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Classification of inelastic deformation and material-intrinsic indices about mechanical performance of general solid matter

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Abstract

The present article is aimed to detect material-intrinsic indices that can be used to supervise the mechanical performance of general solid matter. The novelty carried in this article can be summarised as follows. Firstly, an inelastic deformation state of almost any solid matter can be treated as the combination of two fundamental modes due to different microscopic causation: Mode I inelastic distortion due to the movement of sliding types of defects and Mode II inelastic dilation due to the evolution of voids/bubbles. Secondly, each inelastic deformation mode is characterised by a single principal inelastic deformation descriptor (PIDD): Mode I by a newly introduced quantity of maximum distortional angle change α and Mode II by the logarithm of dilating magnification ω. In particular, the concept of maximum distortional angle change gives rise to a geometrically intuitive yield criterion of α > αc, which in situations of small deformation, is shown to asymptote von Mise’s, and to become Tresca’s in cases of plane stress. Thirdly, the deformation process of a solid matter under monotonic and ambient loads is formulated by means of trajectories of thermodynamic equilibria with respect to the PIDD pair. Then a pair of physical quantities which measure the stresses needed to change the local PIDD state are singled out. Being termed as inelastic deformation resistances (IDRs), these two quantities are shown to depend only on the onsite atomic configurations. It is also shown that key descriptive properties about the mechanical behaviours of materials, such as ductility, are encoded in IDRs as functions of PIDDs. Hence the IDR pair may serve as material performance indices that may be more intrinsic than conventional stress-strain relationships.

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References

  1. Standard Test Methods for Tension Testing of Metallic Materials, ASTM E8-03, 24 (2010).

  2. L. P. Kubin, G. Canova, M. Condat, B. Devincre, V. Pontikis, and Y. Bréchet, Solid State Phenom. 23–24, 455 (1992).

    Article  Google Scholar 

  3. D. Weygand, L. H. Friedman, E. V. Giessen, and A. Needleman, Model. Simul. Mater. Sci. Eng. 10, 437 (2002).

    Article  ADS  Google Scholar 

  4. H. M. Zbib, and T. Diaz de la Rubia, Int. J. Plast. 18, 1133 (2002).

    Article  Google Scholar 

  5. A. Arsenlis, W. Cai, M. Tang, M. Rhee, T. Oppelstrup, G. Hommes, T. G. Pierce, and V. V. Bulatov, Model. Simul. Mater. Sci. Eng. 15, 553 (2007).

    Article  ADS  Google Scholar 

  6. J. A. El-Awady, S. Bulent Biner, and N. M. Ghoniem, J. Mech. Phys. Solids 56, 2019 (2008).

    Article  ADS  Google Scholar 

  7. A. M. Hussein, and J. A. El-Awady, J. Mech. Phys. Solids 91, 126 (2016).

    Article  ADS  Google Scholar 

  8. I. Groma, F. F. Csikor, and M. Zaiser, Acta Mater. 51, 1271 (2003).

    Article  ADS  Google Scholar 

  9. T. Hochrainer, S. Sandfeld, M. Zaiser, and P. Gumbsch, J. Mech. Phys. Solids 63, 167 (2014).

    Article  ADS  Google Scholar 

  10. H. S. Leung, P. S. S. Leung, B. Cheng, and A. H. W. Ngan, Int. J. Plast. 67, 1 (2015).

    Article  Google Scholar 

  11. M. S. Mohamed, B. C. Larson, J. Z. Tischler, and A. El-Azab, J. Mech. Phys. Solids 82, 32 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  12. Y. Zhu, and Y. Xiang, J. Mech. Phys. Solids 84, 230 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  13. H. G. F. Wilsdorf, J. Electron. Mater. 4, 791 (1975).

    Article  ADS  Google Scholar 

  14. A. A. Benzerga, and J.-B. Leblond, Adv. Appl. Mech. 44, 169 (2010).

    Article  Google Scholar 

  15. D. Kondepudi, and I. Prigogine, Modern Thermodynamics: From Heat Engines to Dissipative Structures (John Wiley & Sons, Hoboken, 2014).

    Book  Google Scholar 

  16. B. Wang, Sci. China-Phys. Mech. Astron. 63, 124611 (2020).

    Article  ADS  Google Scholar 

  17. B. Wang, Eng. Fract. Mech. 254, 107936 (2021).

    Article  Google Scholar 

  18. E. H. Lee, J. Appl. Mech. 36, 1 (1969).

    Article  ADS  Google Scholar 

  19. H. Hencky, Z. Angew. Math. Mech. 4, 323 (1924).

    Article  Google Scholar 

  20. A. Nadai, J. Appl. Phys. 8, 205 (1937).

    Article  ADS  Google Scholar 

  21. H. C. Wu, Continuum Mechanics and Plasticity, 1st ed. (Chapman and Hall/CRC, New York, 2004).

    Google Scholar 

  22. Y. L. Bai, M. F. Xia, and F. J. Ke, Statistical Meso-Mechanics of Damage and Failure: How Microdamage Induces Disaster, 1st ed. (Springer, Singapore, 2019).

    Book  Google Scholar 

  23. A. L. Gurson, J. Eng. Mater. Tech. 99, 2 (1977).

    Article  Google Scholar 

  24. V. Tvergaard, Int. J. Fract. 17, 389 (1981).

    Article  Google Scholar 

  25. V. Tvergaard, and A. Needleman, Acta Metall. 32, 157 (1984).

    Article  Google Scholar 

  26. A. Needleman, and V. Tvergaard, J. Mech. Phys. Solids 32, 461 (1984).

    Article  ADS  Google Scholar 

  27. Y. Xiang, J. Mech. Phys. Solids 57, 728 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  28. M. Zaiser, Philos. Mag. Lett. 93, 387 (2013).

    Article  ADS  Google Scholar 

  29. P. M. Anderson, J. P. Hirth, and J. Lothe, Theory of Dislocations, 3rd ed. (Cambridge University Press, New York, 2017).

    Google Scholar 

  30. Y. Zhu, Y. Xiang, and K. Schulz, Scripta Mater. 116, 53 (2016).

    Article  Google Scholar 

  31. Z. Zhou, Y. Zhu, J. Luo, X. Yang, and X. Guo, Int. J. Solids Struct. 198, 57 (2020).

    Article  Google Scholar 

  32. M. Zaiser, Phys. Rev. B 92, 174120 (2015).

    Article  ADS  Google Scholar 

  33. R. Wu, and M. Zaiser, J. Mech. Phys. Solids 159, 104735 (2022).

    Article  Google Scholar 

  34. D. Hull, and D. J. Bacon, Introduction to Dislocations, 5th ed. (Elsevier, Oxford, 2011).

    Google Scholar 

  35. A. A. Griffith, and G. I. Taylor, Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci. 221, 163 (1921).

    ADS  Google Scholar 

  36. G. A. Francfort, and J. J. Marigo, J. Mech. Phys. Solids 46, 1319 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  37. B. Bourdin, G. A. Francfort, and J. J. Marigo, J. Mech. Phys. Solids 48, 797 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  38. E. P. George, W. A. Curtin, and C. C. Tasan, Acta Mater. 188, 435 (2020).

    Article  ADS  Google Scholar 

  39. A. Pineau, A. A. Benzerga, and T. Pardoen, Acta Mater. 107, 424 (2016).

    Article  ADS  Google Scholar 

  40. J. W. Yoon, Y. Lou, J. Yoon, and M. V. Glazoff, Int. J. Plast. 56, 184 (2014).

    Article  Google Scholar 

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Correspondence to Biao Wang.

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Conflict of interest The authors declare that they have no conflict of interest.

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Yichao Zhu was partly supported by the National Natural Science Foundation of China (Grant No. 12172074), the Fundamental Research Funds for the Central Chinese Universities (Grant No. DUT16RC(3)091). Biao Wang was partly supported by the National Natural Science Foundation of China (Grant Nos. 12150001, and 11832019).

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Zhu, Y., Li, S. & Wang, B. Classification of inelastic deformation and material-intrinsic indices about mechanical performance of general solid matter. Sci. China Phys. Mech. Astron. 66, 114611 (2023). https://doi.org/10.1007/s11433-023-2167-5

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  • DOI: https://doi.org/10.1007/s11433-023-2167-5

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