From an atomic perspective, plastic deformation corresponds to the breaking of bonds with original atom neighbors and then re-forming bonds with new neighbors as large numbers of atoms or molecules move relative to one another. As the material is deformed beyond this point, the stress is no longer pro- portional to strain, and permanent, non-recoverable, or plastic deformation occurs. For most metallic materials, elastic deformation persists only to strains of about 0.005. A structure or component that has plastically deformed may not function as intended. Most structures are designed to ensure that only elastic deformation will result when a stress is applied. The remaining discussion of mechani- cal behavior assumes isotropy and polycrystallinity because such is the character of most engineering materials. Because the grain orientation is random in most polycrystalline materials, these may be considered to be isotropic inorganic ceramic glasses are also isotropic. For these materials the elastic properties are completely characterized only by the specification of several elastic constants, their number depending on characteristics of the crystal structure. that is, the elastic behavior (e.g., the magnitude of E) varies with crystallographic direction (see Table 3.3). Many materials are elastically anisotropic. In most metals G is approximately 0.4, therefore if one modulus is known, the other may be approximated. For isotropic materials, shear and elastic moduli are related to each other and to Poisson's ratio according to E= 2G(1+v) If the applied stress is uniaxial (only in the z direction), and the material is isotropic, then ∈(x)= ∈(y). When a tensile stress is imposed on a metal specimen, an elastic elongation and ac- companying strain z result in the direction of the applied stress.As a result of this elongation, there will be constrictions in the lateral (x and y) directions perpendicular to the applied stress. However, for some polymeric materials its magnitude is significant in this case it is termed viscoelastic behavior A parameter termed Poisson's ratio ∨ is defined as.the ratio of the lateral and axial strains. For metals the anelastic component is normally small and is often neglected. This time-dependent elastic behavior is known as anelasticity. That is, elastic deformation will continue af- ter the stress application, and upon load release some finite time is required for com- plete recovery. Anelasticity In most engineering materials, however, there will also exist a time-dependent elastic strain component.
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