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33.2 STRENGTH OF PLASTICALLY DEFORMED MATERIALS
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Methods for strength estimation include the conventional uniaxial tension test, which routinely measures true and engineering yield and ultimate strengths, percentage elongation and reduction in area, true ultimate and fracture strains, strainstrengthening exponent, strain-strengthening coefficient, and Young s modulus. These results are for the material in specimen form. Machine parts are of different shape, size, texture, material treatment, and manufacturing history and resist loading differently. Hardness tests can be made on a prototype part, and from correlations of strength with hardness and indentor size ([33.1], p. 5 35) and surface, ultimate strength can be assessed. Such information can be found in corporate manuals and catalogs or scattered in the literature. Often these are not helpful. In the case of a single plastic deformation in the manufacturing process, one can use the true stress-strain curve of the material in the condition prior to straining provided the plastic strain can be determined. The results are good. For a sequence of successive strains, an empirical method is available which approximates what happens but is sometimes at variance with test results. Cold work or strain strengthening is a common result of a cold-forming process. The process changes the properties, and such changes must be incorporated into the application of a theory of failure. The important strength is that of the part in the critical location in the geometry and at condition of use.
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33.2.1 Datsko s Notation In any discussion of strength it is necessary to identify 1. The kind of strength: ultimate, u; yield, y; fracture, f; endurance, e. 2. The sense of the strength: tensile, t; compressive, c; shear, s. 3. The direction or orientation of the strength: longitudinal, L; long transverse, B; short transverse, D; axial, a; radial, R; circumferential, C. 4. The sense of the most recent prior strain in the axial direction of the envisioned test specimen: tension, t; compression, c. If there is no prior strain, the subscript 0 is used.
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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THE STRENGTH OF COLD-WORKED AND HEAT-TREATED STEELS 33.4
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PERFORMANCE OF ENGINEERING MATERIALS
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33.2.2 Datsko s Rules Datsko [33.1] suggests a notation (S1 )234, where the subscripts correspond to 1, 2, 3, and 4 above. In Fig. 33.1 an axially deformed round and a rolled plate are depicted. A strength (Su )tLc would be read as the engineering ultimate strength Su, in tension (Su )t , in the longitudinal direction (Su )tL, after a last prior strain in the specimen direction that was compressive (Su )tLc. Datsko [33.1] has articulated rules for strain strengthening that are in approximate agreement with data he has collected. Briefly, Rule 1. Strain strengthening is a bulk mechanism, exhibiting changes in strength in directions free of strain. Rule 2. The maximum strain that can be imposed lies between the true strain at ultimate load u and the true fracture strain f. In upsetting procedures devoid of flexure, the limit is f , as determined in the tension test. Rule 3. The significant strain in a deformation cycle is the largest absolute strain, denoted w. In a round w = max(| r|, | |, | x|). The largest absolute strain w is used in calculating the equivalent plastic strain q , which is defined for two categories of strength, ultimate and yield, and in four groups of strength in Table 33.1. Rule 4. In the case of several strains applied sequentially (say, cold rolling then upsetting), in determining qu , the significant strains in each cycle wl are added in decreasing order of magnitude rather than in chronological order. Rule 5. If the plastic strain is imposed below the material s recrystallization temperature, the ultimate tensile strength is given by Su = (Su)o exp qu = 0( qu )
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