A model for predicting plastic strain and surface cracks at steady-state wear and ratcheting regime

Unidirectional plastic strain accumulation (ratcheting) is one of the main causes of surface crack nucleation in rails and wheels in dry condition. It is related to frictional forces which develop at the contact interface due to sliding, especially in curve and in braking. Surface cracks generated by ratcheting can subsequently lead to severe damage when environmental fluid contaminants (such as rain or snow) are added at the contact interface, due to the complex solid-fluid interaction, which can enhance crack growth.
In dry condition, wear and ratcheting can reach an equilibrium, such that the strain field and the crack depth are stationary. Understanding such steady-state deformation regime can be a key factor for predicting the expected crack depth and scheduling a correct maintenance programme.
In this paper a model for predicting the strain field at steady-state regime is proposed. Such model, based on an integral equation, allows predicting the strain field and crack morphology at high cycle number with no need of iterative numerical simulation. The potentiality of the model was proven both in characterizing the cyclic plasticity behaviour of materials and in predicting the maximum expected crack depth in full scale railway wheels.