Three-dimensional elastic-plastic stress analysis of rolling contact

Three-dimentional elastic-plastic rolling contact stress analysis was conducted incorporating elastic and plastic shakedown concepts. The Hertzian distribution was assumed for the normal surface contact load over a circular contact area. The tangential forces in both the rollings and lateral directions were considered and were assumed to be proportional to the Hertzian pressure. The elastic and plastic shakedown limits obtained for the three-dimentional contact problem revealed the role of both longitudinal and lateral shear traction on the shakedown results. An advanced cyclic plasticity model was implemented into a finite element code via the material subroutine. Finite element simulations were conducted to study the influences of the tangential surface forces in the two shear directions on the residual stresses and residual strains. For all the cases simulated, the P₀/k ratio (P₀ is the maximum Hertzian pressure and k is the yield stress in shear) was 6.0. The Q_x/P ratio, where Q_x is the total tangential force on the contact surface in the rolling directional and P is the total normal surface pressure, ranged from 0 to 0.6. The Q_y/P ratio (Q_y is the total tangential force in the lateral direction) was either zero or 0.25. Residual stresses increase with increasing rolling passes but tend to stabilize. Residual strains also increase but the increase in residual strain per rolling pass (ratchetting rate) decays with rolling cycles. Residual stress levels can be as high as 2k when the Q_x/P ratio is 0.6. Local accumulated shear strains can exceed 20 times the yield strain in shear after six rolling passes under extreme conditions, Comparisons of the two-dimensional and three-dimentional rolling contact results were provided to elucidate the differences in residual stresses and ratchetting strain predictions.