- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Materials

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Network approach for the analysis of the irreversible deformation of solids with soft heterogeneities

Tito Andriollo1,*, Varvara Kouznetsova2, and Laura Alessandretti3

  • 1Aarhus University, 8000 Aarhus C, Denmark
  • 2Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
  • 3Technical University of Denmark, 2800 Kgs. Lyngby, Denmark

  • *titoan@mpe.au.dk
PDF

Phys. Rev. Materials 6, L110601 – Published 29 November, 2022

DOI: https://doi.org/10.1103/PhysRevMaterials.6.L110601

Abstract

We introduce the concept of shear band network (SBN) in ductile solids containing soft particles to investigate their irreversible deformation. Drawing on network science tools, we show that the evolution of the SBN explains the material strength at the coarse scale. To gain physical understanding of the activation order of the SBN links during tensile loading, we develop an analytical model based on the continuum theory of irreversible deformation. The results are used to construct an efficient, parameter-free indicator of the material strength that is solely based on the particle size and spatial distribution, thus proving that network science can advance the understanding of strength mechanisms in ductile solids.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (38)

  1. M. Ashby, H. Shercliff, and D. Cebon, Materials: Engineering, Science, Processing and Design (Butterworth-Heinemann, Oxford, UK, 2010).
  2. N. E. Putra, M. J. Mirzaali, I. Apachitei, J. Zhou, and A. A. Zadpoor, Multi-material additive manufacturing technologies for Ti-, Mg-, and Fe-based biomaterials for bone substitution, Acta Biomater. 109, 1 (2020).
  3. J. Aboudi, S. Arnold, and B. Bednarcyk, Micromechanics of Composite Materials: A Generalized Multiscale Analysis Approach (Butterworth-Heinemann, Oxford, UK, 2012).
  4. D. D. Ben, Y. R. Ma, H. J. Yang, L. X. Meng, X. H. Shao, H. Q. Liu, S. G. Wang, Q. Q. Duan, and Z. F. Zhang, Heterogeneous microstructure and voids dependence of tensile deformation in a selective laser melted AlSi10Mg alloy, Mater. Sci. Eng. A 798, 140109 (2020).
  5. T. L. Anderson, Fracture Mechanics – Fundamentals and Applications, 3rd ed. (CRC Press, Boca Raton, 2005).
  6. G. Rousselier, Porous plasticity revisited: Macroscopic and multiscale modeling, Int. J. Plast. 136, 102881 (2021).
  7. J. Faleskog and P. Gudmundson, Analytical predictions of yield stress of a strain gradient plasticity material reinforced by small elastic particles, J. Mech. Phys. Solids 157, 104623 (2021).
  8. J. E. Bishop, J. M. Emery, C. C. Battaile, D. J. Littlewood, and A. J. Baines, Direct numerical simulations in solid mechanics for quantifying the macroscale effects of microstructure and material model-form error, JOM - J. Miner. Met. Mater. Soc. 68, 1427 (2016).
  9. T. Andriollo, Y. Zhang, S. Fæster, J. Thorborg, and J. Hattel, Impact of micro-scale residual stress on in-situ tensile testing of ductile cast iron: Digital volume correlation vs. model with fully resolved microstructure vs. periodic unit cell, J. Mech. Phys. Solids 125, 714 (2019).
  10. K. Matouš, M. G. D. Geers, V. G. Kouznetsova, and A. Gillman, A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials, J. Comput. Phys. 330, 192 (2017).
  11. J. Segurado, R. A. Lebensohn, and J. Llorca, Computational homogenization of polycrystals, in Advances in Crystals and Elastic Metamaterials, Part 1, edited by M. I. Hussein (Elsevier, Cambridge, MA, USA, 2018).
  12. S. Bargmann, B. Klusemann, J. Markmann, J. E. Schnabel, K. Schneider, C. Soyarslan, and J. Wilmers, Generation of 3D representative volume elements for heterogeneous materials: A review, Prog. Mater. Sci. 96, 322 (2018).
  13. H. Villarraga-Gómez, E. L. Herazo, and S. T. Smith, X-ray computed tomography: From medical imaging to dimensional metrology, Precis. Eng. 60, 544 (2019).
  14. T. M. Pollock, Alloy design for aircraft engines, Nat. Mater. 15, 809 (2016).
  15. A. Sola, D. Bellucci, and V. Cannillo, Functionally graded materials for orthopedic applications – an update on design and manufacturing, Biotechnol. Adv. 34, 504 (2016).
  16. P. S. Ghatage, V. R. Kar, and P. E. Sudhagar, On the numerical modelling and analysis of multi-directional functionally graded composite structures: A review, Compos. Struct. 236, 111837 (2020).
  17. X. Wu and Y. Zhu, Heterogeneous materials: A new class of materials with unprecedented mechanical properties, Mater. Res. Lett. 5, 527 (2017).
  18. E. Tejado, W–Cu metal matrix composites for next generation fusion devices, Mater. Today 38, 136 (2020).
  19. S. Tarancón, E. Tejado, M. Richou, and J. Y. Pastor, Evaluation of tensile and elastic properties of W/Cu cold-spray coatings for application to the FGM DEMO divertor concept, Fusion Eng. Des. 171, 112719 (2021).
  20. N. Bilger, F. Auslender, M. Bornert, J. C. Michel, H. Moulinec, P. Suquet, and A. Zaoui, Effect of a nonuniform distribution of voids on the plastic response of voided materials: A computational and statistical analysis, Int. J. Solids Struct. 42, 517 (2005).
  21. F. Fritzen, S. Forest, T. Böhlke, D. Kondo, and T. Kanit, Computational homogenization of elasto-plastic porous metals, Int. J. Plast. 29, 102 (2012).
  22. A. Buljac, L. Helfen, F. Hild, and T. F. Morgeneyer, Effect of void arrangement on ductile damage mechanisms in nodular graphite cast iron: In situ 3D measurements, Eng. Fract. Mech. 192, 242 (2018).
  23. C. L. Xu, T. Andriollo, Y. B. Zhang, J. C. Hernando, J. Hattel, and N. Tiedje, Micromechanical impact of solidification regions in ductile iron revealed via a 3D strain partitioning analysis method, Scr. Mater. 178, 463 (2020).
  24. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevMaterials.6.L110601 for (1) example of shear band network in a real material, (2) description of the finite element model, (3) procedure used to identify the links of the shear band network, (4) shear band network metrics vs. material stiffness variation, (5) shear band network metrics vs. Delaunay network, (6) derivation of the rate of irreversible work for a shear band, and (7) strength indicator vs. material strength data.
  25. N. Limodin, J. Réthoré, J. Y. Buffière, A. Gravouil, F. Hild, and S. Roux, Crack closure and stress intensity factor measurements in nodular graphite cast iron using three-dimensional correlation of laboratory X-ray microtomography images, Acta Mater. 57, 4090 (2009).
  26. L. Papadopoulos, J. G. Puckett, K. E. Daniels, and D. S. Bassett, Evolution of network architecture in a granular material under compression, Phys. Rev. E 94, 032908 (2016).
  27. L. Papadopoulos, M. A. Porter, K. E. Daniels, and D. S. Bassett, Network analysis of particles and grains, J. Complex Networks 6, 485 (2018).
  28. K. P. Krishnaraj and P. R. Nott, Coherent Force Chains in Disordered Granular Materials Emerge from a Percolation of Quasilinear Clusters, Phys. Rev. Lett. 124, 198002 (2020).
  29. V. A. Buryachenko, R. Y. Kim, N. J. Pagano, and J. E. Spowart, Quantitative description and numerical simulation of random microstructures of composites and their effective elastic moduli, Int. J. Solids Struct. 40, 47 (2003).
  30. C. L. Y. Yeong and S. Torquato, Reconstructing random media, Phys. Rev. E 57, 495 (1998).
  31. V.-D. Nguyen, E. Béchet, C. Geuzaine, and L. Noels, Imposing periodic boundary condition on arbitrary meshes by polynomial interpolation, Comput. Mater. Sci. 55, 390 (2012).
  32. E. de Souza Neto, D. Peric, and D. R. J. Owens, Computational Methods for Plasticity: Theory and Applications (Wiley, Chichester, UK, 2008).
  33. K. Sieradzki and R. Li, Fracture Behavior of a Solid with Random Porosity, Phys. Rev. Lett. 56, 2509 (1986).
  34. M. Barthelemy, Morphogenesis of Spatial Networks (Springer International Publishing, Cham, Switzerland, 2018).
  35. M. Newman, Networks: An Introduction (Oxford University Press, Oxford, UK, 2010).
  36. Y. Malkov, A. Ponomarenko, A. Logvinov, and V. Krylov, Approximate nearest neighbor algorithm based on navigable small world graphs, Inf. Syst. 45, 61 (2014).
  37. C. Miehe and M. Lambrecht, Analysis of microstructure development in shearbands by energy relaxation of incremental stress potentials: Large-strain theory for standard dissipative solids, Int. J. Numer. Methods Eng. 58, 1 (2003).
  38. H. Laubie, F. Radjai, R. Pellenq, and F. J. Ulm, Stress Transmission and Failure in Disordered Porous Media, Phys. Rev. Lett. 119, 075501 (2017).

Outline

Information

Phys. Rev. Materials 6, L110601– Published 29 November, 2022
  • Received 28 January 2022
  • Revised 15 June 2022
  • Accepted 15 November 2022
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation