The calculation of effective elastic constants in a composite with 3D orthogonal nonwoven fibers.pdf 1. Introduction Composite materials which consist of two or more constituent materials are commonly used in advanced structural applications, e.g. in the marine and aerospace industry. This is because of appropriate mechanical properties such as high specific strength and stiffness, low density and high resistance to corrosion. However, the limited understanding of the composite material behavior requires more research. This is further complicated by the fact that these materials behavior is dependent on lay-up, loading direction, specimen size and environmental effects such as temperature and moisture. Research on determination of effective elastic constants for anisotropic materials is very important in composite structures. A orthogonal nonwoven fibers reinforced resin matrix composites are used in some structural applications, due to their various reasons especially to their excellent mechanical behavior in terms of their specific stiffness in the direction of the fibers. The prediction of the mechanical properties of composites has been the main objective of many researchers. The well-known models that have been proposed and used to evaluate the properties of cross-ply laminate composites are Voigt [1], 1989 and Reuss [2], 1829 models. The Voigt model is also known as the rule of mixture model or the iso-strain model, while the Reuss model is also known as the inverse of mixture model or the iso-stress model. The study will be using complex functions to determine the effective elastic coefficients of the unidirectional plates as presented by Vanin [3] (1961). Semi empirical models have emerged to correct the rule of mixture model where correcting factors are introduced. Under this category, it is noticed three important models: the modified rule of mixture, the Halpin -Tsai [4] model (Halpin et al., 1976) and Chamis [5] model (Chamis, 1989). The Halpin - Tsai model emerged as a semi-empirical model that tends to correct the transverse Young's modulus and longitudinal shear modulus. The Chamis micromechanical model is the most used and trusted model which give a formulation for all five independent elastic properties. Hashin and Rosen [6] (Hashin et al., 1964) initially proposed a composite cylinder assemblage model to evaluate the elastic properties of cross-ply laminate laminate composites. Alfootov [7] determined the mechanical properties of cross-ply laminate reinforced composites with perpendicular fibers. Christensen [8], 1990 proposed a generalized self-consistent model in order to better evaluate the transversal shear modulus. Also the Mori - Tanaka model [9] (Mori et al., 1990) is a famous model which is widely used for modeling different kinds of composite materials. This is an inclusion model where fibers are simulated by inclusions embedded in a homogeneous medium. The self-consistent model has been proposed by Hill [10], 1965 and Budiansky [11], 1965 to predict the elastic properties of composite materials reinforced by isotropic spherical particulates. Later the model was presented and used to predict the elastic properties of short fibers composites [12] (Chou et al., 1980). Recently, a new micromechanical model has been proposed by Huang [13, 14], 2001. The model is developed to predict the stiffness and the strength of cross-ply laminate composites. Assuming cubic symmetry structure and using ANSYS software, effective characteristics of this composite are studied. Numerical studies are performed for some stress states in a representative unit cell for determination the effective elastic properties of fibers reinforced orthogonal nonwoven composite. 2. Computational procedure 2.1. Definition and elasticity effective parameters in cubic symmetry composite The present approach is based on the theory anisotropic elasticity. A numerical method is able to simplify the problem by satisfy the stress - strain boundary conditions directly into the expression for defining the elastic properties in a composite material. This study considers a composite material with 3D orthogonal nonwoven fibers. In this structure of material fibers are parallel to x, y and z directions as follows and are said to define a cubic symmetry array. Theory of elasticity can be used for investigating the stress - strain state of fiber reinforced composite materials. The generalized Hook's law relating strains to stresses can be written as follows: d = h ]Ы, i, j = !, 2, 3. (1) Where [A] _aijkl] is the compliance matrix and , are the strain and stress components, respectively. In this study, composites with orthogonal nonwoven fibers and constant radius are investigated as cubic symmetry materials. The simplest anisotropic case, that of cubic symmetry has three independent elements. These materials with volume V, stress and strain are described as follows: Ы _ VbdV and M _ V j . ( V V In Cartesian coordinates, Hook's law for cubic symmetry material is as follows: x) _ Mе*) + b12 (еy) + b12 (еz), y) _ b21< е x) + bn( е y) + b12 (е z), л _ Мех>+Ms)+ьп

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