The elongation of a mild steel specimen in the yield (or perfect plasticity) region BC is typically 10–20 times the elongation that occurs between the onset of loading and the proportional limit. The portion of the stress–strain curve extending from A to the point of fracture (E) is the plastic range. In the range CD, an increase in stress is required for a continued increase in strain. This is called the strain hardening or cold working. If the load is removed at a point g in region CD, the material returns to no stress at a point h along a new line parallel to the line OA: a permanent set Oh is introduced. If the load is reapplied, the new stress–strain curve is hgDE. Note that there is now new yield point (g) that is higher than before (point B) but reduced ductility. This process can be repeated until the material becomes brittle and fractures.
Ultimate Tensile Strength
The engineering stress diagram for the material when strained beyond C displays a typi- cal ultimate stress (point D), referred to as the ultimate or tensile strength Su. Additional elongation is actually accompanied by a reduction in the stress, corresponding to fracture strength Sf (point E) in the figure. Failure at E occurs, by separation of the bar into two parts (Figure 2.2), along the cone-shaped surface forming an angle of approximately 45° with its axis that corresponds to the planes of maximum shear stress. In the vicinity of the ultimate stress, the reduction of the cross-sectional area or the lateral contraction becomes clearly vis- ible and a pronounced necking of the bar occurs in the range DE. An examination of the rup- tured cross-sectional surface depicts a fibrous structure produced by stretching of the grains of the material. Interestingly, the standard measures of ductility of a material are defined on the basis of the geometric change of the specimen, as follows: Here, Ao and Lo denote, respectively, the original cross-sectional area and gage length of the specimen. Clearly, the ruptured bar must be pieced together to measure the final gage length Lf. Similarly, the final area Af is measured at the fracture site where the cross section is minimal. Note that the elongation is not uniform over the length of the speci- men but concentrated in the region of necking. Therefore, percent elongation depends on the gage length. The diagram in Figure 2.3a depicts the general characteristics of the stress–strain diagram for mild steel, but its proportions are not realistic. As already noted, the strain between B and C may be about 15 times the strain between O and A. Likewise, the strains from C to E are many times greater than those from O to A. Figure 2.3b shows a stress– strain curve for mild steel drawn to scale. Clearly, the strains from O to A are so small that the initial part of the curve appears to be a vertical line. Offset Yield Strength Certain materials, such as heat-treated steels, magnesium, aluminum, and copper, do not show a distinctive yield point, and it is usual to use a yield strength Sy at an arbitrary strain. According to the so-called 0.2% offset method, a line is drawn through a strain of 0.002 (that is 0.2%), parallel to the initial slope at point O of the curve, as shown in Figure 2.4. The intersection of this line with the stress–strain curve defines the offset yield strength (point B). For the materials mentioned in the preceding discussion, the offset yield strength is slightly above the proportional limit.
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