Niels Vancraeynest1, Steven Cooreman2 and Sam Coppieters1 1Elooi lab, Department of Materials Engineering, KU Leuven 2 Applications & Solutions department, ArcelorMittal Global R&D Gent

1. Identification of the large strain flow curve of high
strength steel via the torsion test and FEMU
ESAFORM 2023
Niels Vancraeynest1, Steven Cooreman2 and Sam Coppieters1
1Elooi lab, Department of Materials Engineering, KU Leuven
2 Applications & Solutions department, ArcelorMittal Global R&D Gent
Elooi
Laboratory

2. 2
Today's overview
• Goal
• Pure torsion test
• Numerical
• FEMU
• Results
• Summary & Outlook

3. 3
Goal – Identify HSS S700MC
• Inversely identify hardening behaviour
• Find a suitable hardening law
• Explore the capabilities of the torsion test

4. 4
Goal – Tension-Torsion machine
Twisting head Weighing head
Capacity loadcell: Torque:100 Nm Force:5 kN
Total length: 3 m
Advandages of the tension-torsion test:
• Minor necking in gauge length
• Boundary condition are good known
• No influence of friction
• Large strains (𝜺𝒆𝒒
𝒑𝒍
> 𝟏 )
• Ability for abrupt strain path changes

5. 5
Pure torsion test – Boundary conditions
Weighing head:
• Free along rotation axis
• Friction in guiding rails (300 N)
Twisting head:
• Rotation until fracture
• Tmax equal to 100 Nm
𝜃
2r =Ø8
L=20
Boundary quasi static test:
• nominal strain rate ≤ 𝟏𝟎−𝟑 𝟏
𝒔
𝜀𝑒𝑞 =
𝛾
3
=
𝑟 ⋅ 𝜃
𝐿 ⋅ 3
→ 𝜃 ≤ 30 ° 𝑚𝑖𝑛

6. 6
Rolling direction
t = 12 mm
Pure torsion test– Experimental work
Test information:
• High strength steel plate S700MC
• Rotation axis along the rolling direction RD
• Repeated 3 times

7. 7
Pure torsion test– Experimental results

8. 8
Numerical – Finite element model
Mesh:
• Hexahedral reduced element
(C3D8R)
• Average element size 0,3 mm
in gauge length
Material model:
• Elastically isotropic
• Plastically isotropic
 von Mises yield criterium
 phenomenological hardening law
Boundary conditions:
• 2 points kinematically
coupled to the grip
surfaces
• Boundary applied on
reference points

9. 9
Numerical – Finite element model Updating
Cost function formulation:
• Defines similarity
with experiment
FEMU algorithms:
• Starting with Gauss-Newton
algorithm with possibility to
transition to Levenberg-
Marquardt
Material model:
• Inversely identified material parameters
for:
 Swift
 Voce
 p-model

10. 10
FEMU – Initial guess based on uniaxial tensile test
Hardening law Amount of parameters Material parameters
Swift 3 𝐾 ; 𝜀0 ; 𝑛
Voce 3 𝐶 ; 𝑚 ; 𝐵
p-model 2 𝑝 ; 𝜀𝑚𝑎𝑥
Hardening law Amount of parameters Material parameters
Swift 3 𝐾 ; 𝜀0 ; 𝑛
Voce 3 𝐶 ; 𝑚 ; 𝐵
p-model 2 𝑝 ; 𝜀𝑚𝑎𝑥
0,12

11. 11
FEMU – Cost function
FEMU boundaries:
• FEMU sees [25° - 600°]
• Step size of 2,5°
Cost function:
• Compare experimental and
numerical torque
𝐶(𝒑) =
1
2
𝑻𝑒𝑥𝑝 − 𝑻𝑛𝑢𝑚(𝒑)
𝑇
⋅ 𝑻𝑒𝑥𝑝 − 𝑻𝑛𝑢𝑚(𝒑)
𝑻𝑛𝑢𝑚(𝒑)
𝑻𝑒𝑥𝑝

12. 12
Results – indication problem statement
PEEQ = 0,12

13. 13
Results – Remark reduced integration elements
Settings:
• Time step: 0,02 s
• Rotation: Smooth step 600°
• Identical model & mesh
Caused by:
• Different default hourglass controls

14. 14
Results – Remark reduced integration elements

15. 15
Results – Identified hardening behaviour

16. 16
Results – Identified hardening behaviour

17. 17
Summary & Outlook
• Be aware of hourglassing
• The Swift hardening law can describe S700MC during
pure torsion
• Limited spiral necking was observed, probably due to
anisotropy

18. Thank you!
Time for questions / discussion.

19. 19
C3D8R
-
More saturation (best: Voce)
C3D8
-
Closer to UTT (best: Swift)
Results – C3D8R vs C3D8

20. 20
Results – Remark reduced integration elements

21. 21
Results – Remark reduced integration elements
Undeformed Deformed

22. 22
Summary & Outlook
Von Mises Barlat2004-p18
Hill48

23. 23
Summary & Outlook