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Development of a methodology for the automated spatial mapping of heterogeneous elastoplastic properties of welded joints
[Développement d’une méthodologie de cartographie automatisée des propriétés élasto-plastiques hétérogènes de joints soudés]
Robert Hamill1, 2 orcid  ; Allan Harte2 ; Aleksander Marek1 orcid ; Fabrice Pierron1, 3 orcid
1Faculty of Engineering and Physical Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, Hampshire, UK
2United Kingdom Atomic Energy Authority, Culham Centre for Fusion Energy, Culham Science Centre, Abingdon OX14 3DB, Oxfordshire, UK
3MatchID NV, Leiekaai 25A, Ghent, East Flanders, BE 0563. 512.491, Belgium
Comptes Rendus. Mécanique, Volume 354 (2026), pp. 561-592

Knowledge of the mechanical properties of materials is required for the design and analysis of engineering products, however, the characterisation of heterogeneous properties using traditional techniques is limited by spatial resolution or insufficient reliability. This paper presents a novel methodology for the characterisation of heterogeneous mechanical properties by extending the virtual fields method through the automated spatial parameterisation of constitutive parameters. Collaboration with the United Kingdom Atomic Energy Authority provided this project with an application focus on the characterisation of the spatially-varying, elastoplastic mechanical properties of welded joints. The developed methodology enables the novel characterisation of welds with assorted geometries, varied loading configurations and dissimilar materials. Numerical verification of the developed method was performed using synthetic data equivalent to that obtained experimentally using optical measurements, where the kinematic fields are known and controlled. The results confirm that the proposed approach converges towards the target parameter maps without any a priori information on the distribution of the properties, successfully demonstrating the established methodology as a proof of concept.

La connaissance des propriétés mécaniques des matériaux est indispensable à la conception et à l’analyse des structures. Il arrive que ces propriétés soient hétérogènes spatialement, comme dans les joints soudés, et dans ce cas, les méthodes d’essai traditionnelles sont limitées par leur manque de résolution spatiale. Cet article présente une méthodologie originale de caractérisation de distributions de propriétés élasto-plastiques basée sur la méthode des champs virtuels enrichie d’un outil de paramétrisation automatique de ces distributions. En collaboration avec l’Autorité Britannique de l’Énergie Nucléaire (UKAEA), les joints soudés ont été choisis comme exemple d’application pour illustrer la méthodologie. Celle-ci est en mesure de traiter des géométries et des cas de chargement complexes, au-delà du cas classique du joint bord-à-bord en traction uniaxiale (cas 1D). Cet article se focalise sur la présentation de la méthodologie et sur sa vérification à partir de données de simulation de champs de déformation, typiquement obtenus par mesure optique comme la corrélation d’images numériques. Les résultats confirment que la méthode converge bien vers les résultats attendus, ceci sans nécessiter d’information a priori sur les distributions spatiales de propriétés mécaniques. Des applications à des données expérimentales sont en cours.

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DOI : 10.5802/crmeca.371
Keywords: Virtual fields method, inverse identification, characterization, welding, materials testing 2.0, heterogeneity
Mots-clés : Méthode des champs virtuels, identification inverse, caractérisation mécanique, soudage, essais matériaux 2.0, hétérogénéité

Robert Hamill  1 , 2   ; Allan Harte  2   ; Aleksander Marek  1   ; Fabrice Pierron  1 , 3

1 Faculty of Engineering and Physical Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, Hampshire, UK
2 United Kingdom Atomic Energy Authority, Culham Centre for Fusion Energy, Culham Science Centre, Abingdon OX14 3DB, Oxfordshire, UK
3 MatchID NV, Leiekaai 25A, Ghent, East Flanders, BE 0563. 512.491, Belgium
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Robert Hamill; Allan Harte; Aleksander Marek; Fabrice Pierron. Development of a methodology for the automated spatial mapping of heterogeneous elastoplastic properties of welded joints. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 561-592. doi: 10.5802/crmeca.371
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[1] Yiqiang Wang; Giacomo Aiello; Gerald Pintsuk; Dmitry Terentyev; Jeong-Ha You; Guangming Zhou; Tyge Schioler; Zsolt Vizvary; Cory Hamelin; David Bowden; Robert Skilton; Sergei L. Dudarev; David Knowles; Chris Waldon; Mark Shannon; Thomas Barrett Ensuring the Structural Integrity of Tokamak Fusion Power Plants: Challenges, Progress and Pathway, Philos. Trans. R. Soc. Lond., Ser. A, Volume 383 (2025) no. 2300, 20240180, 31 pages | DOI

[2] K. Degiorgio; M. Muscat; P. Mollicone RCC-MRx Type P Damage Assessment Methodologies for the Design of Nuclear Fusion Reactor Components, Fusion Eng. Des., Volume 221 (2025), 115407, 12 pages | DOI

[3] Steven M Zuniga; Sheri D Sheppard Determining the Constitutive Properties of the Heat-Affected Zone in a Resistance Spot Weld, Model. Simul. Mat. Sci. Eng., Volume 3 (1995) no. 3, pp. 391-416 | DOI

[4] Wolfgans Bleck; Uwe Reisgen; Oleg Mokrov; Eduardo Rossiter; Thomas Rieger Methodology for Thermomechanical Simulation and Validation of Mechanical Weld-Seam Properties, Adv. Eng. Mater., Volume 12 (2010) no. 3, pp. 147-152 | DOI

[5] Chunhua Wei; Jing Zhang; Shanglu Yang; Wu Tao; Fengshun Wu; Weisheng Xia Experiment-Based Regional Characterization of HAZ Mechanical Properties for Laser Welding, Int. J. Adv. Manuf. Technol., Volume 78 (2015) no. 9–12, pp. 1629-1640 | DOI

[6] Navid Nazemi; Faouzi Ghrib Strength Characteristics of Heat-Affected Zones in Welded Aluminum Connections, J. Eng. Mech., Volume 145 (2019) no. 12, 04019103 | DOI

[7] Idna Wudtke; Hossein Talebi; Mohammad Silani; Frank Werner A Hierarchical Multi-Scale Approach to Mechanical Characterization of Heat Affected Zone in Welded Connections, Comput. Mater. Sci., Volume 96 (2015), pp. 396-402 | DOI

[8] G. Çam; Ç. Yeni; S. Erim; V. Ventzke; M. Koçak Investigation into Properties of Laser Welded Similar and Dissimilar Steel Joints, Sci. Technol. Weld. Joining, Volume 3 (1998) no. 4, pp. 177-189 | DOI

[9] D. A LaVan Microtensile Properties of Weld Metal, Exp. Tech., Volume 23 (1999) no. 3, pp. 31-34 | DOI

[10] David A. LaVan; W. N. Sharpe Local Properties of Undermatched Steel Weld Metal, Metall. Mater. Trans., Volume 32 (2001) no. 4, pp. 913-922 | DOI

[11] Rafal M. Molak; Krystian Paradowski; Tomasz Brynk; Lukasz Ciupinski; Zbigniew Pakiela; Krzysztof J. Kurzydlowski Measurement of Mechanical Properties in a 316L Stainless Steel Welded Joint, Int. J. Press. Vessels Pip., Volume 86 (2009) no. 1, pp. 43-47 | DOI

[12] D. Rao; J. Heerens; G. Alves Pinheiro; J. F. dos Santos; N. Huber On Characterisation of Local Stress-Strain Properties in Friction Stir Welded Aluminium AA 5083 Sheets Using Micro-Tensile Specimen Testing and Instrumented Indentation Technique, Mater. Sci. Eng. A, Volume 527 (2010) no. 18–19, pp. 5018-5025 | DOI

[13] M. Pakdil; G. Çam; M. Koçak; S. Erim Microstructural and Mechanical Characterization of Laser Beam Welded AA6056 Al-alloy, Mater. Sci. Eng. A, Volume 528 (2011) no. 24, pp. 7350-7356 | DOI

[14] H. T. Wang; G. Z. Wang; F. Z. Xuan; C. J. Liu; S. T. Tu Local Mechanical Properties of a Dissimilar Metal Welded Joint in Nuclear Powersystems, Mater. Sci. Eng. A, Volume 568 (2013), pp. 108-117 | DOI

[15] Stijn Hertelé; Nenad Gubeljak; Wim De Waele Advanced Characterization of Heterogeneous Arc Welds Using Micro Tensile Tests and a Two-Stage Strain Hardening (‘UGent’) Model, Int. J. Press. Vessels Pip., Volume 119 (2014), pp. 87-94 | DOI

[16] Pengfei Zheng; Ran Chen; Haiting Liu; Jiming Chen; Zhijie Zhang; Xing Liu; Yao Shen On the Standards and Practices for Miniaturized Tensile Test — A Review, Fusion Eng. Des., Volume 161 (2020), 112006 | DOI

[17] W. C. Oliver; G. M. Pharr An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments, J. Mater. Res. Technol., Volume 7 (1992) no. 6, pp. 1564-1583 | DOI

[18] W. C. Oliver; G. M. Pharr Measurement of Hardness and Elastic Modulus by Instrumented Indentation: Advances in Understanding and Refinements to Methodology, J. Mater. Res. Technol., Volume 19 (2004) no. 1, pp. 3-20 | DOI

[19] M. Dao; N. Chollacoop; K. J. Van Vliet; T. A. Venkatesh; S. Suresh Computational Modeling of the Forward and Reverse Problems in Instrumented Sharp Indentation, Acta Mater., Volume 49 (2001) no. 19, pp. 3899-3918 | DOI

[20] Duyi Ye; Feng Mi; Jianzhong Liu; Yuandong Xu; Yinzheng Chen; Lei Xiao Use of Instrumented Indentation Testing to Study Local Mechanical Properties of 304L SS Welded Joints Subjected to Low-Cycle Fatigue Loadings, Mater. Sci. Eng. A, Volume 564 (2013), pp. 76-84 | DOI

[21] Anton Evdokimov; Aleksei Obrosov; Ralf Ossenbrink; Sabine Weiß; Vesselin Michailov Mechanical Properties of Dissimilar Steel-Aluminum Welds, Mater. Sci. Eng. A, Volume 722 (2018), pp. 242-254 | DOI

[22] Jimmy E. Campbell; Hannah Zhang; Max Burley; Mark Gee; Antony Thomas Fry; James Dean; Trevor William Clyne A Critical Appraisal of the Instrumented Indentation Technique and Profilometry-based Inverse Finite Element Method Indentation Plastometry for Obtaining Stress-Strain Curves, Adv. Eng. Mater., Volume 23 (2021), 2001496, 13 pages | DOI

[23] Damaso M. De Bono; Tyler London; Mark Baker; Mark J. Whiting A Robust Inverse Analysis Method to Estimate the Local Tensile Properties of Heterogeneous Materials from Nano-Indentation Data, Int. J. Mech. Sci., Volume 123 (2017), pp. 162-176 | DOI

[24] Ehsan Javaheri; Janot Lubritz; Benjamin Graf; Michael Rethmeier Mechanical Properties Characterization of Welded Automotive Steels, Metals, Volume 10 (2020) no. 1, 1, 19 pages | DOI

[25] Xi Chen; Nagahisa Ogasawara; Manhong Zhao; Norimasa Chiba On the Uniqueness of Measuring Elastoplastic Properties from Indentation: The Indistinguishable Mystical Materials, J. Mech. Phys. Solids, Volume 55 (2007) no. 8, pp. 1618-1660 | DOI

[26] Stéphane Avril; Marc Bonnet; Anne-Sophie Bretelle; Michel Grédiac; François Hild; Patrick Ienny; Félix Latourte; Didier Lemosse; Stéphane Pagano; Emmanuel Pagnacco; Fabrice Pierron Overview of Identification Methods of Mechanical Parameters Based on Full-Field Measurements, Exp. Mech., Volume 48 (2008) no. 4, pp. 381-402 | DOI

[27] J. M. P. Martins; A. Andrade-Campos; S. Thuillier Comparison of Inverse Identification Strategies for Constitutive Mechanical Models Using Full-Field Measurements, Int. J. Mech. Sci., Volume 145 (2018), pp. 330-345 | DOI

[28] Fabrice Pierron Material Testing 2.0: A Brief Review, Strain, Volume 59 (2023) no. 3, e12434, 20 pages | DOI

[29] M. A. Sutton; J. H. Yan; S. Avril; F. Pierron; S. M. Adeeb Identification of Heterogeneous Constitutive Parameters in a Welded Specimen: Uniform Stress and Virtual Fields Methods for Material Property Estimation, Exp. Mech., Volume 48 (2008) no. 4, pp. 451-464 | DOI

[30] A P Reynolds; F Duvall Digital Image Correlation for Determination of Weld and Base Metal Constitutive Behavior, Welding J., Volume 78 (1999), p. 355s-360s

[31] W. D. Lockwood; A. P. Reynolds Simulation of the Global Response of a Friction Stir Weld Using Local Constitutive Behavior, Mater. Sci. Eng. A, Volume 339 (2003) no. 1, pp. 35-42 | DOI

[32] B. L. Boyce; P. L. Reu; C. V. Robino The Constitutive Behavior of Laser Welds in 304L Stainless Steel Determined by Digital Image Correlation, Metall. Mater. Trans., Volume 37 (2006) no. 8, pp. 2481-2492 | DOI

[33] G. Le Louëdec; F. Pierron; M. A. Sutton; A. P. Reynolds Identification of the Local Elasto-Plastic Behavior of FSW Welds Using the Virtual Fields Method, Exp. Mech., Volume 53 (2013) no. 5, pp. 849-859 | DOI

[34] K. M. Saranath; Abhay Sharma; M. Ramji Zone Wise Local Characterization of Welds Using Digital Image Correlation Technique, Opt. Lasers Eng., Volume 63 (2014), pp. 30-42 | DOI

[35] K. M. Saranath; M. Ramji Local Zone Wise Elastic and Plastic Properties of Electron Beam Welded Ti-6Al-4V Alloy Using Digital Image Correlation Technique: A Comparative Study between Uniform Stress and Virtual Fields Method, Opt. Lasers Eng., Volume 68 (2015), pp. 222-234 | DOI

[36] Marco Rossi; Attilio Lattanzi; Antonio Piccininni; Pasquale Guglielmi; Gianfranco Palumbo Study of Tailor Heat Treated Blanks Using the Fourier-series-based VFM, Procedia Manuf., Volume 47 (2020), pp. 904-909 | DOI

[37] T. T. Nguyen; J. M. Huntley; I. A. Ashcroft; P. D. Ruiz; F. Pierron A Fourier-series-based Virtual Fields Method for the Identification of 2D Stiffness Distributions, Int. J. Numer. Methods Eng., Volume 98 (2014) no. 12, pp. 917-936 | DOI | MR

[38] António Andrade-Campos; Sandrine Thuillier; João Martins; Pierpaolo Carlone; Fausto Tucci; Robertt Valente; Rui M. F. Paulo; Ricardo J. Alves de Sousa Integrated Design in Welding and Incremental Forming: Material Model Calibration for Friction Stir Welded Blanks, Procedia Manuf., Volume 47 (2020), pp. 429-434 | DOI

[39] M. Kartal; Rafal M. Molak; Mark Turski; S. Gungor; Michael E. Fitzpatrick; Lyndon Edwards Determination of Weld Metal Mechanical Properties Utilising Novel Tensile Testing Methods, Appl. Mech. Mater., Volume 7–8 (2007), pp. 127-132 | DOI

[40] M Acar; S Gungor; S Ganguly; P J Bouchard; M E Fitzpatrick Variation of Mechanical Properties in a Multi-Pass Weld Measured Using Digital Image Correlation, Proceedings of the 2009 SEM Annual Conference, Society for Experimental Mechanics (2009), pp. 1868-1875

[41] C. Leitão; I. Galvão; R. M. Leal; D. M. Rodrigues Determination of Local Constitutive Properties of Aluminium Friction Stir Welds Using Digital Image Correlation, Mater. Des., Volume 33 (2012), pp. 69-74 | DOI

[42] Yang Peng; Chao Wu; Jieliang Gan; Jun Dong Determination of the Local Constitutive Properties of the Welded Steel Joints Using Digital Image Correlation Method, Constr. Build. Mater., Volume 171 (2018), pp. 485-492 | DOI

[43] Ruixiang Bai; Hao Jiang; Zhenkun Lei; Da Liu; Yang Chen; Cheng Yan; Wang Tao; Qiaoling Chu Virtual Field Method for Identifying Elastic-Plastic Constitutive Parameters of Aluminum Alloy Laser Welding Considering Kinematic Hardening, Opt. Lasers Eng., Volume 110 (2018), pp. 122-131 | DOI

[44] A. Shahmirzaloo; M. Farahani; M. Farhang Evaluation of Local Constitutive Properties of Al2024 Friction Stir-Welded Joints Using Digital Image Correlation Method, J. Strain Anal. Eng. Des., Volume 56 (2021) no. 7, pp. 419-429 | DOI

[45] Xu Wu; Jian Shuai; Kui Xu; Zhiyang Lv; Ke Shan Determination of Local True Stress-Strain Response of X80 and Q235 Girth-Welded Joints Based on Digital Image Correlation and Numerical Simulation, Int. J. Press. Vessels Pip., Volume 188 (2020), 104232 | DOI

[46] S. Ramachandran; A. K. Lakshminarayanan; P. A. S. Reed; J. M. Dulieu-Barton Application of Imaging Techniques to Determine the Post-Yield Behaviour of the Heterogeneous Microstructure of Friction Stir Welds, Exp. Mech., Volume 61 (2021), pp. 1045-1063 | DOI

[47] Attilio Lattanzi; Antonio Piccininni; Pasquale Guglielmi; Marco Rossi; Gianfranco Palumbo A Fast Methodology for the Accurate Characterization and Simulation of Laser Heat Treated Blanks, Int. J. Mech. Sci., Volume 192 (2021), 106134 | DOI

[48] Aleksander Marek; Frances M. Davis; Fabrice Pierron Sensitivity-Based Virtual Fields for the Non-Linear Virtual Fields Method, Comput. Mech., Volume 60 (2017) no. 3, pp. 409-431 | DOI | MR

[49] Amar Peshave; Fabrice Pierron; Pascal Lava; David Moens; Dirk Vandepitte Metrics to Evaluate Constitutive Model Fitness Based on DIC Experiments, Strain, Volume 60 (2024) no. 5, e12473 | DOI

[50] C. Devivier; F. Pierron; M. R. Wisnom Impact Damage Detection in Composite Plates Using Deflectometry and the Virtual Fields Method, Compos. A. Appl. Sci. Manuf., Volume 48 (2013), pp. 201-218 | DOI

[51] J. M. Considine; F. Pierron; K. T. Turner; P. Lava; X. Tang Smoothly Varying In-Plane Stiffness Heterogeneity Evaluated under Uniaxial Tensile Stress, Strain, Volume 53 (2017) no. 5, e12237 | DOI

[52] ANSYS, Inc. Ansys Workbench (2023) https://www.ansys.com/products/ansys-workbench

[53] M. Rossi; P. Lava; F. Pierron; D. Debruyne; M. Sasso Effect of DIC Spatial Resolution, Noise and Interpolation Error on Identification Results with the VFM, Strain, Volume 51 (2015) no. 3, pp. 206-222 | DOI

[54] MatchID NV MatchID (2023) https://www.matchid.eu/

[55] The MathWorks Inc. MATLAB (2023) https://matlab.mathworks.com/

[56] E. A. de Souza Neto; D. Perić; D. R. J. Owen Computational Methods for Plasticity: Theory and Applications, John Wiley & Sons, 2008 | DOI

[57] Tianchen Hu; Mark C. Messner NEML2: An Efficient and Modular Multiphysics Constitutive Modeling Library for Hybrid Computing Environments, SoftwareX, Volume 31 (2025), 102302, 8 pages | DOI

[58] The MathWorks Inc. MATLAB — Global Optimization Toolbox (2024) https://www.mathworks.com/...

[59] A. Peshave; F. Pierron; P. Lava; D. Moens; D. Vandepitte DIC-Based Finite Element Model Validation: A Practical Case Study for In-Plane Loading of A Composite Laminate, Exp. Mech., Volume 66 (2026) no. 1, pp. 37-66 | DOI

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