در تجاری کردن بین میرایی و سختی در طراحی کامپوزیت تقویت شده با الیاف گسسته

Quasi-static models are first developed, by using a forced balance approach, to define the effects of selected microstructural parameters, e.g. fibre aspect ratio, fibre off-axis angle and fibre volume fraction, on the damping and stiffness of a class of polymeric, discontinuous fibre-composite systems. Simultaneous optimization of damping, stiffness and weight of a class of such material is then carried out by using the so-called inverted utility function method. The obtained results show that discontinuous fibre-reinforced composites have superior design flexibility as compared with those pertaining to continuous fibre-reinforced composites.

It is well known that lightweight fibre-reinforced polymer composite materials have higher specific strength and stiffness when compared with conventional structural materials such as metals. Much effort has been devoted to the improvement and optimization of these properties as pertaining to various classes of composite microstructures. Good vibration damping properties are also particularly important for composite structures to acquire [1] when they are used under dynamic loading, e.g. in aerospace structures. Due in part to the extensive accumulated experience with conventional structural materials, such as metals, which in general have poor internal damping, the potential for the improvement and optimization of damping in fibre-reinforced composites has not yet been fully realized. Meanwhile, the full use of discontinuous fibre-reinforcement has not yet been fulfilled in composite material applications. This may be due to the direct accomplishment of higher specific strength and stiffness in the more familiar continuous fibre composites. The damping properties of continuous fibre composites have been studied by a number of researchers [2] and [3]. There are relatively few publications on damping of discontinuous fibre composites. However, studies reported by, for instance, McLean and Read [4] and Gibson et al. [5] indicate that vibration damping of polymeric fibre-reinforced composites may be significantly improved, and possibly can be readily optimized by using, as a reinforcement, discontinuous fibres rather than continuous ones. In this context, studies carried out by, e.g. Gibson and Yau [5], Gibson et al. [6], Sun et al. [7], and Suarez et al. [8] have confirmed that the damping factor of polymeric discontinuous fibre-composites is a frequency dependant, and it relates strongly with the microstructure's particulars, e.g. fibre aspect ratio, fibre volume fraction and fibre off-axis angle. The research work of Gibson and Yau [5] and Gibson et al. [6], for instance, indicates that by varying the fibre aspect ratio and fibre orientation, superior damping and stiffness could be achieved separately. This observation implies that the optimum conditions, in terms of microstructural parameters, for damping may not be necessarily the same for stiffness. Consequently, it is important to study the influence of the various governing microstructural parameters as pertaining to both damping and stiffness. The optimization, in terms of the microstructure, of this trade-off between damping and stiffness is the main intention of this paper. In this context, the general procedure of the force-balance approach [7] is used to formulate an analytical optimization model, whereby a multi-objective optimization functional is established to optimize the mentioned two properties simultaneously. For this purpose, both the composite laminate and its constituents are assumed to behave in a linear viscoelastic manner. Hence, the elastic–viscoelastic correspondence principle [9], [10] and [11] is assumed to be applicable. The composite laminate is considered to be uniaxially loaded in tension with the loading direction coinciding with the longitudinal axis x of the laminate. In the force-balance approach, the expression for the elastic stiffness of a discontinuous fibre-composite is derived from the average fibre stress using Cox's analytical model concerning fibre stress distribution [12]. In this paper, the analytical model by Cox [12] is followed and extended to include time-dependent behaviour, whereby the elastic–viscoelastic correspondence principle is used to obtain the expressions for the viscoelastic complex moduli from their elastic counterparts. In the case of sinusoidal loading, the expression for the complex modulus would involve both the storage modulus and the associated-with loss modulus. Here, the following complex moduli are dealt with equation(1) where E and G indicate, respectively, the moduli under tensile and shear loading. Meantime, and the over-prime designates the storage modulus and the double over-prime identifies the loss modulus. Meantime, the corresponding damping (or loss) factor is defined as the ratio between the loss modulus and the associated-with storage modulus, i.e. equation(2)

Analytical predictions which were determined by the force-balance method show that damping and stiffness are functions of fibre off-axis angle, fibre volume fraction and fibre aspect ratio. In order to increase the damping, it may be necessary to sacrifice the stiffness, and vice versa. The inverted utility function and simplex methods were found to be suitable to deal with a multiobjective optimization problem with a relatively small number of variables. The use of the variable transformation technique to convert the constrained non-linear optimization to a non-constrained non-linear problem makes such an optimization much easier to handle. For the given E-glass/epoxy composite material, Table 1, the results of optimization of damping, stiffness and specific weight show that, at a fibre off-axis angle of ∼43.75°, by setting the fibre aspect ratio as 1.38 or 85.10, the fibre volume fraction reaches either 62 or 54%, respectively, and one could obtain maximum damping, relatively high stiffness and relatively low specific weight for this class of material. The existence of such multiple local minima gives more flexibility in the design of discontinuous fibre-reinforced composite materials. In this context, both microfibre or whisker composites (l/d≈1.38) and discontinuous fibre-reinforced composites with longer fibre l/d=85.10 can be selected as to the predefined design specifications. It should, however, be pointed out that some of the obtained results in this paper are likely to be more of academic rather of industrial interest particularly when the optimized composites with very low aspect ratio fibres are considered. Current composite manufacturing processes may not be able to achieve a high volume fraction as 0.60 with a controlled fibre orientation like 43.75° for a low aspect ratio of 1.38. High fibre volume fraction and controlled fibre orientations may be only achieved for parallel long or continuous fibres that are closely packed, as in prepreg tapes or filament wound parts.