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FIGURE 29.17 A portion of a 4140 steel shaft quenched in still oil (H = 0.35) and tempered for 2 hours at 1000 F, grain size 7.5.
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The tempered hardness equation becomes RT = (RQ 5.3 10)0.34 + 10 + 11.91 = 0.34RQ + 16.71 The Jominy curve is predicted by noting that the Rockwell C-scale hardness at Jominy station 1 is (RQ)1 = 32 + 60(%C) = 32 + 60(0.40) = 56.0 and a table is prepared as depicted in Table 29.9 for 1000 F tempering temperature. The variation of surface strength with size of round is prepared using equivalent Jominy distances as depicted in Table 29.10. Table 29.11 shows an ultimate-strength traverse of a 11 8-in round. There is only a mild strength profile in the traverse. The significant strength for bending and torsion is at the surface. For the 11 8-in round, the surface ultimate strength is estimated by interpolation to be 164.3 kpsi. The R. R. Moore endurance limit at this location is estimated to be 164.3/2, or 82 kpsi. Steels in large sections or with less alloying ingredients (smaller ideal critical diameters) exhibit larger transverse strength changes. For sections in tension, significant strength is at the center. When testing, machined specimens from the center of a round say little about the strength at the surface. Heat treating a specimen proves little about strengths in the actual part. Some variations in strength attributed to size result from differences in cooling rates. When the number of cycles is less than 107, the endurance strength must be estimated. Reference [29.8] gives a useful curve fit for steels: Sf = Sum m exp (m) mNfcm exp ( f N fc) f Su f N c m f f N c > m f (29.24)
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TABLE 29.9 Surface Ultimate Strength as a Function of Jominy Distance for 4140 Steel Oil Quenched (H = 0.35) and Tempered 2 Hours at 1000 F, Grain Size 71 2
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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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TABLE 29.10 Variation of Surface Strength with Diameter of 4140 Steel Round Quenched in Still Oil (H = 0.35) and Tempered for 2 Hours at 1000 F, Grain Size 71 2
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m= f = c= Nf = Su =
strain-strengthening exponent true strain at fracture an exponent commonly in the neighborhood of 1 2 the number of cycles to failure ultimate tensile strength
Example 3. Estimate the finite-life engineering fatigue strength of an annealed 4340 steel with the following properties: Su = 103 kpsi RA = 0.56 Solution. The endurance limit is estimated as Su/2 = 103/2 = 51.5 kpsi at 107 cycles. Because no strain-hardening information is supplied, it is necessary to estimate m from m Su = Sy (offset) exp 1 or 103 m 65.6 0.002(2.718)
Sy = 65.6 kpsi at 0.2 percent offset
from which m = 0.14. The true strain at fracture can be assessed from the reduction in area: f = ln 1 1 = ln = 0.821 1 RA 1 0.56
TABLE 29.11 Variation of Local Strength in a 1.125-in Round of 4140 Steel Quenched in Still Oil (H = 0.35) and Tempered for 2 Hours at 1000 F, Grain Size 71 2
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.
STRENGTH UNDER DYNAMIC CONDITIONS 29.27
STRENGTH UNDER DYNAMIC CONDITIONS
The true stress coefficient of the strain-strengthening equation = o m is o = Sum m exp m = 103(0.14) 0.14 exp 0.14 = 156.0 kpsi The constructive strain 1 is a root of the equation o m 1 exp ( 1) 1 = 0 Se or alternatively, Su m m exp (m) 1m exp ( 1) 1 = 0 Se When 1 is small, the term exp 1 approaches 1, and 1 can be found explicitly from 1 = From the first, 1 = 51.5 156
1/0.14
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