FEM simulation

1. A dynamic FEM simulation of the nano-impact test on mono- or
multi-layered PVD coatings considering their graded strength properties
determined by experimental–analytical procedures
G. Skordaris, K.-D. Bouzakis ⁎, P. Charalampous
Laboratory for Machine Tools and Manufacturing Engineering, Mechanical Engineering Department, Aristoteles University of Thessaloniki, Greece
a b s t r a c ta r t i c l e i n f o
Article history:
Received 14 November 2014
Accepted in revised form 26 January 2015
Available online 7 February 2015
Keywords:
PVD coating
Graded properties
Brittleness
Nano-impact
FEM simulation
Nano-impact test is a reliable method for assessing the brittleness of PVD coatings with mono- or multi-layer
structures. For the analytical description of this test, an axis-symmetrical Finite Element Method (FEM) model
was developed using the LS-DYNA software. This software was adequate to simulate the progressive superficial
coating fracture induced by the repetitive nano-impacts during the nano-impact test. The coating possesses one
or more individual layers with own mechanical properties, since every layer after its deposition at the PVD pro-
cess temperature is exposed to an annealing affecting its strength data. The annealing duration of each layer is
associated with the rest time, up to the deposition of the overall coating thickness. For simulating this procedure
and estimating the related mechanical properties of the coating layers, cemented carbide specimens with the
same TiAlN PVD (Physical Vapor Deposition) coating of various thicknesses and structures were annealed in
vacuum. The annealing duration was equal to the deposition time required for coating a specimen with a further
layer up to a constant overall thickness. The superficial strength properties of these coatings were determined via
nano-indentations, coupled with FEM calculations to estimate the corresponding stress–strain curves. Results
obtained by the developed FEM model simulating the nano-impact test were compared with experimental
ones. Taking into account the sufficient convergence between them, the introduced numerical procedure can
be effectively employed to evaluate the effect of various coating structures on their brittleness.
© 2015 Elsevier B.V. All rights reserved.
1. Introduction
For improving the mechanical and tribological properties as well as
the chemical stability of coated compounds, multi-layered PVD coatings
even with different mechanical strengths or materials for the individual
layers are used [1]. Moreover, the application of multi-layered PVD coat-
ing structures on cemented carbide inserts has been documented as an
efficient way for prolonging the coated tool life, especially when the
coated surfaces are subjected to repetitive dynamic loads [2–5]. This is
attributed to the ability of layer interfaces to decelerate the propagation
of cracks potentially developed in the coating material under such loads
[2,5,6]. Numerous tests were invented in the past for assessing the
cracking resistance of multi-layered PVD coatings such as of nano-
indentation [7], bending [8] and scratch test [6]. In recent investigations,
by employing nano- and macro-impact tests with modulated force
characteristics, the brittleness and fatigue of mono-and multi-layered
PVD coatings were effectively captured [2,9–11]. According to the
attained results, the increase of the number of coating layers leads to
improved coating fatigue strength and low brittleness.
Since the nano-impact test is a reliable method to characterize the
brittleness of PVD coatings, its analytical description can contribute to
an efficient assessment of the brittleness of various coating structures
and graded properties, thus restricting the experimentation's time.
Efforts for the numerical description of the nano-impact test have
been undertaken in the past by developing a three dimensional (3D)
FEM-model considering uniform or graded strength properties versus
the coating thickness [12,13]. The presented 3D-FEM model in these
publications for describing the nano-impact test led to long calculation
times when using fine discretization networks for attaining a reasonable
accuracy. In this way, its application for a precise description of fine
coating structures is limited. Moreover, the lack of accurate data refer-
ring to strength properties versus the coating thickness further narrows
the calculations' reliability.
Graded mechanical strength properties may be induced in the
coating structure, using diverse superficial treatments as for example
micro-blasting [13]. Hereupon, the initial yield stress is commonly
impaired up to a small depth from the coating surface, whereas the
strength data in the rest coating structure remain unaffected [14].
Graded properties in the coating material may also develop during the
deposition of sputtered PVD coatings, with cone-shaped columnar
structure. The associated with this structure grain's size enlargement,
towards the coating surface, diminishes the strength properties [15]. A
Surface & Coatings Technology 265 (2015) 53–61
⁎ Corresponding author. Tel.: +30 23 10996021; fax: +30 23 10996059.
E-mail address: bouzakis@eng.auth.gr (K.-D. Bouzakis).
http://dx.doi.org/10.1016/j.surfcoat.2015.01.063
0257-8972/© 2015 Elsevier B.V. All rights reserved.
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2. schematic presentation of the columnar grain structure of mono-
layered sputtered TiAlN coatings with different thicknesses is displayed
in Fig. 1a. In the case of a multi-layered coating, the columnar growth
during the PVD process is disrupted with a frequency dependent upon
the number of the deposited layers (see Fig. 1b). Thus, the decrease of
the mechanical data of the coating material versus its thickness is
reduced. Strength property changes also develop in the coating, because
of annealing at the PVD process temperature [16]. The annealing dura-
tion of a certain coating region corresponds to the rest time, up to the
deposition accomplishment over this region. Investigations revealing
the effect of annealing temperature and duration on the superficial
hardness of PVD TiAlN films are described, among others, in [17,18].
For overcoming the problem of determining graded strength
properties of PVD coatings with various structures, appropriate
experimental–analytical procedures were implemented, as explained
in a next section. Moreover, an axis-symmetrical FEM model for the
dynamic simulation of the nano-impact test was developed, enabling
a discretization of the film thickness at least twenty times larger com-
pared to the existing FEM model [12] almost at the same computational
time. The effectiveness of this model is validated by comparing calculated
results with experimental ones in the case of PVD coatings with one or
more layers.
2. Experimental and computational details
PVD deposition process with high ionization sputtering (HIS) was
employed for preparing TiAlN coatings with an Al/Ti ratio of 54/46 and
columnar micro-structure on cemented carbide inserts of HW-K05/K20
SPGN 120408 ISO specifications, using a CEMECON C900 coating ma-
chine [19]. The deposition temperature and the bias voltage amounted
to 450 °C and −110 V respectively. The overall film thickness in all
specimen cases was approximately 8 μm, consisting of one, two or four
Structure Layers (SLs) [2]. The deposition rate was 1 μm/h, applying a
fold rotational speed of roughly 3 rpm. In the case of a coating consisting
of two or four SLs, a coating growth interruption took place after the
deposition of each individual SL with a thickness of 4 μm or 2 μm respec-
tively, followed by an Ar-ion etching for a period of 10 min. During the
PVD deposition process, the temperature was kept constant. Additional-
ly, inserts were coated with a mono-layer film of 2 μm or 4 μm thickness.
Some of these inserts were annealed in vacuum at a temperature of
450 °C, equal to the PVD process one, for a duration of 2 h, as further
discussed in the next section.
For estimating the strength properties of the individual SLs of the
manufactured PVD films, nanoindentations were carried out by means
of a FISCHERSCOPE H100 device. The applied Berkovich indenter tip
geometrical deviations were detected according to methods described
in [20]. An appropriate number of nanoindentations were conducted
for excluding the specimens' roughness effect on the measurements
accuracy [20]. The superficial strength properties of the employed coat-
ings were determined via an analytical evaluation of nanoindentation
results, employing methods documented in the literature [20]. The
nano-impact tests were conducted by a diamond cube indenter using
a Micro Materials Ltd device at a frequency of 1 Hz [9]. The LS-DYNA
software was employed for developing the axis-symmetrical FEM
model, which simulates dynamically the nano-impact test [21,22].
3. Results and discussion
3.1. Determination of graded strength properties of mono- and
multi-layered coatings
A crucial issue for the accuracy of the developed FEM model to pre-
dict the coating structure response during the nano-impact test is the
determination of the strength properties versus the coating thickness.
For determining these properties in the case of a coating thickness of
8 μm with one, two or four layers, it was considered that every layer
after its deposition is exposed to an annealing at the PVD temperature
of a duration corresponding to the rest time, up to the coating process
accomplishment [16].
3.1.1. Determination of superficial strength properties
In the case of a columnar coating structure, during the PVD process,
the coating strength properties may diminish due to the augmentation
of the grain size induced by the columns' diameter growth [15]. More-
over, the columnar coating structure is disrupted and restarts growing
when the deposition of a next layer begins. In this way, it is reasonable
to assume that the superficial hardness of the upper structural layer (SL)
of a multi-layer film corresponds to the one of a mono-layer coating of
the same thickness.
For validating this assumption, nanoindentations at a maximum
load of 15 mN were conducted on mono-layered PVD TiAlN coatings
of 2 μm, 4 μm or 8 μm thickness (see Fig. 2a). For excluding the specimen
roughness effect on the nanoindentation results accuracy, 40 measure-
ments per nanoindentation were conducted for stabilizing the moving
average of the indentation depth versus the indentation force [20].
The lower the film thickness, the better it withstands the indenter
penetration, yielding to decreased maximum indentation depth [15,
16]. Related nanoindentations were also carried out in the case of an
8 μm thick TiAlN coating possessing two or four layers, as displayed in
Fig. 2b. A comparison between the results presented in Fig. 2a and b ver-
ify the assumption that the superficial hardness of a monolayer coating
of 2 μm or 4 μm thicknesses is practically equal to the corresponding one
of a superficial layer of the same thickness.
The superficial strength properties of the investigated coatings were
determined by analytical evaluation of the attained nanoindentation
results, according to the methodologies described in [20]. The obtained
results in the case of mono-layer coatings of various thicknesses are
exhibited in this Table 1. The mechanical properties of the cemented
carbide substrate are also presented in this table. Thicker PVD coatings,
which are associated with coarser superficial film grain sizes, possess
lower yield and rupture stress [15], whereas the film elasticity modulus
remains practically constant in all coating cases. The calculated stress
fields at the constant indentation load of 15 mN show that the depth
of the plastically deformed film regions remains under 2 μm in all
coating cases (see Fig. 3). Moreover, as expected, the size of the plasti-
cally deformed region at the same indentation load increases with the
augmentation of the coating thickness [15,16].
The structure of the 8 μm thick mono-layer coating was analytically
described using four individual layers (Analytical Description's Layers
(ADLs)) of a thickness of 2 μm with own uniform properties. These
properties can be determined, as previously discussed, at an indentation
Fig. 1. Coating columnar microstructures of: (a) mono- and (b) multi-layered coatings of
various thicknesses.
54 G. Skordaris et al. / Surface & Coatings Technology 265 (2015) 53–61

3. load of 15 mN. In this case, the induced film plastic deformation is
restricted in a region of less than 2 μm thickness (see Fig. 3). The rest
coating structure is deformed elastically possessing the same elasticity
modulus. According to comprehensive investigations described in
[16], there is a gradation of the strength properties at the first 2 μm
from the film surface in the case of a 8 μm thick coating. This happens
because in this particular coating case the strength properties are
stabilized after an annealing duration larger than 120 min and the
deposition duration of the upper 2 μm is less than this time [16]. In
this way, mechanisms resulting in hardness changes such as of disloca-
tion movements and atom's diffusions, have not been completed [16]. In
contrast, at larger depths the strength properties are not further affected
since the annealing time is larger than 120 min and the previously
mentioned mechanisms are accomplished. Thus, the film strength
data depend only on the grain size and uniform properties within an
ADL can be considered. In the described investigations, for simplifying
the related calculations, it was assumed that the mechanical strength
properties versus the coating thickness, up to a depth of 2 μm from
the film surface are constant. These properties can be determined as
described in Fig. 3.
In this context, it was necessary to check if the determined superficial
strength properties at an indentation load of 15 mN, assumed as uniform
for an ADL thickness of 2 μm, can be employed for the analytical descrip-
tion of the whole coating structure. For this purpose, nanoindentations
were conducted at a lager indentation load of 45 mN on mono-layer
coatings of 2 μm, 4 μm or 8 μm thickness. A relevant load–displacement
diagram in the case of a coating thickness of 2 μm is exhibited in Fig. 4.
The measured course of the indentation depth versus the indentation
load was compared to the determined one by the FEM-based simulation
of the nanoindentation [20]. In this calculation, the stress–strain data
shown in Table 1 for a film thickness of 2 μm were employed. The max-
imum deviation dmax between the measured and the calculated indenta-
tion load versus the indentation depth is less than 4%. Similar results
were obtained in the further applied mono-layer coatings of 4 μm and
8 μm possessing strength data associated with these film thicknesses
(see Table 1). In this way, the assumption of uniform mechanical proper-
ties within an ADL thickness of 2 μm leads to sufficiently accurate results.
These properties depend on the overall coating thickness and structure
and can be determined as introduced in Figs. 2 and 3.
3.1.2. Determination of internal ADL strength properties
For defining the mechanical properties of internal ADLs, annealings
for 120 min of coated hardmetal inserts with mono-layer coatings of
various thicknesses at a temperature of 450 °C, equal to the deposition
one, were conducted. At annealing durations larger than 120 min, the
maximum indentation depth remains invariant [16]. The attained
maximum indentation depths before and after annealing of the mono-
layered coatings of 2 μm, 4 μm or 8 μm thickness are illustrated in
Fig. 5a. In Fig. 5b, the corresponding yield and rupture stress determined
after [20] are captured. As expected, the indentation depths grow and
the mechanical properties decrease after annealing, whereas the elastic-
ity modulus remains constant. The mechanical properties of a 6 μm
thick coating were determined by linear interpolation between the
corresponding properties at 4 μm and 8 μm film thicknesses.
As previously discussed, the investigated coating structures were
simulated using four ADLs, each one with a thickness of 2 μm and own
mechanical properties. The internal ADL properties were approximated
as explained in Fig. 6. For example, in the case of a 8 μm mono-layer
coating, the yield stress of the superficial layer 1 having a thickness of
2 μm amounts to ca. 3.4 GPa (see Table 1). Furthermore, considering
the coating structure, the ADL's positions within the coating thickness
and the related annealing duration after their deposition, the three
internal layers 2, 3 and 4 possess the superficial strength properties of
a 6 μm, 4 μm and 2 μm thick mono-layer coating, annealed at durations
larger than 120 min respectively (see Fig. 6a). In the same way, as
demonstrated in Fig. 6b and c, for coatings of the same overall thickness
of 8 μm, however with two or four SLs, based on the position of the
individual ADLs within the coating thickness, the related annealing
duration can be estimated. For annealing durations larger than 2 h, the
mechanical data of the ADLs correspond to the ones of annealed
mono-layer coatings of overall thickness equal to that of the individual
SLs, as presented in Fig. 5. The superficial 2 μm thick ADLs of the
prepared coatings are subjected to annealing at durations less than
2 h. The strength properties of these ADLs, according to the SLs' thick-
ness of each coating, are associated with values shown in Table 1.
3.1.3. Verification of the approximated coating mechanical properties
gradations by means of nanoindentations
To check the validity of the predicted coating strength properties
gradations occurring after the PVD process in the case of a 8 μm thick
Fig. 2. Load–displacement diagrams, employing a Berkovich indenter (th/b = 2.2/74 nm/mm),
on coatings: (a) mono-layered and variously thick, (b) with different structures and
constant overall thickness.
Table 1
Superficial strength properties of variously thick PVD mono-layer coatings and
of their substrate.
55G. Skordaris et al. / Surface & Coatings Technology 265 (2015) 53–61

4. film with one, two or four SLs, nanoindentations were conducted at an
increased maximum load of 200 mN. In this way, it was intended that
many ADLs of diverse mechanical properties are plastically deformed.
The related load–displacement diagrams and the attained maximum
indentation depths are exhibited in Fig. 7. The indentation depth dimin-
ishes, as the number of the SLs grows. This is attributed to the increase
of the coating strength properties along with the reduction of the SLs'
thickness, as already explained. Using the measured maximum indenta-
tion depths, as the displacements exercised in the axis-symmetrical
FEM model shown in Fig. 8, the related maximum indentation loads
were calculated. In this FEM model, the kinematic hardening rule was
considered since this leads to a rapid convergence in the corresponding
FEM calculations [23,24]. For the individual ADLs, the strength proper-
ties displayed in Fig. 6 were employed.
According to the calculated von Mises stress field at the maximum
indentation depth in the case of a coating consisting of one SL, all ADLs
are almost plastically deformed (see Fig. 9a). Similar results were also ob-
tained in the other examined coating structures. The calculated reaction
forces for various coating structures are displayed in Fig. 9b. These reac-
tion forces correspond to the maximum indentation depths obtained
in the various coating structures, which are illustrated in Fig. 7. In all
examined cases, the resulting deviations between the applied indentation
load of 200 mN and the calculated reaction forces are less than 5%. If uni-
form coating properties associated with the superficial ones shown in
Table 1 are used, significant deviations of the calculated reaction forces
from the exercised indentation load of 200 mN develop. In this way, the
Fig. 3. Developed stress fields in variously thick mono-layer coatings at a maximum indentation load of 15 mN, employing a Berkovich indenter (th/b = 2.2/74 nm/mm).
Fig. 4. Measured and calculated courses of the indentation depth versus the indentation
load of a Berkovich indenter (th/b = 2.2/74 nm/mm) into a 2 μm thick coating, up to an
indentation load of 45 mN. (The calculations are based on nanoindentation results at
15 mN.).
Fig. 5. Annealing effect on the: (a) maximum attained indentation depths at a maximum
indentation load of 15 mN and (b) strength properties of variously thick mono-layer
coatings.
56 G. Skordaris et al. / Surface & Coatings Technology 265 (2015) 53–61

5. estimated ADL's mechanical properties, as presented in Fig. 6 for the var-
ious coating SL cases, enable an accurate description of the elasto-plastic
behavior of the applied coatings with different structures.
3.2. Nano-impact tests on mono- or multi-layered coatings
Nano-impact tests were conducted on the coated inserts with the
different coating structures by a sharp cube corner indenter [2,9]. The
relevant results in terms of nano-impact depth versus the number of
impacts for an 8 μm thick coating consisting of one, two or four SLs
are illustrated in Fig. 10. It is obvious that by increasing the number of
layers, the growth of the nano-impact depth is significantly decelerated.
This is attributed to the important property of PVD coatings with multi-
layered structure to hinder the crack propagation [2]. These experimental
results will be used for assessing the accuracy of the developed FEM
model to simulate the nano-impact test on coatings with graded strength
properties.
3.3. FEM simulation of the nano-impact test on mono- or multi-layered
coatings
3.3.1. The developed axis-symmetrical FEM model
Since an axis-symmetrical FEM simulation of the nano-impact test
can lead to a significantly reduced computational time compared to a
3D-FEM model [12], it was necessary to replace the cube corner indenter
by an equivalent conical one with axis-symmetrical geometry. The equiv-
alent cone possesses the same projected area versus the indentation
depth hi (see Fig. 11). The angle of the equivalent cone was calculated
according to equations introduced in [25]. Hereupon, the actual spherical
tip radius of the cube corner indenter equal to roughly 75 nm was taken
into account.
The inadequacy of the ANSYS software, introduced in Fig. 8, for de-
scribing sufficiently the indenter penetration during the nano-impact
test is explained in Fig. 12. In both examined nanoindentation cases,
using the indenter geometries displayed at the top of Fig. 12, the same
coating's material laws presented in Fig. 6 were considered. The
diamond indenters were assumed as elastic materials with elasticity
modulus equal to 1100 GPa. According to the results demonstrated in
Fig. 12, at the constant load of 2.5 mN, a comparably larger imprint
depth develops during loading as well as unloading when a cube corner
indenter is employed. This behavior can be attributed to the sharper
form of the latter indenter compared to a Berkovich one. At loads larger
than 2.5 mN, the sharp geometry of the cube corner indenter results in
highly distorted elements and thus non-converged solutions. Further-
more, when the indenter exits from the imprint (unloading stage), a
plastic deformation and residual stresses remain in the coating material,
as exhibited at the bottom of Fig. 12. If the coating is reloaded, as it is the
case during the nano-impact test, the stress fields developed during the
Fig. 6. Predicted graded strength properties of 8 μm thick coatings with different
structures.
Fig. 7. Load–displacement diagrams at a maximum indentation force of 200 mN on coatings
with diverse structures, employing a Berkovich indenter (th/b = 2.2/74 nm/mm).
Fig. 8. The employed FEM model for the determination of stress fields and depths during
the nanoindentation on variously structured coatings considering predicted strength
property gradations.
57G. Skordaris et al. / Surface & Coatings Technology 265 (2015) 53–61

6. loading stage, displayed in the middle of Fig. 12, are re-established
and the same indentation depth is attained. In this way, because the
indentation depth grows progressively during the nano-impact test
(see Fig. 10), the mechanisms taking place during this test cannot be
described by the ANSYS software.
The mechanisms developed during a nano-impact are schematically
illustrated in Fig. 13. As the cube corner indenter penetrates into the im-
print formed during a previous i-impact, superficial stresses equal to the
coating rupture stress occur. Hence, cracks develop, the coating material
fails and film debris are shaken of the contact region between the in-
denter and the coating. In opposite, when the Berkovich indenter is
used, the material stressed at rupture stress level is trapped in a less
loaded coating zone (see also Fig. 12b). Thus, the developed debris are
hindered to be pressed out of the contact region between the indenter
and the coating. As a consequence, in the case of the cube corner indenter,
the imprint is enlarged and the nano-impact depth grows.
For describing these mechanisms, an axis-symmetrical FEM model
was created, using the LS-DYNA software package [22]. The developed
FEM model consisting of individual shell elements is demonstrated in
Fig. 14. The applied element formulation option is characterized in LS-
DYNA as axis-symmetrical solid-area weighted [21]. The actual ADL
strength properties were estimated taking into account the coating
structure shown in Fig. 6. In the calculations, materials with piecewise
linear plasticity and strain rate independent were considered [21,22].
It was reasonable to assume that the film strain rate does not affect
the developed film strains, since the duration of the nano-impact test
lasts 1 s and strains of the applied film material are affected by the strain
rate at impact force durations less than few milliseconds [11]. The
diamond indenter was assumed as rigid [22]. Calculations were also
conducted for an elastic diamond indenter. In both cases, the obtained
results were practically identical. Because the calculation time is compa-
rably shorter in the case of a rigid indenter, this option was employed.
The densities of the involved materials in the FEM model are documented
Fig. 9. (a) Determination of the plastically deformed region during nanoindentation at a
load of 200 mN into a mono-layer coating described using four ADLs. (b) Calculated reac-
tion forces at the maximum indentation depths obtained in various coating structure cases
considering uniform or graded coating properties.
Fig. 10. Nano-impact results on the investigated coatings with different structures,
employing a diamond cube indenter at a frequency of 1 Hz and maximum load of 100 mN.
Fig. 11. Description of a diamond cube corner indenter by means of an equivalent cone.
58 G. Skordaris et al. / Surface & Coatings Technology 265 (2015) 53–61

7. in [26,27,28]. For describing the indenter penetration into the coating
material, it was assumed that the ADLs and the substrate behave as indi-
vidual bodies with own strength properties. Moreover, nodes belonging
to neighborhood elements between two ADLs were joined in one.
In the developed FEM model, a surface to surface contact was applied
for describing the interface between the diamond indenter and the coated
specimen. This is a penalty-based contact with springs placed between all
penetrating nodes and the contact surface [22,29,30]. In addition, an
eroding contact, also a penalty-based contact, was applied between
each individual ADL and the indenter [21]. In this way, elements involved
in the contact definition are subject to erosion (element deletion)
according to a material failure criterion and not directly due to the eroding
contact restrictions. The contact surface is updated as external elements
are deleted. In the performed calculations, it was assumed that each
ADL can withstand the applied load up to a maximum value corre-
sponding to its rupture strain and rupture stress (see Fig. 5). If the
developed element strain exceeds the rupture strain, then the element
is deleted for simulating the crack and debris formation. The accuracy of
discretizising the coating thickness is more than twenty times higher
than that of the developed in the past related FEM model [13], thus
attaining a more detailed description of the coating structure and its
damage. Moreover, due to the axis-symmetrical FEM model structure,
the FEM calculation solving time is comparably significantly shorter.
For attaining the diamond indenter motion, a concentrated nodal
force on the indenter mass center is applied [21]. The time course of
this load is linked to a certain curve representing the time dependent
impact force, as it is shown in Fig. 15. The equilibrium differential
equations are integrated for incremental solution time steps of few
milliseconds. Each solution step is based on the results of the previous
one (explicit method) [22].
3.3.2. Characteristic results obtained by the developed FEM model
An analytical description of the progressive coating failure during
the first impact via the developed FEM model is shown in Fig. 16.
As the indenter penetrates into the coated specimen, the developed
Fig. 12. Calculated stress fields at various nanoindentation's stages employing diverse
indenters onto an 8 μm thick PVD TiAlN mono-layer coating.
Fig. 13. Coating failure mechanisms developed during the nano-impact test.
Fig. 14. The developed axis-symmetrical FEM model for simulating the nano-impact test
using the LS-DYNA software.
59G. Skordaris et al. / Surface & Coatings Technology 265 (2015) 53–61

8. stresses are increased. If the equivalent stress is larger than the element
rupture stress i.e. rupture strain, the failure criterion is met and the
related element is deleted. Up to the completion of the first impact
duration, further elements are overloaded and become inactive. Hence,
in each incremental solution time step the contact region between the
indenter and the coated workpiece is updated. As a consequence, the im-
pact depth grows progressively. The results presented in Fig. 16 describe
this mechanism of the stepwise augmentation of the impact depth. The
exhibited stress fields correspond to loading stages with increasing
stresses after the deletion of some contact elements.
The impact depths and equivalent stress fields after the first, one
hundred and two hundred impacts in various coating structure cases
are exhibited in Fig. 17. These results are associated with coatings
possessing one or four structure layers (SLs). The corresponding to the
coating's structures properties are documented in Fig. 6. As the number
of the impact cycles increases, the indentation depth grows as well.
Due to the lower mechanical properties and higher brittleness of the
mono-layer coating compared to the four-layered one, the related
nano-impact depths are larger.
3.3.3. Comparison between experimental and FEM-calculated results
Comparisons between measured and FEM calculated imprint depths
versus the number of impacts, for two coatings both of 8 μm thickness
but with one or four SLs are illustrated in Fig. 18. Calculations were
carried out assuming that the coating possesses constant properties,
which are associated with the shown ones in Table 1, according to the
SL thickness of the coating. In Fig. 18, the related results monitoring
the developed nano-impact depth versus the number of impacts corre-
spond to the curves 1 and 1′. Moreover, further calculations were
performed, considering for the individual SLs, the strength properties
documented in Fig. 6. These results are described by the curves 2 and
2′ for coating structures with one or four SLs respectively. The FEM
calculated imprint depths converge sufficiently with the measured
ones, if the existing strength property gradations are considered. In the
latter 2 and 2′ cases, the corresponding deviations from the measured re-
sults are less than 5%. These deviations are larger than 15%, if constant
mechanical properties versus the coating thickness are assumed. In this
way, the developed FEM model can be effectively applied for assessing
the brittleness of PVD coatings with various structures and graded
strength properties. Moreover, the obtained experimental and analytical
results ascertain the fact that coatings with multi-layer structures, due to
Fig. 15. Measured time course of the force during the nano-impact test, considered in the
FEM calculations.
Fig. 16. Developed equivalent stress fields at different times and penetration's depths
during the first nano-impact in the case of an 8 μm thick PVD TiAlN coating with 1 struc-
tural layer, employing a diamond cube indenter at a frequency of 1 Hz and a maximum
load of 100 mN.
Fig. 17. Developed equivalent stress fields after various impact numbers in the case of a
8 μm thick PVD coating with 1 or 4 SLs, employing a diamond cube indenter at a frequency
of 1 Hz and a maximum load of 100 mN.
60 G. Skordaris et al. / Surface & Coatings Technology 265 (2015) 53–61

9. their low brittleness, can withstand more effectively impact loads
compared to mono-layer ones. In this context, the presented methods
can be employed to evaluate the efficiency of potential mechanical or
thermal coating treatments for reducing the coating brittleness.
4. Conclusions
The nano-impact test is a reliable method for evaluating the coating
brittleness. An axis-symmetrical FEM model was developed for simulat-
ing dynamically the nano-impact test on mono- and multi-layered PVD
coatings. The graded strength properties gradation of coatings with vari-
ous structures was approximated with the aid of nanoindentations on
as deposited and annealed coating surfaces. By the introduced axis-
symmetrical FEM simulation, compared to an existing 3D-FEM model,
the calculation's time was significantly reduced and moreover, the result's
accuracy increased due to the denser finite element discretization net-
work. In this way, the presented FEM model could be an efficient tool
for assessing film structure's and mechanical properties gradation's
effects on the coating's brittleness. For attaining this target, the distribu-
tion of the strength properties versus the coating thickness has to be
estimated. The described methods facilitate this estimation.
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Fig. 18. Comparison between experimental and FEM-calculated imprint depths versus the number of impacts on variously structured coatings, considering uniform or graded strength
properties versus the film thickness (diamond cube indenter at a frequency of 1 Hz and a maximum load of 100 mN).
61G. Skordaris et al. / Surface & Coatings Technology 265 (2015) 53–61