Nanoindentation Lecture 1 Basic Principle Do Kyung Kim Department of Materials Science and Engineering KAIST
Indentation test (Hardness test)
Hardness – resistance to penetration of a hard indenter
Hardness is a measure of a material’s resistance to surface penetration by an indenter with a force applied to it.
Brinell, 10 mm indenter, 3000 kg Load F /surface area of indentation A
Vickers, diamond pyramid indentation
Vickers microindentation : size of pyramid comparable to microstructural features. You can use to assess relative hardness of various phases or microconstituents.
Microhardness - Vickers and Knoop
Microindentation Optical micrograph of a Vickers indentation (9.8 N) in soda-lime glass including impression, radial cracking, and medial cracking fringes.
Mechanical property measurement in micro-scale (Micro-indentation)
To study the mechanical behavior of different orientations, we need single crystals.
For a bulk sample, it is hard to get a nano-scale response from different grains.
Very little information on the elastic-plastic transition.
Nanoindentation is called as,
The depth sensing indentation
The instrumented indentation
Nanoindentation method gained popularity with the development of,
Machines that can record small load and displacement with high accuracy and precision
Analytical models by which the load-displacement data can be used to determine modulus, hardness and other mechanical properties.
Micro vs Nano Indentation
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.
Basic Hertz’s elastic solution (1890s)
Schematics of indenter tips Vickers Berkovich Knoop Conical Rockwell Spherical
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
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
Sharp indenter (Berkovich)
Sharp and well-defined tip geometry
Well-defined plastic deformation into the surface
Good for measuring modulus and hardness values
Elastic-plastic transition is not clear.
Blunt indenter - spherical tip
Extended elastic-plastic deformation
Load displacement results can be converted to indentation stress-strain curve.
Useful in determination of yield point
Tip geometry is not very sharp and the spherical surface is not always perfect.
P : applied load
h : indenter displacement
h r : plastic deformation after load removal
h e : surface displacement at the contact perimeter
Analytical Model – Basic Concept
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
Analytical Model – Field and Swain
They treated the indentation as a reloading of a preformed impression with depth h f into reconformation with the indenter.
Field, Swain, J Mater Res, 1993
Analytical Model – Oliver and Pharr Oliver & Pharr, J Mater Res, 1992
Continuous Stiffness Measurement (CSM)
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.
Oliver, Pharr, Nix, J Mater Res, 2004
for Berkovich indenter E: modulus of specimen E’: modulus of indenter for Berkovich indenter
One of the most cited paper in Materials Science Nov 28, 2006 No of citation Nov 2003 - 1520, Nov 2005 - 2436
Berkovich indenter Projected area b
Berkovich vs Vickers indenter
Face angle of Berkovich indenter: 65. 3
Same projected area-to-depth ratio as Vickers indenter
Equivalent semi-angle for conical indenter: 70.3
Berkovich projected area
Vickers projected area
Commercial machine implementation
Inductive force generation system
Displacement measured by capacitance gage
Two perpendicular transducer systems
Displacement of center plate capacitively measured
Load via leaf springs by expansion of load actuator
Deflection measured using a force LVDT
Force applied by an electromagnetic actuator
Displacement measured via a capacitive system
Spring-based force actuation
most common means
long displacement range & wide load range
Large and heavy due to permanent magnet
Electrostatic force btwn 3-plate transducer applied
Small size (tenths of mm) & good temperature stability
Limited load(tenths of mN) & displacement(tenths of N)
Tip attached to end of cantilever &
Sample attached to piezoelectric actuator
Displacement of laser determine displacement
Tip on leaf springs are displaced by piezoelectric actuator
Force resolution is very high ( pN range),
As resolution goes up, range goes down & Tip rotation
Optical lever method
Linear Variable Differential Transducer (LVDT)
Measure the difference btwn C 1 and C 2 due to
High precision(resolution < 1 Å) & small size
Relatively small displacement range
Photodiode measures lateral displacement
Popular method in cantilever based system
Detection of deflection < 1 Å
AC voltage proportional to relative displacement
High signal to noise ratio and low output impedance
lower resolution compared to capacitor gage
Beam intensity depends on path difference
Sensitivity < 1 Å & used in hostile environment
Fabry-Perot system used for displacement detection
Factor affecting nanoindentation
Initial penetration depth
Piling-up and sinking-in
Indentation size effect
Drift can be due to vibration or a thermal drift
Thermal drift can be due to
Different thermal expansion in the machine
Heat generation in the electronic devices
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.
Real tip shape
Deviation from perfect shape
Area function calibration
Ideal tip geometry yields the following area-to-depth ratio: A = 24.5 h c 2
Real tips are not perfect!
Calibration Use material with known elastic properties (typically fused silica) and determine its area as a function of contact
New area function A = C 1 h c 2 + C 2 h c + C 3 h c 1/2 + C 4 h c 1/4 + C 5 h c 1/8 + …
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
Pile-up and Sinking-in
Phase transition measurement
Nanoindentation on silicon and Raman analysis
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
High temperature measurement
Nanindentation with or without calibration
Temperature match btw. indenter and sample is important for precision test.
Prior depth calibration and post thermal drift correct are necessary.