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Stochastic modeling of damage evolution in composites under environmental ageing

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Abstract

A mathematical model is proposed for predicting damage evolution and stiffness degradation in composite materials under environmental ageing. Environmental parameters such as moisture, temperature, and ultraviolet (UV) radiation cause hygrothermal loads on the structure, which leads to damage evolution. The present work establishes a constitutive model for treating the damage density as a random variable. A forward stochastic differential equation (FSDE) is proposed to predict the damage density evolution. Damage nucleation and annihilation rates are taken into consideration in terms of Brownian motions. A second-order damage tensor is developed using the solution of the FSDE. The damage tensor is incorporated into the constitutive model for predicting the elastic moduli. Finally, the proposed model is verified against experimental observations under certain hygrothermal conditions.

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References

  1. Chaim R, Baum L, Brandon DG (1989) Mechanical properties and microstructure of whisker-reinforced alumina-30 vol glass matrix composite. J Am Ceram Soc 72(9): 1636–1642

    Article  Google Scholar 

  2. Brinson HF, Morris DH, Yeow YT (1978) A new experimental method for the accelerated characterization of composite materials, Verein Deutscher Ingenieure, 6th Internationale Konferenz ueber experimentelle Spannungsanalyse, presented at Munich, West Germany, Sept 18–22:395-400

  3. Oliveira BF, Creus GJ (2004) An analytical-numerical framework for the study of ageing in fiber reinforced polymer composites. Compos Struct 65(3–4): 443–457

    Article  Google Scholar 

  4. Case SW, Reifsnider KL (1996) Micromechanical analysis of fiber fracture in unidirectional composite materials. Int J Solids Struct (UK) 33(26): 3795–3812

    Article  MATH  Google Scholar 

  5. Talreja R (1985) A continuum mechanics characterization of damage in composite materials. Proc R Soc Lond Ser A Math Phys Sci 399: 195–216

    Article  ADS  MATH  Google Scholar 

  6. Talreja R (1986) Stiffness properties of composite laminates with matrix cracking and interior delamination. Eng Fract Mech 25(5-6): 751–762

    Article  Google Scholar 

  7. Talreja R (1990) Internal variable damage mechanics of composite materials, In: Boehler JP (ed) Yielding, damage and failure of anisotropic solids. EGF 5, London, pp 509–533

  8. Talreja R (1994) Damage characterization by internal variables. In: Talreja R (ed) Damage mechanics of composite materials, Elsevier, London, pp 53–78

  9. Judd NCW, Wright WW (1978) Voids and their effects on mechanical properties of composites-an appraisal. Soc Adv Mater Process Eng (SAMPE) J 14: 10–14

    Google Scholar 

  10. Jones RM (1998) Mechanics of composite materials (5th edn). Taylor and Francis, Philadelphia

  11. Lundgren J, Gudmundson P (1999) Moisture absorbs ion in glass-fiber/epoxy laminates with transverse matrix cracks. Compos Sci Technol 59: 1983–1991

    Article  Google Scholar 

  12. Lu JW, Hutchinson TJ, Rodel DJ (1995) Effect of matrix cracking on the overall thermal conductivity of fiber-reinforced composites. Phil Trans R Soc Phys Sci Appl High-Temp Struct Mater 351(1697): 595–610

    Article  ADS  Google Scholar 

  13. Reynolds TG, McManus HL (1999) Accelerated tests of environmental degradation in composite materials. In: Grant P, Rousseau CQ (eds) Composite structures: theory and practice. ASTM STP 1383, American Society for Testing and Materials, West Conshohocken, PA, pp 513–525

  14. Sobczyk K (2001) Stochastic differential equations with applications to physics and engineering. Springer, New York

    Google Scholar 

  15. Bai Y, Fujiu K, Mengfen X (1991) Formulation of statistical evolution of microcracks in solids. Acta Mechanica Sinica 7(1): 59–66

    Article  ADS  MATH  Google Scholar 

  16. Bai Y, Han W, Bai J (1996) A statistical evolution equation of microdamage and its application. In: McDowell DL (ed) Applications of continuum damage mechanics to fatigue and fracture. ASTM, Orlando, FL, ISBN: 0803124732

  17. Yu Q, Youshi H (1997) A theoretical analysis on stochastic behavior of short cracks and fatigue famage of Metals. Acta Mechanics Solida Sinica 10(4): 352–358

    Google Scholar 

  18. Augusti G, Mariano PM (1999) stochastic evolution of microcracks in continua. Comput Methods Appl Mech Eng 168: 155–171

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Klebaner Fima C. (2005) Introduction to stochastic calculus with applications. Imperial College Press, London

    Google Scholar 

  20. Rahman R (2009) Damage evolution in composite material under environmental aging: a stochastic model with experimental validation. Thesis, The University of Alabama

  21. Rahman R (2010) Damage evolution in composite materials under environmental ageing. VDM Verlag Dr. Müller, Germany, ISBN: 3639322142

  22. Sidney IR (1992) Adventures in stochastic processes. Birkhauser, Boston

    MATH  Google Scholar 

  23. Øksendal BK (2010) Stochastic differential equation: an introduction with applications (5th edn). Springer, New York

    Google Scholar 

  24. Iacus MS (2008) Simulation and inference for stochastic differential equations (1st edn). Springer, New York

    Book  Google Scholar 

  25. Krajcinovic D (1996) Damage mechanics (1st edn). North Holland, Amsterdam

    Google Scholar 

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Authors and Affiliations

  1. Department of Aerospace Engineering and Mechanics, The University of Alabama, Tuscaloosa, AL, 35487, USA

    R. Rahman & A. Haque

  2. Department of Mathematics, The University of Alabama, Tuscaloosa, AL, 35487, USA

    Z. Wu

Authors
  1. R. Rahman
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  2. A. Haque
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  3. Z. Wu
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Correspondence to R. Rahman.

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Rahman, R., Haque, A. & Wu, Z. Stochastic modeling of damage evolution in composites under environmental ageing. J Eng Math 79, 153–166 (2013). https://doi.org/10.1007/s10665-012-9557-x

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  • DOI: https://doi.org/10.1007/s10665-012-9557-x

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