1. Nanoindentation Lecture 1 Basic Principle Do Kyung Kim Department of Materials Science and Engineering KAIST

5. Microhardness - Vickers and Knoop

9. Basic Hertz’s elastic solution (1890s)

10. Schematics of indenter tips Vickers Berkovich Knoop Conical Rockwell Spherical

11. 4-sided indenters

12. 3-sided indenters

13. Cone indenters

14. Indenter geometry 1 0.72   A =  h p 2 tan 2  Cone 1.034 0.75 42.28  35.26  A = 3h p 2 tan 2  Cube Corner 1.012 0.75 77.64   1 =86.25   2 =65  A = 2h p 2 tan  1 tan  2 Knoop 1.012 0.75 70.32  68  A = 4h p 2 tan 2  Vickers 1.034 0.75 70.2996  65.3  A = 3h p 2 tan 2  Berkovich 1 0.75 N/A N/A A   2Rh p Sphere Geometry correction factor (  ) Intercept factor Effective cone angle (  ) Semi angle (  ) Projected area Indenter type

15. Stress field under indenter - contact field Boussinesq fields (point load) Hertzian fields (spherical indenter) Brian Lawn, Fracture of Brittle Solids, 1993, Cambridge Press Anthony Fischer-Cripp, Intro Contact Mechanics, 2000, Springer

20. Analytical Model – Doerner-Nix Model Doerner, Nix, J Mater Res, 1986

22. Analytical Model – Oliver and Pharr Oliver & Pharr, J Mater Res, 1992

25. One of the most cited paper in Materials Science Nov 28, 2006 No of citation Nov 2003 - 1520, Nov 2005 - 2436

26. Material response

27. Nanoindenter tips

28. Berkovich indenter Projected area b

36. Thermal drift calibration Indenter displacement vs time during a period of constant load. The measured drift rate is used to correct the load displacement data. Application of thermal drift correction to the indentation load-displacement data

38. Machine compliance calibration Usually done by manufacturer using materials with known properties (aluminum for large penetration depths, fused silica for smaller depth). Using an accurate value of machine stiffness is very important for large contacts, where it can significantly affect the measured load-displacement data.

42. Pile-up and Sinking-in

45. Fracture toughness measurement Combining of Laugier proposed toughness model and Ouchterlony’s radial cracking modification factors, fracture toughness can be determined. Fracture toughness expression K c = 1.073 x v (a/l) 1/2 (E/H) 2/3 P / c 3/2