vegter yield criterion
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Biaxial test equipment
x
y
3
5
6
Domain in stress space
Principal stress space Local stress space
σ1
σ2
σps
σsh
σps
σsh
4
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Possible deformation modes
Tension Simple shear Non-proportional
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Strain path changes applied to mild steel
0 0.1 0.2 0.3 0.4 0.50
100
200
300
400
equivalent plastic strain (-)
str
ess (
MP
a)
5
9
Stress paths
0 100 200 300 400
0
50
100
150
200
250
tensile stress (MPa)
shear
str
ess (
MP
a)
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Yield surface correspondence
0 0.2 0.40
100
200
300
400
equivalent plastic strain (-)
str
ess (
MP
a)
0 100 200 300 4000
100
200
tensile stress (MPa)
shear
str
ess (
MP
a)
6
11
Different strain paths
0 0.05 0.1 0.15 0.2
0
0.2
0.4
0.6
tensile strain (-)
shear
str
ain
(-)
12 3 4 5 6
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Shear stresses
0 0.05 0.1 0.15 0.2
0
0.2
0.4
0.6
0.8
tensile strain (-)
shear
str
ain
(-)
1 6
0 0.1 0.2 0.3 0.4 0.5 0.60
50
100
150
200
250
equivalent plastic strain (-)
shear
str
ess (
MP
a)
6
1
7
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Tensile stresses
0 0.05 0.1 0.15 0.2
0
0.2
0.4
0.6
0.8
tensile strain (-)
shear
str
ain
(-)
1 6
0 0.2 0.4 0.60
100
200
equivalent plastic strain (-)
shear
str
ess (
MP
a)
6
1
0 0.1 0.2 0.3 0.4 0.5 0.6
0
100
200
300
400
equivalent plastic strain (-)
tensile
str
ess (
MP
a)
1
6
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Stress paths
0 0.05 0.1 0.15 0.2
0
0.2
0.4
0.6
0.8
tensile strain (-)
shear
str
ain
(-)
1 6
0 0.2 0.4 0.60
100
200
equivalent plastic strain (-)
shear
str
ess (
MP
a)
6
1
0 0.2 0.4 0.6
0
200
400
equivalent plastic strain (-)
tensile
str
ess (
MP
a)
1
60 100 200 300 400
0
50
100
150
200
250
1
6
tensile stress (MPa)
shear
str
ess (
MP
a)
8
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Simulation of experiments
Vegter yield criterion
Isotropic hardening (tabular)
Material model:
0 0.05 0.1 0.15 0.2
0
0.2
0.4
0.6
0.8
tensile strain (-)
sh
ea
r str
ain
(-)
1 3 5
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Results in stress space for mild steel
0 0.2 0.4 0.6 0.8 1-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
normalized tensile stress (-)
norm
aliz
ed s
hear
str
ess (
-)
experiment
simulation
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Orthogonal experiments for aluminium
0 0.1 0.2 0.3 0.4 0.5
0
50
100
150
2001
3
equivalent plastic strain (-)
shear
str
ess (
MP
a)
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Results in stress space for aluminium
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
normalized tensile stress (-)
norm
aliz
ed s
hear
str
ess (
-)
experiment
simulation
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Conclusion
• The orthogonal strain path can be used to trace the (current) yield surface
• Influence of strain rate should be corrected
• For DC06 steel the yield locus is distorted by strain
• Aluminium 5182 can be modelled with isotropic hardening
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Acknowledgement
This research was carried out under project number MC1.03158 in the framework of the Strategic Research programme of the Materials Innovation Institute (former NIMR) in the Netherlands (www.m2i.nl)