It has been proposed to surface harden a steel leaf spring with a thickness, t,

Question

It has been proposed to surface harden a steel leaf spring with a thickness, t, to improve its bending fatigue resistance. The steel is initially at 200 BHN and can be hardened to 350BHN to whatever depth, d, is desired. However, the time required for deep hardening is excessive. Ignoring residual stresses, estimate the minimum d/t ratio to achieve the maximum bending fatigue strength at long lives (N>10^6). What would the optimum value of d/t be if this member were to be subjected to cyclic axial loading?

Explanation / Answer

For fatigue life of more than 106 cycles

Endurance limit Se = 0.25 x BHN

If BHN can be increased to 350. Se  = 0.25 x 350 = 87.5 N/mm2 (in reversed bending)

In axial loading Se = 0.7 X 87.5 = 61.25 N/mm2

Also ultimate strength Su = 2xSe = 2 x 87.5 = 175 N/mm2

From ultimate strength to optimum depth of hardness curves

For 175 N/mm2 percent depth is 28%

Hence d/t can be taken as 30%

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