Issue34

C. Ronchei et alii, Frattura ed Integrità Strutturale, 34 (2015) 74-79; DOI: 10.3221/IGF-ESIS.34.07 75 It is important to highlight that the above definitions represent just some of those reported in the literature (a general account on the critical plane orientation is given in Ref. [8]). Among the critical plane fatigue criteria, the modified Carpinteri-Spagnoli (C-S) criterion [9], a simplified version of the original C-S criterion [10], correlates the critical plane orientation with the weighted mean directions of the principal stress through an off-angle,  (which is regarded to be dependent on the ratio between the fatigue limit under fully reversed shear and that under fully reversed normal stress, , 1 , 1 af af     ). Then, the multiaxial fatigue assessment is performed by using a nonlinear combination of the equivalent normal stress amplitude and the shear stress amplitude acting on the critical plane (see Ref. [11] for a general account of the criterion). In accordance with the original idea developed by Carpinteri et al. [9, 10], Łagoda et al. [12] have recently proposed some modifications to the original  expression which, in limit conditions, are pertinent to both mild and very hard metals. The goal of the present paper is to implement the different expressions of the rotational angle  in the modified C-S criterion. In order to verify whether the above expressions are able to improve the fatigue lifetime estimation capability of the criterion, some experimental data available in the literature [13-17] are examined. C RITICAL PLANE ORIENTATION AND FATIGUE LIFE EVALUATION he high-cycle multiaxial fatigue criterion, known as the modified Carpinteri-Spagnoli (C-S) criterion [9], is a simplified version of the original one proposed in Ref. [10]. In particular, the modifications are related to a simplified weighting procedure to determine the averaged principal stress axes, and to the effect of the non-zero normal mean stress on the fatigue limit. Fig. 1 summarizes how to use the modified C-S criterion to estimate fatigue lifetime of structural components failing in high-cycle fatigue regime. Figure 1 : Graphical representation of the modified C-S criterion. In particular, from the stress state at a material point P , the averaged directions of principal stress axes can be determined on the basis of their instantaneous directions by means of the averaged values of the principal Euler angles. The orientation of the critical plane is linked to the above averaged directions through the rotational angle  :   2 1 , 1 , 1 3 2 1 45 af af               (1) T