A modified direct analysis method for problems in repeated contact is presented. This method is shown to be an efficient technique for the determination of the steady state solution under proportional or non-proportional cyclic loading. An elastic-plastic problem is converted into a purely elastic problem and an inelastic problem. Two decomposed problems can be solved separately using the same linear operator, such as finite element method, with different material properties.;The repeated elastic-plastic rolling/sliding contacts on a half plane, half space, quarter space, and an actual rail are considered. The elastic stress history is required in the direct analysis method. Solution to the elastic stress field in a half plane or a half space subjected to the surface contact load are available in closed form. The interior stress field in a quarter space subjected to the Hertzian contact load is simulated by a set of the dual integrals and combined with the direct analysis method. The contact load must be assumed to be off the edge of the quarter space in this solving procedure to ensure that the contact pressure distribution remain Hertzian. To consider the edge effect on the contact load, a point load iteration method is used, which allows an arbitrary surface profile to be the prescribed boundary condition.;A surface-hardened component is modeled as a layered material having inelastic properties that vary with depth. Those material properties are qualitatively converted from material's experimental hardness profile. The steady state residual stresses, residual strains and plastic strain amplitudes are calculated. The present direct method calculates the steady state quantities at a relatively rapid rate and allows assessment of performance by parameter studies in realistic three-dimensional problems which would otherwise be prohibitively lengthy by other techniques.
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