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Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation
- 1. Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 1 Centre for Mechanical Technology and Automation (TEMA) Department of Mechanical Engineering, University of Aveiro Campus Universitário de Santiago, 3810-193 Aveiro, Portugal XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 M. Conde1,*, A. Andrade-Campos1, S. Coppieters2 2 Department of Materials Engineering, KU Leuven Ghent Technology Campus, Gebroeders De Smetstraat 1, Ghent, 9000, Belgium * Corresponding author: Mariana Peneda Conde. E-mail address: marianaconde@ua.pt
- 2. Introduction, framework and literature review XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Engineering design and development framework M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 1 Engineering design and development Simulation predictions Virtual manufacturing
- 3. Introduction, framework and literature review XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Numerical material behaviour reproduction M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 2 Constitutive model Material parameters Numerical material behaviour prediction
- 4. Introduction, framework and literature review XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Observed problem and possible solution M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 3 Classical mechanical tests Fixed stress state [1] Several tests required Time consuming High costs Heterogeneous mechanical tests Several strain and stress states simultaneously Large mechanical information More complex stress states that better represent reality [1, 2] Fewer tests required [3] Reliability proved [1-4] [1] S. Cooreman, D. Lecompte, H. Sol, J. Vantomme, and D. Debruyne, Exp. Mech., vol. 48, no. 4, pp. 421–433, 2008, doi: 10.1007/s11340-007-9094-0. [2] T. Pottier, F. Toussaint, and P. Vacher, Eur. J. Mech. A/Solids, vol. 30, no. 3, pp. 373–382, 2011, doi: 10.1016/j.euromechsol.2010.10.001. [3] Nelson Mineiro Souto. Phd Thesis, University of Aveiro, Portugal, 2015. [4] E. M. C. Jones, J. D. Carrol, K. N. Karlson, S. L. B. Kramer, R. B. Lehoueq, P. L. Reu and D. Z. Turner. Computational Materials Science, 152(June):268-290, 2018.
- 5. Introduction, framework and literature review XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Non-homogeneous mechanical tests from the literature M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 4 [7] T. Pottier, P. Vacher, F. Toussaint, H. Louche and T. Coudert. Experimental Mechanics, 52(7):951-963, 2012. [5] [5] [5] [6] [7] [4] [8] [3] [3] [5] Steven Cooreman. PhD Thesis, Free University of Brussels, Belgium, 2008. [6] J. H. Kim, F. Barlat, F. Pierron and M. G. Lee. Experimental MechanicsI, 54(7):1189-1204, 2014. [4] E. M. C. Jones, J. D. Carrol, K. N. Karlson, S. L. B. Kramer, R. B. Lehoueq, P. L. Reu and D. Z. Turner. Computational Materials Science, 152(June):268-290, 2018. [8] L. Chamoin, C. Jailin, M. Diaz and L. Quesada. International Journal of Solids ans Structures, 2020. [3] Nelson Mineiro Souto. Phd Thesis, University of Aveiro, Portugal, 2015.
- 6. Proposed solution XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Innovative heterogeneous mechanical test M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 5 Design a heterogeneous mechanical specimen Uniaxial loading conditions Several strain and stress states simultaneously Standard tensile testing machine Non-circular interior notch Shape optimisation based on heterogeneity indicators
- 7. Methodology and implementation XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by shape optimisation: general methodology M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 6 Control variables Curve definition Specimen’s shape Virtual mechanical test Strain and stress states Heterogeneity criterion Objective function Optimisation algorithm Iterative process Heterogeneity indicators Plane stress state Best solution Beginning Convergence?
- 8. Methodology and implementation XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Optimisation problem formulation M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 7 The aim is to find r = [ ri ] with i = 1,… n, that: maximises: 𝐻 𝐫, 𝐮 𝑟𝑖 min ≤ 𝑟𝑖 ≤ 𝑟𝑖 max, 𝐊. 𝐮 = 𝐅. 𝐫 ∈ ℝ𝑛 Subjected to: 𝑖 = 1, … , 𝑛,
- 9. Methodology and implementation XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Solution’s evaluation: heterogeneity criterion M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 8 𝐼T1 = 𝑤r1 Std 𝜀2 𝜀1 𝑤a1 + 𝑤r2 𝜀2 𝜀1 𝑅 𝑤a2 + 𝑤r3 Std 𝜀𝑝 𝑤a3 + 𝑤r4 𝜀𝑝 𝑀𝐴𝑋 𝑤a4 + 𝑤r5 𝐴𝑣𝜀𝑝 𝑤a5 𝐼T1 ϵ [0,1] [3] Nelson Mineiro Souto. Phd Thesis, University of Aveiro, Portugal, 2015. 𝐶𝐹T1 = 2 − 𝐼T1 uniaxial tension pure shear uniaxial compression plane strain equibiaxial tension [3]
- 10. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Sensitivity analysis to the element’s dimension and type M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 9 Control points Fixed point Extra points x y
- 11. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Sensitivity analysis to the element’s dimension and type M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation Control points Fixed point Extra points x y 10
- 12. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Sensitivity analysis to the element’s dimension and type M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation Control points Fixed point Extra points x y 10
- 13. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Sensitivity analysis to the element’s dimension and type M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation Control points Fixed point Extra points x y 11
- 14. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 12 Control points Fixed point Extra points x y Analysed parameters Boundary conditions Specimen’s height/width ratio Shape of the initial solution Number of curve control points Constitutive model
- 15. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation Control points Fixed point Extra points x y from 60 mm Analysed parameters Boundary conditions Specimen’s height/width ratio Shape of the initial solution Number of curve control points Constitutive model 13
- 16. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation Control points Fixed point Extra points x y from 60 mm to 120 mm Analysed parameters Boundary conditions Specimen’s height/width ratio Shape of the initial solution Number of curve control points Constitutive model 13
- 17. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation Control points Fixed point Extra points x y Analysed parameters Boundary conditions Specimen’s height/width ratio Shape of the initial solution Number of curve control points Constitutive model 14
- 18. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation Control points Fixed point Extra points x y Analysed parameters Boundary conditions Specimen’s height/width ratio Shape of the initial solution Number of curve control points Constitutive model 14
- 19. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation Control points Fixed point Extra points x y from 4 Analysed parameters Boundary conditions Specimen’s height/width ratio Shape of the initial solution Number of curve control points Constitutive model 15
- 20. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation Control points Fixed point Extra points x y from 4 to 12 control points Analysed parameters Boundary conditions Specimen’s height/width ratio Shape of the initial solution Number of curve control points Constitutive model 15
- 21. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 16 Control points Fixed point Extra points x y Hooke’s Law Swift hardening Law Analysed parameters Boundary conditions Specimen’s height/width ratio Shape of the initial solution Number of curve control points Constitutive model
- 22. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 16 Control points Fixed point Extra points x y Hooke’s Law Swift hardening Law Yld2000-2d yield function Analysed parameters Boundary conditions Specimen’s height/width ratio Shape of the initial solution Number of curve control points Constitutive model
- 23. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation: comparison of the obtained solutions M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 17
- 24. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation: reference solution (circular interior notch) M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 18
- 25. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation: best-obtained solutions M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 19
- 26. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation: best-obtained solutions M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 20
- 27. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation: best-obtained solutions M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 21
- 28. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Specimen design by optimisation: best-obtained solutions M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 22
- 29. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Hardening parameters’ identifiability analysis of the best solutions M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 23 [10] Y. Zhang, S. Gothivarekar, M. Conde, A. V. de Velde, A. Andrade-Campos, S. Coppieters, (Unpublished results) [11] R. Brun, P. Reichert, H. R. K¨unsch, Water Resources Research 37 (4) (2001) 1015-1030. doi:10.1029/2000WR900350 [12] D. N. Gujarati, Basic Econometrics, 4th Edition, Vol. 82, McGrawHiII/lrwin, 2003. doi:10.2307/2230043. [10, 11] [10, 12] Good identifiability Poor identifiability Good identifiability Poor identifiability Moderate identifiability The identifiability indexes are based on the partial derivative of the strain field with respect to the hardening parameters. It demonstrates the influence of the material model parameters in the computed strain fields of the test.
- 30. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Validation of the best solution using a virtual experiment M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 24 Virtual experiment Real speckle pattern (5px dot size) Added heteroscedastic noise Reference image deformed according to the FEA data (nodal coordinates for each load step) Performance analysis (subset size, step size, strain window and order of the fitting polynomial) 𝑁𝑜𝑖𝑠𝑒 𝑓𝑙𝑜𝑜𝑟 = 1.526 × 10−3 𝑁𝑜𝑖𝑠𝑒 𝑙𝑒𝑣𝑒𝑙 = 0.653 %
- 31. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Validation of the best solution using a virtual experiment M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 25 Strain component Average FEA and DIC difference (%) xx 3.283 yy 6.057 xy 14.477 Subset-based DIC process Speckle pattern quality Experimental noise Strain calculation method
- 32. Analysis and results XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 Validation of the best solution using a virtual experiment M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 26
- 33. Conclusions and future works XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 27 Main conclusions Interior notched specimen for a uniaxial loading test using shape optimisation Uniaxial tension, pure shear, uniaxial compression and plane strain states in the plastic regime Larger heterogeneity than a specimen with a circular interior notch Good identifiability of the sought parameters of the Swift hardening Law Validation using a virtual experiment Good agreement on the xx and yy strain components xy strain component exhibited larger differences Larger errors observed in the tip of the interior notch Strains states revealed in the numerical analysis are observed in the virtual experiment
- 34. Conclusions and future works XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 M. Conde, A. Andrade-Campos, S. Coppieters, Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation 28 Future works Influence of the material orientation On the mechanical behaviour of the best solution On the shape optimisation problem Parameter identification using the developed specimen Synthetic images Experimental data Perform the real experimental validation of the designed test
- 35. Design and validation of a heterogeneous interior notched specimen for material mechanical characterisation Thank you! XVI International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2021, Barcelona, Spain, 7-10 September 2021 M. Conde1,*, A. Andrade-Campos1, S. Coppieters2 This project was funded by the Research Fund for Coal and Steel under grant agreement No 888153. The authors acknowledge the financial support of the Portuguese Foundation for Science and Technology (FCT) under the project PTDC/EME-APL/29713/2017 by UE/FEDER through the programs CENTRO 2020 and COMPETE 2020, and UID/EMS/00481/2013-FCT under CENTRO-01-0145-FEDER-022083. * Corresponding author: Mariana Peneda Conde. E-mail address: marianaconde@ua.pt
Editor's Notes
- Greetings Name, University, Counrty Title
- Nowadays…
- Accurate simulations <- robust contitutive model+calibrated material parameters
- These days the classical mechanical tests are used to calibrate the model’s parameters. However, heterogeneous mechanical tests ……
- The heterogeneity is obtain due to a complex specimen geometry, or a complex loading condition, or even the combination of both Here are some exemples from the literature…. Still don’t presente all the strain and stress states These still have some issues like sliping of grips
- It is proposed to develop….
- How does he optimisation problema work? It stars by…. Control variables = optimisation variables Curve definition, … Virtual mechanical test performed in abaqus until rupture in plane stress state conditions There are obtained the strain and stress states that are used for the calculation of the heterogeneity criterion
- CP = optimisation variable Fixed point -> give another point to curve (> flexibility) but not add a optimisation variable Extra points -> unsure slipes continuty in the symmetries The aim is to … That maximizes the heterogenety Subjected to the search space limits of variables and the equilíbrium of forces of the virtual test
- The heterogeneity criterion used was an adaptation of one from the literature It was evaluated in the moment just before rupture and it takes in consideration… strain states. It takes into acount both elastic and plastic strains. It is normalised, so its maximum possible value is 1 and the cost function to be minimised is equal to 2 minus the heterogeneity criterion value
- Conserning the simulation procedure, it …
- It was performed a sensittivy analysis of the heterogeneity criterion to the element dimension and type. For that it was varied each control point individually from 6 to 14, while the other were fixed in 10 and was calculated the heterogeneity criterion value with diferent element dimensions
- It was performed a sensittivy analysis of the heterogeneity criterion to the element dimension and type. For that it was varied each control point individually from 6 to 14, while the other were fixed in 10 and was calculated the heterogeneity criterion value with diferent element dimensions
- It was performed a sensittivy analysis of the heterogeneity criterion to the element dimension and type. For that it was varied each control point individually from 6 to 14, while the other were fixed in 10 and was calculated the heterogeneity criterion value with diferent element dimensions It is observed a similar behaviour with the different element dimentions, with some exceptions with the 0.88mm element edge size So it was perfered a smaller element dimention, expecting more accuracy
- It was taken the same approach for the element type sensitivity evaluation. It is clearlly observed a shift in the curves that will influence the heterogeneity criterion value. However, since the optimisation problema is a comparitive approach, this will not influence finding the best solution. So it was perfered a elemento type that requires less computational time (CPS4R)
- These are the heterogeneity criterion values of each final solution. The best 4 were highlighted for further analysis.
- Here is the reference solution, a specimen with a 20mm diameter perforation in the center. On the left there are the minor and major stress and strain ratio, the von mises stress and the equivalente plastic strain of the specimen in the moment just before rupture. On the right, the same moment is demonstrated in the major and minor stress diagram. It can be observed some heterogeneity specially in the elastic regime. The plsatic regime is dominated by uniaxial tension state, with some uniaxial compression state.
- Here is solution F, with a larger width. It shows mora variaty in the strain and stress states, exhibiting elemento from the plane strain state, until uniaxial compression in the plastic regime. In the elastic regime there are observed elements in the equibiaxial tension state.
- This solution was genetared with an ellipsed-shape interior notch as initial solution of the optimisation problem. It presents one of the largest heterogeneity criterion values, however the strain and stress states observed haven’t got that variety
- This is the solution obtained with the combination of the best parameters. It presentes a similar mechanical behaviour as Sol. F, but a more complex interior notch shape
- Lastly this is the solution obtained with the same parameters as Sol F, but adding the anisotropy behaviour to the material model. The interior notch shape is different from Sol F, demonstrating that dependeing on the material use, the optimium shape is different. The minor and major stress diagram shows a large amount of elements in the plastic regime with a good variety of stress states.
- It was done an identifiability analysis to the hardening parameters of the best solutions. …. It was proved that all the solutions show good identifiability, whereas the reference solution shows a moderate identifiability of the hardening parameters
- A virtual experiment was held with a real speckle pattern….
- Here are presented the strain fields of the FEA and DIC analysis and the normalised difference between the two. The xx (exs) and yy (why) strain components show large similarities, with only some discrepencies in the tip of the notch. Whereas the xy (ex-why) strain ocmponent exhibits larger diffrences with a average of approx. 14%. These differences reflect the influence of the subset-based DIC process, the speckle pattern quality, the experimental noise and the strain calculation method.
- Here are presented the minor and major strain diagrams of the same solution in the moment just before rupture evaluated with the numerical approach and the synthetic images. It is observed a larger number of elements exhibiting pure shear in the virtual experimente and larger strains in the uniaxial tension state