Shake-Down Effect on Fatigue

Going back to the Goodman line we may say that the safety domain of Fig. 5.32 is not totally accessible, meaning that not really all mean stress values may have an effect on fatigue. As matter of fact, not always falls down to zero as goes to r , as Eq. (5.50) would predict. This is because, a stress amplitude value Of ax exists below which, under particular loading conditions, it is not possible to go, whatever the mean stress may be. To understand it, suppose to be dealing with an elastic-ideally plastic material whose characteristic is that of Fig. 5.42. This 

5 Stress-Based Fatigue Analysis High Cycle Fatigue 

It is also evident that the shake-down effect has produced a decrease of the mean stress acting on this new material that will not be any more but a r , median point of line DB of Fig. 5.42 

It is indeed worth to recall that the shake-down effect is possible only when the plastic volume is confined and very small with respect to the elastic one that has to control the process. This is the case of a thin beam in bending or a small hole or a sharp discontinuity whose associate plastic zone is embedded in the elastic surrounding and remains negligible. But when the plastic volume enlarges, as in a thick beam in bending or a large hole, the shake-down effect may not take place completely. Depending on the ratio of the plastic zone volume to 

It must be underlined that the reduction of the mean stress just described with the hypothesis of cycles fluctuating from zero (R — 0) remains valid also in the more general case of g 0. As to these cases, it is worth noting that a very low stress amplitude superposed to a very high mean stress may not get any benefit (no mean stress reduction) if condition 2. in Eq. (5.57) ffa + Cm Oy is not verified. If 

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