Question

The material properties of a machine part are Sut 5 85 kpsi, f 5 0.86, and a fully corrected endurance limit of Se 5 45 kpsi. The part is to be cycled at sa 5 35 kpsi and sm 5 30 kpsi for 12 (103 ) cycles. Using the Gerber criterion, estimate the new endurance limit after cycling

Answer 1

according to Miners method the new endurance limit S
`_e`" is 45 kpsi

Step-by-step explanation:

Given the data in the question;

the amplitude stress σₐ = 35 kpsi

the mean stress for 12(10³) cycles σ
`_m` = 30 kpsi

the ultimate tensile stress S
`_{ut` = 85 kpsi

endurance limit of S
`_e` = 45 kpsi

so, we calculate the reversing stress for Gerber criteria

σ
`_{rev` = σₐ / [ 1 - ( σ
`_m`/S
`_{ut`)²

we substitute

σ
`_{rev` = 35 / [ 1 - ( 30/85)²]

σ
`_{rev` = 35 / [ 1 - 0.124567]

σ
`_{rev` = 35 / 0.875433

σ
`_{rev` = 39.98 kpsi

Using Miners Method;

the reversing stress ( 39.98 kpsi ) is less than endurance limit ( 45 kpsi )

σ
`_{rev` < S
`_e`

According to Miners method, if reversing stress is less than endurance limit, then the endurance limit has not reduced and new endurance limit remains the same.

Hence, according to Miners method the new endurance limit S
`_e`" is 45 kpsi