A. Z. GU[TIN et al.: THE UNCERTAINTY OF HARDNESS MEASUREMENTS RELATED TO THE MEASUREMENT METHOD ...
897–904
THE UNCERTAINTY OF HARDNESS MEASUREMENTS
RELATED TO THE MEASUREMENT METHOD, SURFACE
PREPARATION AND RANGE OF THE MEASUREMENTS
ANALIZA MERILNE NEGOTOVOSTI IN DOLO^ITEV
METODOLOGIJE IZVAJANJ MERITEV TRDOT
Agnieszka Zuzanna Gu{tin
1*
, Borut @u`ek
1
, Bojan Podgornik
1
,
Varu`an Kevorkijan
2
1
Institute of Metals and Technology, Lepi pot 11, 1000 Ljubljana, Slovenia
2
Impol Aluminium Industry, Partizanska 38, 2310 Slovenska Bistrica, Slovenia
Prejem rokopisa – received: 2019-09-12; sprejem za objavo – accepted for publication: 2019-10-20
doi:10.17222/mit.2019.098
The main purpose of this paper is to present the changes in hardness-measurement uncertainty depending on the measurement
method, the number of measurements and the surface preparation. The experiments were executed on the AlCuMgPb aluminium
alloy series 2xxx, manufactured from one batch of homogenous material. The measurements were performed on milled and
polished surfaces using different hardness-test methods: Brinell, Vickers and Rockwell. The goal of this study was to select the
optimum hardness test method together with the surface preparation that provide the best results in terms of measurement
uncertainty. Finally, the results including the effect of the number of performed measurements for different surface preparations
were presented. The statistical deviation in the hardness-measurement results showed a lowest scatter of measured results for the
Rockwell method and the largest for the Brinell test. It was also concluded that the repeatability increased when surface of the
sample was polished, simultaneously only three measurements were needed, using the Brinell and Rockwell methods, to achieve
the minimum required error parameters.
Keywords: hardness measurements, surface preparation, measurement uncertainty, aluminum
Namen raziskave je bil analizirati spremembe vrednosti merilne negotovosti pri meritvah trdote glede na izbrano metodo
merjenja trdote, {tevilo ponovitev ter pripravo povr{ine. Preizkusi so bili izvedeni na aluminijevi zlitini AlCuMgPb serije 2xxx,
iz ene serije homogenega materiala. Meritve trdote z uporabo razli~nih metod merjenja (Brinell, Vickers in Rockwell) so bile
izvedene na poliranih in rezkanih povr{inah vzorcev. Cilj {tudije je bil identificirati optimalno metodo merjenja trdote skupaj z
ustrezno pripravo povr{ine, ki zagotavlja najbolj{e rezultate v smislu merilne negotovosti. Predstavljeni so rezultati, ki
vklju~ujejo vpliv {tevila opravljenih meritev za razli~no pripravo povr{ine. Nihanje rezultatov merjenja trdote je pokazalo
najmanj{i raztros v primeru meritev izvedenih po Rockwellu, najve~je nihanje pa je bilo pri merjenju trdote po Brinellu.
Ugotovili smo, da se je pri polirani povr{ini vzorca pove~ala ponovljivost meritev, obenem pa so bile potrebne pri uporabi
Brinellove in Rockwellove metode le 3 ponovitve za doseganje minimalnih parametrov odstopanja.
Klju~ne besede: meritve trdot, rezkana in polirana povr{ina, merilna negotovost, aluminij
1 INTRODUCTION
Hardness tests are one of the fastest and the least ex-
pensive methods for defining the mechanical properties
of materials.
1
Therefore, hardness testing is often used
for material assessment, during the research and develop-
ment of a material, as well as in the quality control of the
production process. The hardness method selected and
used should be determined by the microstructure, i.e., the
homogeneity of the material, as well as the type of
material, the size of the part and its condition. There are
three main hardness-measurement methods used for
metallic materials, each with their own set of benefits
and requirements, defined by appropriate standards,
which also explain the procedure and application of the
hardness test in details. The three most common inden-
tation hardness testes are: Brinell, Vickers and Rockwell.
The Vickers hardness (HV) is calculated by measuring
the size of an indent (diagonal lengths) left in the sample
material by pressing a diamond pyramid indenter with a
given load. The diagonals of the indent are measured
optically in order to determine the hardness, using a table
or formula. The Rockwell test (HR) is calculated by
measuring the depth of an indent after an indenter has
been forced into the specimen material at a given load.
The Brinell method (HB) requires optical reading of the
diameter of a hard ball indentation and then using a chart
to convert the average measurement to the Brinell
hardness value. The decision for the selection of the type
of the hardness test is significantly affected by the
dimension of the specimen as well as its hardness. For
softer metals and alloys the most appropriate and
accurate hardness method is the Brinell method. Im-
plementation of this method is possible on the specimens
with a relatively smooth surface. A very smooth polished
surface is necessary when the Vickers methods is used in
order to avoid an excessive measurement error.
2
Further-
Materiali in tehnologije / Materials and technology 53 (2019) 6, 897–904 897
UDK 620.1:620.178.151.6:001.82:620.178.1 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 53(6)897(2019)
*Corresponding author's e-mail:
agnieszka.gustin@imt.si (Agnieszka Zuzanna Gu{tin)

more, surface roughness is extremely important in in-
strumented indentation hardness testing, because the
mechanical properties of the tested material are
calculated on the assumption that the sample surface if
flat.
3,4
As mentioned, the surface condition influences both
the measured hardness value as well as the measurement
uncertainty, which is especially important in the
industrial environment, requiring high repeatability. The
characteristics of the empirically developed hardness
tests make it difficult to determine the measurement un-
certainty using methods based on mathematical models.
5
However, the European Association of National Metrol-
ogy Institutes has developed guidelines
6
t h a th e l pi n
estimating the uncertainty in hardness measurements. It
lists four main groups of influencing parameters that
affect the uncertainty of hardness measurements, with
the test piece non-homogeneity and its surface quality
being number one. This is followed by the hardness
testing machine, environment and operator. The surface
quality of the test piece may considerably influence the
results of hardness measurements, with a rougher surface
requiring a greater force and a larger indenter to produce
a larger indentation.
6
Furthermore, in general, the in-
fluence of roughness and material non-homogeneity can
be improved as the number of hardness measurements is
increased.
5
This study is focused on the selection of the most
appropriate hardness method together with a surface
preparation that enables the best results in terms of
measurement uncertainty when measuring the hardness
of Al alloys. Finally, the object is to study the differences
in the hardness results when the measurements are
performed on milled and polished specimens. The statis-
tical deviation in hardness measurement results is then
briefly discussed in order to verify the reliability of the
hardness measurements.
2 EXPERIMENTAL PART
The main goal of this research is to present a statis-
tical analysis of the hardness measurements performed
by three different hardness test methods: Brinell, Vickers
and Rockwell. For an easier comparison of the obtained
results, all the measurements were performed on the
same material and specimens. The used test material,
applied methods and equipment are described in the
sections below.
2.1 Test material
The hardness tests were performed on aluminium
alloy series 2xxx (AlCuMgPb) in T6 condition, manu-
factured from one batch of homogenous material. Test
specimens in the form of square blocks (10×10×100) mm
were cut from extruded rods of a 20 mm diameter and
surface finished by using standard milling and polishing
conditions (Figure 1). Due to the statistical relevance of
the results, ten measurements were carried out on each of
the five successive specimens in the milled and polished
state.
2.2 Test methods and equipment
The hardness measurements were performed by using
three hardness-test methods: Brinell (HBW), Vickers
(HV) and Rockwell (HRBW) according to the latest ISO
standards, which requires that the test shall be carried out
on a surface that is smooth and even, free from oxide
scale, lubricants and foreign material. The Brinell hard-
ness test was performed according to the SIST EN ISO
6506-1:2014 standard
7
using an Innovates NEXUS 7501
testing machine with a 2.5-mm-diameter ball and a load
of 62.5 kgf (HBW2.5/62.5). The Vickers hardness test
was performed according to the SIST EN ISO
6507-1:2018 standard
8
on a Wilson Instrument Tukon
2100B testing machine with a load of 10 kgf (HV10).
The Rockwell hardness test (HRBW) was performed
according to the SIST EN ISO 6508-1:2016 standard
9
using a Wilson Instruments B2000 testing machine, a
load of 100 kgf and a 1.587 mm diameter ball.
2.3 Test parameters
For each group of measurements the statistical
analysis was performed, which includes calculations of
the following parameters:
10
A. Z. GU[TIN et al.: THE UNCERTAINTY OF HARDNESS MEASUREMENTS RELATED TO THE MEASUREMENT METHOD ...
898 Materiali in tehnologije / Materials and technology 53 (2019) 6, 897–904
Figure 1: Examples of tested specimens with milled (left) and polished (right) surfaces

The average value:
x
n
x
i
i
n
=
=
∑
1
1
(1)
where n represents the number of measurements and x
i
the individual measurement.
The standard deviation s:
s
xx
n
i
i
n
=
−
−
=
∑()
2
1
1
(2)
s
s
x
%
=× 100 % (3)
The standard measurement uncertainty u:
u
s
n
= (4)
u
u
x
%
=× 100 % (5)
And the repeatability of measurements b:
b
xx
x
ax
=
−
m min
(6)
x
max
and x
min
represent the minimum and maximum
measured values from the set of measurements.
3 RESULTS
This section presents the results of the statistical
calculations according to the measurements performed
on one sample and then for all the tested samples. For
the discussion we chose one sample with calculated
statistical parameters that were the closest to the average
values.
3.1 Brinell test results
Measurement results from the milled and polished
surface according to the Brinell test are summarized in
Table 1 and graphically presented in Figure 2 and Fig-
ure 3, respectively.
For each of five samples in the milled state (1-M to
5-M) the average measured hardness value is between
116.3 and 117.9 HBW. The standard deviation (s) varies
from 0.48 % to 0.80 %, the estimated standard measure-
ment uncertainty (u) is between 0.15 % and 0.25 % and
the repeatability (b) is between 1.63 % and 2.76 %.
If all 50 individual measurements are taken into the
account, the average hardness value is 117.2 HBW, the
standard deviation (s) increases to 0.83 % and the
repeatability (b) to 3.70 %, while the estimated standard
measurement uncertainty (u) decreases to 0.12 %
(Table 1).
In the case of measurements performed on a polished
surface (1-P to 5-P) the mean hardness values are lower,
between 113.1 and 116.9 HBW. Lower are also the
standard deviation (s), from 0.25 % to 0.57 %, the esti-
mated standard measurement uncertainty (u), between
0.10 % and 0.18 % and the repeatability (b), from
0.85 % to 1.63 %.
Again, if all 50 individual measurements are taken
into account the standard deviation (s) decreases to
1.26 % and the estimated standard measurement uncert-
ainty (u) to 0.18 %, while the repeatability increases to
4.42 %. As can be seen from Figure 2, the hardness
measurements performed on the polished Al surface are
lower by 1–2 % compared to the milled one. Further-
more, for this single sample the standard deviation and
repeatability are reduced by about 40 %, when switching
from milled to polished surface. The standard deviation
was reduced from 0.64 % to 0.38 %, the estimated
measurement uncertainty from 0.20 % to 0.12 % and the
repeatability from 1.92 % to 1.09 % (Figure 3). On the
other hand, in the case of a polished surface, non-homo-
A. Z. GU[TIN et al.: THE UNCERTAINTY OF HARDNESS MEASUREMENTS RELATED TO THE MEASUREMENT METHOD ...
Materiali in tehnologije / Materials and technology 53 (2019) 6, 897–904 899
Figure 3: Influence of surface preparation on measurement error for
Brinell hardness test (Table 1)
Table 1: Statistical calculations according to the measurements per-
formed on five milled and polished specimens using the Brinell test
Deviation
calculations (%)
x sub
MILLED SURFACE
average per sample 117.2 HBW 0.64 0.20 1.92
all measurements 117.2 HBW 0.83 0.12 3.70
POLISHED SURFACE
average per sample 115.8 HBW 0.38 0.12 1.09
all measurements 115.8 HBW 1.26 0.18 4.42
Figure 2: The average Brinell hardness results obtained for milled and
polished specimens
Note: The min and max values of error bars are depicted with a cap
for polished and with no cap for milled samples for all diagrams.

geneity of the material becomes more pronounced,
resulting in a more than doubled standard deviation
(1.26 %), almost no changes of the estimated standard
measurement uncertainty (0.16%) and the repeatability
(4.42 %), when measurements over all five samples are
taken into the account (Figure 3).
3.2 Vickers test results
The results of the Vickers hardness measurements are
summarized in Table 2 and graphically presented in
Figure 4 and Figure 5.
In the case of measurements performed on a milled
surface, the average hardness value is between 119.9 and
123.5 HV10 (Figure 4), the standard deviation (s)i s
between 1.17 % and 2.76 %, the estimated measurement
uncertainty (u) between 0.44 % and 0.96 % and the
repeatability (b) between 3.48 % and 7.97 %. Results
show that in the case of the Vickers method the measure-
ment uncertainty for milled surfaces is considerably
greater (around three times) than in the case of the
Brinell hardness measurements.
If all the individual measurements are considered, the
average hardness value is 122.2 HV10, no changes of
standard deviation (s) 2.35 %, while the repeatability (b)
reaches 9.0 %, the estimated measurement uncertainty
(u) decreases to 0.33 % (Table 2).
In the case of measurements performed on polished
surfaces, again the mean measured hardness values are
lower, between 118.2 and 122.5 HV10, as shown in
Figure 4. Furthermore, also the measurement error has
been reduced by more than 40 %. However, it still
remains considerably larger than for the Brinell method.
The standard deviation is between 0.38 % and 0.80 %,
the estimated measurement uncertainty is between
0.12 % and 0.25 %, and the repeatability is between
1.24 % and 2.55 %.
If all 50 individual measurements are taken into the
account, the standard deviation decreases to 1.31 %, the
estimated uncertainty to 0.29 % and the repeatability to
5.13 % (Table 2).
According to the measurements performed on a
single sample switching from a milled to a polished sur-
face, the results in the standard deviation, the estimated
measurement uncertainty, and the repeatability are
reduced by 3–4 times (Figure 5). Again, in the case of
measurements performed on a polished surface, the
effect of inhomogeneity of the material is observed,
which reflects the same trend as in the case of the Brinell
test. The standard deviation decreases from 2.35 % to
1.31 %, the estimated measurement uncertainty from
0.33 % to 0.29 %, and the repeatability from 9.0 % to
5.13 % when taking all the measurements into account
(Figure 5).
3.3 Rockwell test results
The results of the Rockwell hardness testing per-
formed on milled and polished specimens are
summarized in Table 3 and graphically presented in
Figure 6 and Figure 7.
In the case of the milled surface, the average
measured value is between 67.8 and 68.5 HRB, see
Figure 6, the standard deviation (s) between 0.25 % and
0.91 %, the estimated measurement uncertainty (u)
between 0.07 % and 0.19 % and the repeatability (b)
between 0.74 % and 2.51 %. This is very comparable to
the results of the Brinell hardness measurements.
If all 50 individual measurements are taken into
account, the average hardness value is 68.1 HRB, the
standard deviation (s) increase to 0.74 % and the
repeatability (b) to 3.38 %, while the estimated measure-
ment uncertainty (u) decreases to 0.10 % (Table 3).
In the case of measurements performed on a polished
surface the measurement error has improved compared
to the milled surface. When performing a measurement
A. Z. GU[TIN et al.: THE UNCERTAINTY OF HARDNESS MEASUREMENTS RELATED TO THE MEASUREMENT METHOD ...
900 Materiali in tehnologije / Materials and technology 53 (2019) 6, 897–904
Figure 5: Influence of surface preparation on the measurement error
for the Vickers test method (Table 2)
Table 2: Statistical calculations according to the measurements per-
formed on five milled and polished specimens using the Vickers test
Deviation
calculations (%)
x sub
MILLED SURFACE
average per sample 122.2 HV 2.39 0.75 7.59
all measurements 122.2 HV 2.35 0.33 9.00
POLISHED SURFACE
average per sample 120.9 HV 0.51 0.16 1.78
all measurements 120.9 HV 1.31 0.29 5.13
Figure 4: Average Vickers hardness results obtained for milled and
polished specimens

on a single specimen the standard deviation (s)i sb e t -
ween 0.17 % and 0.56 %, the estimated measurement
uncertainty (u) between 0.05 % and 0.18 % and the
repeatability (b) between 0.58 % and 2.02 %.
Taking into account all 50 individual measurements,
the standard deviation (s) is 1.11 %, the measurement
uncertainty 0.16 % and the repeatability (b) 4.22 %
(Table 3).
According to measurements performed on a single
sample a polished surface provides a lower measurement
reliability. The standard deviation decreased from 0.64 %
to 0.50 %, the estimated measurement uncertainty from
0.20 % to 0.16 %, and the repeatability from 2.06 % to
1.78 % (Figure 7). However, the situation is the opposite
when considering all the measurements performed on
5 samples. In this case the standard deviation being
increased to 1.11 %, the repeatability to 4.22 % and the
estimated measurement uncertainty does not change
(Figure 7).
4 DISCUSSION
Besides the surface preparation and quality, the num-
ber of performed measurements considerably influences
the measurement error and uncertainty. The measured
results for Brinell, Vickers and Rockwell hardness
testing using a different number of measurements are
depicted in Figures 8 to 10.
According to the Brinell test (Figure 8 and Figure 9)
increasing the number of performed measurements from
2 to 10 has only a minor effect on the average value and
repeatability, with the differences being less than 1.0 %
for the milled and even below 0.2 % for the polished
surface. On the other hand, the number of performed
measurements has a significant influence on the
measurement reliability, including the standard deviation
and measurement uncertainty (Figure 9).
If only two HBW measurements are performed on
the milled surface, the standard deviation is above 2 %,
the estimated uncertainty is 1.6 % and repeatability
amounts to 2.7 % (Figure 9). To achieve a standard de-
viation of less than 1 % and a measurement uncertainty
of less than 0.5 %, it is necessary to carry out 7 to 10
measurements (Figure 9). In the case of the polished
surface only three to five measurements are sufficient to
obtain a standard deviation lower than 1 % and a me-
asurement uncertainty lower than 0.5 % (Figure 9).
In the case of the Vickers hardness measurement
(Figure 10), the influence of the number of performed
measurements is even more visible, as well as the
influence of surface preparation. On the milled surface
10 measurements are required to achieve a measurement
uncertainty of less than 1.5 % and a standard deviation of
less than 3.5 %, while on the polished surface already
three measurements provide a standard deviation below
1.5 % and a measurement uncertainty below1%( Fig-
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Materiali in tehnologije / Materials and technology 53 (2019) 6, 897–904 901
Figure 6: Average Rockwell hardness results obtained on milled and
polished specimens
Figure 8: Influence of the number of performed measurements on the
average value for Brinell, Vickers and Rockwell hardness test,
respectively
Figure 7: Influence of surface preparation on the measurement error
for the Rockwell test method (Table 3)
Table 3: Statistical calculations according to measurements performed
on five milled and polished specimens by the Rockwell test
Deviation
calculations (%)
x sub
MILLED SURFACE
average per sample 68.1 HRB 0.64 0.20 2.06
all measurements 68.1 HRB 0.74 0.10 3.38
POLISHED SURFACE
average per sample 68.8 HRB 0.50 0.16 1.78
all measurements 68.8 HRB 1.11 0.16 4.22

ure 10). By increasing the number of measurements on
the polished surface to 7 standard deviation close to 1 %
and a measurement uncertainty less than 0.5 % is
achieved.
In the case of the Rockwell test method the influence
of the number of performed measurements on the
measurement reliability is depicted in Figure 11. Similar
to the Brinell and Vickers methods the change in average
value is minor when increasing the number of measure-
ments from 2 to 10. The difference is less than 0.5 %.
Furthermore, already three measurements are sufficient
to provide a standard deviation of lower than1%( Fig-
ure 11) and a measurement uncertainty lower than 0.5 %
(Figure 11) if the surface is polished. For the milled
surface these values are obtained when performing five
measurements. A further increase in the number of
performed measurements no longer significantly affects
the reliability of the results. A much bigger influence and
improvement is obtained with the surface polishing.
An analysis of measurement uncertainty (u), standard
deviation (s) and repeatability (b) shows that the highest
uncertainty in the hardness measurements performed on
Al alloys occurs for the Vickers hardness test, being
almost three times higher than the Brinell and Rockwell
methods (Figure 12). On the other hand, the best results
in terms of measurement reliability are obtained for the
Rockwell test, with the measurement uncertainty being
between 0.18 % and 0.14 % and for the Brinell from
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902 Materiali in tehnologije / Materials and technology 53 (2019) 6, 897–904
Figure 9: Influence of the number of performed measurements on the
measurement reliability for the Brinell test method
Figure 10: Influence of the number of performed measurements on
the measurement reliability for the Vickers test method

0.20 % to 0.12 %. Looking at different preparations of
the surface (milled or polished), again surface polishing
has the biggest influence in the case of the Vickers test
method, improving the measurement uncertainty by
about 75 % (Figure 12). In the case of the Brinell test
method the improvement is about 40 % and for Rockwell
about 20 %.
5 CONCLUSIONS
The measurement reliability analysis of different
hardness measurement methods applied on an Al 2xxx
series aluminium alloy, including the calculation of the
average value, measurement uncertainty (u), standard
deviation (s) and repeatability (b), has been presented.
The results of the analysis can be summarized in the
following conclusions:
– Surface polishing has a considerable influence on
the measurement uncertainty for Al alloys’ hardness
measurements. The biggest effect is observed in the
case of Vickers hardness measurements, with po-
lished surfaces providing 4–5 times lower measure-
ment uncertainty and deviation.
– Uncertainty in Al alloys hardness measurement is
the highest for the Vickers hardness test, almost
three times higher than the Brinell and Rockwell
measurement methods.
– For the Vickers hardness tests at least 10 measure-
ments on a milled surface have to be performed in
order to achieve a measurement uncertainty below
1.5 %, while for the polished surface 3–5 measure-
ments are enough. On the other hand, the number of
performed measurements has practically no in-
fluence on the average hardness value and repeat-
ability.
– To achieve the same measurement uncertainty of
1.5 %, at least 5 measurements need to be performed
on milled and at least 3 measurements on a polished
surface when using the Brinell and Rockwell
methods, respectively.
– In general, performing hardness measurements on
several samples reduces the measurement uncert-
ainty but emphasizes the material non-homogeneity,
especially in combination with polished surfaces.
Acknowledgment
This research was a part of an interlaboratory pro-
ficiency project carried out between industry and the
materials testing facility at the Institute of Metals and
Technology, which was partly financed by the Slovenian
Research Agency (research core funding No. P2-0050)
and the company Impol.
A. Z. GU[TIN et al.: THE UNCERTAINTY OF HARDNESS MEASUREMENTS RELATED TO THE MEASUREMENT METHOD ...
Materiali in tehnologije / Materials and technology 53 (2019) 6, 897–904 903
Figure 11: Influence of the number of performed measurements on
the measurement reliability for the Rockwell test method
Figure 12: Comparison of measurement reliability for different
hardness test methods and surface preparation when applied to Al
alloys

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904 Materiali in tehnologije / Materials and technology 53 (2019) 6, 897–904