INTRODUCTION
1.6 Graded fiber-reinforced composites
In recent years, the concept of FGM has been further utilized by many researchers to develop light weight, high strength functionally graded fiber-reinforced composites
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for alleviating several structural discrepancies in the use of traditional fiber- reinforced composite laminates. These FG composites are a new class of fiber- reinforced composite materials and generally known as graded fiber-reinforced composites (GFRCs) or functionally graded fiber-reinforced composites (FGFRCs).
Generally, a GFRC/FGFRC has varying fiber volume fraction (FVF) and/or fiber orientation angle (FOA) which create the graded material properties within the domain of the material. Since these parameters (FVF and FOA) could easily be tailored to meet specific requirement in the design of a structural component, GFRCs/FGFRCs have found wide applications especially for reducing thermal deflection of composite laminates, stress concentration near a cut-out within a composite laminate and inter-laminar stress concentration in composite laminates. A considerable number of reports are available in the literature for the design and analysis of graded fiber-reinforced composite (GFRC) lamina with varying fiber volume fraction (FVF) along its in-plane directions. Martin and Leissa (1990) first proposed a GFRC lamina by varying the FVF along one of the in-plane directions and derived exact solutions of a plane stress problem under different boundary conditions. Subsequently, the work was extended to investigate the effects of graded material properties of a GFRC plate on its critical buckling loads and resonant frequencies (Leissa and Martin 1990). The variation of fiber spacing or FVF along in- plane direction of GFRC lamina was also utilized for mitigating some of the structural problems like high stress concentration, reinforcement of shear walls etc.
(Shiau and Cheu 1991; Siau and Lee 1993; Meftah et al. 2007,2008). The variation of FVF along the thickness direction of a GFRC lamina was introduced by Wetherhold et al. (1996) for eliminating or controlling thermal deflections of composite laminates.
In this study, a FG symmetric laminated fiber-reinforced composite beam with varying FVF along the thickness direction is analysed to demonstrate the advantage of creating graded material properties for controlling the thermal deflection of the laminated beam. Kubiak (2005) considered variable FVF across the width of a thin- walled rectangular composite plate and investigated its dynamic response under the in-plane pulse loading. Benatta et al. (2008) considered continuous variation of FVF along the thickness direction of a short FG fiber-reinforced composite beam for demonstrating the effects of different distributions of FVF on the bending response
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of the beam. Bedjilili et al. (2009) presented free vibration characteristics of a symmetric composite beam with the variable FVF along the thickness direction and reported the effect of varying FVF on the natural frequencies. Kuo and Shiau (2009) presented the effect of variation of FVF along the thickness direction of a laminated composite plate on its critical buckling loads and natural frequencies. Oyekoya et al.
(2009) developed a finite element model of a composite plate having functionally variable FVF along any of the axes of reference coordinate system. The study showed enhancement of structural integrity and strength maximization of composite structures through gradation of material properties. Bouremana et al. (2009) performed a thermo-elastic analysis of a symmetric laminated composite beam in order to minimize the thermal deformation of the beam by varying its FVF along the thickness direction. Fu et al. (2010) proposed various gradient-designs across the thickness of the fiber-reinforced composite plates including non-uniform distributions of fiber-orientation and FVF. This three-dimensional analysis demonstrated exact stresses in the proposed kinds of laminated composite plates.
This study also demonstrated the methods for reduction of inter-laminar stress- concentration problem in the composite laminates. Kargarnovin and Hashemi (2012) presented buckling analysis of multilayered cylindrical shell with variable FVF along longitudinal direction. Tahouneh et al. (2013) considered a thick annular graded fiber-reinforced composite plate of variable FVF along the thickness direction and analyzed its free vibration characteristics.
Similar to FVF, the fiber-orientation angle is another important parameter for creating graded material properties along the thickness direction of a fiber-reinforced composite lamina. Batra and Jin (2005) analyzed a graded composite plate of variable fiber-orientation angle along the thickness direction and investigated the effect of the variation of fiber-orientation angle in the plate on its resonant frequencies. Han et al.
(2009) presented linear and nonlinear analyses of composite plates/shells those have variable fiber-orientation angle along the thickness direction according to a sigmoid distribution. This analysis revealed the effect of the varying fiber orientation on the mechanical responses of the structures. Cho and Rowlands (2009) presented an optimized local fiber-orientation angle near the holes or notches of composite structure in order to reduce associated tensile stress concentration. Panda and Ray
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(2009) presented the controlled nonlinear transient responses of laminated composite plates of variable fiber-orientation angle along the thickness direction. Yas and Aragh (2010, 2011) analyzed the free vibration characteristics of cylindrical panels with continuous variations of FVF and fiber-orientation angle along the radial direction. The same authors (Yas and Aragh 2010, 2011) also presented free vibration characteristics of fiber-reinforced plates/panels resting on elastic foundations considering continuous variation of fiber-reinforcement in the thickness direction.
The study indicates the advantages of graded composite laminated plates/panels over the traditional composite laminated plates/panels.
In the aforesaid available studies on the design and analysis of structural behavior of graded fiber-reinforced composite lamina/laminate, the graded material properties are estimated using standard micromechanics theories. Since the implementation of standard micromechanics theories in a straight forward manner may not provide good enough estimation of graded material properties of a GFRC lamina (Aboudi et al. 1995), new micromechanics models have been developed by several researchers particularly for particulate and fiber-reinforced FG composites.
Aboudi et al. (1995,1999) proposed a coupled higher-order theory for functionally graded composites with partial homogenization. Although this higher-order theory provides good estimations of material properties of FG solids, but the requirement of this theory could be justified through a parallel work of Reiter and Dvorak (1997,1998). Reiter and Dvorak (1997, 1998) proposed a micromechanics model for graded composite materials using standard micromechanics theories. This micromechanics model does not support the requirement of higher-order theory in evaluation of graded material properties of FG solid but, it is addressed that the higher-order theory is required only for the locations of low field averages and high gradients within the domain of a FG solid (Dvorak and Zuiker, 1994).