Investigations on a statistical measure of the non-proportionality of stresses

In mechanical engineering fatigue assessment of components, where complex non-proportional loads are acting on, plays an important role to identify critical spots and to predict the lifetime till crack initiation. For this case, a measure for the complexity of local stress states would be very useful to select appropriate criteria or fatigue life calculation methods. In this contribution, a degree of non-proportionality of stresses is investigated, which has been originally proposed by Chu et al. This degree of non-proportionality of stresses is a statistical measure for the variation of principal stress directions. It is shown, how this parameter can be determined for general triaxial stress states, and conditions are derived for mathematical consistency. An example shows that the degree of non-proportionality of stresses can be used even for the compensation of methodical weaknesses of the critical plane criterion, when assessing fatigue effects of local rotating principal stresses for ductile materials such as tempered steel. The critical plane criterion has been used in conjunction with a stress based method (concept of synthetic S/N-curves, which is quite popular in Germany) and linear damage accumulation according Miner’s rule.