This paper describes a design method for the corner radius of a contacting body using the theoretical approach of contact mechanics. A complete contact, as in the case of a sharp-cornered punch, produces singular contact traction: whereas, in an incom...
This paper describes a design method for the corner radius of a contacting body using the theoretical approach of contact mechanics. A complete contact, as in the case of a sharp-cornered punch, produces singular contact traction: whereas, in an incomplete contact, the singular contact traction disappears because of the rounded corners, and the contact edges are within the rounded regions. The design method aims to determine the conditions of the contact force as well as the material properties in an incomplete contact. The incomplete contact changes into the complete contact again when the contact edges exceed the rounded regions owing to either an increased contact force or the compliance of the materials. The contact length of a rounded punch is used as a parameter to derive the required conditions. As a result, a design formula is obtained, which provides a minimum allowable radius when the materials, normal contact force, and the length of a flat region of the punch are predetermined. This work consists of two parts: Part I includes a theoretical background, design method, and formula, and Part II describes the actual process with the investigation of design parameters.