The mechanisms of squat formation on train rails

Figure 1: Computation of tlie initial geometry of a 92 yarn braided rope : (a) starting configura-tion - (b) computed initial configuraconfigura-tion

Figure 2: Cross-sections of the starting (a) and computed initial (b) configurations

sufficient separation between yarns is reached, standard contact conditions are considered, and an initial equilibrium configuration, satisfying the braiding pattern, is obtained (Fig. 1-b, 2-b).

Simulation of test loading cases

Once the initial configuration has been computed, various loading cases can be applied to the model in order to identify the mechanical properties of the structure. Comparisons with experi-mental data will be presented.

References

[1] A. Pickett, J. Sirtautas, and A. Erber. Braiding simulation and prediction of mechanical properties. Applied Composite IVlaterials, 16:345-364, 2009.

[2] D. Durville. Contact modelling in entangled fibrous materials. In Giorgio Zavarise and Peter Wriggers, editors, Trends in Computational Contact Meclianics, volume 58 of Lecture Notes

in Applied and Computational Meciianics, pages 1-22. Springer Berlin / Heidelberg, 2011.

[3] D. Durville. Composite reinforcements for optimum performance, chapter iViicroscopic approaches for understanding the mechanical behaviour of reinforcements in composites. Woodhead Pubhshing Limited, 2011.

182

The mechanisms of squat formation on train rails

Delft University of Technology, Faculty of Civil Engineering and Geosciences, Railway Engineering Group, Stevinweg 1, 2628 CN Delft, the Netherlands. Email: M.J.M.M.Steenhergen@tudelft.nl

Summary: A theory is presented explaining the origination and nature of squat defects on train rails. It is validated with the help of field observations and measurements and destructive microstructural analysis. The analysis involves and combines both metallurgical and mechanical aspects of the wheel-rail contact problem.

Squat railhead defects have been subject of research during the last two decades by different researchers. In recent years investigations have been intensified, particularly in the context of a growing presence of this defect on several rail networks throughout the world. Because unlimited squat growth leads to rail fracture, it constitutes a danger to the railways both in terms of safety and of monitoring and maintenance. Although squats are commonly considered as railhead defects belonging to the Rolling Contact Fatigue (RCF) family, existing views are not uniform, in the sense that the precise nature of the defect and several typical features remain not understood.

A squat defect is characterised by a number of visual criteria (Fig. 1): it appears in the running band of the rail; it shows an unbranched or branched (typically V-shaped) surfacebreaking crack pattern with linear cracks under an angle with the rail axis, and it is -when maturing - accompanied by a local darkening of the surface (in the case of a V-crack showing two lobs) along with a widening of the running band.

Figure 1: Examples of an unbranched and a branched squat

Destructive, microstructural analysis of the top layer of the rail in longitudinal and transverse direction shows a metallurgical key principle of crack initiation: the formation of a white etching layer (WEL) on top of the railhead, formed under repetitive wheel-rail contact introducing high shear tractions on the rail surface. The repetitive contact tractions exceeding the elastic material limit cause a continuous process of plastic strain accumulation and work hardening. Strain saturation of pearlite leads in the final stage, when grain refinement is no longer possible, to cementite decomposition. The WEE has a quasi-amorphous nanocrystalline structure with an extreme hardness and brittleness. It appears in the form of individual and isolated nucleations, forming spatially uniformly distributed islands embedded in the surface, expanding in time and growing together. In this sense, a clearly distinct layer with alternative constitutive properties is formed on top ofthe rail in the contact band as a function of borne tonnage.

Cracks are found to initiate by a double principle: edge delamination of white etching islands and transverse fracture of white etching material.

The microstructural analysis also shows a deeper effect of the response to the moving wheel-rail contact stress field: the pearlitic top layer of about 100 ^im is strongly deformed and has a three-dimensional anisotropic texture. In the longitudinal direction, this is caused by the shear tractions resulting from driven wheels and directed opposite to the running direction, whereas in transverse direction this is caused by the shear stresses arising due to the inclination ofthe rail and directed towards the rail gauge face.

The surface-breaking crack pattern has two general appearance forms: an unbranched pattern, and a branched pattern, typically in the form of a ' V ' . The first pattern shows a single, linear crack, under an angle with both the longitadinal axis and the transverse direction, in the running band of the rail. The latter pattern generally consists of two branches, of which one is leading in magnitude, and the other is trailing. The angles of both branches however in general show symmetry with respect to the transverse direction. The geometrical properties o f t h e leading branch are identical to that of the single branch o f t h e first pattern. . , n + Analysis ofthe three-dimensional crack morphology shows a propagation ot the crack tronts under each surface-breaking crack into the deeper material; the V-shaped defect develops two 'wings', and on the surface two dark-colored lobs appear, enveloping the crack pattern. The crack front o f t h e leading (or single) crack hereby follows the texture o f t h e deformed microstructure, whereas the trailing crack front breaks crosswise through the material texture.

Mechanical interpretation ofthe crack patterns shows that the single or leading crack is a shearinduced fatigue crack, developing perpendicular to the principal tensile direction -associated to the bi-directional shear stresses - in the contact plane, and connecting multiple crack nucleations from white etching material in a straight line.

The trailing crack ofthe branched squat is explained by the following hypothesis. Due to the growth o f t h e shear-induced fatigue crack the shear load redistributes. I f the local material properties and the response under the redistributed contact stress field yield a critical combination, a failure mechanism is formed; the load-bearing surface layer 'collapses', m the form of a wedge, in the contact patch under the transverse shearing load towards the rail gauge face. In the contact patch, the transverse shear stress field forms a semi-ellipsoid according to the Hertzian theory. Within this bi-linear mechanism, one o f t h e branches is given by the shear-induced and pre-existing crack, leading both in time and in magnitude, whereas the trailing one results from brittle fracture, running necessarily crosswise through the microstructure because o f t h e angle of this branch with the rail axis and its anisotropy. Confirmation of this hypothesis is found in the microstructure around the trailing crack tip and in the distinct properties of both crack planes: the fatigue crack has smooth faces, whereas the trailing crack has sharp and rough faces.

Whereas the presence of the trailing crack is important for the contact surface modification, the leading crack dominates the process of fatal crack growth into the rail and rail fracture, as it can propagate over much larger lengths and to larger depths.

The modification of the contact surface during squat growth is a resuh of redistribution of mainly normal contact stresses and of dynamic wheel-rail interaction. The failed material portion gets bordered by an increased hardness envelope, visible on the surface as a dark-colored zone. It is then pressed into the deeper elastic material, accompanied by a gradual expansion of the contact band as a function of the rail surface deformation in normal direction and owing to the transverse curvature ofthe railhead.

The propagation of crack fronts into the deeper material appears to be governed by several factors: oxidation of crack faces and crack tips, the local microstructure of the railhead along the crack path, the longitudinal residual stress field in the rail profile showing strong gradients, and the progressive surface modification, leading to dynamic wheel-rail interaction and continuous redistribution in both the loading and the responsive stress field.

184

A micronechanical approach for the derivation of

a damage-friction interface model

Elio Sacco', Frédéric Lebon^

'Dipartimento di Meccanica, Strutture, Ambiente e Territoria, Universitd di Cassino, Italy (sacco @ unicas. it)

'-LMA, Aix-Marseille Univ, CNRS, UPR 7051, Centrale Marseille, F-13402 Marseille Cedex 20, France {I ebon @ Ima. cnrs-mrs.fr)

Summary: The present paper deals with the derivation of interface model based on a micromechanical analysis, which is able to couple the damage evolution, the non penetration conditions and the friction effect. The solution of the micromechanical problem is determined considering three subproblems and properly superimposing their solutions. Numerical tests are developed.

Introduction

Interface models characterized by nonlinear effects as friction and damage, formulated in the framework of continuum thermodynamics, have been presented in literature [1,2].

A derivation of interface model which takes into account the contact and the friction as well as the evolution of the damage has been presented in [3]. The considered interface damage is governed, at a micromechanical level, by the partial decohesion due to the nucleation of micro-cracks, while the progressive interface damage coiTesponds to the micro-crack growth and coalescence until the formation of macro-cracks, i.e. fracture.

In the present paper, the problem of deriving an interface model from micromechanical studies is investigated, with specific reference to the mortar-brick interphase analysis of masonry material.

The interface mathematical model

Let a typical point of the mortar-brick interphase be considered. A representative volume element (RVE) at that typical point is defined. It is characterized by the presence of microcracks which can evolve, can be open or closed and can develop frictional stresses. The geometry of the RVE is reported in F i g . l . The damage parameter D = alb is introduced.

Three different states can be recognized at the brick-mortar interphase: the mortar-brick bond is absolutely undamaged; partial decohesion between the two contact surfaces of the different materials occurred; the decohesion phenomenon is complete.

In the present study, linear elastic constitutive laws are considered for the mortar and the brick materials. Figure 1: Geometry of the RVE. Unilateral contact and friction laws are assumed to occur at the crack mouths. About the evolution of the damage parameter, i.e. the crack growth, a model which accounts for the couphng of mode I of mode I I of fracture is considered. In particular, it is assumed that the damage evolution is governed by the overall relative displacement acting on the RVE.

In order to recover the interface model by means of the homogenization procedure, the RVE is considered subjected to the average relative displacement, i.e. to an average strain; then.

brick

2a unilateral contact & friction 2b