Basic Theory of Metal Working Machinery's Handbook, 31st Edition
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Fig. 1. A Tensile Specimen with Cross-Sectional Area A Subjected to the Load F Stress-Strain Relationship.— When solid materials are subjected to stress, they usually respond in an elastic fashion; that is, the strain produced by the stress is reversible (the strain goes back to zero when the stress is removed), and the magnitude of the strain is directly proportional to the magnitude of the stress. This relationship between stress and strain is usually referred to as Hooke’s Law and can be written (5) where E = modulus of elasticity (lb/in 2 ). The most common procedure for describing the various relationships between stress and strain is the tensile test, which is used to determine the modulus of elasticity, the elastic limit, the elongation, the proportional limit, the reduction area, the tensile strength, the yield point, the yield strength, and other tensile properties. The stress ( σ ), calculated from the load, and the strain ( e ), calculated from the extension, can either be plotted as 1) nominal (engineering) stress-strain, or 2) true stress-strain The first is more important in design, and the second is more important in manufacturing. The graphs used in each case will be different. Nominal Stress-Strain: Nominal stress, also called engineering stress, is defined as the ratio of the applied load F to the original cross-sectional area A of the specimen: (6) where σ n = nominal stress (lb/in 2 ); F = applied load in the test (lb); and, A 0 = original cross- (7) where e n = nominal strain (in./in.); l 0 = original gauge length (in.); and l = instantaneous length of the specimen (in.). True Stress-Strain: A nominal stress-strain curve does not give a true indication of the deformation characteristic of a solid because it is based on the original cross-sectional area A 0 of the specimen, and this dimension changes continuously during the test. In the solution of technical problems in metalworking, true stress and true strain are much more important. True stress σ is defined as the ratio of the load F to the actual stress-section area A of the specimen: l n ε section area of specimen (in 2 ). Nominal strain is defined as E strain stress constant = = A F n σ = 0 l l l l 0 − = ∆ =
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