The curvilinear integral method: Testing 2 (under non-proportional pulsating axial force and internal pressure)

Abstract The curvilinear integral method suggests another mathematical point of view on life prediction: it does not consider cycles of loading and damage summation on cycles, nor reduction to some ‘equivalent quantity’, nor a critical plane, but rather loading differentials d s and summation of damage differentials d D on d s by means of a (curvilinear) integral. Thus the stress-time functions σ x ( t ), σ y ( t ), τ xy ( t ) (components of plane stress) are allowed to be arbitrary. From such a mathematical point of view, the well-known S - N fatigue line, to which we are all accustomed after Wohler, is not the right basis for life prediction under arbitrary stress-time functions; it is only a concrete integral result under cyclic functions (of constant amplitudes). The right basis is searched for behind the integral sign, i.e. at the differential level, as so-called R r , R c and R τ functions. In the present Testing 2, experimental life data by Bhongbhibhat, Dietmann and Schmid under sinusoidal, triangular and trapezoidal wave forms have been used. The data testify for great influence of the wave forms and mainly their mutuality on fatigue life. They could be a touchstone for each life prediction method. The results of Testing 2 are positive for the integral method.