Micro-Plastic Material Model and Residual Fields in Rolling Contacts

This paper describes a model for the prediction of micro-plastic material transformation and associated residual stress field development in bearing steels during over-rolling. The high and mainly hydrostatic pressure field induced by the rolling element load, leads to the development of micro-plastic deformation in the subsurface layer of the rolling contact. The resulting plastic strain distribution gives rise to an associated self-equilibrating residual stress field that can be experimentally quantified using X-ray diffraction methods. A novel three-dimensional elastic-plastic over-rolling solution is used to evaluate the plastic strains and material transformation. Central to this plastic contact formulation is the incremental approach to deal with nonlinear material behavior. The Prandtl-Reuss constitutive equations in conjunction with Huber-Mises-Hencky yield criterion and Ramberg-Osgood strain-hardening relationships are applied to describe the plastic behavior of common hardened bearing steels. A nonlinear isotropic law is applied to describe the transformation of the retained austenite during stress cycles and changes in the strain-hardening behavior of the material microstructure. Application of this model with an incremental solution scheme based on the Conjugate Gradient Method (CGM) gives good convergence properties and fast solution for each cycle. Comparison between experimentally obtained residual stresses and stress fields derived from the present micro-plastic contact model, indicates good agreement. Numerical simulations, carried out to derive the maximum operating contact pressures in the elastic regime are also in agreement with published data. The model opens new possibilities in the evaluation of steels and heat treatments used in rolling bearings. Furthermore, this micro-plastic contact model may help the interpretation of the load history leading to a given pattern of residual stress measured in bearing rings.