If the value of theoretical stress concentration factor is 1.0, then the value of fatigue stress concentration factor is equal to

Concept: 

Notch sensitivity is defined as the susceptibility of a material to succumb to the damaging effects of stress gassing notches in fatigue loading. The notch sensitivity factor a is defined as

\(q=\frac{increase~of~actual~stress~over~nominal~stress}{increase~of~theoretical~stress~over~nominal~stress}\)

The theoretical Stress concentration factor

\({{K}_{F}}={{\left( \frac{Endurance~limit~of~the~notch~free~specimen}{Endurance~limit~of~the~motched~specimen} \right)}_{actual}}\)

\({{K}_{t}}={{\left( \frac{Endurance~limit~of~the~notch~free~specimen}{Endurance~limit~of~the~notched~specimen} \right)}_{Theoretical}}\)

σ0 = Nominal stress as obtained by elementary equations

Actual stress = Kfσ0

Theoretical stress = Ktσ0

Increase of actual stress over nominal stress = (Kfσ0 - σ0)

Increase of Theoretical stress over nominal stress = (Ktσ0 - σ0)

\(q=\frac{\left( {{k}_{f}}{{\sigma }_{0}}-{{\sigma }_{0}}~ \right)}{\left( {{k}_{t}}{{\sigma }_{0}}-{{\sigma }_{0}}~ \right)}=\frac{{{k}_{f}}-1}{{{k}_{t}}-1~}\)

Calculation:

Given: k_t = 1

\(q=\frac{{{k}_{f}}-1}{{1}-1~}\)

⇒ kf = 1