Alessandro Lambrughi - PhD Researcher ECCOMAS 7th Young Investigators Conference YIC2023

1. Identification through-thickness work hardening
variation of a thick high-strength steel using the
Virtual Field Method
Alessandro Lambrughi - PhD Researcher
Department of Materials Engineering
ECCOMAS 7th Young Investigators
Conference YIC2023

2. 2
Thematic Contextualization
Thermo-Mechanical Controlled Process (TMCP) to produce high-strength steel (HSS) plates
• Controlled rolling + accelerated cooling
• Strength – toughness – weldability
• Industrial application: pipelines

3. 3
Scientific Problematic
Through-thickness properties gradient induced by TMCP - Cause
• Plate surface and center: different cooling rates
1. Microstructural gradient
2. Middle segregation band

4. 4
Scientific Problematic
Through-thickness properties gradient induced by TMCP - Consequence
• Variation mechanical properties: yielding and hardening
• Numerical simulations
• Pipe forming
• Plasticity model: through-thickness hardening behavior

5. 5
Work Objective
Characterization through-thickness hardening behavior of a thick HSS plate
• Tested material: S700MC
• Large plastic strain (post-necking)

6. 6
Solution Approach
Experimental methodology: standard tensile tests combined with Digital Image Correlation (DIC)
• Sheets sliced from thick plate
• Quasi-static conditions
• Stereo DIC setup
• DIC software: MatchID

7. 7
Solution Approach
Numerical methodology: Virtual Field Method (VFM)
• Motivation: post-necking
• MatchID: VFM module
• 2 steps workflow

8. 8
Numerical Methodology
Definition data interval for inverse identification – Motivation
• VFM: plane stress
• Tensile test:
[1] J.-H. Kim et al., Int. J. Solids Struct. 50 (2013) 3829–3842

9. 9
Numerical Methodology
Definition data interval for inverse identification – Selected approach, theoretical principle
• Surface curvature
• Derivation DIC displacement: 𝑘𝑦𝑦 =
𝛿2𝑤𝑵(𝑥,𝑦,𝑧)
𝛿2𝑦

10. 10
Numerical Methodology
Definition data interval for inverse identification – Selected approach, result
• Surface curvature during test
• Illustration along 2 lines
y

11. 11
Numerical Methodology
Inverse identification with VFM – Characteristics
• Ludwick hardening: 𝜎𝑒𝑞= 𝑌0 + 𝐾 𝜀𝑒𝑞
𝑝 𝑛
• Isotropic material
• Virtual fields type: sensitivity-based [1]
[1] A. Marek et al., Int. J. Mater. Form. (2019) 12:457-476

12. 12
Inverse Identification Results
Through-thickness hardening variation of a 12mm thick plate (S700MC-TD)
• Flow curves, surface layers
• Experimental: pre-necking
• VFM: inversely identified

13. 13
Inverse Identification Results
Through-thickness hardening variation of a 12mm thick plate (S700MC-TD)
• Flow curves, surface and central layers
• Experimental: pre-necking
• VFM: inversely identified

14. 14
Conclusion: perspective
More appropriate hardening law to describe post-necking domain
• Numerical application: tensile test thick sample
• Model: through-thickness hardening variation
• Correlation with experiments

15. Thank you!
Thank you!
Time for questions / discussion.
Contact:
Alessandro Lambrughi
KU Leuven technology campus Gent
Gebroeders de Smetstraat 1, 9000 Gent, Belgium
alessandro.lambrughi@kuleuven.be

16. 16
Additional slide
Mismatch hardening law post-necking domain - proof using VFM
• Only 1 slice
• 1 identification pre-necking
• 1 identification pre- and post-necking