The Relationship between the Deformation of Spherical Indentation and Tensile Deformation

Abstract

The paper is devoted to the definition of the deformation during indentation of the sphere and its relationship with the tensile deformation. Proposed by different authors methods of determining the deformation of the contact are considered. The results of their researches may vary significantly. It is shown that in the last decade to determine the deformation, the finite element analysis taking into account the "sink-in/pile-up", i.e. an elastic sinking in and plastic piling up of the material on the edges of the indent during the indentation process is widely used. The purpose of this research is to determine the relationship between tension deformation and sphere indentation deformation with taking into account the last achievements in the field of finite-element modeling of elastic-plastic sphere indentation. It is considered two methods of determining of deformation. One uses the equation proposed by S.I. Bulychev, in which the Mayer’s index is determined from the results of finite element analysis. The second method use the energy concept of hardness. It is based on the assumption that within the range of uniform deformation during uniaxial tension and during sphere indentation, the same energy is consumed to the plastic displacement of the part of the material volume out of limits of initial volume. They have close results. The corresponding graphic relations are shown.

Relation of the Mayer Index to the Characteristics of the Power Law of Metal Hardening

“…To relate the Mayer index m to the hardening exponent n ( [6,7]), the n (m) type dependences proposed in [8,9] were used. As studies have shown [10,11], an unambiguous relationship between m and n is not enough, since ( )…”