Finite element analysis of the penetration depth/tip radius ratio dependence on the correction factor β in instrumented indentation of elastic-plastic materials

Measurements of mechanical properties by instrumented indentation rely heavily upon the relationship between the unloading contact stiffness, S-u, the projected contact area, A(c), and the reduced modulus, E-r. This relationship is written in the form S-u = 2 beta E-r(A(c)/pi)(1/2), where beta is a correction factor that depends on the material properties, the geometry of the indenter and also the penetration depth. Most of the time a constant value of beta is used in experimental measurements, either 1.0 or a value around 1.05, which is not correct since beta strongly depends on the penetration depth as demonstrated by finite element calculations (FEC) on purely elastic materials and also experimentally on the fused quartz, which is the usual sample used for calibration of the contact area function. Here, the dependence of beta on the penetration depth and tip blunting is studied by FEC in the case of elastic-plastic materials generally encountered in engineering. The consequence of not taking into account the influence of beta on hardness and elastic modulus measurements is also investigated.