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STRENGTH UNDER DYNAMIC CONDITIONS 29.10
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FIGURE 29.5 Fatigue-strength diagram for alloy steel, Su = 125 to 180 kpsi, axial loading. Average of test data for polished specimens of AISI 4340 steel (also applicable to other alloy steels, such as AISI 2330, 4130, 8630). (Grumman Aerospace Corp.)
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FIGURE 29.6 Fatigue-strength diagram for 7075-T6 aluminum alloy, axial loading. Average of test data for polished specimens (unclad) from rolled and drawn sheet and bar. Static properties: Su = 82 kpsi, Sy = 75 kpsi. (Grumman Aerospace Corp.)
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ka = kb = kc = kd = ke = Se = Se =
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surface condition modification factor size modification factor loading modification factor temperature modification factor miscellaneous-effects modification factor endurance limit of rotating-beam specimen endurance limit at critical location of part in the geometry and condition of use
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Marin Surface Factor ka
The Marin surface condition modification factor for steels may be expressed in the form
b ka = aSut
(29.7)
Table 29.2 gives values of a, b for various surface conditions. See also Fig. 29.7.
TABLE 29.2 Parameters of Marin Surface Condition Factor a Surface finish Ground Machined, cold-rolled Hot-rolled As-forged kpsi 1.34 2.67 14.5 39.8 MPa 1.58 4.45 58.1 271 b 0.086 0.265 0.719 0.995
Source: Data from C. G. Noll and C. Lipson, Allowable Working Stresses, Society of Experimental Stress Analysis, vol. 3, no. 2, 1946, p. 49, reduced from their graphed data points.
Example 1. A steel has a mean ultimate tensile strength of 520 MPa and a machined surface. Estimate ka. Solution: From Table 29.2, ka = 4.45(520) 0.265 = 0.848 29.3.2 Marin Size Factor kb In bending and torsion, where a stress gradient exists, Kuguel observed that the volume of material stressed to 0.95 or more of the maximum stress controls the risk of encountering a crack nucleation, or growth of an existing flaw becoming critical. The equivalent diameter de of the R. R. Moore specimen with the same failure risk is de = A0.95 0.076 576 (29.8)
where A0.95 is the cross-sectional area exposed to 95 percent or more of the maximum stress. For a round in rotating bending or torsion, A0.95 = 0.075 575d 2. For a round in nonrotating bending, A0.95 = 0.010 462d 2. For a rectangular section b h in
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STRENGTH UNDER DYNAMIC CONDITIONS 29.12
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FIGURE 29.7 Marin endurance limit fatigue modification factor ka for various surface conditions of steels. See also Table 29.2.
bending, A0.95 = 0.05bh. See [29.6], p. 284 for channels and I-beams in bending. Table 29.3 gives useful relations. In bending and torsion, kb =
0.107 (de /0.30) 0.107 = 0.879d e 0.107 (de /7.62) 0.107 = 1.24d e
de in inches de in mm
(29.9) (29.10)
For axial loading, kb = 1. Table 29.4 gives various expressions for kb. The Marin size factor is scalar (deterministic). At less than standard specimen diameter (0.30 in), many engineers set kb = 1. 29.3.3 Marin Loading Factor kc The Marin loading factor kc can be expressed as
kc = Sut
(29.11)
TABLE 29.3 Equivalent Diameters for Marin Size Factor Section Round, rotary bending, torsion Round, nonrotating bending Rectangle, nonrotating bending Equivalent diameter de d 0.37d 0.808bh
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STRENGTH UNDER DYNAMIC CONDITIONS 29.13
STRENGTH UNDER DYNAMIC CONDITIONS
TABLE 29.4 Quantitative Expression for Size Factor
Table 29.5 gives values for , . For axial loading of steel based on Table 29.5, Table 29.6 was prepared. Juvinall [29.12] reports that for steel, 0.75 < kc < 1.0, and suggests using kc = 0.90 for accurate control of loading eccentricity and 0.60 < kc < 0.85 otherwise. The problem of load eccentricity plagues testing as well as the designer. Axial loading in fatigue requires caution. See Fig. 29.8. For torsion, Table 29.7 summarizes experimental experience. In metals described by distortion-energy failure theory, the average value of kc would be 0.577.
29.3.4 Marin Temperature Factor kd Steels exhibit an increase in endurance limit when temperatures depart from ambient. For temperatures up to about 600 F, such an increase is often seen, but above 600 F, rapid deterioration occurs. See Fig. 29.9. If specific material endurance limit temperature testing is not available, then an ensemble of 21 carbon and alloy
TABLE 29.5 Parameters of Marin Loading Factor Mode of loading Bending Axial Torsion kpsi 1 1.23 0.328 MPa 1 1.43 0.258 0 0.078 0.125
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