Li-na Zhu,1,2 Bin-shi Xu,2 Hai-dou Wang,1,3 and Cheng-biao Wang1
Comparison of Four Different Methods toDetermine the Hardness of Plasma-sprayedCr3C2–NiCr Coating by Nano-indentation
Reference
Zhu, Li-na, Xu, Bin-shi, Wang, Hai-dou, and Wang, Cheng-biao, “Comparison of Four Different Methods to
Determine the Hardness of Plasma-sprayed Cr3C2–NiCr Coating by Nano-indentation,” Journal of Testing
and Evaluation, Vol. 43, No. 1, 2015, pp. 108–114, doi:10.1520/JTE20130278. ISSN 0090-3973
ABSTRACT
A Cr3C2–NiCr coating with a thickness of 200 lm was deposited on an AISI 1045 steel
substrate using a supersonic plasma-spray technique. The hardness of the Cr3C2–NiCr
coating was characterized by a nano-indenter equipped with an atomic force microscope
(AFM). The AFM images indicated that the nano-indents on the Cr3C2–NiCr coating
exhibited significant “pile-up” deformation. Such pile-up behavior needs to be taken into
account in hardness determination because the pile-up height accounts for a large
proportion of the indentation depth. In this paper, four different methods are compared to
determine the hardness of the Cr3C2–NiCr coating: the Oliver–Pharr method, two work-of-
indentation methods (total work of indentation and plastic work of indentation), and an
AFM analysis method. The results show that the Oliver–Pharr and work-of-indentation
methods overestimated the hardness, and the AFM analysis method is considered as a more
accurate method for determining the hardness of the Cr3C2–NiCr coating.
Keywords
indentation, hardness, atomic force microscopy
Introduction
Cr3C2–NiCr coatings have been used extensively to resist wear [1–3]. Recently, the supersonic
plasma spray (SPS) process has become preferable for depositing such coatings [4,5]. During
spraying, the velocity of melted particles can exceed sound velocity. The coatings deposited via the
Manuscript received October 25, 2013;
accepted for publication February 12,
2014; published online October 10, 2014.
1 School of Engineering and Technology,
China Univ. of Geosciences, Beijing
100083, China.
2 National Key Lab for Remanufacturing,
Academy of Armored Forces
Engineering, Beijing 100072, China.
3 School of Engineering and Technology,
China Univ. of Geosciences, Beijing
100083, China.
(Corresponding author),
e-mail: [email protected]
Copyright VC 2014 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. 108
Journal of Testing and Evaluation
doi:10.1520/JTE20130278 / Vol. 43 / No. 1 / January 2015 / available online at www.astm.org
SPS process exhibit high density, low porosity, and excellent ad-
hesive strength relative to conventional plasma-sprayed coat-
ings. This can greatly increase the hardness of Cr3C2–NiCr
coatings to improve the wear resistance of various sliding com-
ponents. Thus, it is quite important to determine the hardness
of Cr3C2–NiCr coatings for investigating their wear resistance
and service performance.
Nano-indentation has been used widely to determine the
mechanical properties (hardness, modulus of elasticity, etc.) of
bulk solids, thin films, and coatings [6–8]. The Oliver–Pharr
method [9] is used commonly to measure hardness from force-
depth curves, but it does not take into account the “pile-up”
phenomena in the calculation of contact area, resulting in an
overestimate of the hardness.
Based on the work of indentation, Tuck et al. [10] suggested
two work-of-indentation methods to measure hardness. The
hardness was calculated based on the total work and plastic
work and was expressed as
HWt ¼kP3
max
9W2t
(1)
HWp ¼kP3
max
9W2p
(2)
where:
Pmax¼ peak force,
Wt¼ total work,
Wp¼ plastic work, and
k¼ constant equal to 0.0408 for a Berkovich indenter.
Figure 1 shows the typical force-depth relationship curve.
For the Berkovich indenter, the loading curve has usually been
expressed by Kick’s law,
P ¼ Ch2(3)
where C is a constant.
The total work Wt, given by the area under the loading
curve, can be obtained via integration.
Wt ¼ðhmax
0Pdh ¼
ðhmax
0Ch2dh ¼ Pmaxhmax
3(4)
where hmax is the maximum penetration depth.
The unloading curve is usually well approximated by a
power law relation,
P ¼ a h� hrð Þm(5)
where a and m are power law fitting constants.
The elastic work We, given by the area under the unloading
curve, can be determined by integrating the unloading curve.
We ¼ðhmax
hr
PðhÞdh ¼ðhmax
hr
a h� hrð Þmdh
¼ a hmax � hrð Þmþ1
mþ 1¼ Pmax
mþ 1hmax � hrð Þ
(6)
Thus, the plastic work Wp is the difference between Wt and
We.
Wp ¼Wt �We ¼m� 2ð Þhmax þ 3hr
3 mþ 1ð Þ Pmax(7)
In our previous work [11] the hardness was determined
based on atomic force microscope (AFM) images by consider-
ing the pile-up effect on the real contact area. The hardness was
calculated using the following equation:
A ¼ 14:175hp
120 sin2h2
� 3ctgh2þ
ffiffiffi3p
0B@
1CAðhmax þ havep Þ
2(8)
The value of h can be determined using the geometrical rela-
tionships. In Eq 8, h depends on the material properties of the
coating [12], and havep is the average value of the pile-up heights
around the three sides of the nano-indent.
The projected heights of pile-up material x can be obtained
directly from the AFM cross-section profile of the nano-indent.
In addition, they can be calculated using the geometrical rela-
tionships [11].
x ¼ 3:7651� cos h
2
sinh2
hmax þ havep
� �(9)
By combining Eqs 8 and 9, one can determine the hardness
of pile-up materials.
In this study, the hardness of a Cr3C2–NiCr coating was
determined using the Oliver–Pharr method, work-of-indenta-
tion methods, and the previously proposed AFM method.
FIG. 1 Typical force-depth relationship curve.
ZHU ET AL. ON HARDNESS OF Cr3C2–NiCr COATING 109
Comparisons of the hardness values obtained via these methods
were made in order to determine which method is the more
accurate for calculating hardness for the pile-up material.
Experimental
Cr3C2–NiCr coating was deposited on AISI 1045 steel substrate
using the SPS technique. A high-efficiency plasma spraying sys-
tem with a supersonic gun developed by National Key Lab for
Remanufacturing (Beijing, China) was used to prepare the
Cr3C2–NiCr coating. The system consists of a plasma torch,
power feeder, gas supply, water-cooling circulator, control unit
with a computer interface, and power supply unit. Figure 2
and Table 1 show the morphology and composition of
Cr3C2–25 %NiCr powders, respectively. Aggregate-sintered
Cr3C2–25 %NiCr powders (KF-70) were fabricated by Beijing
General Research Institute of Mining and Metallurgy (China)
with a nominal grain size of 10 to 45lm and a polygonal shape.
Prior to spraying, the substrate was grit blasted using Al2O3
with a particle size of approximately 300lm. Subsequently, a
Ni–Al bond coating was deposited in order to increase the
bond strength between the Cr3C2–NiCr coating and the sub-
strate. Table 2 lists the parameters used in the plasma-spraying
process. Finally, a Cr3C2–NiCr coating with a thickness of
200 lm was obtained, as shown in Fig. 3. Some microporosity
existed in the coating, but no visible microcracks were found.
The porosity of the Cr3C2–NiCr coating was evaluated via the
image analysis method [13]. Some 20 digital scanning electron
microscope (SEM) images with a magnification of 1000� were
taken randomly of the Cr3C2–NiCr coatings to obtain a repre-
sentative porosity value. As an example, the corresponding
image showing the outlines of pores and microcracks after
image processing from the original SEM image in Fig. 3
is shown in Fig. 4. The porosity value obtained for the
Cr3C2–NiCr coatings was 1.68 %.
The sample for hardness measurement was first ground
using emery with a grit size of 6 to 10lm and then polished
further using diamond paste with a particle size of 0.5 to
1.5 lm. The average roughness of the polished surface Ra was
5.46 1.2 nm. The hardness of the Cr3C2–NiCr coating was
characterized using a TriboIndenterVR (Hysitron Corporation,
USA) equipped with a diamond Berkovich indenter that was
also used as an AFM tip with a radius of curvature of <50 nm.
Because the Cr3C2–NiCr coating had some micropores, the
locations of indents were selected so as to keep away from any
micropores. Indents were performed over a range of forces
from 7 to 9mN. A minimum of nine indents was made per
FIG. 2 Morphology of Cr3C2–NiCr powders.
TABLE 1 Composition of Cr3C2–NiCr powders.
Element Cr B Ni Si Fe Cr3C2
wt. % 5 1.8 20 5 5 63.2
TABLE 2 Plasma spraying parameters.
Parameter Ni/Al Cr3C2–NiCr
Primary gas, Ar, m3/h 3.6 4.0
Secondary gas, H2, m3/h 0.3 0.2
Secondary gas, N2, m3/h 0.6 0.6
Powder feed rate, g/min 30 40
Spraying current, A 340 400
Spraying voltage, V 140 140
Spraying distance, mm 150 100
FIG. 3 Morphology of the Cr3C2–NiCr coating.
Journal of Testing and Evaluation110
applied force. The indented surfaces were then imaged after in-
dentation. The hardness at each peak force was averaged over
the nine measurements.
Results and Discussion
FORCE-DEPTH CURVES
Figure 5 shows nine typical force-depth curves for the
Cr3C2–NiCr coating at a peak force of 7mN. Similar force-
depth curves were obtained at other peak forces. As the depos-
ited Cr3C2–NiCr coating had low porosity and the locations of
indents were far from any micropores, the nine force-depth
curves had little dispersion. Figure 6 shows force-depth curves
for the Cr3C2–NiCr coating at different peak forces. For
nano-indentation tests, reproducibility is very important. If the
reproducibility of a nano-indentation test is poor, the data
obtained will have a large scatter and cannot be accurately
analyzed. A good way to check the reproducibility of a nano-
indentation test is to compare force-depth curves at different
peak forces [14]. The loading curves under different peak forces
should be fitted by one curve, and the unloading curves should
exhibit regular spacing. Note that the loading curves of the
Cr3C2–NiCr coating at different peak forces trace each other
very well, thereby showing good repeatability for these
experiments.
In addition, because the contact area in nano-indentation is
measured indirectly from the depth of penetration, the surface
roughness can cause severe errors when determining the
contact area between the nano-indenter and the specimen. The
nano-indentation depth should be at least 20 times the surface
roughness [15]. In the present study, the indentation depth
ranged between 160 and 180 nm at different peak forces that
was more than 20 times greater than the surface roughness of
the Cr3C2–NiCr coating (i.e., 5.46 1.2 nm). Therefore, the
errors caused by the surface roughness can be ignored.
PILE-UP DEFORMATION
The two most common modes of indentation deformation are
pile-up and sink-in. The results of finite element studies by Bol-
shakov and Pharr show that the amount of pile-up or sink-in
depends on the ratio hf/hmax and the work-hardening behavior
[16]. The pile-up is large only when hf/hmax is close to 1 and the
degree of work hardening is small. When hf/hmax< 0.7, very lit-
tle pile-up is observed regardless of the work-hardening behav-
ior of the materials. Figure 7 shows the ratios of hf/hmax of the
Cr3C2–NiCr coating at different peak forces. The ratio hf/hmax
at each peak force is less than 0.7, but significant pile-up was
observed, as shown in Fig. 8. This shows that the deformation
FIG. 4 The corresponding image showing the outlines of pores and
microcracks after image processing of Fig. 3.
FIG. 5 Typical force-depth curves of the Cr3C2–NiCr coating at a peak force
of 7 mN.
FIG. 6 Force-depth curves of the Cr3C2–NiCr coating at different peak
forces.
ZHU ET AL. ON HARDNESS OF Cr3C2–NiCr COATING 111
mode is not determined only by hf/hmax. An accurate determi-
nation of hf/hmax depends on the surface states of the coatings,
surface irregularity, surface heterogeneity, and surface disconti-
nuity. Therefore, an AFM should be used as well to observe the
nano-indents in order to determine the deformation modes.
Figure 9 shows the variation of the pile-up height hp with
peak force. The pile-up height increased with increasing peak
force. The pile-up height ranged between 17 and 26 nm, and it
accounted for a large proportion of the indentation depth of
160 to 180 nm. Therefore, the pile-up height should not be
ignored when calculating the actual contact area. From the
AFM images, the real or actual contact area including the piled-
up deformation area can be calculated based on the idea that
the pile-ups form an arc along the triangular edges [11].
HARDNESS CALCULATION
The hardness of the Cr3C2–NiCr coating was finally determined
using the Oliver–Pharr method, work-of-indentation methods,
and AFM images.
Let HOP be the hardness calculated directly from the force-
depth curve using the Oliver–Pharr method.
HWt: hardness calculated using Eq 1
HWp: hardness calculated using Eq 2
HAFM: hardness calculated using Eqs 8 and 9
In Eqs 8 and 9, the determination of h is an important step.
Figure 10 shows h values of the Cr3C2–NiCr coating at different
peak forces. In this instance it was found that h was approxi-
mately a constant and independent of the peak force. The aver-
age value of h was 96.4�. It is also noted that h may depend on
the inherent properties of the Cr3C2–NiCr coating.
Figure 11 shows the plot of hardnesses HOP, HWt, HWp, and
HAFM versus peak force. The HOP values are nearly the same at
various peak forces, ranging between 9.15 and 9.30GPa. The
hardness values calculated via the plastic work method (i.e.,
HWp) are the greatest. Note that HWp is nearly three times
greater than HOP. Also, HWt is close to HOP, but the former is
slightly greater than the latter. In the present study, HWt and
HWp are both greater than HOP. However, HWt is shown to be
FIG. 8 Typical three-dimensional image of nano-indent at 9 mN.
FIG. 9 Variation of pile-up height with peak force.
FIG. 10 h values at different peak forces.
FIG. 7 hf/hmax at different peak forces.
Journal of Testing and Evaluation112
less than HOP in other publications [8,17]. This may be attrib-
uted to the different methods of calculating We and Wp. For
example, in Refs 8 and 17, We and Wp are calculated based on
the assumption that the ratio of hr/hmax is equivalent to the ratio
of Wp/Wt. In fact, from Eqs 4 and 7, Wp/Wt¼ [(m� 2)/
(mþ 1)]þ 3(hr/hmax).
For pile-up materials, the Oliver–Pharr method does not
consider the pile-up area, and thus overestimates the hardness.
The hardness values HWt and HWp are both greater than
HOP, and it is obvious that the work-of-indentation methods
also lead to an overestimate of the hardness. The work-of-
indentation methods are based on empiricisms or semi-
empirical equations, and the hardness values obtained will be
influenced by many factors such as testing conditions, instru-
mentation, material irregularities, and the initial state of the
material’s surface [8]. Therefore, the Oliver–Pharr method and
work-of-indentation methods are both inaccurate for pile-up
materials.
The value of HAFM is the least amongst those calculated via
the four methods. As HAFM is obtained by analyzing the indent
images and the pile-up area is considered, the AFM hardness
seems closer to the true hardness than the values obtained via
the other three methods considered. It can be concluded that
the AFM analysis method based on the direct observation of
indents and geometrical deduction is the more accurate and
believable for materials that produce pile-up.
It should be noted that the coating microstructure has an
obvious effect on the measured hardness value. Although the
SPS technique can greatly improve the coating quality, micro-
pores and interlamellar boundaries in the Cr3C2–NiCr coating
are unavoidably formed. The interlamellar boundaries can be
regarded as micropores parallel to the coating surface [18]. If
the indentation location is close to micropores or interlamellar
boundaries, the indentation depth will increase. This will lead to
an increase in the contact area and subsequent decrease in
hardness. Therefore, in order to increase the accuracy of the
measurement, the locations of indents should be selected care-
fully through optical microscopy or atomic force microscopy to
avoid micropores or interlamellar boundaries as far as possible.
Conclusions
The hardness of a plasma-sprayed Cr3C2–NiCr coating
has been investigated based on nano-indentation. The experi-
ments showed good repeatability. The nano-indents of the
Cr3C2–NiCr coating exhibited significant pile-up deformation.
The results have been analyzed via the Oliver–Pharr method,
work-of-indentation methods, and the AFM method. The hard-
ness values were overestimated by the Oliver–Pharr method
and work-of-indentation methods. In this paper, the AFM anal-
ysis method based on AFM observations of indents and geomet-
rical perturbations was shown to be the more accurate method
for determining the hardness of a Cr3C2–NiCr coating.
ACKNOWLEDGMENTS
This paper was supported financially by NSF of Beijing
(3120001), NSFC (51275105), Distinguished Young Scholars of
NSFC (51125023), and Fundamental Research Funds for the
Central Universities.
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Journal of Testing and Evaluation114