Physical Theory of Hardness: Function, Calculation Methods, Indentation

By Nikolay Shtyrov

This monograph presents a fundamentally new interpretation of hardness as a physical quantity rooted in energy, kinetics, and structural transformation processes within deformable solids. Moving beyond traditional empirical and geometric definitions, the author develops a rigorous theoretical framework in which hardness is treated as a state function directly related to the specific volumetric power of irreversible deformation processes.
At the core of the work lies the concept of physical hardness as a function derived from the volumetric energy characteristics of a material under loading. The classical indentation diagram F(h) is reinterpreted as a carrier of complete physical information about the deformation process, enabling the calculation of hardness not merely as a number, but as a continuous function reflecting the evolution of material response. This approach establishes a direct connection between indentation, uniaxial tension, and general deformation behavior.
The book introduces two independent methods for determining the hardness function, including analytical evaluation based on indentation curves and a novel approach using the activated volume A(V) as an independent variable. These methods provide a consistent transition between macro-, micro-, and nano-scales of indentation, ensuring continuity of physical interpretation across different testing regimes and indenter geometries.
A significant contribution of the monograph is the development of a universal physical unit of hardness and the formulation of standard functions enabling rigorous comparison between empirical scales such as Brinell and physically defined parameters. The classical Calvert-Johnson method is revisited and interpreted as the first physically consistent macrohardness scale, while new cyclic indentation diagrams (CYMKI) are introduced as an effective tool for evaluating hardness through integral kinetic criteria.
Special attention is given to the role of kinetic parameters, including the generalized rate of force increase and the evolution of the activated deformation volume. The work provides analytical and numerical tools for constructing force functions for both spherical and sharp indenters, including pyramidal and conical geometries. The Rockwell method is reinterpreted within the proposed framework, leading to the formulation of a universal hardness equation applicable across all indentation regimes.
The monograph establishes a unified law of physical hardness, integrating strength, plasticity, damage accumulation, and fracture into a single energy-kinetic description. By linking hardness to measurable physical parameters such as energy flux, deformation rate, and structural evolution, the book offers a new paradigm for hardness measurement and materials characterization.
Intended for researchers, engineers, and advanced students in materials science, solid mechanics, and metrology, this work bridges classical experimental methods with modern physical theory. It provides both conceptual foundations and practical calculation tools, opening перспективу for the development of next-generation hardness standards and testing methodologies in the 21st century.

• Format: Paperback
• Language: English
• ISBN: B0GVD5Y8JL
• ISBN13: 9798254137214
• Release Date: March 2026
• Publisher: Independently Published
• Length: 218 Pages
• Weight: 0.90 lbs.
• Dimensions: 0.6" x 6.0" x 9.0"