Reinforcement unidirectional

Composites. High molecular weight PPS can be combiaed with long (0.6 cm to continuous) fiber to produce advanced composite materials (131). Such materials having PPS as the polymer matrix have been developed by usiag a variety of reinforcements, including glass, carbon, and Kevlar fibers as mat, fabric, and unidirectional reinforcements. Thermoplastic composites based on PPS have found application ia the aircraft, aerospace, automotive, appliance, and recreation markets (see Composite materials, polymer-matrix). 

For a unidirectionally reinforced lamina in the 1-2 plane as shown in Figure 2-7 or a woven lamina as in Figure 2-1, a plane stress state is defined by setting... 

Figure 2-8 Physical Symmetry of a Unidirectionally Reinforced Lamina...

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,... 

As an illustration of the results of the measurements just described, the mechanical properties for four unidirectionally reinforced composite materials, glass-epoxy, boron-epoxy, graphite-epoxy, and Kevlar 49 -... 

For each of the failure criteria, we will generate biaxial stresses by off-axis loading of a unidirectionally reinforced lamina. That is, the uniaxial off-axis stress at 0 to the fibers is transformed into biaxial stresses in the principal material coordinates as shown in Figure 2-35. From the stress-transformation equations in Figure 2-35, a uniaxial loading obviously cannot produce a state of mixed tension and compression in principal material coordinates. Thus, some other loading state must be applied to test any failure criterion against a condition of mixed tension and compression. 

For a unidirectionally reinforced composite material subject to uniaxial load at angle 0 to the fibers (the example problem in Section 2.9.1 on the maximum stress criterion), the allowable stresses can be found from the allowable strains X, Y , etc., in the following manner. 

The foregoing are but examples of the types of mechanics of materials approaches that can be used. Other assumptions of physical behavior lead to different expressions for the four elastic moduli for a unidirectionally reinforced lamina. For example, Ekvall [3-2] obtained a modification of the rule-of-mixtures expression for and of the expression for E2 in which the triaxial stress state in the matrix due to fiber restraint is accounted for ... 

A cross-ply laminate in this section has N unidirectionally reinforced thotropic) layers of the same material with principal material directions srnatingly oriented at 0° and 90° to the laminate coordinate axes. The sr direction of odd-numbered layers is the x-direction of the laminate, e fiber direction of even-numbered layers is then the y-direction of the linate. Consider the special case of odd-numbered layers with equal kness and even-numbered layers also with equal thickness, but not essarily the same thickness as that of the odd-numbered layers, te that we have imposed very special requirements on how the fiber sntations change from layer to layer and on the thicknesses of the ers to define a special subclass of cross-ply laminates. Thus, these linates are termed special cross-ply laminates and will be explored his subsection. More general cross-ply laminates have no such con-ons on fiber orientation and laminae thicknesses. For example, a neral) cross-ply laminate could be described with the specification t/90° 2t/90° 2t/0° t] wherein the fiber orientations do not alter-e and the thicknesses of the odd- or even-numbered layers are not same however, this laminate is clearly a symmetric cross-ply lami-e. 

Fibers are often regarded as the dominant constituents in a fiber-reinforced composite material. However, simple micromechanics analysis described in Section 7.3.5, Importance of Constituents, leads to the conclusion that fibers dominate only the fiber-direction modulus of a unidirectionally reinforced lamina. Of course, lamina properties in that direction have the potential to contribute the most to the strength and stiffness of a laminate. Thus, the fibers do play the dominant role in a properly designed laminate. Such a laminate must have fibers oriented in the various directions necessary to resist all possible loads. 

A simplified performance index for stiffness is readily obtained from the essentials of micromechanics theory (see, for example. Chapter 3). The fundamental engineering constants for a unidirectionally reinforced lamina, ., 2, v.,2, and G.,2, are easily analyzed with simple back-of-the-envelope calculations that reveal which engineering constants are dominated by the fiber properties, which by the matrix properties, and which are not dominated by either fiber or matrix properties. Recall that the fiber-direction modulus, is fiber-dominated. Moreover, both the modulus transverse to the fibers, 2, and the shear modulus, G12. are matrix-dominated. Finally, the Poisson s ratio, v.,2, is neither fiber-dominated nor matrix-dominated. Accordingly, if for design purposes the matrix has been selected but the value of 1 is insufficient, then another more-capable fiber system is necessary. Flowever, if 2 and/or G12 are insufficient, then selection of a different fiber system will do no practical good. The actual problem is the matrix systemi The same arguments apply to variations in the relative percentages of fiber and matrix for a fixed material system. 

Applications. Boron fibers are used as unidirectional reinforcement for epoxy composites in the form of preimpregnated tape. The material is used extensively, mostly in fixed and rotary wing military aircrafts for horizontal and vertical stabilizers, mdders, longerons, wing doublers, and rotors. They are also used in sporting goods. Another application is as reinforcement for metal matrix composites, in the form of an array of fibers pressed between metal foils, the metal being aluminum in most applications. 

ISO 14130 1997 Fibre-reinforced plastic composites - Determination of apparent interlaminar shear strength by short-beam method ISO 15024 2001 Fibre-reinforced plastic composites - Determination of mode I interlaminar fracture toughness, GIC, for unidirectionally reinforced materials... 

This process is adapted to the realization of complex, hollow or solid sections, with high mechanical characteristics thanks to the high unidirectional reinforcement levels. 

ISO 9353 1991 Glass-reinforced plastics - Preparation of plates with unidirectional reinforcements by bag moulding... 

ASTM D 3518 (1991). Practice for in-plane shear stress-strain response of unidirectional reinforced plastics. 

In the case of unidirectionally reinforced layers, or laminae (not to be confused with the similar-looking lamellae, cf. Section 1.3.6.1), a composite is formed by laminating the layers together. If all the layers were to have the same fiber orientation (see Figure 5.117a), the material would still be weak in the transverse direction. Therefore,... 

The characteristic features of a cord—rubber composite have produced the netting theory (67—70), the cord—inextensible theory (71—80), the classical lamination theory, and the three-dimensional theory (67,81—83). From structural considerations, the fundamental element of cord—rubber composite is unidirectionally reinforced cord—mbber lamina as shown in Figure 5. From the principles of micromechanics and orthotropic elasticity laws, engineering constants of tire T cord composites in terms of constitutive material properties have been expressed (72—79,84). The most commonly used Halpin-Tsai equations (75,76) for cord—mbber single-ply lamina L are expressed in equation 5 ... 

Fig. 5. Calendered unidirectionally reinforced single-ply cord—mbber lamina where 0 is...

Figure 21. Translation (utilization) of fiber strength as a function of fiber type and surface treatment (51). Flexural tests on unidirectionally reinforced composites made with phenolic-based matrices carbonized to 1000°C.

For unidirectional reinforced composites (by means of continuous filaments) the following formulae may be used ... 

Unidirectionally reinforced materials are more of a problem to test than multidirectional reinforcements because of the anisotropy of the properties. This anisotropy leads to differences in moduli, strain-to-failure, and other properties of the composite which allow failure of the material to occur in a mode other than that which the researcher may wish to investigate. 

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