■ Basic principle: Repressentative method

 

The relation of the hardness of metals to a uniaxial tensile (or compressive) stress has been extensively studied. In general, the amount of deformation or strain around the indentation varies from point to point. We may, however, expect that when full plasticity is reached, there will be an average or ‘representative’ value in the deformed zone. Empirical and analytical results show that on the specimen surface and at the edge of a spherical indentation the flow stress is highest and its magnitude is related to the mean contact pressure (p_m). Also, these results showed that strain produced at the deformed zone depends only on a/R, where a is the contact radius and R is the spherical indenter radius.

Based on the above results, the following relations were determined for the representative method:

σ_r=p_m/ψ,     ε_{r = f(a/R)}

Here σ_r, ε_r are the ‘representative’ stress and strain induced by indentation, and _ψ is a plastic constraint factor which is obtained from the analysis of stress field underneath the spherical indenter. Thus, by measuring the contact pressure (p_m) at each indentation depth, we can create the p_m – a/R curve (The contact radius (a) can be determined from contact depth (h_c), .) With the representative method, the p_m – a/R curve can be converted to a σ_r – ε_r curve. This algorithm was introduced in ISO in 2008 as Technical Report 29381.

Figure. 2 Principle of evaluation of tensile properties using IIT (Ref. ISO/TR 29381, 2008)