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Keysight Technologies
The Revolutionary Impact of the Oliver and Pharr
Technique on the Science of Hardness Testing
Application Brief
Abstract Background on Vickers Hardness limited by one's ability to measure the
diagonals of the indentation. ASTM E384-
Prior to the advent of instrumented 11 recommends that the test not be used
In 1992, Warren Oliver and George Pharr indentation, the Vickers hardness test
published an article in the Journal of unless it produces an indentation having
was the state-of-the-art in microhard- diagonals of 17m or greater. If the
Materials Research that revolutionized ness testing. The Vickers hardness test
hardness testing [1]. According to Thomas indented material is actually a coating,
is still used today and is governed by two this same standard recommends that the
Reuters Web of Knowledge, this article standards: ASTM E384 and ISO 6507.
has been cited more than 8,500 times, indentation depth be less than 10% of the
The test involves pressing a Vickers coating thickness. Taken together, these
making it one of the most cited works indenter (an oblique, four-sided pyramid)
in all of material science. The genius of two requirements imply that the Vickers
into a surface to a speciic force, P, and hardness test should not be used at all
Oliver and Pharr was this: they devised holding that force for 10 seconds. Once
a way to know the size of a hardness for coatings which are less than about
the indentation process is complete, the 60 m thick.
indentation without imaging it. This de- lengths of the diagonals of the indenta-
velopment disrupted Vickers and Knoop tion are measured optically in order to
microhardness testing which required gage the size of the impression. Vickers
The Origins of Instrumented
direct measurement of the lengths of the hardness (HV) is deined as the applied Indentation
indentation diagonals [2]. Not having to force, P, divided by the surface area of In 1983, Warren Oliver and John Pethica
image the indentation paved the way for the indentation, As: founded a company, Nano Instruments,
fully automated hardness testing. Not
HV = P/As . Eq. 1a Inc., to commercially produce indentation
only was automated testing independent
systems which measured both force and
of human bias, it was also much faster, In terms of the average of the diagonal displacement for the entire time that the
because multiple tests on multiple sam- lengths, this works out to indenter was in contact with the material.
ples could be prescribed and executed
HV = 1854.4 P/d2 . Eq. 1b They were motivated by new possibilities
with no human intervention. Further, the
in micro-mechanical testing, including
Oliver-Pharr method extended hardness where P is the force in units of gf and d is
novel research which showed that the re-
testing to much smaller scales, because the average of the two diagonal mea-
bound of the material upon force removal
one could determine the size of even surements in micrometers. Although it is
was directly related to the Young's modu-
sub-micron indentations with incredible rarely stated explicitly 1, the units of HV as
lus of the material [3]. This rebound could
accuracy. This note explains the theory of calculated above are kgf/mm2.
only be sensed if force and displacement
the Oliver-Pharr method and shows how
were measured continuously throughout
it can be used to obtain an equivalent On the lower end, the force-range of
the indentation process.
Vickers hardness number (HVc). the Vickers hardness test is practically
1. This is often a point of confusion, because ASTM E384-11 states that Eq. 1b gives HV "in terms of" gf per m2. But in fact, the units of HV are kgf/mm2,
because the constant in Eq.1b includes a conversion in force (from gf to kgf) and a conversion in area (from m2 to mm2). Expressed with its units, the
constant multiplier is actually 1854.4 [(kgf-m2)/(gf-mm2)].
02 | Keysight | The Revolutionary Impact of the Oliver and Pharr Technique on the Science of Hardness Testing - Application Brief
In the context of this developing technol-
ogy, Warren Oliver and George Pharr
(both graduates of the doctoral program
at Stanford University under William Nix)
latched on to another idea: perhaps the
size of the indentation could be inferred
from the sensed displacement, thus elimi-
nating the need to image the indentation Figure 1. Schematic of Vickers indentation showing
Figure 2. Schematic of an ideal Vickers pyramid
downward elastic delection of surface outside the
after the fact. The notion that indentation (top) and a real Vickers pyramid. The apical law
contact area.
area would be related to the indentation causes the indentation area to be larger as a
function of indentation depth. ASTM E384 limits
depth was intuitive, but several obstacles the length of the apical law to 0.5 m.
had to be overcome. First, one had to
know the depth over which the indenter lection of the surface outside the contact impression, as imaged through a scanning
actually made contact with the material, area which Oliver and Pharr derived from electron microscope. They found that the
hc. This contact depth could not be taken Sneddon's analysis was: calculated area was virtually identical to
as identical to the displacement sensed the imaged area for all the conditions and
during indentation, h, because during in- h s = 3P/(4S), Eq. 2
materials which they examined (aluminum,
dentation, the material around the contact where P is the applied force, and S is the titanium, sapphire, glass, and quartz).
tended to delect elastically as shown in elastic recovery of the material as the in- They explained that the sharp edges of
Figure 1, making hc less than h. Further, denter is retracted from the sample. Thus, the pyramid served to permanently mark
they had to face the possibility that the the contact depth could be calculated as: the corners of the indentation at the peak
small law at the tip of the indenter (Figure load, so that in fact, the inal indentation
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