Keywords: rolling fatigue contact, stationary modelling, Dang Van fatigue criterion.

The rolling contact fatigue (RCF) of the rail brings about each year, many rail replacement as well as incidents, reducing the speed of the rail network circulation or sometimes even stopping it. Today, the knowledge of the physical phenomena induced and the maintenance procedures required mostly stems from observation and experiments. This however does not allow for the prediction of the damage when the running conditions are changing. The increase in the speed and of the mass of the vehicles, the intensification of the traffic and the wear of the rail profiles have therefore encouraged the SNCF to develop a modelling strategy of the rolling fatigue contact of the rails. The numerical environment will be presented in this paper as well as an application on a specific line.

The contact stresses involved in the RCF depend on the dynamics of the train running on the rail. They are thus changing along the track and depend on many parameters: the track geometry, the wheel and rail profiles, the friction coefficient, but also the masses and suspension characteristics of the train.

The first step is therefore a railway dynamic modelling of the track vehicle interaction [1]. From this simulation, the vector of stress distribution is extracted for a specific zone and is introduced as the loading in a finite element model of the rail.

The second step is the finite element simulation. The mechanical behaviour of the rail is modelled by an elasto-plastic law with kinematic hardening; the asymptotic state of the rail is in general adapted, and in some conditions accommodated. The moving characteristic of the loading plays an important role in the asymptotic state of the rail. But since moving the load at each time step to handle contact would imply either remeshing or a very coarse mesh all along the rail, an Eulerian strategy is adopted. The asymptotic mechanical state is then directly computed using a direct stationary algorithm [2].

The third step is to compute the risk of crack initiation using the meso / macro Dang Van fatigue criterion. Finally, the Miner's rule is used to have an estimation of the mechanical state of the rail.

1

J.B. Ayasse, H. Chollet, "Contact semi hertzien", Technical report, INRETS-LTN, 2002.

2

K. Dang Van, M.H. Maitournam, "Steady-state flow in classical elastoplasticity applications to repeated rolling and sliding contact", Journal of Mechanics and Physics of Solids, 41, 1691-1710, 1993. doi:10.1016/0022-5096(93)90027-D

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