Thin Solid Films 520 (2012) 2375–2389
Contents lists available at SciVerse ScienceDirect
Thin Solid Films
journal homepage: www.elsevier.com/locate/tsf
Critical review
Toughness evaluation of hard coatings and thin films
Sam Zhang ⁎, Xiaomin Zhang
School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
a r t i c l e
i n f o
Available online 24 September 2011
Keywords:
Thin films
Coatings
Fracture toughness
a b s t r a c t
Enormous progress has been achieved over the past decade in evaluating the toughness of hard coatings and
thin films. This paper reviews methodologies developed based on indentation, bending, and microtensile
testing. In addition, we discuss a recent development in fracture toughness measurement which involves
the application of macrotension to a substrate in order to induce microtension in a patterned thin film.
© 2011 Elsevier B.V. All rights reserved.
Contents
1.
2.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Qualitative assessment . . . . . . . . . . . . . . . . . . . . . . . .
2.1.
Indentation plasticity . . . . . . . . . . . . . . . . . . . . .
2.2.
Scratch toughness . . . . . . . . . . . . . . . . . . . . . . .
3.
Quantitative toughness characterization for coatings . . . . . . . . . .
3.1.
Toughness evaluation from radial cracks . . . . . . . . . . . .
3.2.
Toughness evaluation from circumferential cracking and spallation
3.3.
Toughness evaluation from channel cracking . . . . . . . . . .
4.
Microtensile testing of fracture toughness for standalone thin films . . .
4.1.
Inchworm actuation . . . . . . . . . . . . . . . . . . . . . .
4.2.
Membrane deflection . . . . . . . . . . . . . . . . . . . . .
4.3.
Tension by residual stress . . . . . . . . . . . . . . . . . . .
4.4.
Bulging of films . . . . . . . . . . . . . . . . . . . . . . . .
4.5.
Macrotension of substrate . . . . . . . . . . . . . . . . . . .
5.
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.
Hard coatings . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.
Thin films . . . . . . . . . . . . . . . . . . . . . . . . . . .
Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1. Introduction
Toughness is one of the important mechanical properties of a material. The term toughness refers to the ability of a material to absorb
energy during deformation up to fracture [1–2], usually measured in
terms of fracture toughness. In classical mechanics, fracture toughness
refers to the stress resistance of a material to fracture in the presence
of a flaw, i.e. the highest stress intensity that the material can
⁎ Corresponding author. Tel.: + 65 6790 4400; fax: + 65 6791 1859.
E-mail address: msyzhang@ntu.edu.sg (S. Zhang).
0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.tsf.2011.09.036
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withstand without fracture [3]. It is measured as the maximum stress
intensity factor under plane strain condition [4–5]. To meet the “plane
strain” condition, the specimen dimensions, t, a and (W−a), should
respectively satisfy the following inequality:
t; a; ðW−aÞ ≥ 2:5
KIC
σy
!2
;
ð1Þ
where t and W are specimen thickness and width respectively, a is the
flaw size, σy is the yield stress, and KIC is the critical stress intensity
that a material can withstand without fracture. In essence, Eq. (1) requires that the sample thickness should be large enough, while the
2376
S. Zhang, X. Zhang / Thin Solid Films 520 (2012) 2375–2389
initial crack length and the “no-crack” region (i.e., W− a) should not
be too small. For brittle bulk materials, the minimum thickness t is
several to tens of micrometers [5–6]. For thin films, however, where
t usually ranges from nanometers to a few micrometers, the plane
strain condition is not met.
Measurement of fracture toughness for bulk materials is classical,
and is done routinely in research or production using, for example,
the Charpy test, four-point or three-point bending, etc. [7–8]. However, these methods barely apply for a thin film due to the size limitation
of the film thickness. Various methodologies have been developed for
microtensile testing of freestanding thin films, attempting to resolve
the technique difficulties in fabricating a standalone thin film specimen and then clamping and testing. For hard coatings bonded to substrates, researchers make use of nanoindentation on coatings or
bending of ductile substrates to generate different types of coating
cracking, based on which various methods for fracture toughness
measurement are proposed. In fracture mechanics, coating cracking
is a lot more complex. Some hypotheses were put forth for approximation in these methods, resulting in data treatment which is not comparable. It is the aim of this paper to provide an overview of the available
toughness testing methodologies for hard coatings and thin films. Recent developments in microtensile testing of thin films will be
emphasized, especially the application of macrotension to a substrate
in order to induce microtension in a patterned thin film. Commonly
used qualitative methods will be described first.
In this paper, the term “film” refers to a freestanding film (i.e.,
without substrate), while “coating” refers to a film attached to a substrate. It is necessary to make this distinction because a substrate renders support and also brings constraints on the deformation and
fracture of the coating.
In all equations in this paper, K is the stress intensity factor of a
crack in a coating or a film and KC is the fracture toughness (critical
stress intensity factor); for the opening mode of cracking, the subscript ‘I’ is used; σ is the stress in a coating or a film; and t denotes
film thickness. E, H, υ, n are the Young's modulus, hardness, Poisson's
ratio, and the hardening exponent of a coating or a film; in some
cases, subscripts ‘f’ and ‘s’ are added to these symbols to distinguish
coating and substrate. The terms a, b, c, W, l, etc. are used to describe
geometric sizes of testing specimens, and their meanings are defined
in the text.
2. Qualitative assessment
Indentation plasticity [9–11] and scratch toughness or “load-bearing
capacity” [11–14] are, due to their operational simplicity [15], the two
most widely used qualitative methods for determining the toughness
of coatings.
2.1. Indentation plasticity
Plastic
deformation
Elastic
deformation
Fig. 1. Schematic plot of a nanoindentation load–displacement curve. Plasticity is calculated as OA/OB = plastic work / (plastic work + elastic work) [15–16].
plasticity in terms of the mechanical work done during different
stages of indentation measurement,
MDP ¼ plastic work=ðplastic work þ elastic workÞ:
ð3Þ
However, plasticity is not toughness. Plasticity is the capacity to
resist plastic deformation (dislocation movement), while toughness
measures the ability of a material to resist crack propagation.
2.2. Scratch toughness
Scratch testing is most widely used in evaluating the adhesion
strength of hard coatings. During the test, a diamond stylus subjected
to a linearly increasing load is drawn across the coated surface until adhesion failure is induced at a critical load. Generally (but not necessarily), for hard coatings, microcracks appear in the scratch track before
failure occurs [19]. The minimum load at which the first crack occurs
is termed the “lower critical load” Lc1, and the load corresponding to
complete delamination peeling of the coating is the “higher critical
load” Lc2 (Fig. 2). Some researchers have directly used the lower critical
load to indicate crack resistance, or even termed it “scratch toughness”
[9,12,14,20–23]. Zhang et al. [24] pointed out that the coating toughness
should be proportional to both the lower critical load and the difference
between the higher and the lower critical load. Obviously, a coating can
have an early crack, but if it fractures or peels off at very high load, it
means that the coating has a very high “toughness” because, during
the measurement, the coating has successfully resisted the propagation
of the crack. How long the coating can resist delamination and withstand further loading before catastrophic fracture occurs is as important
Indentation plasticity is defined as the ratio of the plastic displacement divided by the total displacement in the load–displacement
curve of a nanoindentation measurement [16] (see, for example,
Fig. 1),
plasticity ¼
εp OA
;
¼
OB
ε
ð2Þ
Total peeling
Cracking occurs
where εp is the plastic deformation and ε is the total deformation. OA
and OB are displacements defined in Fig. 1. Nanoindentation has
found a wide application in evaluating coating “toughness”. As reported,
nc-TiC/a-C coatings (nc = nanocrystalline and a = amorphous) have an
indentation plasticity of 40% [17], while that of nc-TiC/a-C(Al) coatings
is 55% [10].
In a related approach, Fox-Rabinovich et al. [11,18] proposed the
“microhardness dissipation parameter” (see Fig. 1) to express the
Fig. 2. Typical scratch adhesion profile for nc-TiN/a-SiNx coatings deposited on silicon
wafers [15].
S. Zhang, X. Zhang / Thin Solid Films 520 (2012) 2375–2389
P
2377
calculation of the tensile stress induced in the coating during scratch
operation (see example in Fig. 4),
pffiffiffi
KI ¼ σ bf ða; bÞ
F
2R
2a
ð6Þ
σ is the tensile stress which induces the crack, a is the crack length,
and b is the crack spacing. f(a, b) is a nondimensional function dependent on crack length a, and crack spacing b. Practical application of
this method is difficult as there is no general expression for σ
obtained through a three-dimensional finite element model.
3. Quantitative toughness characterization for coatings
Groove track
Fig. 3. Schematic diagram of a microscratch fracture toughness measurement with a
pressure P opening a crack of maximum width 2a out of a groove width 2R [25].
as crack initiation. A new parameter termed “scratch crack propagation
resistance” is thus proposed to directly use the scratch results to indicate coating toughness,
CPRS ¼ Lc1 ðLc1 −Lc2 Þ:
ð4Þ
Hoehn et al. [25] proposed a simplified model of a scratch in order
to formulate an expression for fracture toughness of coatings (see
Fig. 3):
KIC ¼
2pfg a 1=2
−1 R
;
sin
a
R cotθ π
2
ð5Þ
where p is the pressure required to open the crack, R is the radius of
the indenter cone into the groove, 2a is the total crack length, and fg
is the coefficient of grooving friction, which depends on the cone
angle 2θ and can be obtained from the scratch track width and the
depth of penetration. However, the model is oversimplified, and the
actual state of forces in the groove ahead and right below the tip is
much more complex and has to be taken into account for a better
description of the process. Holmberg et al. [26] designed a 3-D finite
element model for the determination of fracture toughness via
For a hard coating well bonded with the substrate, three types of
cracking patterns may be introduced through indentation of the coating
or bending of the substrate: radial cracking, circumferential cracking
and spallation, and channel cracking. All these modes of cracking are
used for quantitative analyses of the fracture toughness of the coating.
3.1. Toughness evaluation from radial cracks
Radial cracks may be introduced at the surface of a ceramic material when indenting with a sharp edge indenter, e.g. a Vickers or a
Berkovich indenter (Fig. 5a). The radial cracking indentation method
was initially proposed for bulk materials [27]. The relationship between the fracture toughness and the length of radial cracks was
established decades ago [28–29]:
1=2 E
P
Kc ¼ α
;
3=2
H
c
ð7Þ
in which P is the peak load at indentation; c is the crack length; and α
is the empirical constant which depends on the geometry of the indenter, α = 0.016 for both a Berkovich and Vickers type indenter.
Elastic/plastic indentation fracture mechanics requires a median and
radial crack pattern being well developed (see Fig. 6 for definition
of median and radial). To ensure the complete formation of a “halfpenny” cracking pattern, geometrically, it is required that c ≥ 2a (a
is the radius of the impression (Fig. 6c)). The derivation of Eq. (7) assumed “unlimited” sample thickness. In practice, the application of
Fig. 4. Schematic illustration of a stylus drawn along a coated sample. The material loading and response can be divided into three phases: ploughing, interface sliding, and pulling a
freestanding coating [26].
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S. Zhang, X. Zhang / Thin Solid Films 520 (2012) 2375–2389
a
Radial
b
Median
c
Half penny
Fig. 5. (a) Schematic illustration of radial cracking upon Vickers indentation, and
(b) ultra-low load nanoindentation radial cracks [27].
Eq. (7) requires that the depth d of the half-penny crack beneath the
surface be less than one-tenth of the thickness of the sample [30].
An ultralow load is applied during nanoindentation of coatings
[27] (Fig. 5b). For a coating with residual stress σr, the following relationship is commonly used [31–32]
1=2 E
P
1=2
þ Zσr c ;
KIC ¼ α
3=2
H
c
ð8Þ
where Z is the crack shape factor given by [32]
pffiffiffi
Z ¼ 1:12 π 3π
8
þ
d=c
π :
2
8 ðd=cÞ
ð9Þ
Z = 1.26 for an idealized half-penny, i.e. the depth d of the crack is
equal to the crack length c, making the half-penny an ideal semicircle.
To meet the geometrical requirements of Eqs. (7) or (8), the indentation depth (smaller than the depth d of the crack induced)
should be much less than 10% of the coating thickness. However, a
load threshold exists for the occurrence of the radial crack during indentation. For most ceramic materials, the threshold load of a Vickers
or Berkovich indentation is 250 mN or more, and the corresponding
impression produced is several micrometers in depth [27,33]. A
sharper angle indenter greatly reduces the threshold load for radial
cracks. For example, indenting with a cube-corner indenter reduces
Fig. 6. Crack patterns in a brittle material upon Vickers indentation: (a) a radial crack;
(b) a median crack; (c) half-penny cracking (a combination of a radial crack and a median crack) [41].
the load threshold by at least an order of magnitude compared with
that with a Vickers indenter [27]. Yet even here, the indentation
depth is still a few hundred nanometers for many brittle materials
in order to induce a radial crack [34]. Therefore, for coatings, to introduce well-developed radial cracks, the depth limitation of nanoindentation to exclude substrate effects is usually very difficult to meet.
Unlike standardized tests with a single well-defined crack in a
well-defined loading configuration (like uniaxial tensile testing)
[35], indentation induces a complex crack network and residual damage around the impression. This makes mechanical analysis extremely difficult [29,36]. The “expanding cavity” model was adopted to
depict the damage zone of an indentation [28,37], but its reliability
is questionable [38–39]: experiments on bulk ceramic materials
revealed that the details of indentation cracking are extremely material dependent. That is, the crack patterns are often not the idealized
half-penny shape as assumed in the model [40–41]. In bulk ceramic
S. Zhang, X. Zhang / Thin Solid Films 520 (2012) 2375–2389
materials, the actual crack pattern is obtained through observing the
cross-section of the median/radial crack (Fig. 6c) [41–42], but it is almost impossible to do the same on coatings. Therefore, it is very difficult to judge the reliability of Eqs. (7) and (8) for coatings.
A substrate indentation method was proposed to tackle the problem
of substrate influence [43]: indentation is conducted on the uncoated
side of the substrate surface such that the radial crack in the substrate
propagates into the coating. In this way, a single through-thickness
crack is induced in the coating (Fig. 7a). The tougher the coating, the
shorter the crack in the coating (Fig. 7b). Based on the energy balance
principle, the following equation is obtained
Af Gf þ As Gs ¼ Asf As þ Ass Gs :
ð10Þ
2379
3.2. Toughness evaluation from circumferential cracking and spallation
Circumferential cracking and spallation describe peeling of the
coating around the indentation (Fig. 8a). For a very brittle coating, it
is generated upon nanoindentation. At spallation, a plateau forms in
the load–displacement curve (see Fig. 8b) [34,44–47], which can be
used to produce a quantitative estimate of the coating fracture toughness. Li et al. (Fig. 8a) [34] suggested that fracture proceeds as follows:
(1) the first circumferential through-thickness crack forms around the
indenter by high stress in the contact area; (2) delamination and
buckling occur around the contact area at the coating/substrate interface due to high lateral pressure; (3) a second circumferential
through-thickness crack forms, and spallation is generated by high
a
Gf and Gs are the strain energy release rates for coating and substrate, Af
and As are true cracked film and substrate areas. Asf, and Ass are cracked
areas when coating properties are identical to those of the substrate.
Through comparing the crack lengths of coated and uncoated sides, an
expression is obtained for the toughness of the coating
First ring-like
through-thickness
crack formation
8 2
3
2
3 91=2
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi 2
ffi 2 >
>
uE uE <
=
2
2
p
ffiffi
1−υ
1−υ
ðϕb−aÞ u f
u f
26
s 7
s 7
t 5 þ 6
5
Kf ¼ Ks 41 þ λ
;
42ψc σr t t >
>
2
2
E
E
t
:
;
s 1−υ
s 1−υ
f
f
ð11Þ
where the subscript f′ refers to the film and s′ to the substrate; Ks is the
fracture toughness of the substrate; a and b are crack lengths as shown
in Fig. 7a; the dimensionless factors λ and ψc are 0.45 and 0.95 respectively, obtained from finite element model (FEM) calculations; and ϕ
is a geometry term obtained from FEM.
Delamination
and buckling
a
Partial spalling
formation
Second ring-like
through-thickness
crack formation
Lateral cracking
during unloading
b
b
= 10 6 No coating
Indenter
-100
-80
-60
-40
-20
-10
-20
0
20
40
60
80
100
Crack growth
-30
-40
-50
Wedge model
-60
Half-infinite plate model -70
-80
Fig. 7. (a) Schematic of indentation geometry; (b) crack growth front for different film
fracture toughnesses Kc [43].
Fig. 8. (a) Schematic illustration of the three stages in nanoindentation fracture for thin
coatings; (b) schematic of a load–displacement curve, showing a step during the loading cycle and associated energy release [34].
2380
S. Zhang, X. Zhang / Thin Solid Films 520 (2012) 2375–2389
bending stresses at the edges of the buckled thin coating. The third
stage, circumferential through-thickness cracking and spallation of
the coating, causes a sudden excursion of the indenter in displacement, which induces a step in the load–displacement curve (Fig. 8b).
Given area ABC in Fig. 8b representing the energy U dissipated upon
coating cracking, the fracture toughness is obtained as
"
KC ¼ EU
1−ν2 A
#1=2
;
ð12Þ
in which A = 2πCRt is the crack area, 2πCR is the crack length in the
coating plane, CR is the radius of circumferential through-thickness
crack formed around the indenter, and t is the coating thickness. E
and ν are Young's modulus and Poisson's ratio of the coating, respectively.In Eq. (12), the coating fracture energy U is the irreversible
work Wirr of the indenter during the excursion from A to B.
However, extraction of the irreversible work Wirr became the focal
point of much debate. denToonder et al. [44] suggested the lower and
upper boundaries of the Wirr as shown in Fig. 9: the areas of OAB and
ABFR, which correspond to the cases of full elastic deformation and full
plastic deformation of the coated system, respectively. Chen and Bull
[47] considered the area ABQE as representing the irreversible work
Wirr, with AE and BQ being the unloading curves at excursion start
point and end point. Further, they provided a method to obtain the
unloading curve AE through the linear relationship between the ratio
of displacement δf/δ1 and that of hardness over Young's modulus (Hs/Es):
δf
H
¼ 1−λ s ;
δ1
Es
ð13Þ
where Hs and Es are the hardness and Young's modulus of the substrate.
λ =4.5 for a Berkovich indenter. δf, and δ1 are the residual displacement
and full displacement of indentation as shown in Fig. 9. Expression (13)
is developed for bulk materials without fracture [48]. It approximately
applies to coated systems in which the substrate dominates the deformation in deep indentations. In this way, the lower boundary ABE and the
upper boundary ABFE of the irreversible work Wirr are obtained.
Michel et al. [46] realized that apart from the fracture energy U of
the coating, the energy consumed in substrate deformation is also included in the work done by the indenter. He proposed ABH in Fig. 10 as
the fracture energy U of the coating. In Fig. 10, ABEF represents the
total work of the indenter during circumferential cracking and
Fig. 9. Schematic illustration of the boundaries of the irreversible work Wirr at the plateau in a nanoindentation load–displacement curve [47].
Fig. 10. Schematic diagram representing the fracture energy U of a coating at the plateau in a nanoindentation load–displacement curve: the segment (GB) represents a
partial loading curve of the Si substrate; the dotted area (ABEF) represents the total
work under the step (done by the indenter); the gray area 1 (ABH) represents the energy released on circumferential cracking and spallation, while the area 2 (BEF) represents the energy of Si deformation [46].
spallation of the coating, and segment GB represents a partial loading
curve of the silicon substrate.
Malzbender et al. [44,49] studied the change of the irreversible energy Wirr versus load P through conducting a set of loading–unloading
cycles before and after the spallation of a coating. They found that the
curve of Wirr vs. P was divided into several segments of straight lines
representing different events during cracking: radial cracking, delamination, circumferential through-thickness cracking, and chipping
(Fig. 11a). Apparently, the irreversible work Wirr was obtained from
the energy difference Ufrc just before and after the circumferential
through-thickness cracking. Further, they found that Wirr is coatingthickness dependent [50]: the thinner the coating is, the larger the irreversible energy dissipation Wirr. The authors claimed that it is due
to the fact that more substrate deformation is involved for a thinner
coating during indentation. Accordingly, the fracture energy U is
obtained through extrapolating Wirr of the coating to infinite coating
thickness (Fig. 11b).
Chen and Bull [45,51] extracted the fracture energy U of a coating
from the curve of total work Wt versus displacement D (see example
Fig. 12). First, the initial Wt vs. D curve is extrapolated from the cracking start point A to the cracking end point C. Then Wt vs. D curve after
cracking is extrapolated back to the cracking start point. Vertical Wt
differences AB and CD are thus obtained. AB represents the work difference consumed in the elastic–plastic deformation of the coating/
substrate system before and after the coating fracture, and CD is the
total work done during the cracking. The difference between CD and
AB is thus deemed the fracture energy U.
Displacement-controlled nanoindentation of thin ceramic coatings with a sharp indenter (cube corner tip with radius of 40 nm
when new) was extensively investigated by Chen and Bull [45,51].
Displacement-controlled indentation was supposed to be more sensitive to the coating cracking because the load drop at coating fracture is
unambiguously related to the loss of the contact of the indenter with
the coating/substrate system. On the contrary, in addition to the indenter movement due to the loss of contact, there is an additional movement
of the indenter due to the deformation of the coating/substrate system
at the fracture load. Fig. 13a shows a typical load–displacement curve
of a displacement-controlled nanoindentation conducted on a 400 nm
TiOxNy coating on a glass substrate, in which the load jump between B
and C is associated with the radial through-thickness cracking of the
coating [45]. The Wt vs. D method was used to obtain the fracture energy
U and the fracture toughness was obtained according to Eq. (12).
The fracture behavior of a thin hard coating in nanoindentation as
described by Li et al. (Fig. 8a) [34] and Malzbender et al. [49] is the
S. Zhang, X. Zhang / Thin Solid Films 520 (2012) 2375–2389
a
a
300
2381
2500
Chipping
250
Radial
cracking Delamination
2000
Load (µN)
200
150
100
1500
1000
50
0
b
0
0.1
500
0.3
0.2
300
100
200
300
400
Depth (nm)
250
b
200
150
100
2000
50
1500
0
0
0.1
0.2
0.3
0.4
0.5
0.6
1000
500
Fig. 11. (a) Energy irreversibly dissipated during indentation as a function of the peak
load applied during the indentation [49]; (b) the energy irreversibly dissipated during
indentation as a function of the inverse coating thickness t [50].
basis for the energy-based nanoindentation methodology. After radial
cracking, delamination and buckling, it is the circumferential throughthickness cracking and spallation that results in a step in the load–
displacement curve which is used to extract the fracture energy U of
the coating. However, not only the circumferential cracking and spallation, but also radial cracking of the coating [52–54], delamination of
the interface [55–56], cracking or spallation of the brittle substrate
0.5
1
1.5
2
Fig. 13. Displacement-controlled nanoindentation of a 400-nm-thick TiOxNy coating on
a glass substrate. In (a), position A is where plastic deformation of the softer substrate
starts; points B and C are the start point and end point of through-thickness cracking; D
and E are the start point and end point of interfacial fracture. The circle in (b) marks an
area of uplift associated with interfacial fracture [45].
5
2
[52,57], and even the dislocation nucleation and phase transformation
of the substrate material [58] induce a step in the loading curve of a
nanoindentation. These steps may overlap in some cases. For example,
the catastrophic delamination of a compressively stressed coating
after buckling overlaps with the circumferential cracking and spallation that follows. This can be explained by the following onedimensional blister model of a coating.
The driving force (energy release rate of the interface) Gi of the interfacial delamination after buckling is [59–61]
1
2 Gi
σ
¼ m 1− c
;
G0
σr
0
where G0 = (1−υ)tσr2/E and m = [1 + 0.9021(1−υ)] − 1; σr is the residual stress of the coating, and
4
3
0
0.5
1
1.5
2
2.5
3
3.5
σc ¼ 1:2235
Fig. 12. Schematic illustration extrapolating the total work vs. displacement curve before and after cracking to determine the fracture dissipated energy CD–AB. Here, the
points A and D are the start and end points of the excursion in the measured work
vs. displacement curve [45].
2
E
t
1−υ2 b
ð14Þ
ð15Þ
is the buckling stress; t is the coating thickness, and b is the radius of
the delaminated zone.
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S. Zhang, X. Zhang / Thin Solid Films 520 (2012) 2375–2389
Eq. (14) is schematically represented by Fig. 14, where Γi(ψ) is the
fracture toughness of the coating/substrate interface. Given an initially delaminated region of width 2bi, the coating will buckle at σr = σc.
The blister (buckled coating) would then spread dynamically when σr
reaches σ* (where Gi = Γi(ψ)), and would be arrested at b = b* (where
Gi = Γi(ψ). The buckling also favors cracking and spallation of the
coating because a tensile stress in the coating on the inner side near
the edge is induced after bending. When the driving force Gf for
cracking of the coating satisfies the equation
Gf
Γf
;
N
Gi Γi ðψÞ
ð16Þ
where Γf is the fracture toughness of the coating, the coating cracks
and spalls away from substrate at a particular angle [62]. Both the dynamic processes, i.e., the interfacial delamination and the cracking
and spallation of the coating, blend together.
More fundamentally, the fracture toughness should be obtained
from the energy release rate (or stress intensity factor) as catastrophic
fracture starts near equilibrium. (With reference to Fig. 14, this would
be at the intersection of the vertical line at bi and the horizontal line at
“1”). In Fig. 14, let A be the area under the curve and above line “1”, the
fracture toughness obtained from the spallation process would then
be equivalent to A/(b* − bi); obviously this grossly overestimates the
energy.
A more recent paper [63] scrutinized, from extensive published
data, the steps and the coating thicknesses, and concluded that the
steps are formed due to loss of contact of the indenter with the sample.
Upon catastrophic fracture of the coating, the indenter undergoes
freefall of a distance approximately equal to the thickness of the coating. The size of such a step has no logical relationship with the energy
dissipation that fractures the coating.
3.3. Toughness evaluation from channel cracking
2
1−ν
πtg
2
!1=2
;
x
Fig. 15. Three-dimensional channeling of a crack across a thin bonded coating [66].
where
g ¼ g α; β;
ð17Þ
Fig. 14. Schematic illustration of instability analysis of a one-dimensional blister [61].
!
σ
; ns ;
σsy
in which σsy and ns are the yielding stress and strain hardening exponents of the substrate; and α and β are Dunders parameters describing the elastic mismatch between the coating and the substrate:
α¼
Channel cracking is “through-thickness cracking” in which the
coating is cracked all the way through to the substrate as the crack
propagates. The “through-thickness” characteristic is maintained during crack propagation, forming a channel-like crack (Fig. 15). In tensile
loading, as the crack length reaches approximately three times the
coating thickness, the channel crack propagates at steady state until
complete fracture [64].
Taking into consideration the substrate constraint on coating
cracking, the stress intensity factor of the coating can be expressed
as [61,64–68]
KI ¼ σ
t
Advancing
crack front
y
E −Es
E þ Es
and β ¼
1 μ ð1−2νs Þ−μs ð1−2νÞ
;
2 μ ð1−νs Þ þ μs ð1−νÞ
where Es and νs are the elastic constants of the substrate, respectively,
μ = E/2(1 + ν) denotes the shear modulus, and E ¼ E= 1−ν2 is a
plane strain tensile modulus.
In Eq. (17), the substrate effect is contained in g. Studies [64,66] of
g indicate that a ductile substrate promotes channel cracking (i.e., at
larger g, as can also seen in the ratio σσsy in the definition of g, ductile
materials have much smaller yielding stress than brittle materials)
and thus requires less stress to reach KI in Eq. (17).
For a thin ceramic coating on a ductile substrate, bending of the ductile substrate causes channel cracking of the coating. Thus multi-strain
flexure tests [69–70] and sphere indentation tests [67–68] have been
proposed for the fracture toughness of this type of coating/substrate
system.
A multi-strain flexure test [69–70] is illustrated in Fig. 16. A ceramic coating is deposited on a ductile (metallic) substrate and the
coating patterned into strips. The sample is then placed under flexure
such that the ceramic coating strips are on the side surface of the
bending beam, and the strips are aligned along the beam axis. During
bending, a linear strain gradient is induced in the beam from the bottom to the top: tensile strain on the top, compressive strain at the
bottom, and zero strain along the neutral plane. Thus, coating strips
at different positions are subjected to different strains. Coating strips
with strains larger than a critical value fracture. As such, the critical
strain can be indentified and the critical stress is thus obtained from
the stress–strain relationship (Hooke's law, assuming the ceramic
coating fractures in purely elastic deformation). Inserting the critical
stress in Eq. (17) yields the fracture toughness of the coating.
In sphere indentation, a spherical indenter of large radius is
indented into the coating to cause circular cracking (Fig. 17) [67–68].
S. Zhang, X. Zhang / Thin Solid Films 520 (2012) 2375–2389
2383
the yielding strain and hardening exponent of the ductile substrate.
The terms m1 and m2 are defined as:
0:14
m1 εsy ¼ 1:45 þ
εsy
m2 εsy ; ns ¼ ½1466−118ns þ ½−22:7 þ 1:8ns þ ½0:075−0:003ns Fig. 16. A multistrain specimen and test configuration [70].
The strain of the coating under the indenter is axisymmetric and is a
function of the location (r), as given by Eq. (18) [21],
r r 3
εr
þ m2 εsy ; ns
¼ m1 εsy
;
D
D
εsy
ð18Þ
1
εsy
1
εsy
!
!2
:
Once the critical strain is identified, the critical stress is obtained
through Hooke's law, thus Eq. (17) yields the ceramic coating's fracture toughness. Expression (18) is suitable for most metallic substrates [67].
The parameter g in Eq. (17) describes the constraint of the substrate on the channel cracking of the coating. It is very complex for
ductile substrates [66], which hinders its application. In practice, it is
difficult to make coating strips on a metallic substrate by lithography.
In the case of the sphere indentation test, accurately locating the first
crack on the unloaded impression is a problem.
For thin hard coatings deposited on rigid (ceramic) substrates,
nanoindentation with a sharp edge indenter can be used to generate
radial channel cracks [19,57], as illustrated in Fig. 18. A hemispherical
plastic zone is generated under the contact at the beginning of indentation; with increasing load, the plastic zone expands further and its
hemispherical shape changes upon impinging with the substrate.
The radial cracks emanate from the sharp corners. With further loading, the plastic zone transforms to cylindrical and the radial cracks become channel cracks (Fig. 18b) [71–72].
According to the rigid substrate hypothesis, the indented volume
of the coating material is solely accommodated via deformation of
a
Plastic zone
where εr is the strain in the radial direction; r and D are the radius of impression and sphere indenter diameter respectively; and εsy and ns are
Radial crack
Film
Sphere
Substrate
Film
a
b
r
Impression
Plastic zone
Substrate
Channel
crack
Film
Circumferential
cracks
Fig. 17. The sphere indentation test: circumferential cracks develop within the indent
[67].
Substrate
Fig. 18. (a) Schematic cross-section of indentation-induced partial-penetration radial
fracture in a mechanically-thick coating. When the coating is thick compared to the
plastic zone, the plastic zone is spherical in shape and radial cracks are seen as surface
traces. (b) Schematic cross-section of indentation-induced channel cracking in a mechanically thin coating. Here, the plastic zone is cylindrically shaped due to the constraint of the substrate and the channel cracks extend through the coating [71–72].
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S. Zhang, X. Zhang / Thin Solid Films 520 (2012) 2375–2389
driving or retarding force. σr results in a stress intensity factor of
the form
1=2
Kr ¼ ψ′σr tf
;
ð21Þ
where ψ′ is a constant that depends on the stiffness mismatch between the coating and the substrate [61,66]. At equilibrium, the fracture toughness can be obtained by summation of Eqs. (19) and (21).
4. Microtensile testing of fracture toughness for standalone thin
films
Fig. 19. SEM image of a coating fracture in tetrahedral amorphous carbon (ta-C). The
coating thickness is 248 nm [71].
the coating. This requires a substrate much harder and tougher than
the coating [73]. Otherwise, the plastic zone may extend into the substrate [58] or, even worse, cause extensive substrate deformation [74].
Assuming there is no deformation in the substrate, the stress intensity
factor of indentation-driven channel cracking is derived as [61,75]
KI ¼ λV
1=3
Ef Hf2
tf
a2
:
c1=2
ð19Þ
The subscript f′ refers to “film” or coating properties and λ is approximately 0.013 for the Vickers geometry and 0.016 for the cubecorner geometry. a is the radius of the indentation, and c is the
crack length. For a well-developed channel crack, Eq. (19) requires
that the crack length is larger than three times of the film thickness
as shown in Fig. 19. The parameter V* is used to exclude the portion
of the indented displaced volume accommodated by the substrate
when the indenter tip penetrates through coating [71],
V ¼
8
>
>
<
>
>
: 1−
1
hp −tf
h3p
3
hp ≤ tf
hp N tf
:
ð20Þ
hp refers to indentation depth and tf is the coating thickness. Residual stresses σr from deposition acts as an additional crack
Uniaxial tensile testing has been established for the measurement
of fracture toughness [7–8]. In a uniaxial tensile test with a central
crack, the stress intensity factor is
pffiffiffiffiffi
KI ¼ σ πl;
ð22Þ
where σ is the sample stress, and l is half the length of the central
crack. For a tensile testing specimen with an edge crack, the stress intensity factor becomes
pffiffiffiffiffiffi a KI ¼ σ πaf
:
W
ð23Þ
The sample dimensional function f ða=W Þ ¼ 1:12−0:23ða=W Þþ
10:55ða=W Þ2 −21:72ða=W Þ3 þ 30:41ða=W Þ4 , in which a is the length
of the edge precrack and W is the width of the gauge region. Eq. (23)
is valid for a/W ≤ 0.6 [76].
The concept of micro-tensile testing is straightforward for measuring the fracture toughness of thin films according to Eqs. (22)
and (23). However, it is very challenging to prepare freestanding
samples with micro-scale size and then conduct tensile tests on
them. Notable progress has been made in micro- and nano-scale tensile testing in recent years [5,77–88]. Photolithographic techniques
are used in the preparation of freestanding films. According to classical fracture toughness measurements, atomically sharp precracks of
known lengths are required. Vickers indentations and focused ion
beams are most commonly used to produce precracks in the film.
Loading of the precracked standalone films can be very delicate and
difficult. Quite a few methods have been proposed: the inchworm actuation by Chasiotis et al. [85], membrane deflection by Espinosa et al.
Fig. 20. Microscale fracture specimen preparation and testing: (a) specimen before indentation of the SiO2 substrate, (b) specimen with edge pre-crack after indentation, (c) freestanding specimen with edge precrack after substrate removal (release), and (d) fracture of specimen at applied force P [84].
S. Zhang, X. Zhang / Thin Solid Films 520 (2012) 2375–2389
2385
4.1. Inchworm actuation
The inchworm actuation method [87] is illustrated in Fig. 20. The
‘dog-bone’ shape film is produced lithographically. An edge precrack is fabricated by indentation of the adjacent free substrate region.
To facilitate griping of the sample, one end of the ‘dog-bone’ is not released from the substrate, while the other end is freestanding. UV glue
and electrostatic suction are combined to provide bonding of the freestanding end of the ‘dog-bone’ to a loading beam. The tensile load is
applied to the film via an inchworm actuator. The resolution of the actuator is 4 nm and the load cell has an accuracy of 10 − 4 N. The fracture
toughness is obtained according to Eq. (23) given the critical stress at
fracture.
The technique was used successfully in the fracture toughness
measurement of diamond-like carbon (DLC) and polycrystalline silicon films [84,86,91].
4.2. Membrane deflection
In the membrane deflection method [88], the film to be tested is
deposited on a silicon wafer and patterned into strips using lithographic techniques. The gauge section of each film strip is made freestanding by etching away the silicon wafer material from the backside
using techniques for micro-electromechanical systems (MEMS)
(Fig. 21). The loading is accomplished vertically using a nanoindenter
with line-load tip at the middle of the free standing span (Fig. 22). A
microscope interferometer positioned directly below the specimen
measures the deflection Δ of the film from the fringes generated as a
result of phase differences of the monochromatic light reflecting off
the film after traveling different path lengths. The angle θ that the
film moves upon deflection is given as
tan θ ¼
Δ
;
LM
ð24Þ
where LM is the initial length of the film strips. The tensile load PM and
the stress σ in the film are obtained through Eqs. (25) and (26)
PM ¼
Fig. 21. (a) Schematic representation of three general microfabrication steps used to
process specimens; (b) optical image of three Au membranes showing characteristic
dimensions. LM is half the membrane length and W is the membrane width [88].
[88], tension by residual stress by Kahn et al. [82–83,89], bulging of
films by Xiang et al. [80–81], and the most recent substrate macrotension by Zhang and Zhang [90]. The key points of these methods are
described below.
Gauge area Membrane
σ¼
PV
2 sin θ
PM
:
A
ð25Þ
ð26Þ
PV is the vertical nanoindentation load on the film and A is the crosssectional area of the film in the gauge section.
At fracture of the film, the fracture toughness is calculated according to Eq. (23). This method has been used for ultrananocrystalline diamond films [92], diamond-like carbon (DLC) films, silicon nitride
Line-load tip Silicon substrate
Mireau
microscope
objective
Fringe pattern
a) Before loading
Fringe pattern
b) After loading
Fig. 22. Schematic drawing of the membrane deflection experiment (MDE) setup and monochromatic images of the bottom side of a membrane in (a) the unloaded state and
(b) under load [93].
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S. Zhang, X. Zhang / Thin Solid Films 520 (2012) 2375–2389
(Si3N4) films [93–94], and single crystal silicon carbide (3C-SiC) [87],
as well as gold, copper, and aluminum films [88,95–96].
4.3. Tension by residual stress
This is an ingenious way of loading: the residual tensile stress in a
thin film is used to serve as the loading to fracture the film in a fracture toughness measurement [82–83,89]. The film to be tested is
made into bridges with lithographic technologies (a film strip that
is freestanding in the center while ends still adhere well to the substrate as shown in Fig. 23b). A sharp precrack is produced by indentation in the film bridges before they are freestanding from substrate
(Fig. 23a, c). The film bridges are stressed automatically due to
unleashing of the residual stress. The stress intensity is related to
the initial crack length as shown by the K versus a curves in
Fig. 23d. The film bridges crack if the stress intensity factor is above
the fracture toughness. Thus, the fracture toughness lies between
the stress intensity factors of the broken and unbroken bridges
Fig. 23. Images of film bridges used to measure fracture toughness and stress corrosion. (a) Schematic top view showing the dimensions. (b) Schematic side view. (c) SEM images of
a 60-μm-wide beam with an indentation placed near its center, a higher magnification SEM of the area near the indent showing the precrack traveling from the substrate into the
beam. The indent was made on the SiO2 release layer, which was subsequently removed by the HF etching. (d) Plot of stress intensity K versus crack length a for polysilicon film
bridges. The solid lines show the relations between K and a for three values of residual stress. The dotted line is the fracture toughness KIC determined from these data [89].
S. Zhang, X. Zhang / Thin Solid Films 520 (2012) 2375–2389
(dotted line in Fig. 23d). For application of this method, the residual
stress must be tensile (not compressive) and the magnitude should
only be in the range of a few tens of MPa.
a
The bulge test was originally proposed for the accurate measurement of elastic properties of freestanding films [97], and was later
used in the measurement of fracture toughness [80–81,98]. In the
bulge test, a rectangular “window” of the silicon substrate is etched
away to reveal the film to be tested (see Fig. 24a). A focused ion
beam is used to prepare a precrack length 2l in the film along the longer side at the middle of the window (Fig. 25). A uniform air or water
pressure is applied at the window to “bulge” the film as shown in
Fig. 24b. If the window's length over width ratio is greater than
four, the stress σ and strain ε of the film will be uniformly distributed
across the width of the bulged film [80] (Fig. 24b):
p a2 þ h2
Si
b
Stress
ð27Þ
2ht
ε ¼ ε0 þ
Focused ion beam
Film
4.4. Bulging of films
σ¼
2387
2
2
a þh
2ah
arcsin 2
−1;
2ah
a þ h2
ð28Þ
where p is the applied pressure, h is the membrane deflection, t is the
film thickness, 2a is the width of the membrane, and ε0 is the residual
strain in the film.
At critical pressure, Eq. (27) gives rise to the critical stress σC
when the film fractures. Inserting the critical stress σC into Eq. (22)
yields the fracture toughness of the film.
Stress
Fig. 25. (a) Schematic illustration of the micro-fabrication of a precrack of length 2l at
the center of a freestanding membrane using a focused ion beam and (b) SEM image of
a typical precrack in an AlTa coating on a silicon wafer substrate. The arrows indicate
the transverse direction of the membrane [81].
4.5. Macrotension of substrate
A recently proposed method is microtensile testing of film microbridges via macrotension to a substrate [90]. In this method, the film
is deposited on a rectangular silicon wafer substrate, in which an initial edge crack is introduced using a diamond cutter with a manual
application of a small force. After film deposition, a section of the
film ahead of the substrate crack is patterned into strips as shown
in Fig. 26. Precracks on each film strip are made with Vickers indentation into the adjacent substrate region. The film strips are then released from the substrate by etching away a ZnO sacrificial layer to
form film microbridges; i.e. the middle of the strip is released while
both ends are still affixed to the substrate. As the surface tension of
the etchant would fracture the microbridges easily when the sample
is taken out of the liquid, a sample holder is made to allow testing
a
P=0
b
P >0
Fig. 24. Schematic illustration of the bulge test for a section of a long rectangular membrane: perspective views of the freestanding film, (a) before and (b) after a pressure P
is applied [81].
Fig. 26. Schematic of the testing configuration for the substrate macrotension technique: a rectangular silicon wafer substrate containing an edge crack and two pinholes; a series of film strips just ahead of the tip of the substrate crack. Just before testing, the film strips are released from the substrate through etching of a sacrificial layer
between the film and the substrate; upon loading, the substrate crack extends in a stable manner and travels beneath film bridges [90].
2388
S. Zhang, X. Zhang / Thin Solid Films 520 (2012) 2375–2389
in water. On testing, a displacement controlled loading is applied to
the substrate by manually dialing a micrometer. The tensile loading
opens the substrate crack beneath the microbridges, causing the bridges to fracture (Fig. 26).
The film strain ε is measured through the extension δ of the film
during testing,
ε¼
δ
:
L0
ð27Þ
L0 is the original length of the microbridge before loading. The extension δ of the microbridge is measured by the extension of the substrate
crack opening, which gives rise to a critical stress through Hooke's law,
σ = Eε, as the ceramic film is assumed to fracture elastically. The fracture toughness is then calculated according to the Eq. (23).
The first advantage of the tension on substrate method lies in the
fact that expensive equipment such as a focused ion beam is not required. Only a precision micrometer is needed to carry out the test.
Technically, using a ZnO release layer as a sacrificial layer (and thus
0.25% HCl as the etchant) instead of a SiO2 layer (thus toxic HF as
the etchant) not only reduces the toxicity, but also allows testing of
almost all ceramic films and even metallic films. The shortcoming of
the method is its requirement of testing in water (to circumvent the
surface tension problem of the liquid etchant).
5. Summary
This article reviewed recent advances in fracture toughness measurements for hard coatings and thin films.
5.1. Hard coatings
For a hard coating well bonded on the substrate, the most common qualitative methods used include indentation plasticity and
scratch resistance; quantitatively, different methods are used based
on the type of cracking patterns upon indentation: radial cracking,
channel cracking, and circumferential cracking and spallation.
The most common radial cracking method consists of the ultralow
load indentation of the coating and measuring the lengths of resulting
radial cracks. Once the length c is measured, the fracture toughness is
calculated via Eq. (7):
KC ¼ α
1=2 E
P
:
3=2
H
c
1−ν2
πtg
2
"
#1=2
EU
KC ¼ :
1−ν2 A
Many authors obtain the fracture energy U from extrapolation of
the load–displacement curve in which a step appears upon fracture.
However, extraction of U from the step is controversial.
5.2. Thin films
The most straightforward and reliable way of testing a thin film is to
apply tension directly to the film when it is “freestanding”. A number of
“microtensile” methods have been used: inchworm actuation, membrane deflection, tension by residual stress, bulging, and the most recent “macrotension of substrate”. In all these method, the key is p
the
ffiffiffiffiffi
determination of the critical stress σ of the film; then KI ¼ σ πl
pffiffiffiffiffiffi
Eq. (22) for a central crack or KI ¼ σ πaf ða=W Þ Eq. (23) for an edge
crack characterizes the fracture toughness. The formulation in microtensile testing is indeed very simple, but the difficulty lies in making
the film freestanding, introducing a sharp precrack in the film, and
clamping the film and applying a minute testing force. Technically, all
these are difficult to accomplish and usually require specific and dedicated apparatus.
The “macrotension of substrate” method developed recently provides an extremely simple alternative, in which fracture forces are applied to freestanding “microbridges” through macrotension of the
substrate via a simple micrometer. This method cleverly solves the
problems of clamping a freestanding film and applying minute forces
on it.
Acknowledgments
This work was supported by Project No. T208A1218 of the Ministry of Education, Singapore, and partly by Project No. 51001084 of the
National Natural Science Foundation, China.
References
This equation was adopted from indentation of bulk ceramics. To
apply on coatings, the load P has to be ultralow in order to avoid substrate effects. To use Eq. (7), however, the crack length must be at
least 2a (where a is half of the diagonal length of the indent). Therefore, problems always emerge in dealing with the substrate influence
and/or generation of a valid crack length.
When cracking starts with a “through-thickness” crack, it is termed
“channel cracking”. The key to determine the fracture toughness of a
coating is to obtain the critical stress σ; Eq. (17) is then used:
KI ¼ σ
is simple, but the assumption of rigidity of the substrate usually
does not apply.
Circumferential cracking and spallation take place during nanoindentation of hard, thus brittle, coatings on ceramic substrates. If the
energy released per fractured area (U/A) is obtained, the fracture
toughness of the coating is calculated through Eq. (12):
!1=2
:
Bending of the substrate (multi-strain flexure) and sphere indentation of the coating, etc., have been used to generate channel cracking. The critical stress is obtained through the critical strain via
Hooke's law. The method appears simple, but the parameter g in the
equation is not explicit, which hinders the application of this method.
Channel cracking has also been generated through nanoindentation of hard coatings on rigid substrates. The resultant formulation
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