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

Abstract

The issues of determining the Mayer index depending on the parameters of strain hardening of an elastoplastic body described by the Hollomon equation are considered. The analysis of expressions connecting the engineering uniform deformation with the Mayer index is carried out. A new expression is obtained, a particular case of which is the result obtained by V.M. Matyunin et al. Applying the ratio of the maximum Mayer hardness to the Brinell hardness, the relationship of the ultimate strength to the Brinell hardness, and the Hollomon equation, a new expression of the Mayer law is obtained. The description of the radius of the contact area by a power function of the depth of the indenter insertion allowed us to represent the Mayer index as a ratio of known parameters obtained by finite element modeling for other purposes. The graphical dependences of the results obtained are presented.

Determination of the Tensile Strain by Indenting the Sphere

“…The content of Section 2 allows us to rethink the essence of the parameter m (Eq. 10), which was obtained by the authors in the previous work [18] from the analytical definition of the conditional uniform deformation (Eq. 9).…”

“…The present studies are a logical continuation of our previous work [18], therefore we use the same notation. To describe an elastoplastic body, we use the Hollomon equation:…”