Notch sensitivity factor (A) is related as [A = Notch sensitivity factor, B = Theoretical stress concentration factor, C = Fatigue stress concentration factor]

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  1. A = [B - 1] [C - 1]
  2. B = 1 + A [C - 1]
  3. A = BC
  4. C = 1 + A [B - 1]

Answer (Detailed Solution Below)

Option 4 : C = 1 + A [B - 1]
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Detailed Solution

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Explanation:

Notch sensitivity:

Notch sensitivity is defined as the susceptibility of a material to succumb to the damaging effect of stress raising notches in fatigue loading

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

Key Parameters:

  • A = Notch Sensitivity Factor
  • B = Theoretical Stress Concentration Factor (Kt)
  • C = Fatigue Stress Concentration Factor (Kf)

actual stress = Kσo, theoretical stress = Kσo

where, σ= nominal stress, Kf = actual stress concentration factor Kt = theoretical stress concentration factor.

Increase of actual stress = (Kσ- σo)

Increase of theoretical stress = (Kσ- σo)

\({\bf{q}} = \frac{{\left( {{{\bf{K}}_{\bf{f}}}{{\bf{\sigma }}_{\bf{o}}}\; - \;{{\bf{\sigma }}_{\bf{o}}}} \right)}}{{\left( {{{\bf{K}}_{\bf{t}}}{{\bf{\sigma }}_{\bf{o}}}\; - \;{{\bf{\sigma }}_{\bf{o}}}} \right)}} = \frac{{\left( {{{\bf{K}}_{\bf{f}}}\; - \;1} \right)}}{{\left( {{{\bf{K}}_{\bf{t}}}\; - \;1} \right)}}\)

⇒ C = 1 + A [B - 1]

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