"NUMERICAL SIMULATION OF ELASTIC-PLASTIC CONTACT WITH ISOTROPIC HARDENING "

Abstract

The contacts of mechanical components transmit loads that lead to subsurface stresses developing in the contacting bodies. In an efficient tribological design, these stresses are expected to remain under the yield strength of the softer contacting material. When this condition is not met, plastic flow occurs in the softer body. Under the assumption of isotropic hardening, the yield strength increases with the development of additional plastic strains. As plastic flow processes are dissipative and therefore path dependent, the elastic-plastic problem is unsolvable through analytical endeavours, but can be approached with a numerical algorithm capable of simulating the loading history. The Betti’s reciprocal theorem provides the theoretical framework for the application of superposition principle to elastic-plastic stresses and displacement. An algorithm consisting in three nested loops is assembled from the solutions of simpler problems: (1) the purely elastic rough contact problem, (2) the inclusion problem and (3) the problem of the plastic strain increment. The numerical simulations suggest that the residual stresses decrease the intensity of the total stresses, thus delaying additional plastic flow. With increasing load, the heart-shaped plastic strain volume advances toward the surface, enveloping a plastic core near the initial point of contact. Compared to the purely elastic case, the elastic-plastic pressure shows a flatter distribution, while the contact radius is increased.