Simplified direct method for cyclic strain calculation: repeated rolling/sliding contact on a case-hardened half plane

A direct analysis method for problems in repeated elastic-plastic rolling/sliding contact is presented. The method is shown to be an efficient technique for the determination of the steady-state solution under proportional or nonproportional cyclic loading and can provide such results as residual stress, residual strain, and cyclic strain range. Furthermore, the method is valid for both elastic and plastic shakedown. A two-dimensional rolling/sliding contact problem is considered with emphasis on the calculation of cyclic plastic strains. Several numerical techniques are employed to simplify and reduce the computational effort. These techniques consist of an operator split, the modified incremental projection method, middle-loading state, and decomposition into residual steady-state and cyclic parts. The resulting scheme is highly efficient and is ideally suited for parameter studies. To demonstrate the practical application of the approach, a two-dimensional contact problem, assuming a case-hardened material, is solved.