A Finite Element Study of an Elasto-Plastic Disk or Cylindrical Contact Against a Rigid Flat in Plane Stress with Bilinear Hardening

This work presents a finite element study of elasto-plastic cylindrical contact. The geometry could also be described as a vertically aligned disk whose axis of symmetry is parallel to the contact surface. The cylinder is considered to be in the plane stress state. The material of the cylinder is modeled as elasto-plastic with bilinear hardening (also known as linear hardening). Simulations for a range of material properties and deflections typical to engineering applications are carried out. A mesh convergence study has also been performed. By employing symmetry, the cylinder has been modeled as a quarter circle and a straight line is used to model the opposing rigid flat surface. The finite element results for the elastic and fully plastic cylindrical contact cases are compared to other existing models such as Hertz contact and spherical elasto-plastic models. Since the case considered is plane stress, the stress distribution is significantly different from elasto-plastic spherical contacts, which would be closer to a plane strain case. An empirical relationship is fit to the results to allow for prediction of the contact width as a function of displacement and force.