Issue 37

I.Llavori et alii, Frattura ed Integrità Strutturale, 37 (2016) 87-93; DOI: 10.3221/IGF-ESIS.37.12 88 In general, the study of fretting is divided into two stages, the crack initiation and its subsequent propagation. On the one hand, due to the non-proportional multiaxial state of contact stress field, the use of multiaxial fatigue parameters has become a very popular technique for fatigue life assessment [2]. On the other hand, several studies analyses the propagation phase in terms of the Linear Elastic Fracture Mechanics (LEFM) for brittle materials. In this regard, works such as Vázquez [3] employs analytical methods to estimate cycles to failure. Other works like the one of Giner et al. [4] studies the mechanics of the contact in presence of a crack in a single numerical model due to the advantage of the eXtended Finite Element Method (X-FEM) [5]. However, these studies are mainly focused in the partial slip regime where the removal of material is not important and therefore, do not need to employ wear simulation techniques. In the presence of wear, one of the most prominent works is presented by Madge et al . [6]. First, the numerical simulation of the process of material removal using the Abaqus FEA user subroutine UMESHMOTION is performed. Then, crack initiation analysis using the Smith-Watson-Topper (SWT) multiaxial fatigue parameter coupled with the Miner-Palmgren accumulation damage framework to account the effect of wear is carried out. Finally, the propagation phase is analyzed via submodelling technique. This method allows to transfer the stress state of the contact surface from global wear model to crack submodel. Consequently, the explicit interaction between the fretting contact and the crack can’t be modelled. The aim of this paper is to employ the X-FEM methodology implemented by Giner et al . [4] to explicitly model the interaction between the fretting contact and the crack, to explain the same set of numerical problems analyzed by Madge et al . [4.] Therefore, the developed method combines the Archard wear model, a critical-plane implementation of the SWT multiaxial fatigue criterion coupled with the Miner-Palmgren accumulation damage rule for crack initiation prediction, and the X-FEM developed by Giner et al. [7] in addition to the Level Set Method (LSM) [8] in order to detect the extended elements, for crack propagation prediction. Therefore, the sum of the two stages gives a total life prediction. R EVIEW OF WEAR , CRACK INITIATION AND PROPAGATION CRITERIA Wear law criterion he wear simulation algorithm used in this work is the one presented by McColl et al. [9] for 2D numerical model and used also by Cruzado et al. [10] for 3D simulations. The simulation methodology is based on the Archard wear law, an iterative process in which the local Archard equation is resolved by means of the finite element contact stresses and slip distribution results. However, this process requires a high computational performance, therefore the cycle jump technique is employed [9,10], where it is made the assumption that wear remains constant over a small number of cycles. Thus, the Archard local equation (Eq. 1) is defined as Δh (x,t)=Δn×k×p(x,t)×Δs(x,t) (1) where Δh ( x,t ), Δn , k , p ( x,t ) y Δs ( x,t ) are the incremental wear depth, the cycle jump, Archard wear coefficient, the contact pressure and the relative slip for a specific point at specific time. The wear coefficient used in this work is based on the experimental results of Magaziner et al. [11] which was estimated by McColl et al. [9] and employed later by Madge et al. [6]. Crack Nucleation Criteria As it has been mentioned in the introduction, due to the non-proportional multiaxial state of stress field, the use of multiaxial fatigue parameters has become a popular technique. In this paper the SWT (Eq. 2) criterion [12] is used to predict the location, plane and cycles to crack nucleation.     b b c N N E 2 2 f máx f f f f máx ´ SWT 2 ´ ´ 2 2                 (2) where σ f ´ is the fatigue strength coefficient, ε f ´ is the fatigue ductility coefficient, b is the fatigue strength exponent and c is the fatigue ductility exponent. The fatigue constants used in this paper are the same as the ones employed by Madge et al. [6]. The stress state in the contact zone varies during the test due to wear phenomenon, thereby the SWT value is different for each wear state. One of the most commonly used techniques to take into account these states is the damage accumulation rule of Miner-Palmgren (Eq. 3), defined as T