Rail surface crack initiation analysis using multi-scale coupling approach

A concurrent multi-scale computational strategy for rail surface crack initiation analysis is introduced in current paper. It attempts to take advantage of the efficiency of macroscopic models and the accuracy of the mesoscopic models. The solving procedure is , through the coupling of individual approaches, beginning from the largest scale to the smaller scale, making use of multi-body dynamic(MBS) simulation, explicit finite element(FEM) analysis, sub-modelling technique as well as crack initiation analysis. The main idea of the seamless handshaking algorithms at the interface of the respective approaches is presented. A unified description of crack initiation analysis is built up by linking the models at different scales. Moreover, the surface and sub-surface stress/strain distributions under the wheel-rail rolling contact loads are obtained from coupled simulations. Based on the stress/strain response, the critical plane orientation of surface crack initiation is predicted. It can be concluded that the proposed numerical procedure can provide much accurate and realistic outcomes for rail surface crack initiation analysis in comparison with performing an simulation only on one scale level. of such FE models is not allowed to be refined to a desired level for crack initiation analysis resulting from the fact that the dimensions of wheels and rails are considerably bigger than the ones of the crack. A study in(Liu et al., 2006) introduced a sub-modelling technique into fatigue life prediction on wheels to overcome this problem. While the feasibility of sub-modelling technique on W/R rolling contact analysis has not yet been verified. Moreover, quasi static loads instead of dynamic loads are applied on the sub-model, which is questionable for the accuracy and effectiveness of sub-modelling approach. In order to overcome the above mentioned restrictions, a multi-scale coupling approach for rail surface crack initiation analysis is proposed in current study. This paper is organized as follows: the main procedure of computational multi-scale coupling strategy is presented in section 2, which is followed by wheel-rail interaction analysis in macro scale and mesoscale. Moreover, crack initiation analysis will be demonstrated in section 4. Finally, concluding remarks will be presented. 2 COMPUTATIONAL MULTI-SCALE COUPLING STRATEGY In many problems related to material science, the interactions among ultimate microscopic constituents of materials determine the behavior of the material at macroscopic scale(Lu and Kaxiras, 2004). In order to capture the multi-scale behavior present at a material, numerous multi-scale modelling approaches has been proposed to fulfill different purpose of engineering applications(Li et al., 2010, Yang et al., 2014, Bertolino et al., 2007). However, in the research field of railway engineering, few investigations on wheel-rail interaction using multi-scale approach have been reported so far. 2.1 Multi-scale definition In the context of simulations on wheel-rail interaction, different idealizations and numerical approaches are used to model its response behaviour under variable length scale, wherein one can distinguish four characteristic length levels: 1) Complete macro-scale – vehicle-track interaction, built with MBS model, where a complete vehicle-track system as shown in figure 1(a) is considered and the length of the track normally can be ranged from one to a couple of kilometres. 2) Component macro-scale – wheel/rail components interaction denoted as figure 1 (b), where the dimensions of the wheel and rail model is limited to the order of meter. In this scale, explicit FEM method is routinely utilized to examine the dynamic response between two contact bodies. Sophisticated constitutive laws instead of rigid or elastic assumptions made in MBS simulation, are always employed to describe the material behaviour of the physical system. 3) Mesoscopic scale – rail FEM sub-model as shown in figure 1(c), in which the study on surface initiated crack can be implemented at a desired mesh refining level in the order of 0.1mm. The crack initiation mechanism resulting from dislocations, grain boundaries, and other microstructural defects are able to be unveiled by running the sub-model simulations. 4) Microscopic scale ( in the order of a few micro-meters as shown in figure 1(d)) goes one step further, where atoms are the major players and their interactions can be highlighted by classical interatomic potentials(Lu and Kaxiras, 2004). Herein, our study is only limited from macroscopic to mesoscopic scales, the micro-scale analysis is beyond the scope of this research. Since none of the methods alone would suffice to describe the entire wheel-rail contact system, the goal becomes to develop a coupled macroscopic–to-mesoscopic computational approach which means coupling different methods specialized at different length scales, effectively distributing the computational power where it is needed the most, as well as taking advantage of the efficiency of macroscopic models and the accuracy of the mesoscopic models. Figure 1. Schematic graph of multi-scale coupling strategy for crack initiation analysis. a) Complete macro scale –vehicle/track interaction; b) Component macro scale – wheel/rail interaction; c) Mesoscale – Rail sub-model crack initiation analysis; d) Micro scale – Rail micro-crack analysis(Franklin et al., 2011, Steenbergen and Dollevoet, 2013). 2.2 Interface handshaking algorithm Conceptually, two categories of multi-scale simulations can be envisioned, sequential and concurrent. The differences between the definition of sequential and concurrent approaches can be found from (Lu and Kaxiras, 2004). In this paper, a concurrent approach integrating with MBS simulation, explicit FEM analysis, sub-modelling technique as well as crack initiation procedure is developed. A smooth coupling between different scales is organized as below: 1) Complete MBS analysis / Component explicit FEM coupling: To achieve the MBS and explicit FEM hand-shaking, a complete MBS model should be generated firstly. Using the surface crack initiation criteria proposed by (Ekberg et al., 2002), the most critical region over the global track for surface crack to occur will be identified. Following that, a limited length of rail FE model together with a wheel component FE model is produced to simulate the dynamic stress/strain response over the most critical region. The relative contact positions between wheel and rail, wheel running velocities, real-time wheel axle loads obtained from MBS simulation will be transformed into a FE load-vector and applied on the wheel component as dynamic boundary conditions. 2) Component Explicit FEM / Meso – Sub-model coupling: The nodal interface loads ( restored in NCFORC result file) obtained from transient wheel-rail explicit FEM analysis will be used as a input for the settlement of coarse full-model boundary conditions. Here, only the rail is considered in the coarse full-model analysis and the nodal interface loads in substitution for the functionality of the wheel are applied on the rail contact patches. After finishing the coarse full-model analysis, refined sub-model as shown in figure 1(c) will be created and its boundary nodes will be stored into a file for displacement interpolation with the full-model result file. The calculated displacement on the cut boundary of the full-model will be used as boundary conditions for sub-modelling analysis. By doing the cut boundary verification and stress-strain post-processing analysis, the coupling between component explicit FEM analysis and sub-modelling simulation will be fulfilled. The validity of the sub-modelling procedure should be further confirmed through comparison with the dynamic simulation results. 3) Meso – Sub-model / Crack initiation analysis coupling: The material planes that are candidate for the maximum damage critical plane is determined by computing the transformation matrices for a given set of angles. The stress tensor and strain tensor at each history point obtained from sub-modelling analysis will be imported to crack initiation procedure. The fatigue parameters defined by critical plane approaches will be computed by rotating the material planes. In the end, the material planes with the maximum fatigue parameters will be viewed as the potential orientation for the crack to initiate. 3 RESULTS AND DISCUSSION Following the computational multi-scale coupling strategy discussed in section 2, numerical simulations will be implemented at different scales. As a consequence, results and discussions will be presented in this section. 3.1 Complete macro-scale – MBS In this scale, vehicle bodies, suspensions, subgrade, wheelset represented by springs, dashpots and masses are all assumed to be rigid or elastic bodies. Running through the simulation, it is possible to determine the contact conditions, track load and vehicle stability performance. Typical examples can be found in (Shevtsov, 2008, Wan et al., 2013). 3.1.1 MBS model A three-dimensional MBS model for a specific Dutch railway curved line is built up in the multi-body simulation software Adams/VI Rail. For the vehicle model, standard Manchester passenger wagon with double wheel-sets in the front and the rear of the car body is utilized, in which the wheel profile is chosen as standard S1002 and the rail profile is UIC54E1. Simulations are implemented with a train speed of 140 km/h over the track, which is considered as a total length of 1000m involving a 400m curved track with the radius of 1000m. The transition region between curves and tangent track is assumed to be 100m. Regarding the contact mode, General Contact Element (WRGEN) using actual wheel and rail profile to calculate the actual contact kinematics at each simulation step is used in the simulations. WRGEN evaluates the local contact stiffness based on geometry and materials properties. 3.1.2 Dangerous region identification The fatigue index for surface initiated fatigue is based on the theory of elastic and plastic shakedown in general, and shakedown map theory in particular. The fatigue index is expressed as: