Question 5.5: Determine the cumulative damage experienced by a ground circ...

Given: SAE 4340, HB 275 alloy steel rod. s_u = 1048 MPa D = 38 mm. Ground surface.
Endurance strength data (S-N) shown in Figure 5–10 s_n = 430 MPa.
Loading is reversed, repeated bending. Load history shown in Table 5–5.

Analysis: First adjust the S-N data for actual conditions using methods of Section 5–6. Use Miner’s rule to estimate the portion of life used by the loading pattern.

Results:

For SAE 4340, HB 275, s_{u}=1048 \mathrm{MPa}
From Figure 5-11, basic s_{n}=475 \mathrm{MPa} for ground surface
Material factor, C_{m}=1.00 for wrought steel
Type-of-stress factor, C_{s t}=1.0 for reversed, rotating bending stress
Reliability factor, C_{R}=0.81 (Table 5-3) for R=0.99 (Design decision)
Size factor, C_{s}=0.84 (Figure 5-12 and Table 5-4 for D=38 \mathrm{~mm} )
Estimated actual endurance limit, s_{n}^{\prime}- Computed:
s_{n}^{\prime}=s_{n} C_{m} C_{s t} C_{R} C_{s}=(475 \mathrm{MPa})(1.0)(1.0)(0.81)(0.84)=323 \mathrm{MPa}
This is the estimate for the actual endurance limit of the steel. In Figure 5-10, the endurance limit for the standard specimen is 430 \mathrm{MPa}. The ratio of the actual to the standard data is 323 / 430=0.75. We can now adjust the entire S-N curve by this factor. The result is shown in Figure 5-23.

Now we can read the number of cycles of life, N_{i}, corresponding to each of the given loading levels from Table 5-5. The combined data for the number of applied load cycles, n_{j}, and the life cycles, N_{j}, are now used in Miner’s rule, Equation 5-35, to determine the cumulative damage, D_{c}. Results are shown in Table 5-6.

Comment: We can conclude from this number that approximately 57% of the life of the component has been accumulated by the given loading. For these data, the greatest damage occurs from the 650 MPa loading for 2000 cycles. An almost equal amount of damage is caused by the 500 MPa loading for 10 000 cycles. Note that the cycles of loading at 300 MPa contributed nothing to the damage because they are below the endurance limit of the steel.