A New Numerical Procedure for Determination of Effective Elastic Constants in Unidirectional Composite Plates

Journal of Solid Mechanics

مقاله 8، دوره 8، شماره 1، خرداد 2016، صفحه 104-115   

نوع مقاله: Research Paper

نویسندگان

S Daryazadeh¹؛ L Lvov Gennadiy¹؛ M Tajdari^{* 2}

¹National Technical University , Kharkov Polytechnic Institute, Ukraine, Kharkov

²Department of Mechanical Engineering, Islamic Azad University, Arak Branch, Arak, Iran

چکیده

In this paper a composite plate with similar unidirectional fibers is considered. Assuming orthotropic structure, theory of elasticity is used for investigating the stress concentration. Also, complex variable functions are utilized for solving the plane stress problems. Then the effective characteristics of this plate are studied numerically by using ANSYS software. In this research a volume element of fibers in square array is considered. In order to investigate the numerical finite element modeling, the modeling of a quarter unit cell is considered. For determining the elasticity coefficients, stress analysis is performed for considered volume with noting to boundary conditions. Effective elasticity and mechanical properties of composite which polymer epoxy is considered as its matrix, are determined theoretically and also by the proposed method in this paper with finite element method. Finally, the variations of mechanical properties with respect to fiber-volume fraction are studied.

کلیدواژه‌ها

Composite plate؛ Unidirectional fibers؛ Effective elastic constants؛ Orthotropic plate

مراجع

[1] Voigt W., 1889, Uber die beziehung zwischen den beiden elastizitatskonstanten isotroper korper, Wiedemann's Annalen 38 : 573-587.
[2] Reuss A., 1929, Berechnung der fliessgrense von mischkristallen auf grund der plastizitatsbedingun fur einkristalle, Zeitschrift Angewandte Mathematik und Mechanik 9 : 49-58.
[3] Halpin J.C., Kardos J.L., 1976, The halpin-tsai equations: a review, Polymer Engineering and Science 16(5): 344-352.
[4] Chamis C.C., 1989, Mechanics of composite materials: past, present and future, The Journal of Composites Technology and Research 11: 3-14.
[5] Hashin Z., Rosen B.W., 1964, The elastic moduli of fiber reinforced materials, Journal of Applied Mechanics 31: 223-232.
[6] Christensen R.M., 1990, A critical evaluation for a class of micromechanical models, Journal of Mechanics and Physics of Solids 38(3): 379- 404.
[7] Mori T., Tanaka K., 1973, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica 21: 571-574.
[8] Hill R., 1965, Theory of mechanical properties of fiber-strengthen materials-3 self-consistent model, Journal of Mechanics and Physics of Solids 13 :189-198.
[9] Bubiansky B., 1965, On the elastic modulli of some heterogeneous materials, Journal of Mechanics and Physics of Solids 13: 223-227.
[10] Chou T.w., Nomura S., Taya M., 1980, A self- consistent approach to the elastic stiffness of short-fiber composites, Journal of Composite Materials 14: 178-188.
[11] Huang Z.M., 2001, Simulation of the mechanical properties of fibrous composites by the bridging micromechanics model, Composites: Part A 32: 143-172.
[12] Huang Z.M., 2001, Micromechanical prediction of ultimate strength of transversely isotropic fibrous composites, International Journal of Solids and Structures 38: 4147-4172.
[13] Vanin G. A., 1985, Micro-Mechanics of Composite Materials, Nauka Dumka, Kiev.
[14] Carpeenosa D. M., 1985, Composite Materials, Nauka Dumka, Kiev.