A three-dimensional elastic-plastic contact code based on semi-analytical method is presented and validated. The contact is solved within a Hertz framework. The reciprocal theorem with initial strains is then introduced, to express the surface geometry as a function of contact pressure and plastic strains. The irreversible nature of plasticity leads to an incremental formulation of the elastic-plastic contact problem, and an algorithm to solve this problem is set up. Closed form expression, which give residual stresses and surface displacements from plastic strains, are obtained by integration of the reciprocal theorem. The resolution of the elastic-plastic contact using the finite element (FE) method is discussed, and the semi-analytical code presented in this paper is validated by comparing results with experimental data from the nano-indentation test. Finally, the resolution of the rolling elastic-plastic contact is presented for smooth and dented surfaces and for a vertical or rolling loading. The main advantage of this code over classical FE codes is that the calculation time makes the transient analysis of three-dimensional contact problems affordable, including when a fine mesh is required.

Tests have been performed on a two-disk machine in order to evaluate the role of inclusions, surface roughness and operating conditions on rolling contact fatigue of AISI 52100 and M50 bearing steels. Important parameters—such as nature and location of inclusions, small and large wavelengths of surface roughness, normal loading or sliding conditions—on crack initiation and propagation stages have been identified. The operating conditions have been selected to encompass typical jet engine applications. Tests have been carried out up to 4.2 GPa, for two different surface finishes. Surface distress and sub-surface damage which could result in catastrophic failure have been observed. Indeed, surface initiated deep spalling (observed at 3.5 GPa for unpolished surfaces and under rolling plus sliding conditions) as well as sub-surface initiated deep spalling (at 4.2 GPa for polished specimens) have been observed. Sub-surface micro-cracks were detected early and followed during some interrupted tests by the means of an ultrasonic echographic device. Results of our experiments are analyzed and discussed in relation to the rolling contact fatigue theories.