Microindentation A prescribed load appled to an indenter in contact with a specimen and the load is then removed and the area of the residual impression is measured. The load divided by the by the area is called the hardness.
Nanoindentation A prescribed load is appled to an indenter in contact with a specimen. As the load is applied, the depth of penetration is measured. The area of contact at full load is determined by the depth of the impression and the known angle or radius of the indenter. The hardness is found by dividing the load by the area of contact. Shape of the unloading curve provides a measure of elastic modulus.
Nearly all of the elements of this analysis were first developed by workers at the Baikov Institute of Metallurgy in Moscow during the 1970's (for a review see Bulychev and Alekhin). The basic assumptions of this approach are
Deformation upon unloading is purely elastic
The compliance of the sample and of the indenter tip can be combined as springs in series
The contact can be modeled using an analytical model for contact between a rigid indenter of defined shape with a homogeneous isotropic elastic half space using
where S is the contact stiffness and A the contact area. This relation was presented by Sneddon. Later, Pharr, Oliver and Brotzen where able to show that the equation is a robust equation which applies to tips with a wide range of shapes.
Analytical Model – Doerner-Nix Model Doerner, Nix, J Mater Res, 1986
The nanoindentation system applies a load to the indenter tip to force the tip into the surface while simultaneously superimposing an oscillating force with a force amplitude generally several orders of magnitude smaller than the nominal load.
It provides accurate measurements of contact stiffness at all depth.
The stiffness values enable us to calculate the contact radius at any depth more precisely.
Drift might have parallel and/or a perpendicular component to the indenter axis
Thermal drift is especially important when studying time varying phenomena like creep.
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
Displacement arising from the compliance of the testing machine must be subtracted from the load-displacement data
The machine compliance includes compliances in the sample and tip mounting and may vary from test to test
It is feasible to identify the machine compliance by the direct measurement of contact area of various indents in a known material
Anther way is to derive the machine compliance as the intercept of 1/total contact stiffness vs 1/ sqrt(maximum load) plot, if the Young’s modulus and hardness are assumed to be depth-independent
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.
As sample roughness does have a significant effect on the measured mechanical properties, one could either try to incorporate a model to account for the roughness or try to use large indentation depths at which the influence of the surface roughness is negligible.
A model to account for roughness effects on the measured hardness is proposed by Bobji and Biswas.
Nevertheless it should be noticed that any model will only be able to account for surface roughnesses which are on lateral dimensions significantly smaller compared to the geometry of the indent
Plastic deformation in all materials is time and temperature dependent
Important parameter to determine is the strain rate sensitivity
The average strain rate can be given by
It can be done by experiments at different loading rate or by studying the holding segment of a nanoindentation.
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