Nanoindentation of engineering materials is commonly used to study, at small length scales, the continuum mechanical properties of elastic modulus and yield strength. However, it is difficult to measure strain hardening via nanoindentation. Strain hardening, which describes the increase in strength with plastic deformation, affects fracture toughness and ductility, and is an important engineering material property. The problem is that the load-displacement data of a single nanoindentation do not provide a unique solution for the material's plastic properties, which can be described by its stress-strain behaviour. Three-dimensional mapping of the displacement field beneath the indentation provides additional information that can overcome this difficulty. We have applied digital volume correlation of X-ray nanotomographs of a nanoindentation to measure the sub-surface displacement field and so obtain the plastic properties of a nano-structured oxide dispersion strengthened steel. This steel has potential applications in advanced nuclear energy systems, and this novel method could characterise samples where proton irradiation of the surface simulates the effects of fast neutron damage, since facilities do not yet exist that can replicate this damage in bulk materials.