The ultimate tensile conditions of high temperature

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Unformatted text preview: strength and the advantages of strengthening bonded or joined together by atomic m by the fibers will be less than fully realized. critical nucleus Nucleus of therequired for effective strengthening is interface accomplished by solid-state size such that either The minimum or critical fiber length lc a growth or dissolution will decrease its free fiber d, function of several variables including the diameter of the energy.the ultimate tensile conditions of high temperature and pr critical resolved shear stress ( CRSS) The shear stress diffusion coefficient The constant i resolved in the slip plane in the slip direction at which relating mass flux per unit area to the gradient. It obeys an Arrhenius-type e |plastic deformationMenu | Textbook Table of Contents | e-Text Main occurs. such is strongly temperature-depende crosslinks Primary bonds formed between adjacent coefficient describes the ease of atom polymer chains. These atomic “bridges” are often the solid state. composed of small chains of either oxygen or sulfur but can be composed of many other small groups of atoms. direct dissolution mechanism A d mechanism in which the solid dissolve crystal lattice The framework on which atoms are surrounding liquid without substantial placed in periodic three-dimensional structures. dislocation A linear defect in a cry crystalline Having atoms or ions arranged on a responsible for plastic deformation. three-dimensional lattice having long-range order. pg583 [R] G1 7-27060 / IRWIN / Schaffer iq Chapter 14 12.01.98 plm QC3 rps MP Composite Materials 583 FIGURE 14.3–1 (a) Isolated fiber embedded in a matrix, (b) the distortions associated with tensile loading of the composite in part a, and (c) the distribution of shear and normal stresses on the outer fiber surface (also the interface region) along the fiber length in response to the loading. (a) σ σ (b) l lc /2 σ max = ε Ef lc /2 σ τ (c) strength of the fibers f u , and the matrix shear yield strength my . The second factor sets the limit on the load carried by the fibers, and the third factor describes the ability of the matrix to transmit the load from one fiber to the next. The relationship among these variables is found using a force balance. The force carried by the fibers is equal to the normal stress in the fibers multiplied by their cross-sectional area. This force is transferred to the fibers via a shear stress acting on the fiber surface. Mathematically, the force balance is: d lc 2 d2 4 my (14.3–1) fu or, equivalently, lc d fu 2 (14.3–2) my The quantity lc d is known as the critical aspect ratio. Typically, the critical aspect ratio ranges from 20 to 150 for most fiber and matrix materials. Since a typical fiber diameter is between 10 and 30 m, critical fiber lengths are on the order of 0.2–4.5 mm. In most practical instances, the fiber length l is much larger than lc . 14.3.2 Characteristics of Fiber Materials | v v The most common geometrical shape for the reinforcing phase in a high-performance structural composite is a fiber. The reason for this is that the strength of a brittle material is inversely related to the sq...
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