Modelling the role of length scales in the indentation testing of metals

The strength of materials is related to their intrinsic (microstructural) length scale. Small scale testing also introduces an extrinsic length scale effect, such as the widely reported indentation size effect (ISE). These length scale effects have been studied and modelled both analytically and numerically.

Finite element models have been developed in COMSOL and Abaqus to incorporate the ISE into hardness models for different indenter profiles and validated against fundamental theories.

A novel analytical model has been developed for the ISE in a flat punch indenter under plain strain conditions and validated using experimental data and numerical models developed in this thesis. It was found from the loading and unloading curves generated by this model that the hardness depends on two length scales, the punch width and the indentation depth.

A strain gradient crystal plasticity model has been developed in Abaqus using a User Material (UMAT) routine to investigate the ISE for different crystal structures. Spherical and conical hardness simulations were performed for materials with different intrinsic length scales.

An analytical model has been developed as an extension of the Nix and Gao [1] to consider the hardness in polycrystalline alloys. This model has been validated against existing experimental data and used to analyse a bespoke series of experimental hardness tests provided for this project by UKAEA.