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: wanghaidou@aliyun.com

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