Influence of equi-biaxial residual stress on unloading behaviour of nanoindentation

Finite element simulations have been used to investigate the influence of equi-biaxial residual stress on the unloading behaviour of nanoindentation on elastic–plastic strain-hardening materials. It is found that the real contact area and the elastic recovery of indentation can be correlated to the existing residual stress and that there is a linear relationship between the Ac/Ag or he/hmax ratio and the σr/σy ratio. The slope of the Ac/Ag vs. σr/σy curve is only dependent on the strain-hardening behaviour of materials but independent of the E/σy ratio; while the slope of the he/hmax vs. σr/σy curve is only dependent on the E/σy ratio but independent of the strain-hardening behaviour of materials. The existence of residual stress has a slight effect on the hardness measured by nanoindentation while it has no effect on the measured elastic modulus.