On the pressure dependence of the indentation modulus

The influence of the pressure distribution beneath a spherical indenter onto the resulting penetration depth and consequently its impact onto the derived apparent indentation modulus has been modelled theoretically. It turns out that the pressure distribution has the same effect as a constant hydrostatic pressure of one half of the contact pressure within the entire sample. The effect is particularly important in situations of high contact pressure as during elastic indentation loading before the occurrence of the first pop-in. Furthermore, for all materials with a high ratio between hardness and elastic modulus the indentation modulus should differ from the "zero-pressure elastic modulus" in an experimentally verifiable way. A quantitative assessment delivers a possible increase up to 15 %.