For steels, the endurance limit is approximately 1/2 of the tensile strength, and the fatigue strength at 103 cycles is approximately 90% of the tensile strength. The S-N curves can be approximated by a straight lines between 103 and 106 cycles when plotted as log(S ) versus log(N). Beyond 106 cycles the curves are horizontal.
A. Write a mathematical expression for S as a function of N for the sloping part of the S-N curve, evaluating the constants in terms of the approximations above.
B. A steel part fails in 12,000 cycles. Use the above expression to ?nd what % decrease of applied (cyclic) stress would be necessary to increase in the life of the part by a factor of 2.5 (to 30,000 cycles).
C. Alternatively, what % increase in tensile strength would achieve the same increase in life without decreasing the stress?