Stiffness composite

Key Words —Nanotubes, mechanical properties, thermal properties, fiber-reinforced composites, stiffness constant, natural resonance. 

Just as there must be some rationale for selecting a particular stiffness and/or strength of material for a specific structural application, there must also be a rationale for determining how best to achieve that stiffness and strength for a composite of two or more materials. That is, how can the percentages of the constituent materials be varied so as to arrive at the desired composite stiffness and strength ... 

Coating thickness should be chosen to optimize the benefit in toughness and minimize the loss in strength and some other properties. As a rule of thumb, the thickness of the coating should be kept minimum compared to the fiber diameter in order to eliminate any reductions of composite stiffness and strength in both... 

Flexural modulus is a convenient measure of composite stiffness. Fillers can con-tribute significantly to a stifmess increase. 1 he... 

Predictions of 2D and 3D woven composite stiffness properties have the adequacy level necessary for their use in practical design optimisations. Meso-level predictors for composite stiffness are integrated with macro-level FE tools for structural analysis. 

Figure 2.1 Mechanical degradation with temperature for typical fibers (strength), polymers, and composites (stiffness), values normalized by those at 20°C. (Data reproduced from [1-4].)...

It is well established in the literatme, that the incorporation of rigid micro-scaled fillers usually increases composite stiffness, but at the expense of ductility. This is due to the stress concentration regions that exist in close proximity of the reinforcement. In the case of nanoscaled fillers, in contrast, the stress concentrations are significantly reduced. Hence, composite ductility can be retained at a constant level or even improved, in comparison to neat polymer [8]. It has been shown that some nanocomposites may lead to significant and simultaneous improvements in stiflhess, fracture toughness, impact energy absorption and vibration damping. These characteristics could be of particular importance in some structural apphca-tions such as in the automotive and aircraft industries [4]. 

For two-dimensional randomly oriented fibers in a composite, approximating theory of elasticity equations with experimental results yielded this equation for the planar isotropic composite stiffness and shear modulus in terms of the longitudinal and transverse moduli of an identical but aligned composite system with fibers of the same aspect ratio ... 

More refined models of macroscale composite stiffness have been developed (such as the Halpin-Tsai equations [91]) that take into account some of the assumptions made above, e.g., fiber length, orientation, and inefficiencies in... 

Furthermore, the stifihess of the composites increased by inserting higher fiber content. This difference in composite stiffness can be explained by the chemical modification performed on the fibers. Figme 10.5 evidences tensile modulus obtained in composites reinforced with in-natme and modified fibers and with different amounts of fibers reinforced in the matrix. 

Consider a subunit that comprised of fully aligned short fibers. The subunit is said to be transversely isotropic, if it is isotropic in all planes perpendicular to the fiber direction, and the fiber axis is the axis of asymmetry. For a transversely isotropic unidirectional stiffness tensor Cijki, orientation averaging can be done to give the composite stiffness, Cijki), as follows (Advani and Tucker 1987) ... 

This chapter is devoted to the analysis of the elastic properties and their characterization for laminated advanced composites. It starts with a general overview of composite stiffness and then moves to lamina analysis focused on unidirectional reinforced composites. The analysis of laminated composites is addressed through the classical lamination theory (CLT). The last section describes full-field techniques coupled with inverse identification methods that can be employed to measure the elastic constants. 

The stiffness of polymer-based composite systems depends on numerous factors such as the stiffness of constituents, the volume fraction of each component, and the size, shape and orientation of reinforcements. As a whole there are three distinct types of polymer composites continuous fibre-reinforced polymer composites, short fibre-reinforced polymer composites, and polymer nanocomposites. Theoretical models based on micromechanical models are well developed and provide an adequate representation of composite stiffness. These micromechanical models are formulated based on assumptions of continuum mechanics. However, for nanocomposite materials, with fillers of size approximately 1 nm compared to the typical carbon fibre diameter of 50 tm, the rules and requirements for continuum... 

Figure 13.9 Physical representations, coordinate systems, and corresponding (a) Halpin-Tsal and (b) Morl-Tanaka equations used for the calculation of composite stiffness based on fiber and disk-llke platelet reinforcement.

Using the above concepts and equations, the average composite stiffness can be obtained from the strain concentration tensor A and the filler and matrix properties ... 

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