Issue 37

J. Vázquez et alii, Frattura ed Integrità Strutturale, 37 (2016) 38-45; DOI: 10.3221/IGF-ESIS.37.06 40 Fig. 2 shows the fretting scar and the fracture surface in this test on the opposite side of the main crack. Three semi- elliptical cracks can be clearly seen. The initiation points are marked with a red dot. The fretting pad surface roughness caused the appearance of the scar with vertical bands. The black area corresponds to the slip zones of the contact. Also, it can be seen that the cracks initiated at the contact trailing edge ( x = a) or inside the slip zone. In order to measure the crack initiation angles and path, the fracture surface was analysed with a confocal microscope, obtaining the image shown in Fig. 3, where colour code means the distance from the failure surface to a reference plane. The resolution of the data obtained is 0.65 μm in the plane of the crack ( yz plane) and 2 - 3 μm in the x direction. The initiation point is marked with a white dot. This image shows that the initiation point appears at the top of a “hill”, i.e. the crack grows around the initiation point with a certain angle towards the inside of the contact and then becomes perpendicular to the contact surface. This paper pays attention to the first zone, which appears red coloured in the image. The surface data was exported to a text file. Afterwards, several straight radial lines were drawn starting at the initiation point and at different angles (-45º, -35º, -25º, -15º, -5º, 5º, 15º, 25º, 35º, 45º), being 0º the line perpendicular to the surface. The crack surface along these lines is shown in Fig. 4 for each of the three cracks in the specimen. The cracks profile are adimensionlised with the fictitious (from a linear elastic analysis) semi-width of the contact, a = 2.33 mm in Fig. 1. This dimension is calculated assuming that the real contact length is not 7 mm but 3.45 mm, as explained later. It can be seen how the crack grows almost perpendicular to the surface for the first 20 μm and then turns towards the inside of the contact with an angle between 20 and 28 degrees from the line perpendicular to the contact. Figure 3 : Confocal microscope image of crack 2. C RACK INITIATION ANALYSIS n this section, an attempt to reproduce the experimentally observed crack initiation path is made. Three different crack initiation procedures are used in this analysis. The three of them are based on the well known Fatemi-Socie (FS) [[16]] and Smith-Watson-Topper (SWT) [[17]] multiaxial fatigue parameters and will be described later. As mentioned earlier, the fretting surface scar, Fig. 2, is not ideal and it is obvious that the contact zone is far from being uniform due to an excessive roughness -along the horizontal direction- in the specimen surface and mainly in the fretting pad. To consider this effect in the crack initiation procedures, it is assumed that both normal and tangential loads per unit length are obtained dividing the total load by the real contact length in the horizontal direction. By a digital image processing it is obtained that the real contact length in the horizontal direction is 3.45 mm, leading to a normal and tangential loads per unit length of 1682.2 and 246.4 N/mm respectively. A 2D (plain strain) linear-elastic analysis using the analytical equations for the mechanical contact between a half-plane and a cylinder [[19]], and considering the above loads with an axial stress of 50 MPa, shows that the maximum von Mises stress produced is less than the yield stress for this material. If in addition, it is considered that the crack initiation phase is only influenced by the very-near surface strain/stress field, therefore, the use of the above linear-elastic model can be justified to analyse the crack initiation process. First Crack Initiation Analysis Procedure A scheme of such a procedure is shown in Fig. 5. First, at the trailing edge ( x = a , y =0) the direction which gives the maximum value of the parameter (critical plane) is obtained. The search for this maximum is only done in the xy plane and using increments of 0.1 degrees for the search. Once the critical plane at the trailing edge is found, it is assumed that I 0 100 200 μm