In analysis and design, the mechanical behavior of materials under load is of primary importance. Experiments, mainly in tension or compression tests, provide basic information about overall response of specimens to the applied loads in the form of stress–strain diagrams. These curves are used to explain a number of mechanical properties of materials. Data for a stress–strain diagram are usually obtained from a tensile test. In such a test, a specimen of the material, usually in the form of a round bar, is mounted in the grips of a testing machine and subjected to tensile loading, applied slowly and steadily or statically at room temperature (Figure 2.1). The ASTM specifies precisely the dimensions and constriction of standard tension specimens. The tensile test procedure consists of applying successive increments of load while taking corresponding electronic extensometer readings of the elongation between the two gage marks (gage length) on the specimen. During an experiment, the change in gage length is noted as a function of the applied load. The specimen is loaded until it finally ruptures. The force necessary to cause rupture is called the ultimate load. Figure 2.2 illustrates a steel specimen that has fractured under load and the extensometer attached at the right by two arms to it. Based on the test data, the stress in the specimen is found by dividing the force by the cross-sectional area, and the strain is found by dividing the elongation by the gage length. In this manner, a complete stress–strain diagram, a plot of strain as abscissa and stress as the ordinate, can be obtained for the material. The stress strain diagrams differ widely for different materials. Stress–Strain Diagrams for Ductile Materials. A typical stress strain plot for a ductile material such as structural or mild steel in tension is shown in Figure 2.3a. Curve OABCDE is a conventional or engineering stress strain diagram. The other curve, OABCF, represents the true stress–strain. The true stress refers to the load divided by the actual instantaneous cross-sectional area of the bar; the true strain is the sum of the elongation increments divided by the corresponding momentary length. For most practical purposes, the conventional stress–strain diagram provides satisfactory information for use in design. We note that engineering stress (σ) is defined as load per unit area, and for the tensile, specimen is calculated from. The stress is assumed to be uniformly distributed across the cross section. The engineering strain (ε) is given by Equation 1.20. A detailed analysis of stress and strain will be taken. Yield Strength the portion OA of the diagram is the elastic range. The linear variation of stress–strain ends at the proportional limit, a marked increase in strain without corresponding increase in stress is referred to as the yield point or yield strength Sy. For most cases, in practice, the proportional limit and yield point are assumed to be one: Sp ≈ Sy. In the region between B and C, the material becomes perfectly plastic, meaning that it can deform without an increase in the applied load.
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