Investigation of sharp contact at rigid–plastic conditions

Sharp contact problems are examined theoretically and numerically. The analysis is focused on elastic–plastic material behaviour and in particular the case when the local plastic zone arising at contact is so large that elastic effects on the mean contact pressure will be small or negligible. It is shown that, save for the particular case of a rigid–plastic power-law material, at such conditions, there is no single representative value on the uniaxial stress-strain curve that can be used in order to evaluate the global parameters at contact. However, the present numerical results indicate that good accuracy predictions for the mean contact pressure can be achieved when this variable is described by two parameters corresponding to the stress levels at, approximately, 2 and 35% plastic strain. Regarding the size of the contact area, it is shown that this quantity is very sensitive to elastic effects and any general correlation with material properties is complicated at best. The numerical analysis is performed by using the finite element method and the theoretical as well as the numerical results are compared with relevant experimental ones taken from the literature. From a practical point of view, the presented results are directly applicable to material characterization or measurements of residual mechanical fields by sharp indentation tests, but also for situations such as contact in gears or in electronic devices.