Of unidirectional

Fig. 2. Three layers of unidirectional material stacked together to form a laminate.

The difference between the bounds defined by the simple models can be large, so that more advanced theories are needed to predict the transverse modulus of unidirectional composites from the constituent properties and fiber volume fractions (1). The Halpia-Tsai equations (50) provide one example of these advanced theories ia which the rule of mixtures expressions for the extensional modulus and Poisson s ratio are complemented by the equation... 

Fig. 12. (a) The variation of the tensile strength of unidirectional carbon-fiber-reinforced epoxy resin as a function of the fiber volume fraction, (b) The variation of the tensile strength of unidirectional carbon-fiber-reinforced epoxy resin as a function of the fiber volume fraction for low fiber volume... 

Example 3.2 PEEK is to be reinforced with 30% by volume of unidirectional carbon fibres and the properties of the individual materials are given below. Calculate the density, modulus and strength of the composite in the fibre direction. 

Typical elastic properties of unidirectional fibre reinforced plastics... 

In this Example the angle, 6, was set at 25°. Fig. 3.11 shows the variation of the moduli and Poisson s Ratio values for all angles between 0° and 90°. This gives an interesting overview of the performance of unidirectional composites when subjected to off-axis loading. 

The previous analysis has shown that the properties of unidirectional fibre composites are highly anisotropic. To alleviate this problem, it is common to build up laminates consisting of stacks of unidirectional lamina arranged at different orientations. Clearly many permutations are possible in terms of the numbers of layers (or plies) and the relative orientation of the fibres in each... 

It is also worthy of note that large values of Poisson s Ratio can occur in a laminate. In this case a peak value of over 1.5 is observed - something which would be impossible in an isotropic material. Large values of Poisson s Ratio are a characteristic of unidirectional fibre composites and arise due to the coupling effects between extension and shear which were referred to earlier. 

First, consider uniaxial tension loading in the 1-direction on a flat piece of unidirectionally reinforced lamina where only the gage section is shown in Figure 2-20. The specimen thickness is not just one lamina, but several laminae all of which are at the same orientation (a single lamina would be too fragile to handle). The strains and E2 are measured so, by definition,... 

Hong T. Hahn and Stephen W. Tsai, Nonlinear Elastic Behavior of Unidirectional Composite Laminae. Journal of Composite Materials, January 1973, pp. 102-118. 

J. M. Whitney, Elastic Moduli of Unidirectional Composites with Anisotropic Filaments, Journal of Composite Materials, April 1967, pp. 188-193. 

R. L. Foye, An Evaluation of Various Engineering Estimates of the Transverse Properties of Unidirectional Composites, Proceedings of the 10th National Sympo-... 

The individual laminae used by Tsai [4-6] consist of unidirectional glass fibers in a resin matrix (U.S. Polymeric Co. E-787-NUF) with moduli given in Table 2-3. A series of special cross-ply laminates was constructed with M = 1,2,3,10 for two-layered laminates and M = 1,2,5,10 for three-layered laminates. The laminates were subjected to axial loads and bending moments whereupon surface strains were measured. Accordingly, the stiffness relations as strains and curvatures in terms of forces and moments, that is. 

Other researchers have substantially advanced the state of the art of fracture mechanics applied to composite materials. Tetelman [6-15] and Corten [6-16] discuss fracture mechanics from the point of view of micromechanics. Sih and Chen [6-17] treat the mixed-mode fracture problem for noncollinear crack propagation. Waddoups, Eisenmann, and Kaminski [6-18] and Konish, Swedlow, and Cruse [6-19] extend the concepts of fracture mechanics to laminates. Impact resistance of unidirectional composites is discussed by Chamis, Hanson, and Serafini [6-20]. They use strain energy and fracture strength concepts along with micromechanics to assess impact resistance in longitudinal, transverse, and shear modes. 

G. C. Sih and E. P. Chen, Fracture Analysis of Unidirectional Composites, Journal of Composite Materials, April 1973, pp. 230-244. 

C. C. Chamis, M. P. Hanson, and T. T. Serafini, Impact Resistance of Unidirectional Fiber Composites, in Composite Materials Testing and Design (Second Conference), H. T. Corten (Chairman), Anaheim, California, 20-22 April 1971, ASTM STP 497, American Society for Testing and Materials, 1972, pp. 324-349. 

The fiber content in mat or random fiber RPs is usually somewhat lower than for an isotropic laminate which is comprised of a number of unidirectional plies. Both laminates may, for example, be planar-isotropic. The random criss-cross nature of chopped fibers in a mat does not permit close packing of the bundles, and thus the fiber content is usually lower. With a lay-up of unidirectional plies, the packing of fibers within a ply may be very close, and the fiber content can be very high. The higher fiber content made from individual plies tends to make it stiffer and stronger than the mat construction. 

Therefore, all the theory, sketched previously for particulates, is also valid for the fiber composites, the only difference being in the evaluation of the radius rs of the mesophase. Indeed, in order to define the radius rs of the cylindrical layer, corresponding to the mesophase for the fiber composites, we express it as r, = (rf + Ar) and we modify the respective relation given by Lipatov 11) for particulates to the appropriate relation for cylindrical inclusions. For the cases of unidirectional fiber-reinforced composites, it may be shown that the following relation holds ... 

Numerical methods have been developed by replacing the differential equation by a finite difference equation. Thus in a problem of unidirectional flow of heat ... 

A large block of material of thermal diffusivity Du — 0.0042 cm2/s is initially at a uniform temperature of 290 K and one face is raised suddenly to 875 K and maintained at that temperature. Calculate the time taken for the material at a depth of 0.45 m to reach a temperature of 475 K on the assumption of unidirectional heat transfer and that the material can be considered to be infinite in extent in the direction of transfer. 

Ultrasonic methods can also be applied to velocity measurements based on measurement of the Doppler shift in the frequency of an ultrasonic wave scattered from a moving particle. The angle between the velocity vector and the direction of ultrasound propagation must be known, which practically limits the appHcation of the technique to the measurement of unidirectional flows. However, this Hmitation may be overcome again by the use of an array of transducers [11]. 

Kai, K. and Karthaus, O. (2007) Growth of unidirectionally oriented pentacene nanofibers by a roller method . e-J. Surf. Sci. Nanotechnol, 5, 103-105. 

SSPM of unidirectionally oriented A-S-D triads in alternate mono-layers for detection of photo-induced charge separation... 

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