lecture06 - 5.1 Why Use Fibers? When subjected to any...

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5.1 Why Use Fibers? When subjected to any loading, particulate composites experience high stress concentrations around the reinforcing particles and result in poor strengths to the composites. However, unidirectional fiber-reinforced composite materials are free of high stress concentrations if the loading is in the direction along the axis of fibers. When loaded in a direction transverse to the fiber direction, the stress concentrations in the unidirectional composite will be similar to that in the particulate composites. The maximum size of flaw in a material is proportional to the maximum dimension of the material. Hence, the maximum possible size of a flaw in a plate is much greater than that in a fiber made of the same material. Because the greater the size of flaw, the lower the strength of material, materials in fiber form are much stronger than those in bulk form due to the smaller size of flaw. Hence, in order to reduce the size of flaw and to have higher strength, a material can be made in fiber form with small cross-sectional dimensions than in bulk form. However, it should be noted that composites made of long fibers are primarily designed for being loaded along the fiber direction. If the unidirectional composites are subjected to transverse loading, the disadvantages similar to those particulate composites will occur. The primary reasons for using long fibers as reinforcement for composite materials can be summarized as follows: A. The smaller the fiber diameter, the smaller the imperfection it can have. From fracture mechanics, c K o I π σ = where K I is the stress intensity factor of open mode (first mode), and o is the tensile stress exerted on the specimen which has a central crack with a dimension of 2c. If the stress level is high enough, the fracture of the fiber will take place. The above equation can then be rewritten as c K c Ic = where c is the critical stress while Ic K is the critical stress intensity factor, or so-called fracture toughness. Given Ic K as a material constant, c will decrease as c increases. Since a bulk material usually has larger defects than a small fiber, the stress to cause failure of the bulk material is smaller than that of the fiber. B. The smaller the fiber diameter, the larger the interfacial area for load transferring between fiber and matrix. Given a constant cross-sectional area 2 r A = , a fiber bundles consisting of fibers with a small diameter have a larger total surface area, r c 2 = , than the bundle with fibers of a large diameter. The efficiency of load transferring mechanism on the fiber interface can be greatly improved by increasing the contact area between fibers and matrix. This is very important in the reinforcement process since there are always weak fibers in composite materials. When they are damaged, the load they used to carry should be passed on to the fibers in the surrounding area through matrix. C.
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This note was uploaded on 07/25/2008 for the course ME 426 taught by Professor Liu during the Spring '06 term at Michigan State University.

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lecture06 - 5.1 Why Use Fibers? When subjected to any...

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