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deforms elastically until the load reaches Lz (10 000 lb) and then it deforms plastically. But Lz is also the maximum value of load that this specimen reaches on reloading. It never again will support a load of Lu = 12 000 lb. On this basis, the yield strength of this specimen is (Sy)W = Lz 10 000 = = 99 200 psi Az 0.101
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And the tensile strength of this previously deformed specimen is (Su)W = Lz 10 000 = = 99 200 psi Az 0.101
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32.11.6 Ratio of Tensile Strength to Brinell Hardness It is commonly known by mechanical-design engineers that the tensile strength of a steel can be estimated by multiplying its Brinell hardness number by 500. As stated earlier, this fact led to the wide acceptance of the Brinell hardness scale. However, this ratio is not 500 for all materials it varies from as low as 450 to as high as 1000 for the commonly used metals. The ratio of the tensile strength of a material to its Brinell hardness number is identified by the symbol KB, and it is a function of both the load used to determine the hardness and the strain-strengthening exponent of the material. Since the Brinell hardness number of a given material is not a constant but varies in proportion to the applied load, it then follows that the proportionality coefficient KB is not a constant for a given material, but it too varies in proportion to the load used in determining the hardness. For example, a 50 percent cobalt alloy (L605 or HS25) has a Brinell hardness number of 201 when tested with a 3000-kg load and a hardness of only 150 when tested with a 500-kg load. Since the tensile strength is about 145 000 psi for this annealed alloy, the value for KB is about 970 for the low load and about 730 for the high load. Since the material is subjected to considerable plastic deformation when both the tensile strength and the Brinell hardness are measured, these two values are influenced by the strain-strengthening exponent m for the material. Therefore, KB must also be a function of m. Figure 32.21 is a plot of experimental data obtained by this author over a number of years that shows the relationships between the ratio KB and the two variables strain-strengthening exponent m and diameter of the indentation, which is a function of the applied load. From these curves it is apparent that KB varies directly with m and inversely with the load or diameter of the indentation d. The following examples will illustrate the applicability of these curves. A test was conducted on a heat of alpha brass to see how accurately the tensile strength of a material could be predicted from a hardness test when the strainstrengthening exponent of the material is not known. Loads varying from 200 to 2000 kg were applied to a 10-mm ball, with the following results:
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Load, kg Diameter, mm 200 2.53 500 3.65 1000 4.82 1500 5.68 2000 6.30
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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 32.21 Relationships between the Su /HB ratio (KB) and the strain-strengthening exponent m. D = diameter of the ball, and d = diameter of the indentation. Data are based on experimental results obtained by the author.
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When plotted on log-log paper, these data fall on a straight line having a slope of 2.53, which is the Meyer strain-hardening exponent n. The equation for this straight line is L = 18.8d 2.53 Since, for some metals, m = n 2, the value of m is 0.53. For ease in interpreting Fig. 32.21, the load corresponding to an indentation of 3 mm is calculated from Eq. (32.2) as 43. KB can now be determined from Fig. 32.21 as 890. Thus the tensile strength is Su = KBHB = 890(43) = 38 300 psi. In a similar fashion, the load for a 5-mm diameter is 110 kg, and the corresponding Brinell hardness number is 53. From Fig. 32.21, the value of KB is found to be 780, and the tensile strength is estimated as Su = KBHB = 780(53) = 41 300 psi. The average value of these two calculated tensile strengths is 39 800 psi. The experimentally determined value of the tensile strength for this brass was 40 500 psi, which is just 2 percent lower than the predicted value. As another example, consider the estimation of tensile strength for a material when its typical strain-strengthening exponent is known. Annealed 3003 aluminum has an average m value of 0.28. What is the tensile strength of a heat that has a Brinell hardness number of 28 when measured with a 500-kg load The diameter of the indentation for this hardness number is 4.65.Then from Fig. 32.21 the value of KB is determined as 535. The tensile strength can then be calculated as Su = KBHB = 535(28) = 15 000 psi.
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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