CRITICAL PLANE APPROACHES IN HIGH-CYCLE FATIGUE: ON THE DEFINITION OF THE AMPLITUDE AND MEAN VALUE OF THE SHEAR STRESS ACTING ON THE CRITICAL PLANE

Critical plane approaches are useful methods when designing against long-term fatigue of machine components made from metals. Somewhat surprisingly, the very basic problem of the evaluation of the amplitude and mean value of the shear stress acting on the critical plane is still not resolved satisfactorily for non-proportional cyclic loading conditions. In the present paper, existing proposals for solving this problem are briefly reviewed and their weaknesses highlighted. Then it is shown, through particular examples, that application of these proposals can lead to ambiguous results. Therefore, new definitions of the amplitude and mean value of the shear stress acting on the critical plane are formulated here. These new definitions are free from any ambiguity because they are based on the construction of the unique minimum-circumscribed circle to the path described by the shear stress on the critical plane. The centre of this circle defines the mean shear stress, whereas its radius provides the corresponding shear stress amplitude. The algorithm yielding this minimum-circumscribed circle is presented in some detail.