Issue 30

F. Curà et alii, Frattura ed Integrità Strutturale, 30 (2014) 446-453; DOI: 10.3221/IGF-ESIS.30.54 448 XFEM MODELS n this work the crack propagation path has been investigated by means of extended finite element (XFEM) models. Fracture mechanics isnot properly implemented in the classical FEM models. As a matter of fact crack propagation is defined by geometric entities which are treated as the new endpoints of the structure. It follows that the mesh must be consistent with the crack position. In order to consider the singular stress field near the crack tip, it is necessary to provide an area with a particular mesh. This start point involves a complication in the mesh management, especially when studying the crack growth, as this requires a redefinition of both geometry and mesh at each calculation step. These limitations may be overcome by the technique eXtended Finite Element Method (XFEM) [14]. With this technique, the finite element mesh is enriched by incorporating local functions to represent the jump in the displacements along the crack and near the tip. The mesh does not have to match the position of the crack and it is no longer necessary to define an area of the crack in the mesh, as the singular stress field is included in the problem. The study of the crack propagation can be done without proceeding with a new phase of re-meshing, but simply making sure that the mesh is fine enough in the area of the crack tip in order to obtain accurate results. This investigation has been carried on by using a thin rim gear made of steel, which main characteristics are resumed in Tab. 1. Modulus [mm] 7.4 Teeth number 28 Pitch Diameter [mm] 206.4 Pressure Angle [°] 20 Face width [mm] 8 Table 1 : Gear parameters. m B W [mm] Full Gear 8 1 4 0.5 4 0.4 4 0.3 4 Figure 2 : Gear geometric parameters: tooth height (H), rime thickness (B), web thickness (W). Table 2 : Gear geometric parameters. Different models have been created by varying rim thickness B, crack position and crack orientation. From the geometrical point of view, five rim thickness values have been considered, referred to the tooth height, as generally reported in literature. This geometrical parameter is known as backup ratio m B and it is indicated as the ratio between rim thickness B and tooth height H: m B = B/H. Two different web thickness values have been also considered. The above quoted geometrical parameters are resumed in Tab. 2. Cracks have been positioned on five points equally distributed along the tooth root fillet, starting from the involute up to the middle of the tooth vane (Fig. 3). So for each gear geometry (see Tab. 2), five cases have been run. The effect of the initial crack orientation has been taken into account, in the full gear, by considering three different conditions: the first one with the crack perpendicular to the tangent of the tooth root fillet, second and third ones respectively with 45° clockwise and counterclockwise directions (Fig. 4). I