Advanced Structural Analysis/Part I - Theory/Failure Modes/Fatigue/Crack Initiation/Loading/Influence of Mean Stress/Algebraic Models

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The effect of mean stress, \sigma_m,can be modeled by the following relations:

  • Soderberg:  \sigma_a = \sigma_{a, \sigma_m = 0} (1 - \frac{\sigma_m} {\sigma_y}) ;
    which is conservative for most engineering alloys
  • Modified Goodman:  \sigma_a = \sigma_{a, \sigma_m = 0} (1 - \frac{\sigma_m}{\sigma_u}) ;
    which is nonconservative when  \sigma_m < 0 . It is however, a good approximation for brittle materials and conservative for ductile alloys, when  \sigma_m \leq 0
  • Gerber:  \sigma_a = \sigma_{a, \sigma_m = 0} (1 - {\frac{\sigma_m}{\sigma_u}}^2) ;
    which is only valid when \sigma_m \geq 0 , as a result of the quadratic term. It is a good approximation for ductile alloys