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Keysight Technologies
Rapid Calibration of Area Function and
Frame Stiffness with Express Test1
Application Note
Introduction calibrations are distinctive because
they involve actually using the
The Keysight Technologies, Inc. indenter to make indentations into a
G200 NanoIndenter performs a standard material. Thus, they are the
specific kind of mechanical test last calibrations to be performed and
known as instrumented indentation. they are often performed by the user.
Instrumented indentation testing These calibrations are not unique
(IIT) involves pressing a hard to Keysight systems--they are a
indenter of known shape and elastic necessary aspect of testing with any
properties into a test material while instrumented indentation system.
continuously measuring both force
and displacement. Mechanical Conceptually, one may think about
properties, including Young's modulus the instrument frame as a spring in
and hardness, are derived from these series with the contact as illustrated
fundamental measurements. Because schematically in Figure 1. Physically,
IIT naturally lends itself to evaluating the instrument frame includes the
materials on the scale of nanometers, indenter column, fixturing for the
it is also commonly known as indenter tip and sample, translation
"nanoindentation". mechanisms, gantry, and connections
between all these parts. The objective
A number of calibration processes of the frame-stiffness calibration is to
are required in order to bring an determine a single value, Kf, which
instrumented indentation system characterizes the composite elastic
online. For example, the mechanism stiffness of the testing equipment.
for sensing the motion of the indenter Once the frame stiffness, Kf, is
must be calibrated by associating known, then we can determine the
the output of the sensor with deformation which occurs in the
known dimensions (we use laser equipment and subtract it from the
interferometry for this task). Most total measured displacement so as to
Figure 1. Schematic representation of frame
(Kf) and contact (S) as two springs in series of these calibrations are performed isolate the deformation which occurs
with an effective stiffness K*. at the factory and are transparent to in the test sample. This is our purpose
the user. However, two calibrations behind the calibration of frame
deserve special attention. They stiffness. (Note: "Frame stiffness"
are the "frame-stiffness" and is also commonly referred to as
"area-function" calibrations. These "machine stiffness" or "instrument
stiffness".)
1. A video presentation of this material is available online:
https://keysighteseminar.webex.com/keysighteseminar/lsr.php?AT=pb&SP=EC&rID=5138702&r
Key=1be38082f71e07ff
Eq. 4 expresses a linear relation
between the independent variable A-2
and the dependent variable 1/K*; the
intercept of this line is 1/Kf.
In theory, one could determine
frame compliance3 from a series
of indentations as the intercept of
a plot of (1/K*) vs. A-2 . However,
Figure 2. Schematic representation of indenter area function, A = f(d). in practice, this leads to a problem
of interdependence between the
frame-stiffness calibration and the
As depicted schematically in Figure 2, performed at 400 different sites in area-function calibration -- the area
the area function, A = f(d), is a less than 7 minutes. In addition to the function is required in order to obtain
mathematical description of the obvious benefit of speed, ultra-fast frame stiffness by Eq. 4, but we
geometry of that part of the indenter testing actually improves calibration cannot calibrate the area function
which is designed to be in contact accuracy by allowing more indents to without first knowing the frame
with the test material. It expresses be included (since they are so fast) stiffness (next section). To resolve
the relationship between the distance and by rendering the influence of this circularity, we use the fact that
(d) from the apex of the indenter thermal drift inconsequential 2. hardness (H) is defined as force (P)
(along the indenter axis) and the divided by contact area (A):
cross-sectional area (A) of the Theory of Calibrating H = P/A Eq. 5
indenter at that distance. Although
we determine the area function Frame Stiffness Solving Eq. 5 for A and substituting in
by making indents into a standard Eq. 4 yields
material, it is important to note that With reference to Figure 1, it is clear
the area function is a property of the that what is actually measured during . Eq. 6
indenter tip alone. Knowledge of the an indentation test is the composite
area function is required in order to stiffness, K*. The composite stiffness, Thus, if we indent a material having
be able to calculate contact area from K*, is related to its components uniform hardness and reduced
the fundamental measurements of through a summation of compliances: modulus, using a variety of applied
force and displacement. (Note: "Area 1/K* = 1/S + 1/Kf . Eq. 1 forces, we can determine the frame
function" is also commonly referred to compliance as the intercept of a
as a "tip function," "tip area function", From elastic contact mechanics [3◦ Jabse Service Manual Search 2025 ◦ Jabse Pravopis ◦ onTap.bg ◦ Other service manual resources online : Fixya ◦ eServiceinfo