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Correlation between the internal length, the fracture process zone and size effect in model materials

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Abstract

In this paper, we examine the correlation between the width of the fracture process zone, the parameters entering in the description of size effect (related to the dimension of the specimen especially), and the internal length in non local constitutive relations for a model mortar material with a controlled macro-porosity. Experimental investigations on this material in compression, bending, acoustic emission measurements and their analysis are detailed. The experiments show a good agreement between the evolution of Bažant's size effect parameterd 0 and the evolution of the width of the FPZ. The internal length obtained with the help of inverse finite element analysis is also proportional to these quantities. This correlation provides a reasonable approximation of the internal length, from an experimental test on specimens of a single size directly, equipped with acoustic emission localization devices.

Résumé

Dans cet article, nous examinons les corrélations entre la largeur de la zone de microfissuration (FPZ), les paramètres entrant dans la description de l'effet d'échelle et la longueur interne du modèle d'endommagement non local pour un mortier à macro-porosité contrôlée. Des résultats expérimentaux sur ce matériau en comparession, en flexion ainsi que des mesures d'émission acoustiques et leur analyse sont présentés. Les résultats d'essais montrent une bonne corrélation, entre l'évolution du paramètre d0, paramètre de la loi d'effet d'échelle de Bažant, et la largeur de la PFZ. La longueur interne obtenue numériquement par analyse inverse est aussi proportionnelle à ces paramètres. Une bonne approximation de la longueur interne à partir d'essais sur une seule taille d'éprouvette équipée d'un système d'émission, acoustique est aussi obtenue.

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References

  1. Bažant, Z.P. and Planas, J., ‘Fracture and size effect in concrete and other quasibrittle materials’,CRC Press (1998).

  2. Hillerborg, A., Modéer, M., and Petersson, P.E., ‘Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements’,Cem. Concr. Res. 6 (1976) 773–781.

    Article  Google Scholar 

  3. Bažant, Z.P. and Pijaudier-Cabot, G., ‘Measurement of the characteristic length of non local continuum’,J. Engrg Mech. ASCE 115 (1989) 755–767

    Google Scholar 

  4. Mazars, J. and Pijaudier-Cabot, G., ‘From damage to fracture mechanics and conversely: a combined approach’Int. J. Solids. Struct. 33 (1996) 3327–3342.

    Article  MATH  Google Scholar 

  5. Sluys, L.J., ‘Wave propagation, localization and dispersion in softening solids’ PhD thesis, Delft University of Technology, Delft, The Netherlands (1992).

    Google Scholar 

  6. Peerlings, R.H., de Borst, R., Brekelmans W.A.M. and de Vree, J.H.P., ‘Gradient enhanced damage for quasi-brittle materials’,Int. J. Num. Meth. Engrg.,39 (1996) 3391–3403.

    Article  MATH  Google Scholar 

  7. Carmeliet, J., ‘Optimal estimation of gradient damage parameters from localization phenomena in quasi-brittle materials’,Int. J. Mech. Cohesive Frict. Mats. 4 (1999) 1–16.

    Article  Google Scholar 

  8. Le Bellégo, C., Dubé, J.F., Pijaudier-Cabot, G. and Gérard, B., ‘Calibration of non local damage from size effect tests’,European J. of Mech. 22 (2003) 33–46.

    Article  MATH  Google Scholar 

  9. Hild, F., Berthaud, Y. and Roux, S., ‘Measurement of displacement field using a correlation method in white light’ OASIS 1999—1er Congrès européen de l'Organisation pour l'Application des Sciences de l'Ingénieur au Sport, Palaiseau, France (1999).

  10. Geers, M.G.D., de Borst, R., Brekelmans, W.A.M. and Peerlings, R.H.J., ‘On the use of local strain fields for the determination of the intrinsic length scale’,Journal de Physique IV 8 (1998) 167–174.

    Google Scholar 

  11. Otsuka, K., ‘Detection of fracture process zone in concrete by means of x-ray with contrast medium’ Fracture mechanics of concrete structures, Proc. FRAMCOS 1, Z.P. Bažant editor, Elsevier applied science (1992) 485–490.

  12. Berthaud, Y., ‘Damage measurements in concrete via an ultrasonic technique. Part 1 Experiments’,Cem. Concr. Res. 21 (1991) 73–82.

    Article  Google Scholar 

  13. Selleck, S.F., Landis, E.N., Peterson, M.L., Shah, S.P. and Achenbach, J.D., ‘Ultrasonic investigation of concrete with distributed damage’,ACI Materials Journal 95 (1998)m 27–36.

    Google Scholar 

  14. Maji, A.K. and Shah, S.P., ‘Process zone and acoustic emission in concrete’,Experimental mechanics 28 (1988) 27–33.

    Article  Google Scholar 

  15. Berthelot, J.M. and Robert, J.L., ‘Modelling concrete damage by acoustic emission’,Journal of Acoustic Emission 7 (1987) 43–60.

    Google Scholar 

  16. Mihashi, H., Nomura, N. and Niiseki, S., ‘Influence of Aggregate size on fracture process zone of concrete detected with three dimensional acoustic emission technique’,Cem. Concr. Res. 21 (1991) 737–744.

    Article  Google Scholar 

  17. Otsuka, K., Date, H. and Kurita, T., ‘Fracture process zone in concrete tension specimens by X-ray and AE techniques’. Fracture Mechanics of Concrete Structures; Proceedings of FRAMCOS-3 (1998) 3–16.

  18. Haidar, K., ‘Damage modelling of concrete structures— Numerical approaches and microstructure effects on the rupture properties’, Ph.D thesis, Ecole Centrale de Nantes and Université de Nantes, France (2002) [in French].

  19. Sussman, V., ‘Lightweight plastic-aggregate concrete’,Journal American. Concr. Inst. 72 (1975) 321–323.

    Google Scholar 

  20. Yamura, K. and Yamauchi, M., ‘Use of polystyrene pieces for aggregate of concrete’, Proc. Annual Conf. of Chugoku-Shikoku branch of JSCE (1982) 346–347 [in Japanese].

  21. Perry, S.H., Biscoff, P.H. and Yamura, K., ‘Mix details behaviour of polystyrene aggregate concrete’,Magazine of Concrete Research 43 (1991) 71–76.

    Article  Google Scholar 

  22. Kendall, J., Howard, A.J. and Birchall, J.D., ‘The relation between porosity, microstructure and strength, and the approach to advanced cement-based materials’, Phil. Trans. R. Soc., London, A 310 (1983) 139–153.

    Google Scholar 

  23. zimmerman, W., ‘Elastic moduli of solid containing spherical inclusions’,Mechanics of Materials 12 (1991) 17–24.

    Article  Google Scholar 

  24. RILEM Draft Recommendations, ‘Size effect method for determining fracture energy and process zone size of concrete’,Mater. Struct. 23 (1990) 461–465.

    Article  Google Scholar 

  25. Tada, H., Paris, P.C. and Irwin, G.R., ‘The stress analysis of cracks handbook’, 2nd Edition (Paris production, St. Louis, 1985).

    Google Scholar 

  26. Pijaudier-Cabot, G. and Bažant, Z.P., ‘Non local damage theory’,J. of Engrg. Mech. ASCE 113 (1987) 1512–1533.

    Article  Google Scholar 

  27. Mazars, J., ‘Application de la mécanique de l'endommagement au comportement non linéaire et à la rupture du béton de structure’, Thèse de Doctorat ès Sciences, Université Paris 6, France (1984) [in French].

    Google Scholar 

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Authors and Affiliations

  1. R&DO-Institut de Recherche en Génie Civil et Mécanique (GeM), UMR CNRS 6183, Ecole Centrale de Nantes, France

    K. Haidar, G. Pijaudier-Cabot & A. Loukili

  2. LMGC, UMR5508, Université Montpellier, France

    J. F. Dubé

Authors
  1. K. Haidar
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  2. G. Pijaudier-Cabot
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  3. J. F. Dubé
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  4. A. Loukili
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Additional information

Editorial Note Prof. Gilles Pijaudier-Cabot and Dr. Ahmed Loukili are RILEM Senior Members. Dr. Loukili participates in RILEM TC 195-DTD ‘Recommendation for test methods for autogeneous deformation and thermal dilation of early age concrete’.

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Haidar, K., Pijaudier-Cabot, G., Dubé, J.F. et al. Correlation between the internal length, the fracture process zone and size effect in model materials. Mat. Struct. 38, 201–210 (2005). https://doi.org/10.1007/BF02479345

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  • DOI: https://doi.org/10.1007/BF02479345

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