PSI - Issue 39

A.L. Pinto et al. / Procedia Structural Integrity 39 (2022) 409–418 Author name / Structural Integrity Procedia 00 (2019) 000–000 3 where, Δ ℎ is the threshold stress intensity factor range and Δ −1 is the uniaxial plain fatigue limit range, both obtained under fully reversed loading configurations. 3. Methodology This work presents two different methodologies for predicting the crack initiation direction when fretting under partial slip conditions takes place. In one of them, the CDM is used in conjunction with the SWT parameter. Alternatively, one also investigates a methodology based on LEFM crack propagation principles, which also relies on the SWT model. The LEFM approach here investigated is often applied to model Stage II cracks. Here, on the other hand, one tests the applicability of this theory in modelling early crack propagation. In the next subsections, more details are given concerning methods here investigated. 3.1. Method 1: Critical Direction Method Consider a 2 length line oriented by an angle with respect to the axis perpendicular to the contact surface, Figure 1. In this case, the CDM basically consists in averaging stresses and strains over each possible line for further application in some multiaxial fatigue parameter. In this setting, the critical direction, i.e., the crack initiation orientation, is given by the angle that maximizes the considered multiaxial fatigue parameter. It is worth noting that during the averaging process along any oriented line, stresses and strains are always computed on the same planes. For the application of the CDM in conjunction with SWT parameter one needs to compute average normal stresses and strains for each possible orientation over time: � ( , ) = 2 1 ∫ ( , , ) 0 2 , (3) ̅ ( , ) = 2 1 ∫ ( , , ) 0 2 , (4) where � ( , ) and ̅ ( , ) are the average normal stress and strain components, respectively, for a given line at the time . Now, the obtaining of terms appearing in the SWT parameter (Eq. 1) is straightforward: � , ( ) = � ( , ), (5) ̅ , ( ) = 1 2 � ̅ ( , ) − ̅ ( , ) � . (6) where � , ( ) and ̅ , ( ) are the maximum normal stress and normal strain range, respectively, for a given direction. According to the critical plane definition considered in this work, crack initiation direction can be found by maximizing Eq. 6 with respect to . 411