- Email: [email protected]
Contact mechanics of coating-substrate systems: Monolayer and multilayer coatings
archives of civil and mechanical engineering 12 (2012) 464–470
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/acme
Original Research Article
Contact mechanics of coating-substrate systems: Monolayer and multilayer coatings M. Kotn AGH University of Science and Technology, Faculty of Mechanical Engineering and Robotics, Al. Mickiewicza 30, 30-059 Krako´w, Poland
ar t ic l e in f o
abs tra ct
Article history:
The paper presents issues related to contact mechanics of coating-substrate systems and
Received 20 May 2012
problems with analysis of their mechanical properties. The author’s model of deforma-
Accepted 17 July 2012
tions of such systems based on a complex analysis of nanoindentation tests and FEM
Available online 25 July 2012
modeling is also presented. This model allows identification of the areas submitted to the
Keywords:
highest stress concentration with their quantitative analysis. Studies were carried out on
Contact mechanics
TiN monolayer and Ti/TiN multilayers deposited on steel substrates. For multilayers the
Hard coatings
impact of soft Ti layers on coating fracture was investigated.
Multilayers
& 2012 Politechnika Wrocławska. Published by Elsevier Urban & Partner Sp. z o.o. All rights
FEM modeling
reserved.
Instrumented indentation
1.
Introduction
Hard ceramic coatings are used in many branches of industry to extend the lifetime and improve the load bearing capacity of machine elements, tools and bioimplants. The most frequently applied are transition metal nitrides like titanium nitride (TiN) [1]. Ceramic coatings are hard, wear resistant but have rather low fracture toughness and this is the main application problem particularly when they are deposited on softer substrates (eg. steels and titanium alloys). They are also characterized by high elastic modulus what leads to high stress concentration at interfaces in a case of high elastic properties mismatch between coating and substrate. Under contact loading of coating-substrate systems this stress can cause coatings delamination. However, high elastic modulus corresponds to high hardness of coatings. Higher hardness according to classical theories of wear indicates higher abrasive wear resistance of materials. On the other side very hard coatings exhibit low fracture toughness.
Hence the best solution from tribological point of view are hard and at the same time susceptible coatings. Coatings that can fulfill both demands are built on metal/ ceramic multilayer concept. Such coatings are becoming more popular. Multilayers are composed of a stack of few to hundreds thin layers built usually on two alternately deposited materials. Between multilayers Ti/TiN coatings are one of the most frequently studied [2,3] and used in tribological applications. In that manner also other multilayers are under examinations like Cr/CrN [4,5], W/WN [6], Al/AlN [7], W/ZrN [8], Fe/TiC [9] and Mo/TiC [10]. Mechanical properties of multilayers offer advantages over single nitride coatings—higher toughness and in some cases higher hardness. Proper selection of materials and architecture can also improve significantly their tribological properties. Despite the common applications of various types of coatings there are still no complex studies on the strength of the coating-substrate systems especially for coatings with sophisticated architecture. It is the consequence of complex
n
Tel.: þ48502307899. E-mail address: [email protected]
1644-9665/$ - see front matter & 2012 Politechnika Wrocławska. Published by Elsevier Urban & Partner Sp. z o.o. All rights reserved. http://dx.doi.org/10.1016/j.acme.2012.07.004
archives of civil and mechanical engineering 12 (2012) 464–470
state of stress due to the mismatch of coating and substrate properties and the residual stresses that occur in the system after the deposition [11]. Studies on contact mechanics of coating-substrate systems in elastic–plastic regime of deformations presented in this paper were conducted according to complex procedure based on indentation tests and FEM modeling results. The main aims were analysis of maximum tensile stress concentration areas and their quantitative evaluation for TiN monolayer system and Ti/TiN multilayers.
2. Contact mechanics of coating-substrate systems
where F—load, R—ball radius, and ER—reduced elastic modulus defined as: 1n2i 1n2m 1 ¼ þ ER Ei Em
1ðl þ k þ 4ka2 H2 Þe2aH þ lke4aH 1 þ 4kaHe2aH lke4aH
They compared the deformation of the coating-substrate system with deformation of the hypothetical infinite thick coating and proposed the scaling coefficient a. This parameter depends on the properties of coating and substrate and deformation range. Therefore meaning of a is the same as Em in Eq. (3) and can be calculated from the formula ð5Þ
where l1 and l2 are the functions of t/aC presented in [15]. Similar analysis of elastic deformations were also performed by Gao et al. [16]. When plastic yield of substrate occurs all of these analysis and relations cannot be used anymore. However, many studies conducted by the author and also articles presented in the literature show that the fracture and destruction of hard, wear resistant coatings start when substrate is already plastically deformed. Hence, it is necessary to conduct analysis of deformation, stress distribution and strength of coating-substrate systems within plastic deformation regime of the system.
ð2Þ
In Eq. (2) v is Poisson ratio and subscripts i and m denote a ball (indenter in nanoindentation tests) and material of a flat element (specimen). In the case of coated surface, when coating has different properties than substrate these relations cannot be used. Elastic modulus of specimen Em is not a constant value and varies with the displacement h. At low indentation depth for Em and nm the coatings properties Ec, nc can be taken into calculations, what represents indentation of an infinite thick coating t-1. For large displacements the substrate carries almost all load and its properties should be adopted Es and ns. This situation corresponds to indentation of the system with extremely thin coating t-0. Thus, to built an analytical relation and then predict a, h and pm for intermediate thickness t, it is necessary to define the reduced modulus of elasticity varying with the penetration depth. The relation for Em was given by Liu et al. [13] Em ¼ EC
substrate. A similar relations for the elastic state of deformation of coated elements, binding load and penetration depth, was given by Hsueh and Miranda [15] pffiffiffiffiffi 4Ec Ri ac h ð4Þ P¼a 3ð1n2c Þ
1 Ec ð1 þ ns Þ ð32nc Þl1 þ l2 ½ð32ns Þl1 þ l2 ¼1þp a Es ð1 þ nc Þ pð1nc Þ
Load bearing capacity of coated elements cannot be calculated from Hertz equations [12] usually applied for homogeneous materials. According to Hertz theory, for a contacting ball and a flat surface the contact radius (a), displacement (h) and average pressure (pm) in the contact area can be found from following relations: sffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3 6FE 9F2 3 3FR 3 R , pm ¼ ð1Þ , h¼ a¼ 2 3 4ER 16RER p R2
465
ð3Þ
where l ¼ 14ð1nc Þ=1 þ mð34nc Þ, k ¼ 1ðm1Þ=ðm þ ð34nc ÞÞ, m ¼ Ec ð1 þ ns Þ=Es ð1 þ nc Þ, a ¼ Ft=H. The parameter H is the dimensionless thickness of the coating defines as H ¼t/a0s for elastic substrates and H¼ t/a0c for rigid substrate. The contact area a0s and a0c can be calculated from Eq. (1) as well as for indentation of uncoated substrate and the infinitely thick coating respectively. The whole analysis presented in [13,14] is based on the results of many numerical calculations. Introduction of a few correction factors (Figs. 3 and 4 in [13]) allows to determine the contact parameters for coating-substrate systems by comparing them with a contact of infinitely thick coating or
3. Procedure of complex analysis of coatingsubstrate mechanical properties The instrumental indentation method is extremely helpful for analysis in a field of contact mechanics of complex coating-substrate systems. Quantitative evaluation of the nanoindentation test results compared with the finite element method modeling allows to determine the critical stress level leading to substrate yield and coatings fracture. The scheme of the procedure developed by the author and used for analysis carried out for tested coating-substrate systems is given in Fig. 1. The result of indentation is penetration depth–load curve obtained from indenter displacement and applied load measured continuously during loading and unloading. More information about the mechanical response of coating-substrate systems is obtained after the transformation of penetration depth–loads curves into stress–strain curves (se) plotted using following equations [17,18]: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F 0:2aC , aC ¼ 2hC Ri h2C ð6Þ s ¼ pm ¼ 2 , e ¼ Ri paC where pm—average pressure, F—load, aC—contact radius, Ri—indenter tip radius, and hC—contact depth.
4.
Experimental
Ti/TiN multilayers and TiN monolayer system were deposited on austenitic steel substrates by Pulsed Laser Deposition (PLD) technique with an additional magnetron source [19]. High purity targets (99.9% Ti) were used in the ablation
466
archives of civil and mechanical engineering 12 (2012) 464–470
Fig. 1 – Diagram of a complex analysis of spherical indentation using the experiment and FEM modeling results.
experiments with a pulsed Nd:YAG laser system, operating at a 1064 nm wavelength with 0.6 J pulse energy and 10 ns pulse duration at a repetition rate of 50 Hz. The targets were rotated during laser irradiation in order to avoid the formation of deep craters. To provide homogenous coating thickness over the whole coated surface, the substrates were moved through the plasma plumes during deposition. Metal layers (Ti) were deposited in argon atmosphere (99.99), when nitride TiN in—ArþN2 (99.99). Titanium layers were first deposited on substrates, which provides better adhesion and avoid high residual stress in multilayers. Multilayer 8 Ti/TiN consists eight Ti and TiN layers all 62 nm thick, while total thickness of all tested coating is 1 mm. TEM studies have shown columnar microstructure of TiN monolayer (Fig. 2a) with microcracks formed along the column boundaries due to high compressive residual stress. In multilayers both metallic Ti and ceramic TiN layers also have columnar microstructure as well. TEM image presents well defined layered architecture of 8 Ti/TiN multilayer (Fig. 2b). Width of columns in TiN is smaller in multilayer E20 nm than in monolayer E250 nm. Author’s studies on different multilayer systems like Cr/CrN, TiN/CrN and Ti/TiN exhibited direct scaling of the grain size with thickness of individual layers. Detailed analysis of the microstructure of investigated coatings were presented in previous publications [20,21].
Fig. 2 – TEM micrographs of the cross-section of: (a) TiN and (b) 8 Ti/TiN coatings. Spherical nanoindentation tests were conducted using indenter with 20 mm tip radius and MCT-CSM Instruments equipment. Maximum applied load was 500 mN. Real state of stress during spherical indentation was defined from comparison of experimental results and FEM modeling. The software ANSYS 11 was used to perform the FEM models that comprises of elastic coating, elastic–plastic substrate and rigid ball with Ri ¼20 mm radius pressed into them (Fig. 3). Due to the axial symmetry of problem two dimensional models were analyzed. An accurate analysis of strain and stress fields demands applying a very fine mesh in the coating
archives of civil and mechanical engineering 12 (2012) 464–470
and the substrate near the contact zone. That allows also precise determination of contact geometry. The models were at least 40 times higher than radius of contact area hence the influence of the model size on computational results seems to be excluded. Thanks to that even under maximum load the elastic strain field did not reach right and bottom plane of model. The boundary conditions were specified so that the model matches the real indentation process. The nodes in the bottom surface of the specimen have been fixed and in the symmetry axis of model cannot be deformed in the radial direction. Normal load was gradually applied within 50 steps during loading and unloading down to zero.
Fig. 3 – Part of the finite element model of indenter pressed into coated substrate, with the refined meshes in the region around contact zone.
467
Three coatings of t ¼ 1 mm total thickness were modeled: monolayer, multilayer with two elastic materials and multilayer with softer layers prone to yield. Ceramic TiN monolayer and TiN layers in multilayer have elastic modulus ETiN ¼ 420 GPa, while for softer Ti layers ETi ¼ 160 GPa. Yield strength of Ti layers YTi ¼HTi/3E2 GPa was assumed. Substrate properties ES ¼ 210 GPa and YS ¼0.8 GPa meet properties of X20Cr13 steel. All materials properties are taken from indentation results and catalogs.
5.
Indentation and FEM modeling results
Fig. 4a presents indentation curves for both tested coatings. These curves (Fig. 4b) were transformed into stress–strain curves according to the procedure presented in Fig. 1. A higher stress (mean pressure) level was found for TiN single coating. When relative indentation depth hR ¼hmax/t reaches 0.14 at pm ¼ 3.5 GPa, a drop of contact stresses is observed, which corresponds to first ring crack formation. For multilayer the stable level of pm ¼2.5 GPa starting at hR ¼0.1 reveals deformations controlled by continuous substrate yield with minor coating fracture. The FEM modeling results allowed to find the stress field at certain deformation and contact pressure pm. The maximum tensile stresses were found in two areas: on the surface just outside contact area and in the indenter symmetry axis at coating-substrate interface. The ratio of these tensile stresses to mean contact pressure s/pm is presented in Fig. 5 for both locations. In a whole range of hR
Fig. 4 – Indentation results of TiN and 8 Ti/TiN coatings: (a) indentation curves and (b) stress–strain curves.
Fig. 5 – Tensile stress concentration coefficient at: (a) coating surface and (b) coating-substrate interface.
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archives of civil and mechanical engineering 12 (2012) 464–470
stresses at the surface are higher in multilayers than in single layer (Fig. 5a). It could be explained by easier bending of external TiN layer. Using s/pm ratio the real tensile stress concentrations at both TiN and 8 Ti/TiN coatings surfaces were calculated (Fig. 6). The maximum stress for TiN monolayer system is 10–20% higher than for multilayer. First crack appeared in TiN monolayer when tensile stress reached 7 GPa. But in this calculations the residual stress was not taken into account. The total stress sT in real specimens is a sum of residual stress sR and stress induced by external load sIND: sT ¼ sIND þ sR
systems cracks nucleated in surface propagate down to interface throughout the entire thickness. For coatings with columnar microstructure these cracks develop at column borders (Fig. 7a). These mechanisms of deformation is called
ð7Þ
For TiN monolayer residual stress measured by XRD technique is sRE4 GPa. When this stress was subtracted the coating strength 3 GPa was assumed (Fig. 6 open arrow). If the strength of TiN layers in multilayer is the same and measured residual stress is sRE2 GPa, then the first crack in external ceramic layer should be formed at 5 GPa tensile stress found from FEM modeling (Fig. 6 filled circle). This stress level is at similar hR to TiN monolayer system when first fracture appeared. At the interface stresses are higher for monolayer than for multilayer (Fig. 5b), what is caused by additional stress arising from higher elastic modulus mismatch of coating and substrate. In multilayer, metal layers play an important role on mechanical response, reducing the residual stress and increasing the fracture resistance. Microscopic studies of deformation and fracture mechanisms of such coatings are presented in previous papers [2,20]. For thin, monolayer
Fig. 6 – Tensile stress evolution on coating surfaces.
Fig. 8 – FEM modeling results—indentation of 4 Ti/TiN multilayer: (a) plastic deformations of Ti layers and steel substrate and (b) tensile stress field in TiN layers.
Fig. 7 – TEM cross-section images—deformation mechanisms of: (a) TiN and (b) 8 Ti/TiN multilayer coatings.
archives of civil and mechanical engineering 12 (2012) 464–470
intercolumnar sliding. TEM analyses showed that the deformation mechanism of Ti/TiN multilayers was followed by the sequence of fracture of ceramic layers and yield of metallic ones (Fig. 7b). This deformation mechanism is confirmed by the results of FEM modeling. The maximum plastic deformations of Ti layers (Fig. 8a) and the maximum tensile stress in TiN layers (Fig. 8b) are slightly shifted in the direction of symmetry axis what corresponds to TEM image. The next problem considered in multilayers was the plastic yield of soft layers. Do they lead to stress reduction or leading to higher deformation of the coating induce higher stress in ceramic layers? Fig. 9 presents the comparison of maximum stress concentration in a subsequent ceramic layers in 4 Ti/TiN
Fig. 9 – Tensile stress concentration at subsequent TiN layers in 4 Ti/TiN multilayers.
469
multilayers with elastic (hard) and plastic (plast) Ti layers under two deformations h/t¼ 0.25 and 2. The stress concentration is getting smaller on successive TiN layers. For higher deformation s/pm ratio is 6.8 and 3.5 on first and second TiN layer respectively. Assuming that the cracks are created in the ceramic layers when the tensile stress exceeds their strength, the applied load for crack initiation has to be twice as large in the second TiN layer than in the external one. For the third and fourth layer, the maximum tensile stresses are in the symmetry axis of the contact, while stresses on the edge of contact area are compressive. Therefore, only two external ceramic layers should break under such a deformation. Comparing models where Ti layers are totally elastic and prone to yield, the lack of effect of this plasticity on the stress concentration in TiN ceramic layers under lower deformation h/t¼ 0.25 was found. But under higher deformation, the higher plastic deformations within Ti layers start to play an important role reducing by 20% tensile stress in successive TiN layers. This reduction is due to ‘slipping’ of ceramic layers on metallic ones, what results on lower coating’s bending at the contact edge. Alternately stacked hard and soft layers in the multilayer coatings improve the fracture resistance compared to single ceramic coatings. This advantage of multilayers is confirmed by SEM images of TiN and 8 Ti/TiN coatings’ surfaces with indents induced by 20 mm tip radius indenter (Fig. 10). First circular crack for TiN monolayer system appears at 130 mN load, what corresponds to pop-in on indentation curve (Fig. 4a). Fig. 10a shows the surface of this coating after indentation performed at 200 mN load. However, the same load does not lead to fracture of
Fig. 10 – SEM images of coating surfaces after spherical indentations: (a) TiN at 200 mN, (b) TiN at 1 N, (c) 8 Ti/TiN at 200 mN, and (d) 8 Ti/TiN at 1 N.
470
archives of civil and mechanical engineering 12 (2012) 464–470
8 Ti/TiN multilayer (Fig. 10c) and first crack is formed at about 350 mN load. But in contrast to monolayer, cracks formation in multilayers is not seen on indentation curves. Nevertheless SEM image of 8 Ti/TiN coating after indentation at 1 N load shows small cracks but only inside the indent (Fig. 10d). The TiN monolayer system after this test is highly cracked and last cracks are even beyond the contact area (Fig. 10b). The higher fracture resistance of multilayers than monolayers has also a strong influence on their higher wear resistance. Wear rate of Ti/TiN and Cr/CrN multilayers can be significantly lower than for TiN and CrN monolayer systems, what was presented in previous papers [2,5].
6.
Conclusions
1. Developed by author complex procedure based on transformation of indentation curves into stress–strain curves with subsequent FEM modeling is an effective tool of contact stress analysis in coating-substrate systems. 2. Introduction of soft metallic layers in multilayer results higher tensile stress concentration on coating surface and lower at coating-substrate interface. 3. Metallic layers in Ti/TiN multilayer improve their fracture resistance. Tensile stress at subsequent TiN layers is reduced and external load must significantly rise to induce crack formation at the surface of the following ceramic layer. 4. Comparing two FEM models of multilayers favorable impact of local plastic deformation of metallic layers on stress reduction at heavy duty is clearly seen.
Acknowledgment The author would like to acknowledge Dr. habil J.M. Lackner for coatings deposition at Joanneum Research Forschungsgesellschaft mbH, Leoben, Austria, Dr. Ł. Major for TEM, and M.Sc P. Indyka for SEM analysis.
references
[1] W. Feng, D. Yan, J. Li, Y. Dong, Reactive plasma sprayed TiN coating and its tribological properties, Wear 258 (2005) 806–811. [2] M. Kot, Ł. Major, J. Lackner, W. Rakowski, Enhancement of mechanical and tribological properties of Ti/TiN multilayers over TiN single layer, Journal of Balkan Tribological Association 18 (2012) 92–105. [3] Y.H. Cheng, T. Browne, B. Heckerman, C. Bowman, V. Gorokhovsky, E.I. Meletis, Mechanical and tribological properties of TiN/Ti multilayer coatings, Surface and Coatings Technology 205 (2010) 146–151.
[4] Ł. Major, J. Morgiel, J.M. Lackner, M.J. Szczerba, M. Kot, B. Major, Microstructure, design and tribological properties of Cr/CrN and TiN/CrN multilayer films, Advanced Engineering Materials 10 (2008) 617–621. [5] M. Kot, W. Rakowski, B. Major, Ł. Major, J. Morgiel, Effect of bilayer period on properties of Cr/CrN multilayer coatings produced by laser ablation, Surface and Coatings Technology 202 (2008) 3501–3506. [6] L. Maille, P. Aubert, C. Sant, P. Garnier, A mechanical study of W–N/W multilayers, Surface and Coatings Technology 180–181 (2004) 483–487. [7] G.A. Zhang, Z.G. Wu, M.X. Wang, X.Y. Fan, J. Wang, P.X. Yan, Structure evolution and mechanical properties enhancement of Al/AlN multilayer, Applied Surface Science 253 (2007) 8835–8840. [8] S.A. Barnett, A. Madan, Hardness and stability of metal– nitride nanoscale multilayers, Scripta Materialia 50 (2004) 739–744. [9] C.H. Liu, W.-Z. Li, H.-D. Li, Structure and hardness enhancement of Fe/TiC multilayered films, Nuclear Instruments and Methods in Physics Research B 95 (1995) 323–326. [10] J. Wang, W.-Z. Li, H.-D. Li, Preparation and characterization of superhard TiC/Mo multilayers, Journal of Materials Science 35 (2000) 2689–2693. [11] K. Holmberg, A. Matthews, Coatings Tribology: Properties, Mechanisms, Techniques and Applications in Surface Engineering, Elsevier, Amsterdam, 2009. [12] H. Hertz, Miscellaneous Papers, in: D.E. Jones, G.A. Schott (Eds.), Macmillan, London, 1863. [13] S. Liu, A. Peyronnel, Q.J. Wang, L.M. Keer, An extension of the Hertz theory for 2D coated components, Tribology Letters 18 (2005) 505–511. [14] S.B. Liu, A. Peyronnel, Q.J. Wang, L.M. Keer, An extension of the Hertz theory for three-dimensional coated bodies, Tribology Letters 18 (2005) 303–314. [15] C.-H. Hsueh, P. Miranda, Combined empirical-analytical method for determining contact radius and indenter displacement during Hertzian indentation on coating/substrate systems, Journal of Materials Resources 19 (2004) 2774–2781. [16] H. Gao, C.-H. Chiu, J. Lee, Elastic contact versus indentation modeling of multi-layered materials, International Journal of Solids and Structures 29 (1992) 2471–2492. [17] M. Kot, W. Rakowski, J.M. Lackner, Ł. Major, Analysis of spherical indentations of coating-substrate systems: experiments and finite element modeling, Materials and Design 43 (2012) 99–111. [18] E. Martinez, J. Esteve, Nanoindentation hardness measurements using real-shape indenters: application to extremely hard and elastic materials, Applied Physics A 72 (2001) 319–324. [19] J.M. Lackner, Industrially-Scaled Hybrid Pulsed Laser Deposition at Room Temperature, Orekop, Cracow, 2005. [20] J.M. Lackner, Ł. Major, M. Kot, Microscale interpretation of tribological phenomena in Ti–TiN soft–hard multilayer coatings on soft austenite steel substrates, Bulletin of Polish Academy of Sciences Technical Sciences 59 (2011) 343–355. [21] Ł. Major, J. Morgiel, J.M. Lackner, M.J. Szczerba, M. Kot, B. Major, Microstructure design and tribological properties of Cr/CrN and TiN/CrN multilayer films, Advanced Engineering Materials 10 (2008) 617–621.
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/acme
Original Research Article
Contact mechanics of coating-substrate systems: Monolayer and multilayer coatings M. Kotn AGH University of Science and Technology, Faculty of Mechanical Engineering and Robotics, Al. Mickiewicza 30, 30-059 Krako´w, Poland
ar t ic l e in f o
abs tra ct
Article history:
The paper presents issues related to contact mechanics of coating-substrate systems and
Received 20 May 2012
problems with analysis of their mechanical properties. The author’s model of deforma-
Accepted 17 July 2012
tions of such systems based on a complex analysis of nanoindentation tests and FEM
Available online 25 July 2012
modeling is also presented. This model allows identification of the areas submitted to the
Keywords:
highest stress concentration with their quantitative analysis. Studies were carried out on
Contact mechanics
TiN monolayer and Ti/TiN multilayers deposited on steel substrates. For multilayers the
Hard coatings
impact of soft Ti layers on coating fracture was investigated.
Multilayers
& 2012 Politechnika Wrocławska. Published by Elsevier Urban & Partner Sp. z o.o. All rights
FEM modeling
reserved.
Instrumented indentation
1.
Introduction
Hard ceramic coatings are used in many branches of industry to extend the lifetime and improve the load bearing capacity of machine elements, tools and bioimplants. The most frequently applied are transition metal nitrides like titanium nitride (TiN) [1]. Ceramic coatings are hard, wear resistant but have rather low fracture toughness and this is the main application problem particularly when they are deposited on softer substrates (eg. steels and titanium alloys). They are also characterized by high elastic modulus what leads to high stress concentration at interfaces in a case of high elastic properties mismatch between coating and substrate. Under contact loading of coating-substrate systems this stress can cause coatings delamination. However, high elastic modulus corresponds to high hardness of coatings. Higher hardness according to classical theories of wear indicates higher abrasive wear resistance of materials. On the other side very hard coatings exhibit low fracture toughness.
Hence the best solution from tribological point of view are hard and at the same time susceptible coatings. Coatings that can fulfill both demands are built on metal/ ceramic multilayer concept. Such coatings are becoming more popular. Multilayers are composed of a stack of few to hundreds thin layers built usually on two alternately deposited materials. Between multilayers Ti/TiN coatings are one of the most frequently studied [2,3] and used in tribological applications. In that manner also other multilayers are under examinations like Cr/CrN [4,5], W/WN [6], Al/AlN [7], W/ZrN [8], Fe/TiC [9] and Mo/TiC [10]. Mechanical properties of multilayers offer advantages over single nitride coatings—higher toughness and in some cases higher hardness. Proper selection of materials and architecture can also improve significantly their tribological properties. Despite the common applications of various types of coatings there are still no complex studies on the strength of the coating-substrate systems especially for coatings with sophisticated architecture. It is the consequence of complex
n
Tel.: þ48502307899. E-mail address: [email protected]
1644-9665/$ - see front matter & 2012 Politechnika Wrocławska. Published by Elsevier Urban & Partner Sp. z o.o. All rights reserved. http://dx.doi.org/10.1016/j.acme.2012.07.004
archives of civil and mechanical engineering 12 (2012) 464–470
state of stress due to the mismatch of coating and substrate properties and the residual stresses that occur in the system after the deposition [11]. Studies on contact mechanics of coating-substrate systems in elastic–plastic regime of deformations presented in this paper were conducted according to complex procedure based on indentation tests and FEM modeling results. The main aims were analysis of maximum tensile stress concentration areas and their quantitative evaluation for TiN monolayer system and Ti/TiN multilayers.
2. Contact mechanics of coating-substrate systems
where F—load, R—ball radius, and ER—reduced elastic modulus defined as: 1n2i 1n2m 1 ¼ þ ER Ei Em
1ðl þ k þ 4ka2 H2 Þe2aH þ lke4aH 1 þ 4kaHe2aH lke4aH
They compared the deformation of the coating-substrate system with deformation of the hypothetical infinite thick coating and proposed the scaling coefficient a. This parameter depends on the properties of coating and substrate and deformation range. Therefore meaning of a is the same as Em in Eq. (3) and can be calculated from the formula ð5Þ
where l1 and l2 are the functions of t/aC presented in [15]. Similar analysis of elastic deformations were also performed by Gao et al. [16]. When plastic yield of substrate occurs all of these analysis and relations cannot be used anymore. However, many studies conducted by the author and also articles presented in the literature show that the fracture and destruction of hard, wear resistant coatings start when substrate is already plastically deformed. Hence, it is necessary to conduct analysis of deformation, stress distribution and strength of coating-substrate systems within plastic deformation regime of the system.
ð2Þ
In Eq. (2) v is Poisson ratio and subscripts i and m denote a ball (indenter in nanoindentation tests) and material of a flat element (specimen). In the case of coated surface, when coating has different properties than substrate these relations cannot be used. Elastic modulus of specimen Em is not a constant value and varies with the displacement h. At low indentation depth for Em and nm the coatings properties Ec, nc can be taken into calculations, what represents indentation of an infinite thick coating t-1. For large displacements the substrate carries almost all load and its properties should be adopted Es and ns. This situation corresponds to indentation of the system with extremely thin coating t-0. Thus, to built an analytical relation and then predict a, h and pm for intermediate thickness t, it is necessary to define the reduced modulus of elasticity varying with the penetration depth. The relation for Em was given by Liu et al. [13] Em ¼ EC
substrate. A similar relations for the elastic state of deformation of coated elements, binding load and penetration depth, was given by Hsueh and Miranda [15] pffiffiffiffiffi 4Ec Ri ac h ð4Þ P¼a 3ð1n2c Þ
1 Ec ð1 þ ns Þ ð32nc Þl1 þ l2 ½ð32ns Þl1 þ l2 ¼1þp a Es ð1 þ nc Þ pð1nc Þ
Load bearing capacity of coated elements cannot be calculated from Hertz equations [12] usually applied for homogeneous materials. According to Hertz theory, for a contacting ball and a flat surface the contact radius (a), displacement (h) and average pressure (pm) in the contact area can be found from following relations: sffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3 6FE 9F2 3 3FR 3 R , pm ¼ ð1Þ , h¼ a¼ 2 3 4ER 16RER p R2
465
ð3Þ
where l ¼ 14ð1nc Þ=1 þ mð34nc Þ, k ¼ 1ðm1Þ=ðm þ ð34nc ÞÞ, m ¼ Ec ð1 þ ns Þ=Es ð1 þ nc Þ, a ¼ Ft=H. The parameter H is the dimensionless thickness of the coating defines as H ¼t/a0s for elastic substrates and H¼ t/a0c for rigid substrate. The contact area a0s and a0c can be calculated from Eq. (1) as well as for indentation of uncoated substrate and the infinitely thick coating respectively. The whole analysis presented in [13,14] is based on the results of many numerical calculations. Introduction of a few correction factors (Figs. 3 and 4 in [13]) allows to determine the contact parameters for coating-substrate systems by comparing them with a contact of infinitely thick coating or
3. Procedure of complex analysis of coatingsubstrate mechanical properties The instrumental indentation method is extremely helpful for analysis in a field of contact mechanics of complex coating-substrate systems. Quantitative evaluation of the nanoindentation test results compared with the finite element method modeling allows to determine the critical stress level leading to substrate yield and coatings fracture. The scheme of the procedure developed by the author and used for analysis carried out for tested coating-substrate systems is given in Fig. 1. The result of indentation is penetration depth–load curve obtained from indenter displacement and applied load measured continuously during loading and unloading. More information about the mechanical response of coating-substrate systems is obtained after the transformation of penetration depth–loads curves into stress–strain curves (se) plotted using following equations [17,18]: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F 0:2aC , aC ¼ 2hC Ri h2C ð6Þ s ¼ pm ¼ 2 , e ¼ Ri paC where pm—average pressure, F—load, aC—contact radius, Ri—indenter tip radius, and hC—contact depth.
4.
Experimental
Ti/TiN multilayers and TiN monolayer system were deposited on austenitic steel substrates by Pulsed Laser Deposition (PLD) technique with an additional magnetron source [19]. High purity targets (99.9% Ti) were used in the ablation
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Fig. 1 – Diagram of a complex analysis of spherical indentation using the experiment and FEM modeling results.
experiments with a pulsed Nd:YAG laser system, operating at a 1064 nm wavelength with 0.6 J pulse energy and 10 ns pulse duration at a repetition rate of 50 Hz. The targets were rotated during laser irradiation in order to avoid the formation of deep craters. To provide homogenous coating thickness over the whole coated surface, the substrates were moved through the plasma plumes during deposition. Metal layers (Ti) were deposited in argon atmosphere (99.99), when nitride TiN in—ArþN2 (99.99). Titanium layers were first deposited on substrates, which provides better adhesion and avoid high residual stress in multilayers. Multilayer 8 Ti/TiN consists eight Ti and TiN layers all 62 nm thick, while total thickness of all tested coating is 1 mm. TEM studies have shown columnar microstructure of TiN monolayer (Fig. 2a) with microcracks formed along the column boundaries due to high compressive residual stress. In multilayers both metallic Ti and ceramic TiN layers also have columnar microstructure as well. TEM image presents well defined layered architecture of 8 Ti/TiN multilayer (Fig. 2b). Width of columns in TiN is smaller in multilayer E20 nm than in monolayer E250 nm. Author’s studies on different multilayer systems like Cr/CrN, TiN/CrN and Ti/TiN exhibited direct scaling of the grain size with thickness of individual layers. Detailed analysis of the microstructure of investigated coatings were presented in previous publications [20,21].
Fig. 2 – TEM micrographs of the cross-section of: (a) TiN and (b) 8 Ti/TiN coatings. Spherical nanoindentation tests were conducted using indenter with 20 mm tip radius and MCT-CSM Instruments equipment. Maximum applied load was 500 mN. Real state of stress during spherical indentation was defined from comparison of experimental results and FEM modeling. The software ANSYS 11 was used to perform the FEM models that comprises of elastic coating, elastic–plastic substrate and rigid ball with Ri ¼20 mm radius pressed into them (Fig. 3). Due to the axial symmetry of problem two dimensional models were analyzed. An accurate analysis of strain and stress fields demands applying a very fine mesh in the coating
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and the substrate near the contact zone. That allows also precise determination of contact geometry. The models were at least 40 times higher than radius of contact area hence the influence of the model size on computational results seems to be excluded. Thanks to that even under maximum load the elastic strain field did not reach right and bottom plane of model. The boundary conditions were specified so that the model matches the real indentation process. The nodes in the bottom surface of the specimen have been fixed and in the symmetry axis of model cannot be deformed in the radial direction. Normal load was gradually applied within 50 steps during loading and unloading down to zero.
Fig. 3 – Part of the finite element model of indenter pressed into coated substrate, with the refined meshes in the region around contact zone.
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Three coatings of t ¼ 1 mm total thickness were modeled: monolayer, multilayer with two elastic materials and multilayer with softer layers prone to yield. Ceramic TiN monolayer and TiN layers in multilayer have elastic modulus ETiN ¼ 420 GPa, while for softer Ti layers ETi ¼ 160 GPa. Yield strength of Ti layers YTi ¼HTi/3E2 GPa was assumed. Substrate properties ES ¼ 210 GPa and YS ¼0.8 GPa meet properties of X20Cr13 steel. All materials properties are taken from indentation results and catalogs.
5.
Indentation and FEM modeling results
Fig. 4a presents indentation curves for both tested coatings. These curves (Fig. 4b) were transformed into stress–strain curves according to the procedure presented in Fig. 1. A higher stress (mean pressure) level was found for TiN single coating. When relative indentation depth hR ¼hmax/t reaches 0.14 at pm ¼ 3.5 GPa, a drop of contact stresses is observed, which corresponds to first ring crack formation. For multilayer the stable level of pm ¼2.5 GPa starting at hR ¼0.1 reveals deformations controlled by continuous substrate yield with minor coating fracture. The FEM modeling results allowed to find the stress field at certain deformation and contact pressure pm. The maximum tensile stresses were found in two areas: on the surface just outside contact area and in the indenter symmetry axis at coating-substrate interface. The ratio of these tensile stresses to mean contact pressure s/pm is presented in Fig. 5 for both locations. In a whole range of hR
Fig. 4 – Indentation results of TiN and 8 Ti/TiN coatings: (a) indentation curves and (b) stress–strain curves.
Fig. 5 – Tensile stress concentration coefficient at: (a) coating surface and (b) coating-substrate interface.
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stresses at the surface are higher in multilayers than in single layer (Fig. 5a). It could be explained by easier bending of external TiN layer. Using s/pm ratio the real tensile stress concentrations at both TiN and 8 Ti/TiN coatings surfaces were calculated (Fig. 6). The maximum stress for TiN monolayer system is 10–20% higher than for multilayer. First crack appeared in TiN monolayer when tensile stress reached 7 GPa. But in this calculations the residual stress was not taken into account. The total stress sT in real specimens is a sum of residual stress sR and stress induced by external load sIND: sT ¼ sIND þ sR
systems cracks nucleated in surface propagate down to interface throughout the entire thickness. For coatings with columnar microstructure these cracks develop at column borders (Fig. 7a). These mechanisms of deformation is called
ð7Þ
For TiN monolayer residual stress measured by XRD technique is sRE4 GPa. When this stress was subtracted the coating strength 3 GPa was assumed (Fig. 6 open arrow). If the strength of TiN layers in multilayer is the same and measured residual stress is sRE2 GPa, then the first crack in external ceramic layer should be formed at 5 GPa tensile stress found from FEM modeling (Fig. 6 filled circle). This stress level is at similar hR to TiN monolayer system when first fracture appeared. At the interface stresses are higher for monolayer than for multilayer (Fig. 5b), what is caused by additional stress arising from higher elastic modulus mismatch of coating and substrate. In multilayer, metal layers play an important role on mechanical response, reducing the residual stress and increasing the fracture resistance. Microscopic studies of deformation and fracture mechanisms of such coatings are presented in previous papers [2,20]. For thin, monolayer
Fig. 6 – Tensile stress evolution on coating surfaces.
Fig. 8 – FEM modeling results—indentation of 4 Ti/TiN multilayer: (a) plastic deformations of Ti layers and steel substrate and (b) tensile stress field in TiN layers.
Fig. 7 – TEM cross-section images—deformation mechanisms of: (a) TiN and (b) 8 Ti/TiN multilayer coatings.
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intercolumnar sliding. TEM analyses showed that the deformation mechanism of Ti/TiN multilayers was followed by the sequence of fracture of ceramic layers and yield of metallic ones (Fig. 7b). This deformation mechanism is confirmed by the results of FEM modeling. The maximum plastic deformations of Ti layers (Fig. 8a) and the maximum tensile stress in TiN layers (Fig. 8b) are slightly shifted in the direction of symmetry axis what corresponds to TEM image. The next problem considered in multilayers was the plastic yield of soft layers. Do they lead to stress reduction or leading to higher deformation of the coating induce higher stress in ceramic layers? Fig. 9 presents the comparison of maximum stress concentration in a subsequent ceramic layers in 4 Ti/TiN
Fig. 9 – Tensile stress concentration at subsequent TiN layers in 4 Ti/TiN multilayers.
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multilayers with elastic (hard) and plastic (plast) Ti layers under two deformations h/t¼ 0.25 and 2. The stress concentration is getting smaller on successive TiN layers. For higher deformation s/pm ratio is 6.8 and 3.5 on first and second TiN layer respectively. Assuming that the cracks are created in the ceramic layers when the tensile stress exceeds their strength, the applied load for crack initiation has to be twice as large in the second TiN layer than in the external one. For the third and fourth layer, the maximum tensile stresses are in the symmetry axis of the contact, while stresses on the edge of contact area are compressive. Therefore, only two external ceramic layers should break under such a deformation. Comparing models where Ti layers are totally elastic and prone to yield, the lack of effect of this plasticity on the stress concentration in TiN ceramic layers under lower deformation h/t¼ 0.25 was found. But under higher deformation, the higher plastic deformations within Ti layers start to play an important role reducing by 20% tensile stress in successive TiN layers. This reduction is due to ‘slipping’ of ceramic layers on metallic ones, what results on lower coating’s bending at the contact edge. Alternately stacked hard and soft layers in the multilayer coatings improve the fracture resistance compared to single ceramic coatings. This advantage of multilayers is confirmed by SEM images of TiN and 8 Ti/TiN coatings’ surfaces with indents induced by 20 mm tip radius indenter (Fig. 10). First circular crack for TiN monolayer system appears at 130 mN load, what corresponds to pop-in on indentation curve (Fig. 4a). Fig. 10a shows the surface of this coating after indentation performed at 200 mN load. However, the same load does not lead to fracture of
Fig. 10 – SEM images of coating surfaces after spherical indentations: (a) TiN at 200 mN, (b) TiN at 1 N, (c) 8 Ti/TiN at 200 mN, and (d) 8 Ti/TiN at 1 N.
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8 Ti/TiN multilayer (Fig. 10c) and first crack is formed at about 350 mN load. But in contrast to monolayer, cracks formation in multilayers is not seen on indentation curves. Nevertheless SEM image of 8 Ti/TiN coating after indentation at 1 N load shows small cracks but only inside the indent (Fig. 10d). The TiN monolayer system after this test is highly cracked and last cracks are even beyond the contact area (Fig. 10b). The higher fracture resistance of multilayers than monolayers has also a strong influence on their higher wear resistance. Wear rate of Ti/TiN and Cr/CrN multilayers can be significantly lower than for TiN and CrN monolayer systems, what was presented in previous papers [2,5].
6.
Conclusions
1. Developed by author complex procedure based on transformation of indentation curves into stress–strain curves with subsequent FEM modeling is an effective tool of contact stress analysis in coating-substrate systems. 2. Introduction of soft metallic layers in multilayer results higher tensile stress concentration on coating surface and lower at coating-substrate interface. 3. Metallic layers in Ti/TiN multilayer improve their fracture resistance. Tensile stress at subsequent TiN layers is reduced and external load must significantly rise to induce crack formation at the surface of the following ceramic layer. 4. Comparing two FEM models of multilayers favorable impact of local plastic deformation of metallic layers on stress reduction at heavy duty is clearly seen.
Acknowledgment The author would like to acknowledge Dr. habil J.M. Lackner for coatings deposition at Joanneum Research Forschungsgesellschaft mbH, Leoben, Austria, Dr. Ł. Major for TEM, and M.Sc P. Indyka for SEM analysis.
references
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