Keywords: tribological transformations of surface, wheel/rail contact, thermo-mechanical modelling, transformation induced plasticity, finite element analysis.

The tribological transformations of surface (TTS) are observed on some metallic materials, mainly when the mechanical loading applied to the sample is a repeated, compressive one. From a metallurgical point of view, they correspond to irreversible (permanent) solid-solid phase transformations. TTS initiate and develop on the surface, and in its immediate vicinity, where the mechanical loading is applied.

The main conjecture of this study is that TTS arise from a thermo-mechanical coupling. As a consequence, the aims of the study are: (i) to propose a thermo-mechanical model taking into account the main features of irreversible, solid-solid phase transformations, such as the plastic strain state which it is associated with; (ii) to briefly present the main steps of the numerical algorithm which is used to solve the set of partial derivative equations associated with the constitutive equations of the proposed model, that of quasi-static equilibrium and the heat equation; (iii) to illustrate the potential of the proposed model via the results of a two-dimensional finite element analysis.

Beside the absolute temperature and the strain tensor, the rate-dependent model uses two other internal, state variables: the mass fraction of the daughter phase and a plastic strain tensor. It is clearly based on previous works on transformation induced plasticity, see e.g. Taleb and Sidoroff [1], which are simply extended for a thermo-mechanical coupling to be taken into account. The main ingredients are the state potential and a yield function which are such that the Clausius-Duhem inequality is systematically satisfied.

The numerical implementation of the constitutive equations of the proposed model is based on a return mapping algorithm, see e.g. Nguyen [2]. The main step of the algorithm is the computation of the viscoplastic multiplier, which turns out to be one of the roots of a quadratic equation. On the other hand, the global, equilibrium problem is solved using a classical Newton-Raphson algorithm. The discretized model has been implemented in a finite element software (CodeAster; EdF)

Numerical results for a structural problem, square domain with pressure and/or temperature as boundary conditions on a "small" part of the boundary, are eventually presented. They clearly show that: (i) TTS can not develop in the purely mechanical case, i.e. when the thermal effects are not taken into account; (ii) TTS can initiate when the structural problem is considered as a thermo-mechanical one, which is in line with the main conjecture of the study. The same numerical results, however, suggest that the pressure could also play a part in the development of TTS. The proposed model will have to be extended to such a "pressure sensitivity" in future works.

1

L. Taleb, F. Sidoroff, "A micromechanical modeling of the Greenwood-Johnson mechanism in transformation induced plasticity", International Journal of Plasticity, 19, 1821-1842, 2003. doi:10.1016/S0749-6419(03)00020-2

2

Q.S. Nguyen, "On the elastic-plastic initial-boundary value problem and its numerical integration", International Journal for Numerical Methods in Engineering, 11(5), 817-832, 1977. doi:10.1002/nme.1620110505

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