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SOLID MATERIALS 32.34
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FIGURE 32.18 Stress-strain curve for annealed A40 titanium plotted on logarithmic coordinates. The data are the same as in Fig. 32.17.
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the same manner in which Young s modulus E is related to elastic behavior. Young s modulus E is the value of stress associated with an elastic strain of unity; the strength coefficient 0 is the value of stress associated with a plastic strain of unity. The amount of cold work necessary to give a strain of unity is determined from Eq. (32.14) to be 63.3 percent. For most materials there is an elastic-plastic region between the two straight lines of the fully elastic and fully plastic portions of the stress-strain curve. A material that has no elastic-plastic region may be considered an ideal material because the study and analysis of its tensile properties are simpler. Such a material has a complete stress-strain relationship that can be characterized by two intersecting straight lines, one for the elastic region and one for the plastic region. Such a material would have a stress-strain curve similar to the one labeled I in Fig. 32.19. A few real materials have a stress-strain curve that approximates the ideal curve. However, most engineering materials have a stress-strain curve that resembles curve O in Fig. 32.19. These materials appear to overyield ; that is, they have a higher yield strength than the ideal value, followed by a region of low or no strain strengthening before the fully plastic region begins.Among the materials that have this type of curve are steel, stainless steel, copper, brass alloys, nickel alloys, and cobalt alloys. Only a few materials have a stress-strain curve similar to that labeled U in Fig. 32.19. The characteristic feature of this type of material is that it appears to underyield ; that is, it has a yield strength that is lower than the ideal value. Some of the fully annealed aluminum alloys have this type of curve.
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32.10 TENSILE PROPERTIES
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Tensile properties are those mechanical properties obtained from the tension test; they are used as the basis of mechanical design of structural components more frequently than any other of the mechanical properties. More tensile data are available for materials than any other type of material property data. Frequently the design engineer must base his or her calculations on the tensile properties even under
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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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FIGURE 32.19 Schematic representation of three types of stressstrain curves. I is an ideal curve, and O and U are two types of real curve.
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cyclic, shear, or impact loading simply because the more appropriate mechanical property data are not available for the material he or she may be considering for a specific part. All the tensile properties are defined in this section and are briefly discussed on the basis of the tensile test described in the preceding section.
32.10.1 Modulus of Elasticity The modulus of elasticity, or Young s modulus, is the ratio of stress to the corresponding strain during elastic deformation. It is the slope of the straight-line (elastic) portion of the stress-strain curve when drawn on cartesian coordinates. It is also known, as indicated previously, as Young s modulus, or the proportionality constant in Hooke s law, and is commonly designated as E with units of pounds per square inch (pascals) or the equivalent. The modulus of elasticity of the titanium alloy whose tensile data are reported in Table 32.3 is shown in Fig. 32.15, where the first four experimental data points fall on a straight line having a slope of 16.8 Mpsi.
32.10.2 Proportional Limit The proportional limit is the greatest stress which a material is capable of developing without any deviation from a linear proportionality of stress to strain. It is the point where a straight line drawn through the experimental data points in the elastic region first departs from the actual stress-strain curve. Point P in Fig. 32.16 is the proportional limit (20 kpsi) for this titanium alloy. The proportional limit is very seldom used in engineering specifications because it depends so much on the sensitivity and accuracy of the testing equipment and the person plotting the data.
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