A notification of local minimum pressure at deep elastic–plastic indentation and its application

Indentation techniques are widely employed to measure material hardness by calculating the mean pressure within contact area. This paper reassesses the spherical indentation of an elastic–perfectly plastic material through finite element analysis, but focuses mainly on the variation of mean pressure at deep indentation. In the fully plastic deformation regime, our results reveal that the pressure does not decrease monotonously, but increases again after reaching a local minimum value. It is found that this minimum mean pressure is about 2.23 times of the yield strength and independent of any other material parameters. Moreover, the contact radius and the indentation depth at this minimum pressure are determined analytically. This work can be readily used to measure the strength of materials by indentation tests.