Does anyone have an idea on separating the elastic depth and plastic depth from the nanoindentation load vs displacement curve? An equation of elastic and plastic depth should be established for all the indentation depths.
You can separate elastic depth or elastic displacement from plastic depth/displacement in nanoindentation techniques using the Sakai model. I have used the model in my several papers as displayed below:
1. Alao and Yin, 2016. Assessment of elasticity, plasticity and resistance to machining-induced damage of porous pre-sintered zirconia using nanoindentation techniques. Journal of Materials Science and Technology 32 (5), 402-410.
2. Alao and Yin, 2015. Nanoindentation characterization of the elasticity, plasticity and machinability of zirconia. Materials Science and Engineering: A 628, 181-187.
3. Alao, 2019. Elasticity, plasticity and analytical machinability prediction of lithium metasilicate/disilicate glass ceramics. Journal of the Mechanical Behavior of Biomedical Materials 96, 9-19.
4. Alao et al. 2022. Effect of polymer amount on the mechanical behavior of polymer-infiltrated zirconia-ceramic composite at different pre-sintering temperatures. Materials Research Express 9 (8), 085401.
If you don't have access to any of the above papers, get in touch so that I can provide their soft copies for you.
In the axisymmetric case (for a cone and a ball), you can estimate the elastic displacement of the probe during indentation in four stages:
1. solve the problem for elastic-plastic indentation;
2. define the projection (circle) of the contact area;
3. solve the problem in an elastic formulation for a uniformly distributed load in a circle, which is a projection of the contact area are riached at step 2;
4. determine the elastic displacements of projection of contact area (for the task of step 3).
When you will solve the boundary value problem of step 4, the total force of a uniformly distributed load must be equal to the applied to the indenter (step 1).
In addition you can define plastic displasements by subtraction from elastic-plastic contact displacements (step 1) purely elastic ones (step 4).