1

1

Measurements and calculations on yield

surfaces in tension–simple shear experiments

Ton van den Boogaard and Maarten van Riel

2

Contents

• Vegter yield criterion

• Biaxial experiments

• Non-proportional deformation paths

• Discussion of results

• Comparison experiments / simulations

• Conclusion

2

3

The Vegter yield criterion

4

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

7

Possible deformation modes

Tension Simple shear Non-proportional

8

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)

10

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

12

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

13

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

14

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

15

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

16

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

9

17

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)

18

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

10

19

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

20

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)