Issue 16

L. Susmel, Frattura ed Integrità Strutturale, 16 (2011) 5-17; DOI : 10.3221/IGF-ESIS.16.01 8 where  n,min and  n,max denote the minimum and the maximum value of the stress perpendicular to the plane of maximum shear stress amplitude, respectively. In order to estimate mean stress sensitivity index m, assume now that endurance limits  A and  A are known from the experiments, so that, the only unknown material property in Eq. (6) is m itself. By observing now that both  A and  A are material fatigue properties generated under fully-reversed loading (i.e., R CP =-1), it is logical to argue that material constant m has to be estimated from a third endurance limit determined under a value of R CP larger than -1. Accordingly, if * a  , * , mn  and * , an  are the critical plane stress components referred to the above endurance limit condition, by rearranging Eq. (6), it is trivial to derive the following identity [11, 19]:             * * , * * , * 2 2 a an A A a A mn a m         (9) which allows m to be calculated directly. As to the expected values for m, it can be said that, since m quantifies the portion of the mean normal stress relative to the critical plane which effectively opens the micro/meso cracks by favouring their propagation [11], such a material fatigue property is expected to vary in the range 0-1: when m is equal to unity, the material being assessed is assumed to be fully sensitive to the mean stress perpendicular to the critical plane; on the contrary, an m value equal to zero implies that the investigated material is not sensitive at all to the presence of superimposed static tensile stresses. With regard to the estimation of the mean stress sensitivity index, it is not superfluous to notice here that, in situations of practical interest, the above material constant can easily be determined by directly using a uniaxial endurance limit generated under a load ratio, R=  x,min /  x,max (Fig. 2), larger than -1. In more detail, under axial or bending fatigue loading with superimposed static stress, it is straightforward to see that the relevant stress quantities relative to the critical plane take on the following values [11]: 2 , , ax an a      ; 2 , , mx mn    (10) where  x,a and  x,m are the amplitude and the mean value of the applied stress, respectively. Figure 2 : Cylindrical specimen and adopted frame of reference. From a physical point of view, the meaning of mean stress sensitivity index m can be explained by taking full advantage of the outcomes summarised by Kaufman and Topper in Ref. [27]. In more detail, by performing an accurate experimental investigation they have observed that, when the mean stress perpendicular to the Stage I planes is larger than a certain material threshold value, an increase of the mean stress itself does not result in any further increase of fatigue damage. This experimental evidence was ascribed by Kaufman and Topper themselves to the fact that, in the presence of large values of the mean stress perpendicular to the growth direction, micro/meso shear cracks are already fully open, so that, the shearing forces are directly transmitted to the crack tips by favouring the Mode II growth. On the contrary, when the mean stress normal to the Stage I planes is lower than the above material threshold value, the effect of the shearing forces pushing the crack tips is reduced due to the interactions amongst the asperities characterising the two faces of the cracks themselves. Since the microstructure morphology varies from material to material by resulting in a different roughness of x y z O