The relationship of stress and strain in materials characterizes the deformation behaviour from the elastic loading at low stresses to the stages of deformation with increasing stresses and strains – yielding, work hardening and failure. The relationship is typically found by tensile tests using macroscopic samples.

Nanoindentation hardness and reduced modulus values are related to the materials stress and strain relationship. The indentation strain is controlled by the indentation depth of spherical indentations. The deformation zone around a hardness test is however nonuniform in stress and strain unlike the uniaxial tensile test that is designed for uniformity in stress and strain.

This paper discusses the transition from elastic to plastic deformation in spherical indentation [1,2,3] and the importance of Constrain Factor that plays significant role in relationship between hardness and yield strength, and which is material dependent as well [4]. Comparison between spherical nanoindentation stress – strain method, macroscale tensile tests and microscale pillar compression tests in-situ SEM will be cross-referenced for Cu and several alloys of steel.