skordaris 2015 a dynamic fem simulation of the nano-impact test on mono- or

Surface & Coatings Technology 265 (2015) 53–61

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A dynamic FEM simulation of the nano-impact test on mono- ormulti-layered PVD coatings considering their graded strength propertiesdetermined by experimental–analytical procedures

G. Skordaris, K.-D. Bouzakis ⁎, P. CharalampousLaboratory for Machine Tools and Manufacturing Engineering, Mechanical Engineering Department, Aristoteles University of Thessaloniki, Greece

⁎ Corresponding author. Tel.: +30 23 10996021; fax: +E-mail address: [email protected] (K.-D. Bouzakis

http://dx.doi.org/10.1016/j.surfcoat.2015.01.0630257-8972/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t
a r t i c l e i n f o
Article history:Received 14 November 2014Accepted in revised form 26 January 2015Available online 7 February 2015

Keywords:PVD coatingGraded propertiesBrittlenessNano-impactFEM simulation

Nano-impact test is a reliable method for assessing the brittleness of PVD coatings with mono- or multi-layerstructures. For the analytical description of this test, an axis-symmetrical Finite Element Method (FEM) modelwas developed using the LS-DYNA software. This software was adequate to simulate the progressive superficialcoating fracture induced by the repetitive nano-impacts during the nano-impact test. The coating possesses oneor 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 isassociated with the rest time, up to the deposition of the overall coating thickness. For simulating this procedureand estimating the related mechanical properties of the coating layers, cemented carbide specimens with thesame TiAlN PVD (Physical Vapor Deposition) coating of various thicknesses and structures were annealed invacuum. The annealing duration was equal to the deposition time required for coating a specimen with a furtherlayer up to a constant overall thickness. The superficial strength properties of these coatingswere determined vianano-indentations, coupled with FEM calculations to estimate the corresponding stress–strain curves. Resultsobtained by the developed FEM model simulating the nano-impact test were compared with experimentalones. Taking into account the sufficient convergence between them, the introduced numerical procedure canbe 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 asthe chemical stability of coated compounds,multi-layered PVD coatingsevenwith differentmechanical strengths or materials for the individuallayers are used [1].Moreover, the application ofmulti-layered PVD coat-ing structures on cemented carbide inserts has been documented as anefficient way for prolonging the coated tool life, especially when thecoated surfaces are subjected to repetitive dynamic loads [2–5]. This isattributed to the ability of layer interfaces to decelerate the propagationof cracks potentially developed in the coatingmaterial under such loads[2,5,6]. Numerous tests were invented in the past for assessing thecracking 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 forcecharacteristics, the brittleness and fatigue of mono-and multi-layeredPVD coatings were effectively captured [2,9–11]. According to theattained results, the increase of the number of coating layers leads toimproved coating fatigue strength and low brittleness.

30 23 10996059.).

Since the nano-impact test is a reliable method to characterize thebrittleness of PVD coatings, its analytical description can contribute toan efficient assessment of the brittleness of various coating structuresand graded properties, thus restricting the experimentation's time.Efforts for the numerical description of the nano-impact test havebeen undertaken in the past by developing a three dimensional (3D)FEM-model considering uniform or graded strength properties versusthe coating thickness [12,13]. The presented 3D-FEM model in thesepublications for describing the nano-impact test led to long calculationtimeswhenusingfine discretization networks for attaining a reasonableaccuracy. In this way, its application for a precise description of finecoating structures is limited. Moreover, the lack of accurate data refer-ring to strength properties versus the coating thickness further narrowsthe calculations' reliability.

Graded mechanical strength properties may be induced in thecoating structure, using diverse superficial treatments as for examplemicro-blasting [13]. Hereupon, the initial yield stress is commonlyimpaired up to a small depth from the coating surface, whereas thestrength data in the rest coating structure remain unaffected [14].Graded properties in the coating material may also develop during thedeposition of sputtered PVD coatings, with cone-shaped columnarstructure. The associated with this structure grain's size enlargement,towards the coating surface, diminishes the strength properties [15]. A

54 G. Skordaris et al. / Surface & Coatings Technology 265 (2015) 53–61

schematic presentation of the columnar grain structure of mono-layered sputtered TiAlN coatings with different thicknesses is displayedin Fig. 1a. In the case of a multi-layered coating, the columnar growthduring the PVD process is disrupted with a frequency dependent uponthe number of the deposited layers (see Fig. 1b). Thus, the decrease ofthe mechanical data of the coating material versus its thickness isreduced. Strength property changes also develop in the coating, becauseof annealing at the PVD process temperature [16]. The annealing dura-tion of a certain coating region corresponds to the rest time, up to thedeposition accomplishment over this region. Investigations revealingthe effect of annealing temperature and duration on the superficialhardness of PVD TiAlN films are described, among others, in [17,18].

For overcoming the problem of determining graded strengthproperties of PVD coatings with various structures, appropriateexperimental–analytical procedures were implemented, as explainedin a next section. Moreover, an axis-symmetrical FEM model for thedynamic simulation of the nano-impact test was developed, enablinga discretization of the film thickness at least twenty times larger com-pared to the existing FEMmodel [12] almost at the same computationaltime. The effectiveness of thismodel is validated by comparing calculatedresults with experimental ones in the case of PVD coatings with one ormore layers.

2. Experimental and computational details

PVD deposition process with high ionization sputtering (HIS) wasemployed for preparing TiAlN coatings with an Al/Ti ratio of 54/46 andcolumnar micro-structure on cemented carbide inserts of HW-K05/K20SPGN 120408 ISO specifications, using a CEMECON C900 coating ma-chine [19]. The deposition temperature and the bias voltage amountedto 450 °C and −110 V respectively. The overall film thickness in allspecimen cases was approximately 8 μm, consisting of one, two or fourStructure Layers (SLs) [2]. The deposition rate was 1 μm/h, applying afold rotational speed of roughly 3 rpm. In the case of a coating consistingof two or four SLs, a coating growth interruption took place after thedeposition of each individual SL with a thickness of 4 μmor 2 μm respec-tively, followed by an Ar-ion etching for a period of 10 min. During thePVD deposition process, the temperature was kept constant. Additional-ly, inserts were coatedwith amono-layer film of 2 μmor 4 μm thickness.Some of these inserts were annealed in vacuum at a temperature of450 °C, equal to the PVD process one, for a duration of 2 h, as furtherdiscussed in the next section.

For estimating the strength properties of the individual SLs of themanufactured PVD films, nanoindentations were carried out by meansof a FISCHERSCOPE H100 device. The applied Berkovich indenter tip

Fig. 1. Coating columnar microstructures of: (a) mono- and (b) multi-layered coatings ofvarious thicknesses.

geometrical deviations were detected according to methods describedin [20]. An appropriate number of nanoindentations were conductedfor excluding the specimens' roughness effect on the measurementsaccuracy [20]. The superficial strength properties of the employed coat-ings were determined via an analytical evaluation of nanoindentationresults, employing methods documented in the literature [20]. Thenano-impact tests were conducted by a diamond cube indenter usinga Micro Materials Ltd device at a frequency of 1 Hz [9]. The LS-DYNAsoftware was employed for developing the axis-symmetrical FEMmodel, which simulates dynamically the nano-impact test [21,22].

3. Results and discussion

3.1. Determination of graded strength properties of mono- andmulti-layered coatings

A crucial issue for the accuracy of the developed FEMmodel to pre-dict the coating structure response during the nano-impact test is thedetermination of the strength properties versus the coating thickness.For determining these properties in the case of a coating thickness of8 μm with one, two or four layers, it was considered that every layerafter its deposition is exposed to an annealing at the PVD temperatureof a duration corresponding to the rest time, up to the coating processaccomplishment [16].

3.1.1. Determination of superficial strength propertiesIn the case of a columnar coating structure, during the PVD process,

the coating strength properties may diminish due to the augmentationof the grain size induced by the columns' diameter growth [15]. More-over, the columnar coating structure is disrupted and restarts growingwhen the deposition of a next layer begins. In this way, it is reasonableto 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 ofthe same thickness.

For validating this assumption, nanoindentations at a maximumload of 15 mN were conducted on mono-layered PVD TiAlN coatingsof 2 μm, 4 μmor 8 μmthickness (see Fig. 2a). For excluding the specimenroughness effect on the nanoindentation results accuracy, 40 measure-ments per nanoindentation were conducted for stabilizing the movingaverage of the indentation depth versus the indentation force [20].The lower the film thickness, the better it withstands the indenterpenetration, yielding to decreased maximum indentation depth [15,16]. Related nanoindentations were also carried out in the case of an8 μm thick TiAlN coating possessing two or four layers, as displayed inFig. 2b. A comparison between the results presented in Fig. 2a and b ver-ify the assumption that the superficial hardness of a monolayer coatingof 2 μmor 4 μmthicknesses is practically equal to the corresponding oneof a superficial layer of the same thickness.

The superficial strength properties of the investigated coatings weredetermined by analytical evaluation of the attained nanoindentationresults, according to the methodologies described in [20]. The obtainedresults in the case of mono-layer coatings of various thicknesses areexhibited in this Table 1. The mechanical properties of the cementedcarbide substrate are also presented in this table. Thicker PVD coatings,which are associated with coarser superficial film grain sizes, possesslower yield and rupture stress [15], whereas the film elasticity modulusremains practically constant in all coating cases. The calculated stressfields at the constant indentation load of 15 mN show that the depthof the plastically deformed film regions remains under 2 μm in allcoating cases (see Fig. 3). Moreover, as expected, the size of the plasti-cally deformed region at the same indentation load increases with theaugmentation of the coating thickness [15,16].

The structure of the 8 μm thick mono-layer coating was analyticallydescribed using four individual layers (Analytical Description's Layers(ADLs)) of a thickness of 2 μm with own uniform properties. Theseproperties can be determined, as previously discussed, at an indentation

Fig. 2. Load–displacementdiagrams, employing aBerkovich indenter (th/b=2.2/74nm/mm),on coatings: (a) mono-layered and variously thick, (b) with different structures andconstant overall thickness.

55G. Skordaris et al. / Surface & Coatings Technology 265 (2015) 53–61

load of 15 mN. In this case, the induced film plastic deformation isrestricted in a region of less than 2 μm thickness (see Fig. 3). The restcoating structure is deformed elastically possessing the same elasticitymodulus. According to comprehensive investigations described in[16], there is a gradation of the strength properties at the first 2 μmfrom the film surface in the case of a 8 μm thick coating. This happensbecause in this particular coating case the strength properties arestabilized after an annealing duration larger than 120 min and thedeposition duration of the upper 2 μm is less than this time [16]. Inthis way, mechanisms resulting in hardness changes such as of disloca-tionmovements and atom's diffusions, have not been completed [16]. Incontrast, at larger depths the strength properties are not further affectedsince the annealing time is larger than 120 min and the previouslymentioned mechanisms are accomplished. Thus, the film strength

Table 1Superficial strength properties of variously thick PVD mono-layer coatings andof their substrate.

data depend only on the grain size and uniform properties within anADL can be considered. In the described investigations, for simplifyingthe related calculations, it was assumed that the mechanical strengthproperties versus the coating thickness, up to a depth of 2 μm fromthe film surface are constant. These properties can be determined asdescribed in Fig. 3.

In this context, it was necessary to check if the determined superficialstrength properties at an indentation load of 15mN, assumed as uniformfor an ADL thickness of 2 μm, can be employed for the analytical descrip-tion of the whole coating structure. For this purpose, nanoindentationswere conducted at a lager indentation load of 45 mN on mono-layercoatings of 2 μm, 4 μm or 8 μm thickness. A relevant load–displacementdiagram in the case of a coating thickness of 2 μm is exhibited in Fig. 4.The measured course of the indentation depth versus the indentationload was compared to the determined one by the FEM-based simulationof the nanoindentation [20]. In this calculation, the stress–strain datashown in Table 1 for a film thickness of 2 μmwere employed. The max-imumdeviation dmax between themeasured and the calculated indenta-tion load versus the indentation depth is less than 4%. Similar resultswere obtained in the further applied mono-layer coatings of 4 μm and8 μm possessing strength data associated with these film thicknesses(see Table 1). In thisway, the assumption of uniformmechanical proper-tieswithin an ADL thickness of 2 μm leads to sufficiently accurate results.These properties depend on the overall coating thickness and structureand can be determined as introduced in Figs. 2 and 3.

3.1.2. Determination of internal ADL strength propertiesFor defining the mechanical properties of internal ADLs, annealings

for 120 min of coated hardmetal inserts with mono-layer coatings ofvarious thicknesses at a temperature of 450 °C, equal to the depositionone, were conducted. At annealing durations larger than 120 min, themaximum indentation depth remains invariant [16]. The attainedmaximum indentation depths before and after annealing of the mono-layered coatings of 2 μm, 4 μm or 8 μm thickness are illustrated inFig. 5a. In Fig. 5b, the corresponding yield and rupture stress determinedafter [20] are captured. As expected, the indentation depths grow andthemechanical properties decrease after annealing, whereas the elastic-ity modulus remains constant. The mechanical properties of a 6 μmthick coating were determined by linear interpolation between thecorresponding properties at 4 μm and 8 μm film thicknesses.

As previously discussed, the investigated coating structures weresimulated using four ADLs, each one with a thickness of 2 μm and ownmechanical properties. The internal ADL properties were approximatedas explained in Fig. 6. For example, in the case of a 8 μm mono-layercoating, the yield stress of the superficial layer 1 having a thickness of2 μm amounts to ca. 3.4 GPa (see Table 1). Furthermore, consideringthe coating structure, the ADL's positions within the coating thicknessand the related annealing duration after their deposition, the threeinternal layers 2, 3 and 4 possess the superficial strength properties ofa 6 μm, 4 μm and 2 μm thick mono-layer coating, annealed at durationslarger than 120 min respectively (see Fig. 6a). In the same way, asdemonstrated in Fig. 6b and c, for coatings of the same overall thicknessof 8 μm, however with two or four SLs, based on the position of theindividual ADLs within the coating thickness, the related annealingduration can be estimated. For annealing durations larger than 2 h, themechanical data of the ADLs correspond to the ones of annealedmono-layer coatings of overall thickness equal to that of the individualSLs, as presented in Fig. 5. The superficial 2 μm thick ADLs of theprepared coatings are subjected to annealing at durations less than2 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 propertiesgradations by means of nanoindentations

To check the validity of the predicted coating strength propertiesgradations occurring after the PVD process in the case of a 8 μm thick

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).


film with one, two or four SLs, nanoindentations were conducted at anincreased maximum load of 200 mN. In this way, it was intended thatmany ADLs of diverse mechanical properties are plastically deformed.The related load–displacement diagrams and the attained maximumindentation depths are exhibited in Fig. 7. The indentation depth dimin-ishes, as the number of the SLs grows. This is attributed to the increaseof the coating strength properties along with the reduction of the SLs'thickness, as already explained. Using themeasuredmaximum indenta-tion depths, as the displacements exercised in the axis-symmetricalFEM model shown in Fig. 8, the related maximum indentation loadswere calculated. In this FEM model, the kinematic hardening rule wasconsidered since this leads to a rapid convergence in the correspondingFEM 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 maximumindentation depth in the case of a coating consisting of one SL, all ADLs

Fig. 4. Measured and calculated courses of the indentation depth versus the indentationload of a Berkovich indenter (th/b = 2.2/74 nm/mm) into a 2 μm thick coating, up to anindentation load of 45 mN. (The calculations are based on nanoindentation results at15 mN.).

are almost plastically deformed (see Fig. 9a). Similar resultswere also ob-tained in the other examined coating structures. The calculated reactionforces for various coating structures are displayed in Fig. 9b. These reac-tion forces correspond to the maximum indentation depths obtainedin the various coating structures, which are illustrated in Fig. 7. In allexamined cases, the resulting deviations between the applied indentationload of 200mN and the calculated reaction forces are less than 5%. If uni-form coating properties associated with the superficial ones shown inTable 1 are used, significant deviations of the calculated reaction forcesfrom the exercised indentation load of 200 mN develop. In this way, the

Fig. 5. Annealing effect on the: (a) maximum attained indentation depths at a maximumindentation load of 15 mN and (b) strength properties of variously thick mono-layercoatings.

Fig. 6. Predicted graded strength properties of 8 μm thick coatings with differentstructures.

Fig. 8. The employed FEM model for the determination of stress fields and depths duringthe nanoindentation on variously structured coatings considering predicted strengthproperty gradations.


estimated ADL's mechanical properties, as presented in Fig. 6 for the var-ious coating SL cases, enable an accurate description of the elasto-plasticbehavior 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 thedifferent coating structures by a sharp cube corner indenter [2,9]. Therelevant results in terms of nano-impact depth versus the number ofimpacts for an 8 μm thick coating consisting of one, two or four SLsare illustrated in Fig. 10. It is obvious that by increasing the number oflayers, 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 experimentalresults will be used for assessing the accuracy of the developed FEM

Fig. 7. Load–displacement diagrams at a maximum indentation force of 200mN on coatingswith diverse structures, employing a Berkovich indenter (th/b = 2.2/74 nm/mm).

model to simulate the nano-impact test on coatingswith graded strengthproperties.

3.3. FEM simulation of the nano-impact test on mono- or multi-layeredcoatings

3.3.1. The developed axis-symmetrical FEM modelSince an axis-symmetrical FEM simulation of the nano-impact test

can lead to a significantly reduced computational time compared to a3D-FEMmodel [12], it was necessary to replace the cube corner indenterby an equivalent conical onewith axis-symmetrical geometry. The equiv-alent cone possesses the same projected area versus the indentationdepth hi (see Fig. 11). The angle of the equivalent cone was calculatedaccording to equations introduced in [25]. Hereupon, the actual sphericaltip radius of the cube corner indenter equal to roughly 75 nmwas takeninto account.

The inadequacy of the ANSYS software, introduced in Fig. 8, for de-scribing sufficiently the indenter penetration during the nano-impacttest is explained in Fig. 12. In both examined nanoindentation cases,using the indenter geometries displayed at the top of Fig. 12, the samecoating's material laws presented in Fig. 6 were considered. Thediamond indenters were assumed as elastic materials with elasticitymodulus equal to 1100 GPa. According to the results demonstrated inFig. 12, at the constant load of 2.5 mN, a comparably larger imprintdepth develops during loading aswell as unloading when a cube cornerindenter is employed. This behavior can be attributed to the sharperform of the latter indenter compared to a Berkovich one. At loads largerthan 2.5 mN, the sharp geometry of the cube corner indenter results inhighly distorted elements and thus non-converged solutions. Further-more, when the indenter exits from the imprint (unloading stage), aplastic deformation and residual stresses remain in the coatingmaterial,as exhibited at the bottom of Fig. 12. If the coating is reloaded, as it is thecase during the nano-impact test, the stress fields developed during the

Fig. 9. (a) Determination of the plastically deformed region during nanoindentation at aload of 200 mN into a mono-layer coating described using four ADLs. (b) Calculated reac-tion forces at themaximum indentation depths obtained in various coating structure casesconsidering 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 andmaximum load of 100mN.

Fig. 11. Description of a diamond cube corner indenter by means of an equivalent cone.


loading stage, displayed in the middle of Fig. 12, are re-establishedand the same indentation depth is attained. In this way, because theindentation depth grows progressively during the nano-impact test(see Fig. 10), the mechanisms taking place during this test cannot bedescribed by the ANSYS software.

The mechanisms developed during a nano-impact are schematicallyillustrated in Fig. 13. As the cube corner indenter penetrates into the im-print formed during a previous i-impact, superficial stresses equal to thecoating rupture stress occur. Hence, cracks develop, the coatingmaterialfails and film debris are shaken of the contact region between the in-denter and the coating. In opposite, when the Berkovich indenter isused, the material stressed at rupture stress level is trapped in a lessloaded coating zone (see also Fig. 12b). Thus, the developed debris arehindered to be pressed out of the contact region between the indenterand 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 modelwas created, using the LS-DYNA software package [22]. The developedFEM 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 ADLstrength properties were estimated taking into account the coatingstructure shown in Fig. 6. In the calculations, materials with piecewiselinear plasticity and strain rate independent were considered [21,22].It was reasonable to assume that the film strain rate does not affectthe developed film strains, since the duration of the nano-impact testlasts 1 s and strains of the appliedfilmmaterial are affected by the strainrate at impact force durations less than few milliseconds [11]. Thediamond indenter was assumed as rigid [22]. Calculations were alsoconducted for an elastic diamond indenter. In both cases, the obtainedresultswere 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 involvedmaterials in the FEMmodel are documented

Fig. 12. Calculated stress fields at various nanoindentation's stages employing diverseindenters 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 testusing the LS-DYNA software.


in [26,27,28]. For describing the indenter penetration into the coatingmaterial, it was assumed that the ADLs and the substrate behave as indi-vidual bodies with own strength properties. Moreover, nodes belongingto neighborhood elements between two ADLs were joined in one.

In the developed FEMmodel, a surface to surface contact was appliedfor describing the interface between the diamond indenter and the coatedspecimen. This is a penalty-based contactwith springs placed between allpenetrating nodes and the contact surface [22,29,30]. In addition, aneroding contact, also a penalty-based contact, was applied betweeneach individual ADL and the indenter [21]. In this way, elements involvedin the contact definition are subject to erosion (element deletion)according to amaterial failure criterion andnot directly due to the erodingcontact restrictions. The contact surface is updated as external elementsare deleted. In the performed calculations, it was assumed that eachADL can withstand the applied load up to a maximum value corre-sponding to its rupture strain and rupture stress (see Fig. 5). If thedeveloped element strain exceeds the rupture strain, then the elementis deleted for simulating the crack and debris formation. The accuracy ofdiscretizising the coating thickness is more than twenty times higherthan that of the developed in the past related FEM model [13], thusattaining a more detailed description of the coating structure and itsdamage. 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 nodalforce on the indenter mass center is applied [21]. The time course ofthis load is linked to a certain curve representing the time dependentimpact force, as it is shown in Fig. 15. The equilibrium differentialequations are integrated for incremental solution time steps of fewmilliseconds. Each solution step is based on the results of the previousone (explicit method) [22].

3.3.2. Characteristic results obtained by the developed FEM modelAn 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. 15.Measured time course of the force during the nano-impact test, considered in theFEM calculations.


stresses are increased. If the equivalent stress is larger than the elementrupture stress i.e. rupture strain, the failure criterion is met and therelated element is deleted. Up to the completion of the first impactduration, further elements are overloaded and become inactive. Hence,in each incremental solution time step the contact region between theindenter and the coatedworkpiece is updated. As a consequence, the im-pact depth grows progressively. The results presented in Fig. 16 describethis mechanism of the stepwise augmentation of the impact depth. Theexhibited stress fields correspond to loading stages with increasingstresses after the deletion of some contact elements.

Fig. 16. Developed equivalent stress fields at different times and penetration's depthsduring 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 maximumload of 100 mN.

The impact depths and equivalent stress fields after the first, onehundred and two hundred impacts in various coating structure casesare exhibited in Fig. 17. These results are associated with coatingspossessing one or four structure layers (SLs). The corresponding to thecoating's structures properties are documented in Fig. 6. As the numberof the impact cycles increases, the indentation depth grows as well.Due to the lower mechanical properties and higher brittleness of themono-layer coating compared to the four-layered one, the relatednano-impact depths are larger.

3.3.3. Comparison between experimental and FEM-calculated resultsComparisons betweenmeasured and FEM calculated imprint depths

versus the number of impacts, for two coatings both of 8 μm thicknessbut with one or four SLs are illustrated in Fig. 18. Calculations werecarried out assuming that the coating possesses constant properties,which are associated with the shown ones in Table 1, according to theSL thickness of the coating. In Fig. 18, the related results monitoringthe developed nano-impact depth versus the number of impacts corre-spond to the curves 1 and 1′. Moreover, further calculations wereperformed, considering for the individual SLs, the strength propertiesdocumented in Fig. 6. These results are described by the curves 2 and2′ for coating structures with one or four SLs respectively. The FEMcalculated imprint depths converge sufficiently with the measuredones, if the existing strength property gradations are considered. In thelatter 2 and 2′ cases, the corresponding deviations from themeasured re-sults are less than 5%. These deviations are larger than 15%, if constantmechanical properties versus the coating thickness are assumed. In thisway, the developed FEM model can be effectively applied for assessingthe brittleness of PVD coatings with various structures and gradedstrength properties. Moreover, the obtained experimental and analyticalresults ascertain the fact that coatingswithmulti-layer structures, due to

Fig. 17. Developed equivalent stress fields after various impact numbers in the case of a8 μmthick PVD coatingwith 1 or 4 SLs, employing a diamond cube indenter at a frequencyof 1 Hz and a maximum load of 100 mN.

Fig. 18. Comparison between experimental and FEM-calculated imprint depths versus the number of impacts on variously structured coatings, considering uniform or graded strengthproperties versus the film thickness (diamond cube indenter at a frequency of 1 Hz and a maximum load of 100 mN).


their low brittleness, can withstand more effectively impact loadscompared to mono-layer ones. In this context, the presented methodscan be employed to evaluate the efficiency of potential mechanical orthermal coating treatments for reducing the coating brittleness.

4. Conclusions

The nano-impact test is a reliable method for evaluating the coatingbrittleness. An axis-symmetrical FEMmodelwas developed for simulat-ing dynamically the nano-impact test on mono- and multi-layered PVDcoatings. The graded strength properties gradation of coatings with vari-ous structures was approximated with the aid of nanoindentations onas deposited and annealed coating surfaces. By the introduced axis-symmetrical FEM simulation, compared to an existing 3D-FEM model,the calculation's timewas significantly reduced andmoreover, the result'saccuracy increased due to the denser finite element discretization net-work. In this way, the presented FEM model could be an efficient toolfor assessing film structure's and mechanical properties gradation'seffects on the coating's brittleness. For attaining this target, the distribu-tion of the strength properties versus the coating thickness has to beestimated. The described methods facilitate this estimation.

References

[1] A. Rizzo, L. Mirenghi, M. Massaro, U. Galietti, L. Capodieci, R. Terzi, L. Tapfer, D.Valerini, Surf. Coat. Technol. 235 (2013) 475–483.

[2] G. Skordaris, K.-D. Bouzakis, P. Charalampous, E. Bouzakis, R. Paraskevopoulou, O.Lemmer, S. Bolz, CIRP Ann. Manuf. Technol. 63 (2014) 93–96.

[3] K.-D. Bouzakis, J. Anastopoulos, A. Asimakopoulos, N. Michailidis, G. Erkens, Surf.Coat. Technol. 201 (2006) 4395–4400.

[4] S. PalDey, S.C. Deevi, Mater. Sci. Eng. A 342 (2003) 58–79.[5] Y.L. Su, W.H. Kao, J. Mater. Eng. Perform. 7 (1998) 601–612.[6] P. Panjan, M. Čekada, B. Navinšek, Surf. Coat. Technol. 174–175 (2003) 55–62.[7] N.J.M. Carvalho, J.Th.M. De Hosson, Acta Mater. 54 (2006) 1857–1862.

[8] U. Wiklund, P. Hedenqvist, S. Hogmark, Surf. Coat. Technol. 97 (1997) 773–778.[9] B.D. Beake, G.S. Fox-Rabinovich, S.C. Veldhuis, S.R. Goodes, Surf. Coat. Technol. 203

(2009) 1919–1925.[10] B.D. Beake, G.S. Fox-Rabinovich, Surf. Coat. Technol. 255 (2014) 102–111.[11] K.-D. Bouzakis, G. Maliaris, S. Makrimallakis, Int. J. Fatigue 44 (2012) 89–97.[12] K.-D. Bouzakis, S. Gerardis, G. Skordaris, E. Bouzakis, Surf. Coat. Technol. 206 (2011)

1936–1940.[13] K.-D. Bouzakis, G. Skordaris, S. Gerardis, E. Bouzakis, Mater. Werkst. 44 (2013)

684–690.[14] K.-D. Bouzakis, G. Skordaris, F. Klocke, E. Bouzakis, Surf. Coat. Technol. 203 (2009)

2946–2953.[15] K.-D. Bouzakis, S. Hadjiyiannis, G. Skordaris, I. Mirisidis, N. Michailidis, K. Efstathiou,

E. Pavlidou, G. Erkens, R. Cremer, S. Rambadt, I. Wirth, Surf. Coat. Technol. 177–178(2004) 657–664.

[16] K.-D. Bouzakis, G. Skordaris, S. Hadjiyiannis, I. Mirisidis, N. Michailidis, G. Erkens, I.Wirth, Surf. Coat. Technol. 200 (2006) 4500–4510.

[17] G.S. Fox-Rabinovich, J.L. Endrino, B.D. Beake, M.H. Aguirre, S.C. Veldhuis, D.T. Quinto,C.E. Bauer, A.I. Kovalev, A. Gray, Surf. Coat. Technol. 202 (2008) 2985–2992.

[18] K.D. Bouzakis, M. Pappa, G. Skordaris, E. Bouzakis, S. Gerardis, Surf. Coat. Technol.205 (2010) 1481–1485.

[19] CemeCon AG, Website, www.cemecon.de/index_eng.html.[20] K.-D. Bouzakis, N. Michailidis, S. Hadjiyiannis, G. Skordaris, G. Erkens, Mater. Charact.

49 (2002) 149–156.[21] LS-DYNA Keyword user's manual, Version 971, 2007. (Livermore Software Technol-

ogy Corp.).[22] J.O. Hallquist, LS-DYNA Theoretical Manual, Livermore Software Technology Corp.,

1998[23] ANSYS Release 11.0, 2007.[24] J.F. Besseling, E. Van DerGiessen, Mathematical Modelling of Inelastic Deformation,

Chapman & Hall, 1994, ISBN 0412452804.[25] K.-D. Bouzakis, M. Pappa, G. Maliaris, N. Michailidis, Surf. Coat. Technol. 215 (2013)

218–223.[26] J.E. Graebner, Diam. Relat. Mater. 5 (1996) 1366–1370.[27] Inge L. Rasmussen, Optical Monitoring and X-Ray Absorption Spectroscopy for

Studies of Wear on Thin Films, PhD thesis, University of Copenhagen, Denmark,2011.

[28] ISO 3369:2006 (standard EN 23 369) Impermeable sintered metal materials andhardmetals-Determination of density.

[29] G. Skordaris, J. Mater. Eng. Perform. 22 (2013) 3192–3198.[30] G. Skordaris, J. Mater. Eng. Perform. 23 (2014) 3497–3504.