Under compressive loads combined with friction, some materials undergo Tribological Surface Transformations (TSTs) on the surface of the loaded parts and in the immediately vicinity, which in the case of metals, are known as irreversible solid-solid phase transformations. During the solid-solid phase transformations occurring under mechanical loads, TRansformation Induced Plasticity (TRIP) processes are generated at much lower stress levels than those associated with the yield strength of the material in classical plasticity. In order to assess the effects of thermomechanical coupling in these TSTs, a one-dimensional modelling based on irreversible solid-solid phase transformations and classical plasticity is presented and discussed.

The TSTs which have been affecting some rails of the French railroad for the last twenty years consist of irreversible solid-solid phase transformations resulting in the development of a “White Etching Layer” (WELs) on the rail tread and which grows in depths from several nanometers to more than 100

Based on the previous TRIP studies, which are extended here to the thermomechanical coupling associated with TSTs [

the absolute temperature

the mass fraction of the daughter phase (i.e., the “white” martensite phase) is:

the total infinitesimal strain

^{−3}, and that of martensite (material after phase transformation)

^{−3}.

The material in question is initially nontransformed (

Neglecting the viscoelastic effects and noting that the specific entropy

Using (

The Second Principle of Thermodynamics must be checked, whatever the local thermomechanical state

(i) In the irreversible solid-solid phase transformation (TST) process:

It must be stressed that: (i) TSTs (or WELs), which correspond to the ferrite-pearlite

(ii) In the classical plasticity process:

Combining (

It is worth noting the thermodynamic consistency of this model [

This example will be addressed in order to assess the thermomechanical coupling occurring in the TSTs using the approach presented in Section

(a) Numerical example of TSTs: bar subjected to a thermomechanical loading (where

Assuming that the convective terms of particular derivative are zero, (

Neglecting the effects of both the inertia and gravity, the local expression of quasi-static equilibrium reduces to:
^{−3}; ^{−1}·K^{−1}; ^{−3}·K^{−1}. Note that ^{−3} and martensite ^{−3}). Therefore, based on these experimental data, the transformation ferrite

From (

The results of the numerical simulations are presented in Figures

(a)

(a)

(a) Distribution of mass fraction

Stress/strain curve (solid line) and stress/TRIP-like strain curve (dashed line) in

The results presented in Section

The thermodynamically consistent model presented in this study can be used to simulate the initiation and development of Tribological Surface Transformations (TSTs). The results obtained here show that the thermomechanical coupling can generate a thin layer of fully irreversible solid-solid phase transformation in the immediate vicinity of the point on the bar where the thermomechanical loading is applied. These results also highlight that the layer thickness transformed is in line with the experimental available data on TSTs since a depth of around one hundred micrometers has been reached. In the future studies, it is proposed to test the present thermomechanical model in more realistic numerical simulations involving issues relatied to wheel/rail contact problems.

The author is indebted to Professor Thierry Désoyer and Professor Frédéric Lebon for the valuable discussions.