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3. (20 pts) A shaft with a step in diameter is made of AISI 4340 (aircraft quality) steel of Table 9.1. It is required to withstand 107 cycles of an axial force amplitude Pa = 16 kN applied along with a mean force of Pm = 8 kN. The shaft has dimensions, as in Figure A.12(a), di = 25 mm, da = 30 mm, and p = 0.625 mm. Modification factors shall be applied for the following: • The notch radius p has a machined finish (see Figure 10.10). • Size factor from Fig.10.9. a. Determine kt and estimate ky. Use the typical value of a for quenched and tempered steels for this high strength steel alloy (equation 10.6). b. Determine the fatigue strength (Sar) at 107 cycles of the stepped (notched) shaft applying modification factors for size and surface finish. c. Determine the equivalent completely reversed service stress amplitude (Sar) using the service axial force amplitude, service mean force, and the Walker relationship (Eq. 10.28) with the Walker constant, y = 0.062. d. Determine the safety factor in stress for the life of 107 cycles (Xs\Ny=10cycles).
Table 9.1 Constants for Stress-Life Curves for Various Ductile Engineering Metals, from Tests at Zero Mean Stress on Unnotched Axial Specimens Yield Ultimate True Fracture 0,= 0;(21,9° = AN Strength Strength Strength Material OB of b=B (a) Steels SAE 1015 228 415 726 1020 927 -0.138 (normalized) (33) (60.2) (105) (148) (134) Man-Ten 322 557 990 1089 1006 -0.115 (hot rolled) (46.7) (80.8) (144) (158) (146) RQC-100 683 758 1186 938 897 -0.0648 (roller Q&T) (99.0) (110) (172) (136) (131) SAE 4142 1584 1757 1998 1937 1837 -0.0762 (Q & T, 450 HB) (230) (255) (290) (281) (266) AISI 4340 1103 1172 1634 1758 1643 -0.0977 (aircraft quality) (160) (170) (237) (255) (238) (b) Other Metals 2024-T4 AI 303 476 631 900 839 -0.102 (44.0) (69.0) (91.5) (131) (122) Ti-6A1-4V 1185 1233 1717 2030 1889 -0.104 (solution treated (172) (179) (249) (295) (274) and aged) Notes: The tabulated values have units of MPa (ksi), except for dimensionless b = B. See Table 15.1 for sources and additional properties.
Brinell Hardness 120 160 200 240 280 320 360 400 440 480 520 1.0 Mirror-polished 0.9 Fine-ground or 0.8 commercially polished 0.7 Machined 0.6 ms, Surface Factor 0.5 0.4 Hot-rolled 0.3 As forged 0.2 Corroded in tap water 0.1 Corroded in salt water 60 80 100 120 140 160 180 200 220 240 260 Oy, Ultimate Tensile Strength, ksi 0 Figure 10.10 Effect of various surface finishes on the fatigue limit of steel. Values are plotted of my, the ratio of the fatigue limit to that for polished specimens. (Adapted from R.C. Juvinall, Stress, Strain, and Strength, 1967; (Juvinall 67] p. 234; reproduced with permission; 1967 the McGraw-Hill Companies Inc.)
d, in 1.2 0.4 0.8 1.6 2.0 2.4 2 1.3 2 0 Steels, smooth rotating bending o 1.1 md. Size Factor 28 1.0 edhe 8 E 0.9 0.8 d=7.62 mm 0.7 10 20 30 40 d. Diameter of Test Section, mm 50 60 Figure 10.9 Effect of size on the fatigue limit of smoothly polished specimens of steels tested in rotating bending. Values are plotted of md, the ratio of the fatigue limit to that for the frequently used 7.62 mm (0.3 in.) specimen diameter. (Data from [Heywood 62] p. 23.) where a is a material constant having dimensions of length, with some typical values being as follows: a=0.51 mm (0.02 in) (aluminum alloys) a=0.25 mm (0.01 in) (annealed or normalized low-carbon steels) (10.6) a = 0.064 mm (0.0025 in) (quenched and tempered steels) Ser = Schus max Sar = Smar «(?)" (a, b) (10.28)