E. Giner et alii, Frattura ed Integrità Strutturale, 35 (2016) 285-294; DOI: 10.3221/IGF-ESIS.35.33 286 contacting body is constant with time, whereas the substrate is subjected to cyclic fatigue load. As shown in experimental tests carried out by the authors [1] (see Fig. 1) and in many works in the literature, cracks emanating from the edge of a contact pressing onto a surface tend to grow with a slight deviation inwards beneath the contact and not fully perpendicular to the applied bulk stress. This slight deviation from the normal direction cannot be predicted using a conventional orientation criterion, such as the maximum tangential stress criterion (MTS) and this is the main motivation of this research. Figure 1 : Micrographs for the propagation of non-failure cracks of four tests [1], emanating from the edge of contact. As a result of previous investigations [1], the nonproportional character of the load evolution precludes the application of conventional crack orientation criteria in LEFM for propagating cracks. In a previous work [1], we proposed an orientation criterion based on the minimum range of the shear stress ahead the crack tip, min( ). This criterion has been successfully applied to the prediction of the orientation of long cracks in nonproportional configurations found in fretting fatigue. Continuing with this study, we analyze in this work the influence of several a priori relevant parameters on the crack orientation, such as the normal contacting load, fatigue bulk load, stress ratio R , stiffness of the materials involved, etc. We have found that the amount of contacting normal load is not a relevant magnitude affecting the crack orientation. Contrary to previous expectations, the relative difference in stiffness between indenter and substrate is the parameter that has the greatest effect on the direction of crack propagation. The numerical analysis is performed using the standard finite element method (FEM) and extended finite element method (X-FEM), taking into account the crack face contact along the loading cycle, as implemented by the authors [2]. To predict the crack direction in each step of the crack growth simulation, we use the criterion of min( ) [1], as reviewed in the next section. T HE CRITERION OF THE MINIMUM SHEAR STRESS RANGE rom the numerical analyses and for the geometric and loading configuration considered in this work, it is found that the crack remains closed during a large part of the loading cycle. The application of some of the criteria previously reported and reviewed in [1] did not lead to good predictions of the actual crack path as observed in the experimental tests performed. Consequently, it can be argued that the stress state existing under a crack face contact condition has an important influence to be considered. Assuming an elastic behaviour, the stress state under crack face contact conditions must be essentially controlled by K II , the only stress intensity factor that can exist for a totally closed crack in 2D. The criterion proposed here is a generalization for non-proportional loading of the so-called “criterion of local symmetry” well established for proportional loading, see Cotterell and Rice [3]. The criterion of local symmetry states that the crack F

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