Issue 33

M. Cova et alii, Frattura ed Integrità Strutturale, 33 (2015) 390-396; DOI: 10.3221/IGF-ESIS.33.43 391 More simple cases are given by a static loading combined with one time-variable component; in these cases, a proportional variability is combined with a non-proportional static loading; this is a generalization of the loading condition initially investigated in [7]. The overall stress condition is non-proportional, but it is less complex than previous general case. The presented research addresses this last case. It is explicitly established for fatigue damage assessment of materials dependent on principal stress variations. Anyway, its application to more general cases is possible. More precisely, the following discussion deals with the problem of determining the direction of maximum damage in cases of an external static loading combined with one or several variable loading, ranging from null to a maximum value (in the following called pulsating loadings). - In the first case, we will deal with the treatment of one single external pulsating loading combined with a static load. - In the second case, superimposed to a static load, there will be the combination of two pulsating loading; the time variable loading shall act separately, i.e. disjoint in time. S UPERPOSITION OF INDEPENDENT STATIC AND PULSATING LOADING et us consider a point C of a structural component, loaded, in a period 0-T, by a static loading superimposed to an independent time-variable loading. The resulting stress tensor will be the sum of a constant value [σ] S and a time variable component. Assuming that the time variable components ranges from zero to a value [σ] V , the overall stress tensor can be indicated as:           1 S V t f t      (1) Where, the function f 1 varies continuously from zero to 1 and back to zero, in the time interval from t 1 to t 3 ; elsewhere f 1 is null, see Fig. 1. Figure 1 : qualitative trend of function f1, related to the case of a single time variable component. The versor “n” defines a generic direction at point C. The normal stress σ n , acting on the plane defined by the versor “n”, is given by:             1 T T T n S V t n t n n n n n f t        (2) Due to the properties of the time variable function, the maxima and minima will necessarily occur at t 1 and t 2 alternatively. It is possible to evaluate the mean value and the amplitude of the normal stress:     ,max ,min , 1 2 2 n n T T n m S V n n n n          (3) L