Issue34

R. Citarella et alii, Frattura ed Integrità Strutturale, 34 (2015) 514-523; DOI: 10.3221/IGF-ESIS.34.57 515 From the analysis of the SIF results related to the initial cracked configuration (for such scenario also SIF results obtained by the FEM code ZenCrack have been added for cross comparison), it is possible to assess the impact of the press fit condition when superimposed to the bending load case. Due to the symmetry of the problem a nearly pure mode I crack propagation is realised (K II and K III turn out to be negligible) with no kinking of the propagating crack. The crack growth analysis is nonlinear because of normal gap elements used to model the press fit condition with added friction, and is developed in an iterative-incremental procedure. P ROBLEM DESCRIPTION AND DBEM MODEL Introduction he case study, designed by Sander et Al. [14], represents a four point bending hollow axle in a symmetric configuration (Figs. 1, 2), so that just half axle needs to be modeled in the DBEM environment. Three different load cases have been considered: - bending load case; - press fit load case; - combined load case with simultaneous allowance for bending and press fit . Figure 1 : Drawing of the hollow axle and hub, with highlight of the symmetry plane. Symmetry plane Figure 2 : Drawing of the cracked hollow axle with detail view of crack and fillet double radius. Uncracked DBEM model The DBEM model is made up of two different zones, one for the axle and the other for the hub; the mesh is based on quadrilateral or triangular elements with quadratic shape functions and is not needed on the symmetry plane (Fig. 3). The bending load is obtained by applying a uniform traction distribution on one axle side, whose resultant force is equal to 200 kN, and a point force, equal to 200 kN, in the hub; springs of negligible stiffness are added (on the internal diameter, close to the symmetry plane) in X, Y, Z directions to apply the rigid body constraints (Fig. 3). The modelling of press fit loading due to an interference of 0.28 mm related to the axle’ diameter, comes from the use of gap elements (the corresponding normal gap value is equal to 0.14 mm) at the axle-hub interface (Fig. 3); moreover a frictional contact is considered with friction coefficient μ = 0.6. The latter kind of nonlinear loading involves an incremental-iterative solution procedure. T Symmetry plane