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Chapter 3 Mechanics

# Chapter 3 Mechanics - 3 Mechanics The mechanics of...

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3 Mechanics The mechanics of materials deal with stresses, strains, and deformations in engineering structures subjected to mechanical and thermal loads. A common assumption in the mechanics of conventional materials, such as steel and aluminum, is that they are homogeneous and isotropic continua. For a homo- geneous material, properties do not depend on the location, and for an iso- tropic material, properties do not depend on the orientation. Unless severely cold-worked, grains in metallic materials are randomly oriented so that, on a statistical basis, the assumption of isotropy can be justified. Fiber-reinforced composites, on the other hand, are microscopically inhomogeneous and non- isotropic (orthotropic). As a result, the mechanics of fiber-reinforced composites are far more complex than that of conventional materials. The mechanics of fiber-reinforced composite materials are studied at two levels: 1. The micromechanics level, in which the interaction of the constituent materials is examined on a microscopic scale. Equations describing the elastic and thermal characteristics of a lamina are, in general, based on micromechanics formulations. An understanding of the interaction between various constituents is also useful in delineating the failure modes in a fiber-reinforced composite material. 2. The macromechanics level, in which the response of a fiber-reinforced composite material to mechanical and thermal loads is examined on a macroscopic scale. The material is assumed to be homogeneous. Equa- tions of orthotropic elasticity are used to calculate stresses, strains, and deflections. In this chapter, we look into a few basic concepts as well as a number of simple working equations used in the micro- and macromechanics of fiber-reinforced composite materials. Detailed derivations of these equations are given in the references cited in the text. ß 2007 by Taylor & Francis Group, LLC.

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3.1 FIBER–MATRIX INTERACTIONS IN A UNIDIRECTIONAL LAMINA We consider the mechanics of materials approach [1] in describing fiber–matrix interactions in a unidirectional lamina owing to tensile and compressive load- ings. The basic assumptions in this vastly simplified approach are as follows: 1. Fibers are uniformly distributed throughout the matrix. 2. Perfect bonding exists between the fibers and the matrix. 3. The matrix is free of voids. 4. The applied force is either parallel to or normal to the fiber direction. 5. The lamina is initially in a stress-free state (i.e., no residual stresses are present in the fibers and the matrix). 6. Both fibers and matrix behave as linearly elastic materials. A review of other approaches to the micromechanical behavior of a composite lamina is given in Ref. [2]. 3.1.1 L ONGITUDINAL T ENSILE L OADING In this case, the load on the composite lamina is a tensile force applied parallel to the longitudinal direction of the fibers.
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Chapter 3 Mechanics - 3 Mechanics The mechanics of...

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