Short note on the effect of a pressure-induced increase in Young's modulus

Abstract

It will be shown how relatively simple models simulating bond interactions in solids using effective potentials, such as Lennard–Jones and Morse, can be used to investigate the effect of pressure-induced stiffening or enhancement in these solids. The value of the current study is the possibility of deriving relatively simple dependencies of the bulk-modulus B on the pressure P in a way that is completely free of microscopic material parameters wherever the solid bond interaction can be described, or at least partially described, by Lennard–Jones potential approaches. Instead of bond energies and length, only specific integral constants, such as Young's modulus and Poisson's ratio, are required. The influence of the pressure-induced Young's modulus change is discussed, especially with respect to mechanical contact experiments.

Keywords:

• ultra-hardness
• diamond
• contact mechanics
• nanoindentation
• hardness

Acknowledgements

The author acknowledges helpful discussions with A.C. Fischer-Cripps, Fischer-Cripps Laboratories, Australia, S.J. Bull, Newcastle University, and W.J. Clegg, University of Cambridge. He especially thanks Professor Fischer-Cripps for also providing the indentation data used within the discussion of “ultra-hard coatings”. The author is also thankful to one of the reviewers for suggesting the list describing the possible compensating effects in a compact manner.