On the relationship between plastic zone radius and maximum depth during nanoindentation

The relationship between plastic zone size and plastic depth during indentation has been studied by a number of workers and an expression relating the plastic zone radius to the residual indentation depth (assumed to be the plastic depth) was developed by Lawn et al. [B.R. Lawn, A.G. Evans and D.B. Marshall, J. Am. Ceram. Soc. 63 (1980)198.] based on microindentation testing. In this study, the relationship between the plastic zone radius and residual indentation depth was examined using finite element analysis for conical indentation in elastic-perfectly-plastic bulk materials. The simulations show that the Lawn method overestimates the plastic zone size for different materials with a wide range of Young's modulus over hardness ratio and for indenters with different geometries and it does not consider tip rounding effects. Therefore, an analytical expression is outlined which agrees well with finite element data. For practical application, the relationship between the radius of the plastic deformation zone and the maximum penetration depth is developed here which has been used to modify the energy-based model developed at Newcastle University to predict the hardness and Young's modulus of coated systems. It is found that the new relationship is easy to apply and predictions of the hardness and Young's modulus of coated glass show good agreement with experimental results.