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Inequality Indices Applied to Statistical Physics of Criticality in an Impregnated Fiber Bundle Model

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Mechanics of Composite Materials Aims and scope

Inequality indices (Hirsch and Kolkata) are used in social science and scientometrics. Previously, they were shown to have useful applications in statistical physics of criticality in a Fiber Bundle Model (FBM) with an Equal Load Sharing (ELS). The indices offer potentially useful techniques for predicting the imminent failure of the bundle. In this paper, the same indices are calculated for the case of an Impregnated Fiber Bundle Model (IFBM) with physically based load redistributions around fiber breaks based on finite element model stress fields. It is shown that the behavior of the Hirsch and Kolkata indices in this case are similar to the behavior in the FBM with ELS, including similar critical values for the final failure of the bundle.

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References

  1. S. L. Phoenix, and I. J. Beyerlein, Statistical Strength Theory for Fibrous Composite Materials, Ch. 1.19 in Comprehensive Composite Materials, A. Kelly and C. Zweben (eds), Pergamon, Oxford (2000), pp. 559-639.

  2. A. Hansen, P. C. Hemmer, and S. Pradhan, The Fiber Bundle Model: Modeling Failure in Materials, John Wiley & Sons, Weinheim (2015)

    Book  Google Scholar 

  3. S. G. Abaimov, Statistical Physics of Non-Thermal Phase Transitions: from Foundations to Applications, Springer, New York (2015).

    Book  Google Scholar 

  4. B. W. Rosen, “Tensile failure of fibrous composites”. AIAA J., 2, No. 11, 1985-1991 (1964)

    Article  Google Scholar 

  5. S. B. Batdorf, “Tensile strength of unidirectionally reinforced composites — I,” J. of Reinf. Plastics and Compos., 1, No. 2, 153-164 (1982)

    Article  Google Scholar 

  6. Y. Swolfs, I. Verpoest, and L. Gorbatikh, “A review of input data and modelling assumptions in longitudinal strength models for unidirectional fiber-reinforced composites”, Compos. Struct., 150, 153-172 (2016).

    Article  Google Scholar 

  7. A. Bunsell, L. Gorbatikh, H. Morton, S. Pimenta, I. Sinclair, M. Spearing, Y. Swolfs, and A. Thionnet, “Benchmarking of strength models for unidirectional composites under longitudinal tension,” Compos., Part A, 111, 138-150 (2018).

    Article  CAS  Google Scholar 

  8. C. Breite, A. Melnikov, A. Turon, A.B. de Morais, C. Le Bourlot, E. Maire, E. Schroberl, F. Otero, F. Mesquita, I. Sinclair, J. Costa, J. A. Mayugo, J. M. Guerrero, L. Gorbatikh, L. N. McCartney, M. Hajikazemi, M. Mehdikhani, M. Mavrogordato, P. P. Camanho, R. P. Tavares, S. M. Spearing, S. V. Lomov, S. Pimenta, W. Van Paepegem, and Y. Swolfs, “Detailed experimental validation and benchmarking of six models for longitudinal tensile failure of unidirectional composites,” Compos. Struct., 279, 114828 (2022).

    Article  Google Scholar 

  9. C. Breite, A. Melnikov, A. Turon, A. B. de Morais, F. Otero, F. Mesquita, J. Costa, J. A. Mayugo, J. M. Guerrero, L. Gorbatikh, L. N. McCartney, M. Hajikazemi, P. P. Camanho, R. P. Tavares, S. V. Lomov, S. Pimenta, W. Van Paepegem, and Y. Swolfs, “Blind benchmarking of seven longitudinal tensile failure models for two virtual unidirectional composites,” Compos. Sc. and Technol., 202, 108555 (2021).

    Article  CAS  Google Scholar 

  10. P. Bak, How Nature Works: The Science of Self-Organized Criticality, Copernicus, New York (1996).

    Book  Google Scholar 

  11. P. Bak, C. Tang, and K. Wiesenfeld, “Self-organized criticality: An explanation of the 1/f noise,” Physical Review Letters, 59, No. 4, 381-384 (1987).

    Article  CAS  Google Scholar 

  12. Sornette, D., Chaos, Fractals, Self-organization and Disorder: Concepts and Tools. Springer Series in Synergetics, Vol. XXII, Springer-Verlag, Berlin-Heidelberg (2006).

  13. S. Biswas and B. K. Chakrabarti, “Social inequality analysis of fiber bundle model statistics and prediction of materials failure,” Physical Review E, 104, No. 4, 044308 (2021).

  14. J. E. Hirsch, “An index to quantify an individual’s scientific research output,” Proceedings of the National Academy of Sciences, 102, No. 46, 16569-16572 (2005).

    Article  CAS  Google Scholar 

  15. S. Alonso, F. J. Cabrerizo, E. Herrera-Viedma, and F. Herrera, “h-Index: A review focused in its variants, computation and standardization for different scientific fields”, J. Informetrics, 3, No. 4, 273-289 (2009).

    Article  Google Scholar 

  16. A. Ghosh, N. Chattopadhyay, and B. K. Chakrabarti, “Inequality in societies, academic institutions and science journals: Gini and k-indices,” Physica A: Statistical Mechanics and its Applications, 410, 30-34 (2014).

    Article  Google Scholar 

  17. S. Banerjee, B. K. Chakrabarti, M. Mitra, and S. Mutuswami, “Inequality measures: The Kolkata index in comparison with other measures,” Frontiers in Physics, 8, No. 540, 562182 (2020).

    Google Scholar 

  18. Y. Swolfs, R. M. McMeeking, V. P. Rajan, F. W. Zok, I. Verpoest, and L. Gorbatikh, “Global load-sharing model for unidirectional hybrid fiber-reinforced composites,” J. Mech. and Physics of Solids, 84, 380-394 (2015).

    Article  CAS  Google Scholar 

  19. Y. Swolfs, R. M. McMeeking, I. Verpoest, and L. Gorbatikh, “Matrix cracks around fiber breaks and their effect on stress redistribution and failure development in unidirectional composites,” Compos. Sci. and Technol., 108, 16-22 (2015).

    Article  CAS  Google Scholar 

  20. S. V. Lomov, C. Breite, A. Melnikov, F. Mesquita, Y. Swolfs, and S. G. Abaimov, “Clusters and avalanches of fiber breaks in a model of an impregnated unidirectional fiber bundle under tension,” Int. J.Solids and Struct., 225, 111061 (2021).

    Article  CAS  Google Scholar 

  21. S. V. Lomov, C. Breite, A. Melnikov, F. Mesquita, Y. Swolfs, and S. G. Abaimov, “Discussion of the statistical representativeness of the results in: Lomov, Breite, Melnikov, Mesquita, Swolfs and Abaimov [Int. J. Solids Struct 225 (2021) 111061],” Int. J.Solids and Struct., 236-237, 111356 (2022).

  22. T. Okabe, K. Ishii, M. Nishikawa, and N. Takeda, “Prediction of tensile strength of unidirectional CFRP composites,” Adv. Compos. Mater., 19, No. 3, 229-241 (2010).

    Article  CAS  Google Scholar 

  23. S. Pradhan, A. Hansen, and P. C. Hemmer, “Crossover behavior in burst avalanches: signature of imminent failure,” Physical Review Letters, 95, No.12, 125501 (2005).

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Acknowledgement

A. Melnikov and F. Mesquita have created the dataset, used for the analysis presented in this paper. Christian Breite kindly acknowledges his postdoctoral fellowship project COCOMI (application number 1231322N), which has been funded by the Research Foundation - Flanders (FWO).

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Authors and Affiliations

  1. Department of Materials Engineering, KU Leuven, Kasteelpark Arenberg, 44, 3001, Leuven, Belgium

    S. V. Lomov, C. Breite & Y. Swolfs

  2. Center for Petroleum Science and Engineering, Skolkovo Institute of Science and Technology, Bolshoy blvd., 30, bld.1, Skolkovo, 121205, Moscow, Russian Federation

    S. V. Lomov & S. G. Abaimov

Authors
  1. S. V. Lomov
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  2. S. G. Abaimov
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  3. C. Breite
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  4. Y. Swolfs
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Correspondence to S. V. Lomov.

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Lomov, S.V., Abaimov, S.G., Breite, C. et al. Inequality Indices Applied to Statistical Physics of Criticality in an Impregnated Fiber Bundle Model. Mech Compos Mater 59, 841–846 (2023). https://doi.org/10.1007/s11029-023-10137-3

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  • DOI: https://doi.org/10.1007/s11029-023-10137-3

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