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( Strength of materials) In materials science, the strength of a material refers to the material's ability to resist an applied stress. The applied stress may be tensile, compressive, or shear.

A material's strength is a function of engineering processes, and scientists employ a variety of strengthening mechanisms to alter the strength of a material. These mechanisms include work hardening, solid solution strengthening, precipitation hardening and grain boundary strengthening and can be quantified and qualitatively explained. However, strengthening mechanisms are accompanied by the caveat that mechanical properties of the material may degenerate in an attempt to make the material stronger. For example, in grain boundary strengthening, although yield strength is maximized with decreasing grain size, ultimately, very small grain sizes make the material brittle. In general, the yield strength of a material is an adequate indicator of the material's mechanical strength. Considered in tandem with the fact that the yield strength is the parameter that predicts plastic deformation in the material, one can make informed decisions on how to increase the strength of a material depending its microstructural properties and the desired end effect. Strength is considered in terms of compressive strength, tensile strength, and shear strength, namely the limit states of compressive stress, tensile stress and shear stress, respectively. The effects of dynamic loading is probably the most important practical part of the strength of materials, especially the problem of fatigue. Repeated loading often initiates brittle cracks, which grow slowly until failure occurs.

However, the term strength of materials most often refers to various methods of calculating stresses in structural members, such as beams, columns and shafts, when the equations of equilibrium are not sufficient to solve the problem. In such problems, known as statically indeterminate problems, the elastic or plastic resistance of the material to deformation must be considered when calculating stresses. In this sense, the word "strength" could well be replaced by "stiffness", but the usage goes back to at least 1930 and is not likely to go away any time soon.

Uniaxial stress is expressed by

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