Gradient effects in micro-/nanoindentation

Abstract

During micro-/nanoindentation, sharp deformation gradients are developing in the neighbourhood of the indenter’s tip. These gradients should be taken into account in interpreting related measurements of hardness versus indentation characteristics, such as penetration depth, contact radius and plastic zone size. One way to do this is to resort to mechanism based dislocation arguments by utilising, for example, Ashby’s concept of geometrically necessary dislocations, the density of which is directly related to plastic strain gradients, as shown by Nix and Gao. Another mechanics based approach is to utilise a gradient plasticity formulation, for example, the one advanced by Aifantis and co-workers, which, in conjunction with Johnson’s cavity model, seems to be more flexible in interpreting the indentation size effect (ISE). For very small indentation depths, plastic flow does not occur until the equivalent strain, in the gradient elasticity (GE) region surrounding the hydrostatically pressurised core beneath the indenter’s tip, reaches a critical yield value. In this latter case, the observed ISE effect is interpreted through GE considerations.

Keywords:

• Nanoindentation
• Microindentation
• Indentation size effect
• Deformation gradient
• Plastic flow

Acknowledgements

The authors are indebted to the reviewer for his sharp comments on an earlier version of the manuscript and to L. M. Brown for bringing to their attention some of his recent excellent work that they were not aware of.