Issue 16

L. Susmel, Frattura ed Integrità Strutturale, 16 (2011) 5-17; DOI: 10.3221/IGF-ESIS.16.01 9 the crack faces, it is logical to presume that the value of the mean stress sensitivity index changes as the microstructural features of the material being assessed vary. To conclude, it is worth observing that not only to estimate m correctly but also to apply the MWCCM properly, a multi- parameter optimisation process has to be run to unambiguously determine the orientation of the critical plane [28]. As to such a tricky aspect of the multiaxial fatigue issue, it has to be said that this laborious modus operandi is a direct consequence of the classical fatigue damage model on which the MWCM is based [11, 29]. In fact, independently from the complexity of the time-variable stress state damaging the material point at which the stress analysis is performed, there always exist two or more material planes experiencing the maximum shear stress amplitude, so that, amongst all the potential critical planes, the one which has to be used to calculate mean stress sensitivity index m as well as to perform the fatigue assessment is the plane experiencing the largest value of the maximum normal stress. V ALIDATION BY EXPERIMENTAL RESULTS n order to show the accuracy of the MWCM in estimating high-cycle fatigue strength under multiaxial fatigue loading, a systematic bibliographical investigation was carried out to select an appropriate set of fatigue results. In more detail, initially attention was focused on multiaxial endurance limits generated by testing un-notched samples. In the most general case, the applied loading paths included in-phase and out-of-phase situations (combined axial loading, bending, torsion and internal/external pressure) with and without superimposed static stresses, the applied stress components being defined as follows (see Fig. 2 for the adopted frame of reference):   xxy xy axy mxy xy xy y ay my y x ax mx x t t t t t t , , , , , , , , sin )( ) sin( )( ) sin( )(                        (11) In the above sinusoidal stress signals, subscript m and a denote the mean value and the amplitude of any stress components, respectively,  x ,  y and  xy are the angular velocities, whereas  y,x and  xy,x are the out-of-phase angles, both measured with respect to signal  x (t). Further, also a number of results generated under the complex loading paths sketched in Fig. 3 were considered in the validation exercise discussed in the present section. Tab. 1 summarises the static and fatigue properties of the materials of which the unnotched samples tested under multiaxial fatigue loading were made. Tab. 2 instead lists the experimental values of mean stress sensitivity index m for those materials having m lower than unity. Figure 3 : Investigated complex loading paths.