Issue 37

I.Llavori et alii, Frattura ed Integrità Strutturale, 37 (2016) 87-93; DOI: 10.3221/IGF-ESIS.37.12 89 k i i i n N 1     , (3) where ω is the total accumulated damage (nucleation is defined to have occurred when the parameter reaches the value of 1), n i is the number of cycle completed in each wear stress state and N i is the theoretical number of cycles to failure predicted by the SWT parameter for each wear stress state. In this paper, the implementation of the Miner’s rule presented by Cruzado et al . [13] has been employed. Crack Propagation Criteria To estimate the second phase of the presented method, a crack growth law of the type da/d N = f (Δ K ) based on the LEFM has been used to determine the crack propagation rate. The model relies the correct calculation of the Stress Intensity Factor (SIF) on the X-FEM, using the J integral through the interaction integral. Thus, the effect of the crack/fretting-contact evolution can be analyzed in a single numerical model as shown by Giner et al . [4]. The fracture constants used in this paper are the same as the ones employed by Madge et al . [6]. In this work, it is assumed that the crack propagation takes place under mode I, e.g. Δ K = K I max , since K I min is almost 0 due to stress ratio being R = 0.03 and perpendicular to the initial contact surface. E XPERIMENTAL TEST DESCRIPTION he fretting fatigue experimental tests selected for comparison purpose is reported in the literature by Magaziner et al. [11]. The test machine shown in Fig. 1 consists of two servo-hydraulic actuators. The main actuator controlled the alternating axial load ( σ ) of the fatigue specimen, while the secondary actuator controlled the tangential load ( Q ). Thus, the test machine is capable to perform a combined fretting fatigue and wear test. The selected tests are 9A and 10A, and the amplitude of displacement between the fretted bodies are δ = 36 µm and δ = 104 µm respectively. Figure 1: Schematic of cylinder on flat fretting fatigue test configuration [11]. N UMERICAL MODEL he model shown in Fig. 2 has been developed in the commercial code Abaqus FEA. Due to the typical fretting fatigue testing geometry, half the specimen has been modelled as in references [2,3,4,6]. The model consists of linear quadrilateral elements of 4 nodes (CPE4), with further refinement on the contact neighborhood by the partition technique. In order to obtain a precise slip distribution, the Coulomb and the Lagrange multipliers methods have been used to model the tangential contact. Fig. 3 shows the developed coupled wear, crack initiation and crack propagation numerical flow chart. T T