Orientation efficiency factor

When fibers are not perfectly aligned with the direction of the modulus estimate, an orientation-efficiency factor, %i, is added to (15.4) [25] and Young s modulus will be then deduced from (15.5). 

The orientation-efficiency factor was theoretically determined by Krenchel [26]. For in-plane uniformly distributed fiber orientations, the factor is 3/8 and for 3D uniform fiber orientation distribution is 1/5. In practice, the determination of fiber orientation distribution is normally done by image analysis of different sections of the composites [27]. In the case of all-cellulosic based composites this would be impossible, due to their thickness. In this case, the value of the orientatirai-effi-ciency factor was taken as the value of the order parameter, S, determined by SALS. 

Results obtained using the order parameter determined by SALS, as the value of the orientation efficiency factor, are always closer to the lower bound values of the Young s modulus of the composites. The order parameter is determined as a function of the angle of the fibers to the shear direction, meaning that its value will be more accurate for an in-plane distribution of the fibers. This would probably be the case if the fibers had higher aspect ratio. Nevertheless, SALS seems to be a promising... 

Table 3.6 Orientation efficiency factors in the post-cracking case ...

Figure 3.21 for cementitious composites with different fibres. The maximum is obtained at intermediate values of 8 it ranges from about 7-15 for glass and carbon fibres, respectively. This implies that the stress that could be supported by inclined fibres at such an angle would be smaller by about an order of magnitude than that calculated assuming a constant fibre angle across the crack, that is, the fibre orientation efficiency factor would be considerably smaller than that calculated in Section 3.3.1. 

Laws [4] concluded that the combined efficiency factors, due to both length and orientation, cannot be simply calculated as the product of the length efficiency factor and the orientation efficiency factor. That is, the orientation efficiency factor is also a function of the length in the case of short fibres. For a random, 2D fibre array. Laws [4] derived the following relations ... 

Like e, t is the product of two contributions the concentration N/V of the centers responsible for the effect and the contribution per particle to the attenuation. It may help us to become oriented with the latter to think of the scattering centers as opaque spheres of radius R. These project opaque cross sections of area ttR in the light path. The actual cross section is then multiplied by the scattering efficiency factor optical cross... 

The most efficient factor in stabilizing the electronic state is the dipole-dipole interaction. This creates a local electric field (reactive field) around the excited dye interacting with its dipole [14]. If the charges are present in its vicinity, they create an electric field that interacts with the dye dipole and induces electrochromic shifts of absorption and fluorescence spectra. The direction of these shifts depends on the relative orientation of the electric field vector and the dye dipole. These effects of electrochromism are overviewed in [15]. 

Where q0 is the length efficiency factor related to the aspect ratio of the filler and thus the stress build-up along its length it can take values from 0 to 1 and can be calculated using theoretical models, q, is an orientation factor that takes values of 1 for perfect alignment, 3/8 for alignment in the plane and 1/5 for random orientation. Equation (8.1) can be arranged as ... 

In-plane alignment of the fibres Due to the very nature of the technique used for processing the NW composites, inplane alignment of the NWs is a realistic possibility. From the Krenchel theory of short-fibre reinforcements [20], the orientation and length effects can be incorporated using an efficiency factor to evaluate E,... 

The efficiency is set by the pump manufacturer when the final pump selection is made. It is usually based on their shop tests for the same model and size pumps. The pump efficiency can vary between 10% and 80%. Pump electric motor specifications require mechanical and electrical requirements. Motors can vary in size depending upon power, speed (RPM), frame size, area classification, orientation, service factor and type of enclosure (e.g. totally enclosed fan closure). 

Efficiency of reinforcement (fiber-efficiency factor) n. The percentage of fiber in a rein-forced-plastic structure or part contributing to the property of concern. For example, in a unidirectionally reinforced bar, the theoretical efficiency for Young s modulus and fiber-direction tensile strength is 100%. For a sheet molded from chopped-strand mat with all fibers randomly oriented in the sheet plane, the efficiency for in-plane properties is 37%. With chopped strands randomly oriented in three dimensions, efficiency fells to 20%. 

On the other hand, the method of flow birefringence, of course, allows one to study how the hydrodynamic field influences the formation of the new phase particles. Besidata interpretation using this method. The effect of flow birefringence in a system with colloidal particles, measured by the method traditional for polymers, has several components as in the case of macromolecules the proper anisotropy of particles, the effects of macro- and microforms (Tsvetkov et al., 1964), and conservative dichro-ism, i.e. the light scattering efficiency factor K of oriented anisodiametric, anisotropic particles differs in different observation planes (Onuki and Doi, 1986 Khlebtsov, 1988ab Khlebtsov and Melnikov, 1990). 

The equations for the unrestrained case are more complex, since the orientation efficiency depends on the fibre volume content, Poisson s ratio of the matrix and the ratio between the elastic moduli of the fibre and matrix. They may be found in refs. [48] and [2]. Krenchel noted that the differences in the results obtained using the two assumptions are small. This is demonstrated in Table 3.5 which compares the efficiency factors derived by Krenchel for the constrained assumption and those derived by Cox [2] for the unconstrained case. 

In many engineering applications, the fibre efficiency is expressed in terms of an efficiency factor, which is a value between 0 and 1, expressing the ratio between the reinforcing effect of the short, inclined fibres and the reinforcement expected from continuous fibres aligned parallel to the load. These factors, t]i and rje for length and orientation efficiency, respectively, can be determined either empirically, or on the basis of analytical calculations. They are frequently used in combination with properties that can be accounted for by the rule of mixtures (Section 4.3). In this section, various analytical treatments to account for efficiency factors will be reviewed, with special emphasis on the effects of bond. The effects of length and orientation will be described separately. 

The composite materials approach is usually based on the rule of mixtures, which models the composite as shown in Figure 4.7. It states that the properties of the composite are the weighted average of the properties of its individual components. For mechanical properties such as strength and modulus of elasticity, the concept of the rule of mixtures is valid only if the two components are linear, elastic and the bond between them is perfect. Therefore, the rule of mixtures can only be applied in the elastic, pre-cracked zone of the fibre reinforced cement, and even in this zone it should be considered as an upper iimit, since in practice the bond is not perfect, Taking into account the effects of fibre orientation and length (using the efficiency factors described in Section 4.2), the rule of mixtures can be used... 

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