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Effects of moisture-dependent properties of constituents on the hygroscopic stresses in composite structures

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Mechanics of Composite Materials Aims and scope

The effects related to the evolution of the moisture-dependent hygroelastic properties of composite plies constituting a fiber-reinforced epoxy laminate on the predicted stress states in the structure during the transient stage of hygroscopic loading are investigated. The approach proposed involves the coupling of the classical continuum mechanics formalism to the Eshelby–Kröner self-consistent scale transition model. An inverse scale transition model is used to describe the evolution of local hygroelastic properties of the epoxy matrix as the process of moisture diffusion proceeds. The scale transition relations allow one to determine the local distribution of stresses in the constituents (fiber and matrix) of each ply of the laminates considered from the distribution of macroscopic stresses. Numerical simulations show that the account (or not) of softening of the composite structure under hygroscopic loadings significantly affects the multiscale stress states predicted.

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References

  1. S. W. Tsai, Composite Design, Think Composites (1987).

  2. A. Agbossou and J. Pastor, “Thermal stresses and thermal expansion coefficients of n-layered fiber-reinforced composites,” Compos. Sci. Technol., 57, 249-260 (1997).

    Article  CAS  Google Scholar 

  3. P. D. Soden, M. J. Hinton, and A. S. Kaddour, “Lamina properties lay-up configurations and loading conditions for arange of fiber-reinforced composite laminates,” Compos. Sci. Technol., 58, 1011-1022 (1998).

    Article  CAS  Google Scholar 

  4. J. Crank, The Mathematics of Diffusion, Clarendon Press, Ox ford (1975).

    Google Scholar 

  5. B. P. Patel, M. Ganapathi, and D. P. Makhecha, “Hygrothermal effects on the structural behaviour of thick composite laminates using higher-order theory,” Com pos. Struct., 56, 25-34 (2002).

    Article  Google Scholar 

  6. D. E. Bowles, D. Post, C. T. Herakovich, and D. R. Tenney, “Moiré interferometry for thermal expansion of composites,” Exp. Mech., 21, 441-447 (1981).

    Article  Google Scholar 

  7. S. R. A. Dyer, D. Lord, I. J. Hutch in son, I. M. Ward, and R. A. Duckett, “Elastic anisotropy in unidirectional fibre reinforced composites,” J. Phys. D: Appl. Phys., 25, 66-73 (1992).

    Google Scholar 

  8. C. Ferreira, P. Casari, R. Bouzidi, and F. Jacquemin, “Identification of Young’s modulus pro file in PVC foam core thickness using speckle interferom etry and inverse method,” in: Proc. SPIE — The International Society for Optical Engineering (2006).

  9. C. Ferreira, F. Jacquemin, and P. Casari, “Measurement of the nonuniform thermal expansion coefficient of a PVC foam core by speckle interferometry — influence on the mechanical behavior of sandwich structures,” J. Cell. Plast., 42, No. 5, 393-404 (2006).

    Article  CAS  Google Scholar 

  10. C. T. Herakovitch, Mechanics of Fibrous Composites, John Wiley & Sons Inc., New York (1998).

    Google Scholar 

  11. G. D. Sims, G. D. Dean, B. E. Read, and B. C. Western, “Assessment of damage in GRP laminates by stress wave emission and dynamic mechanical measurements,” J. Mater. Sci., 12, No. 11, 2329-2342 (1997).

    Article  ADS  Google Scholar 

  12. C. L. Tsai and I. M. Daniel, “Measurement of longitudinal shear modulus of single fibers by means of a torsional pendulum,” in: 38th Int. SAMPE Symp. (1993), pp. 1861-1868.

  13. J. A. DiCarlo, “Creep of chemically vapor deposited SiC fiber,” J. Mater. Sci., 21, 217-224 (1986).

    Article  CAS  ADS  Google Scholar 

  14. C. L. Tsai and C. H. Chiang, “Characterization of the hygric behavior of single fibers,” Compos. Sci. Technol., 60, 2725-2729 (2000).

    Article  CAS  Google Scholar 

  15. S. Fréour, D. Gloaguen, M. Francois, R. Guillén, E. Girard, and J. Bouillo, “Determination of the macroscopic elastic constants of a phase embedded in a multiphase polycrystal — application to the beta-phase of Ti-17 titanium based alloy,” Ma ter. Sci. Forum, 404-407, 723-728 (2002).

    Article  Google Scholar 

  16. S. Fréour, D. Gloaguen, M. Francois, A. Perronnet, and R. Guillén, “Estimation of Ti-17 β-phase single-crystal elasticity constants using X-ray diffraction measurements and inverse scale transition modelling,” J. Appl. Crystallogr., 38, 30-37 (2005).

    Article  Google Scholar 

  17. S. Fréour, D. Gloaguen, M. Francois, and R. Guillén, “Application of inverse models and XRD anal y sis to the de termination of Ti-17 β-phase coefficients of thermal expansion,” Scripta Mater., 54, 1475-1478 (2006).

    Article  Google Scholar 

  18. S. Fréour, D. Gloaguen, M. Francois, and R. Guillén, “Study of the coefficients of thermal expansion of phases embedded in multiphase materials,” Mater. Sci. Forum, 426-432, 2083-2088 (2003).

    Article  Google Scholar 

  19. S. Fréour, D. Gloaguen, M. Francois, and R. Guillén, “Thermal properties of polycrystals — X-ray diffraction and scale transition modelling,” Phys. Stat. Solidi (a), 201, 59-71 (2003).

    Article  ADS  Google Scholar 

  20. S. Matthies, S. Merkel, H. R. Wenk, R. J. Hemley, and H. Mao, “Effects of texture on the determination of elasticity of polycrystalline e-iron from diffraction measurements,” Earth Planet. Sci. Lett., 194, 201-212 (2001).

    Article  CAS  ADS  Google Scholar 

  21. J. Han, A. Bertram, J. Olschewski, W. Hermann, and H. G. Sockel, “Identification of elastic constants of alloys with sheet and fibre textures based on resonance measurements and finite element analysis,” Ma ter. Sci. Eng., A191, 105-111 (1995).

    Article  CAS  Google Scholar 

  22. W. Voigt, Lehrbuch der Kristallphysik, Teubner, Leipzig–Berlin (1928).

  23. A. Reuss, “Berechnung der Fliessgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle,” Z. Angew. Math. Mech., 9, 49-58 (1929).

    Article  MATH  CAS  Google Scholar 

  24. H. Neerfeld, “Zur Spannungsberechnung aus röntgenographischen Dehnungsmessungen,” Mitt. Kai ser-Wilhelm-Inst. Eisenforschung Düsseldorf, 24, 61-70 (1942).

    Google Scholar 

  25. R. Hill, “The elastic behaviour of a crystalline aggregate,” Proc. Phys. Soc., 65, 349-354, (1952).

    Article  ADS  Google Scholar 

  26. S. W. Tsai and H. T. Hahn, Introduction to Composite Materials, Technomic Publ. Co., Inc., Lancaster, Pennsylvania (1980).

    Google Scholar 

  27. K. Tanaka and T. Mori, “The hardening of crystals by non-deforming particles and fibers,” Acta Metall., 18, 931-941 (1970).

    Article  CAS  Google Scholar 

  28. T. Mori and K. Tanaka, “Average stress in matrix and average elastic energy of materials with misfitting inclusions,” Acta Metall., 21, 571-574 (1973).

    Article  Google Scholar 

  29. J. D. Eshelby, “The determination of the elastic field of an ellipsoidal inclusion, and related problems,” Proc. Roy. Soc. London, A241, 376-396 (1957).

    MathSciNet  ADS  Google Scholar 

  30. E. Kröner, “Berechnung der elastischen Konstanten des Vielkristalls aus des Konstanten des Einkristalls,” Z. Phys., 151, 504-518 (1958).

    Article  ADS  Google Scholar 

  31. F. Jacquemin, S. Fréour, and R. Guillén, “A self-consistent approach for transient hygroscopic stresses and moisture expansion coefficients of fiber-reinforced composites,” J. Reinf. Plast. Compos., 24, 485-502 (2005).

    Article  CAS  Google Scholar 

  32. A. C. Loos and G. S. Springer, Environmental Effects on Composite Materials, Moisture Absorption of Graphite — Epoxy Composition Immersed in Liquids and in Humid Air, Technomic Publ. (1981), pp. 34-55.

  33. A. Morawiec, “Calculation of polycrystal elastic constants from single-crystal data,” Phys. Stat. Solidi (b), 154, 535-541 (1989).

    Article  CAS  Google Scholar 

  34. S. Matthies and M. Humbert, “The realization of the concept of a geometric mean for calculating physical constants of polycrystalline materials,” Phys. Stat. Solidi (b), 177, K47-K50 (1993).

    Article  CAS  Google Scholar 

  35. S. Matthies, M. Humbert, and Ch. Schuman, “On the use of the geometric mean approximation in residual stress analysis,” Phys. Stat. Solidi (b), 186, K41-K44 (1994).

    Article  CAS  Google Scholar 

  36. U. F. Kocks, C. N. Tome, and H. R. Wenk, Texture and Anisotropy, Cam bridge Univ. Press (1998).

  37. S. Fréour, F. Jacquemin, and R. Guillén, “On the use of the geometric mean approximation in estimating the effective hygro-elastic behaviour of fiber-reinforced composites,” J. Mater. Sci., 47, 7537-7543 (2007).

    Article  ADS  Google Scholar 

  38. R. Morris, “Elastic constants of polycrystals,” Int. J. Eng. Sci., 8, 49, (1970).

    Article  CAS  Google Scholar 

  39. R. Hill, “Continuum micro-mechanics of elastoplastic polycrystals,” J. Mech. Phys. Solids, 13, 89-101 (1965).

    Article  MATH  CAS  ADS  Google Scholar 

  40. T. Mura, Micromechanics of Defects in Solids, Martinus Nijhoff Publishers, The Hague, Netherlands (1982).

    Google Scholar 

  41. K. S. Sai Ram and P. K. Sinha, “Hygrothermal effects on the bending characteristics of laminated composite plates,” Comput. Struct., 40, No. 4, 1009-1015 (1991).

    Article  Google Scholar 

  42. F. Jacquemin and A. Vautrin, “A closed-form solution for the internal stresses in thick composite cylinders induced by cyclical environmental conditions,” Compos. Struct., 58, 1-9 (2002).

    Article  Google Scholar 

  43. S. Fréour, F. Jacquemin, and R. Guillén, “On an analytical self-consistent model for internal stress prediction in fiber-reinforced composites submitted to hygro-elastic load,” J. Reinf. Plast. Compos., 24, 1365-1377 (2005).

    Article  Google Scholar 

  44. U. Welzel, S. Fréour, and E. J. Mittemeijer, “Direction-dependent elastic grain-interaction models — a comparative study,” Philos. Mag., 85, 2391-2414 (2005).

    Article  CAS  ADS  Google Scholar 

  45. O. Gillat and L. J. Broutman, “Effect of external stress on moisture diffusion and degradation in a graphite-reinforced epoxy laminate,” in: ASTM STP 658 (1978), pp. 61-83.

    Google Scholar 

  46. Y. Weitsman, “A continuum diffusion model for viscoelastic materials,” J. Phys. Chem., 94, 961-968 (1990).

    Article  CAS  Google Scholar 

  47. Y. Weitsman, “Moisture in composites: sorption and damage,” in: K. L. Reifsnider (ed.), Fatigue of Composite Materials, Elsevier Science Publ. (1990), pp. 385-429.

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Russian translation in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 4, pp. 539–554, July–August, 2009.

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Youssef, G., Fréour, S. & Jacquemin, F. Effects of moisture-dependent properties of constituents on the hygroscopic stresses in composite structures. Mech Compos Mater 45, 369–380 (2009). https://doi.org/10.1007/s11029-009-9098-1

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  • DOI: https://doi.org/10.1007/s11029-009-9098-1

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