Problem $2$

A flat leaf spring has fluctuating stress of ${}_{\text{m}\text{a}\text{x}}=300$MPa and ${}_{\text{m}\text{i}\text{n}}=150$MPa applied for $1{10}^4$

cycles, and ${}_{\text{m}\text{a}\text{x}}=350$MPa and ${}_{\text{m}\text{i}\text{n}}=-150$MPa applied for $1{10}^3$ cycles. If the load changes to

${}_{\text{m}\text{a}\text{x}}=200$MPa and ${}_{\text{m}\text{i}\text{n}}=-200$MPa, how many cycles should the spring survive?

The material is AISI $1020$ CD and has a fully corrected endurance strength of $S_e=175$MPa.

Assume that $f=0\mathrm{.}9.$