Zr multilayer coating

    Role of interface curvature on stress distribution under indentation for ZrN/Zr multilayer coating Nisha Verma, Vikram Jayaram PII: DOI: Reference:

S0040-6090(14)00644-0 doi: 10.1016/j.tsf.2014.06.001 TSF 33510

To appear in:

Thin Solid Films

Received date: Revised date: Accepted date:

3 January 2014 30 May 2014 1 June 2014

Please cite this article as: Nisha Verma, Vikram Jayaram, Role of interface curvature on stress distribution under indentation for ZrN/Zr multilayer coating, Thin Solid Films (2014), doi: 10.1016/j.tsf.2014.06.001

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ACCEPTED MANUSCRIPT Role of interface curvature on stress distribution under

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indentation for ZrN/Zr multilayer coating. Nisha Verma11,Vikram Jayaram

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Department of Materials Engineering, Indian Institute of Science, Bangalore-560012, India.

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Abstract

Contact damage in curved interface nano-layered metal/nitride (150 (ZrN)/10 (Zr) nm)

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multilayer is investigated in order to understand the role of interface morphology on

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contact damage under indentation. A finite element method (FEM) model was formulated

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with different wavelengths of 1000 nm, 500 nm, 250 nm and common height of 50 nm, which gives insight on the effect of different curvature on stress field generated under indentation. Elastic-plastic properties were assigned to the metal layer and substrate while the nitride layer was assigned perfectly elastic properties. Curved interface multilayers show delamination along the metal/nitride interface and vertical cracks emanating from the ends of the delamination. FEM revealed the presence of tensile stress normal to the interface even under the contact, along with tensile radial stresses, both present at the

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Corresponding author: Nisha Verma, [email protected] University of California Santa Barbara Building 189 room #137, Department of Materials engineering, University of California Santa Barbara

ACCEPTED MANUSCRIPT valley part of the curve, which lead to vertical cracks associated with interfacial

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delamination. Stress enhancement was seen to be relatively insensitive to curvature.

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1. Introduction

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Metal/nitride multilayers have shown promising results in terms of increasing crack

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resistance, corrosion resistance and adhesion [1, 2, 3]. Considerable influence on multilayer performance must arise from the microstructures of the phases and the

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interface morphology; hence a systematic study of all these parameter is technologically

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important. Such a study on ZrN/Zr reported before [1] has shown how volume fraction

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and thickness of metal influences the deformation mode under indentation in metal/nitride multilayers. Finite element method (FEM) was used to generate stress fields responsible for the various cracking modes, such as the radial stress responsible for edge and radial cracks and the shear stress responsible for columnar sliding. With increasing metal thickness, an increase in radial tensile stress was seen in each nitride layer leading to edge cracking at each interface, while the shear stress responsible for column sliding was seen to reduce, hence suppressing columnar sliding. A volume fraction of 13% Zr of 30 nm thickness was seen to lead to the least cracking. Further reduction of metal volume fraction/thickness was not explored in detail because preliminary studies indicated that interface planarity could not be maintained at such low metal layer thicknesses of 6 and 10 nm [4]. Here we report damage modes in 10 nm metal multilayer with curved interface morphology.

ACCEPTED MANUSCRIPT Stress/strain field under indentation is usually complicated for these heterogeneous nanolayered composites. FEM has shown to explain many details when indentation

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modeling is done with true multilayer constituents and structure. In case of Al/SiC

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multilayer, plastic deformation was noticed in Al layer even during unloading and hence unloading curve could not be correlated simply to the elastic recovery that is usually

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noticed in homogeneous materials [5]. A less complicated stress state generated under

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pure compression by pillar compressions is also studied using FEM for Al/SiC multilayer [6]. The hardening rate was reported to reduce by half for 100 0C compared to 23 0C;

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even though in both the cases plastic deformation of Al was the dominant deformation

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mechanism, interfacial sliding was allowed in former case.

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Most of the studies on multilayers have been limited to planar interfaces whereas it has been shown that interface asperities can play an important role, e.g., in thermal barrier coatings, the residual stress was shown to be tensile along the normal to the interface in a top coat, and increases with increase in curvature and height of asperity. Such a normal stress would be zero for a flat interface [7, 8]. A tensile residual stress at the interface may lead to decohesion of coating. Occasionally coatings are deposited on rough surfaces to get better adhesion when residual stress are compressive, making interfacial crack propagation under mixed mode energetically unfavorable. A critical curvature for decohesion has been reported for a particular thickness, residual stress and fracture resistance of interface [9]. Stess/ strain field under indentation for wavy interface in Al/SiC system is reported to be drastically different compared to flat interface multilayer

ACCEPTED MANUSCRIPT [10]. FEM showed 10% variation in hardness and modulus value for wavy interface in contrast with flat interface, whereas unloading plastic strain in Al layer was seen to

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increase compared to flat interface.

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Rough substrates or deposition conditions may influence the interface morphology.

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Waviness of the interface has been explained by the model of Bales and Zangwill [11]

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who show that an angular variation in the incident flux (J), can lead to waviness for amorphous films deposited by sputtering. The waviness comes about from the limited

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surface mobility (occurring due to low deposition temperature and high base air pressure) and shadowing effect (due to initial surface roughness), which implies that a few areas

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would receive more flux compared to the others.

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While much has been reported on the influence of the coating substrate interface on residual stress in the coating, there are no reports on the influence of curvature on stresses under contact loading. In this paper we have tried to understand how the distribution and magnitude of stress is influenced by the periodicity of curved interfaces under contact load. We have chosen ZrN/Zr multilayers as this is a model metal-nitride system without any intermediate nitrides. FEM analysis was carried out to understand the role of curvature on stress distribution and was correlated with experimental findings.

2. Experimental Details

2.1. Film deposition and characterization

ACCEPTED MANUSCRIPT Coatings were deposited by magnetron sputtering (TEER Coating, UK) with 5 micron total thickness and various bilayer spacings out of which the present paper examines 150

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nm/10 nm ZrN/Zr multilayers. Similar observations were made on metal thicknesses

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extending to 6 nm. A depth sensing microhardness indenter (CSM-MHT, Switzerland) was used to carry out Vickers indentations with a load of 1N. Focussed ion beam imaging

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(FIB P200XP, FEI, USA) was used to view subsurface damage around indents and to

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prepare TEM lamella from indentation cross sections. The craters near the indents were milled initially at 2600 pA and subsequently, to create a smooth surface, polishing was

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done first with 1 nA and then 350 pA. To reduce ion damage which may degrade the

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image quality, imaging was done at lower currents of ~11 pA.

Transmission electron microscope (TEM) (Tecnai F-30, FEI Inc., USA) was used to view

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the deformed microstructure to get more clarity on deformation modes of curved interfaces under contact loading. The H bar technique [12] was used to prepare TEM lamellae of the area of interest by trimming the sample.

2.2. FEM

A curved interface multilayer model (Fig. 1) was used to calculate the stress within the multilayer under indentation loading which is explained in more detail elsewhere [1]. Being realistic with respect to the experimental parameters, the nitride layer thickness was kept at 150 nm along with metal layer thickness of 10 nm, keeping total thickness of coating 5 microns. The present analysis was carried out using ABAQUS version 6.5. Convergence in stress value was reached with considerable mesh refinement near the

ACCEPTED MANUSCRIPT contact, while further refinement was found to have no significant effect on the precision of stress values. Isoparametric quadrilateral elements were used for the model. The

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calculations were done with 2D axisymmetric model, which has shown good agreement with our experimental findings reported earlier [1]. The dimensions of the sample were

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kept sufficiently large (50 m* 50 m) to eliminate edge effects and top surface was restricted to follow the indenter surface. Contact between surfaces, including indenter and

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coating was defined using two- dimensional point-to-surface contact element, which is defined with a highly nonlinear force-displacement relation. Boundary conditions on

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bottom and left surface were defined to restrict them from rotation and movement along z and x direction respectively to mimic more realistic case due to the presence of substrate.

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Owing to the high stiffness of diamond, the indenter tip was assumed to be rigid with 5 microns radius, ZrN was assigned isotropic elastic properties whereas Zr and steel

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substrate (SS 304) were modeled with elastic-plastic constitutive relation, assuming kinematic work-hardening and a von Mises yield criterion [1]. Loading and unloading was done through a defined reference point inside the indenter for a maximum load of 1N, as performed during experiments. Good agreement between the experimental and model output was used to validate the model by making comparisons at low loads at which cracking was absent [1]. Properties assigned to get good correlation are given in table 1 [1, 13-16]. To understand the role of varying periodicity, three different configurations were considered, with wavelengths of 1000 nm (I), 500 nm (II) and 250 nm (III) with common amplitude of 50 nm.

3. Results and Discussion

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3.1. Microstructure: As received (150/10 nm)

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The presence of Zr layer is confirmed for the multilayer coatings from Fig. 2 for 150/10 layer thicknesses. Similar observations are made for 6 nm metal layers as well. The

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coating shows curved interfaces with periodicity ~250-300 nm and an amplitude of 50

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nm which is used in the FEM model.

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3.2. Contact Damage

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Cross-sectioning of indents can be used to evaluate the compatibility of the coating with the substrate, as the coating damage is mostly driven by the mismatch stress field

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generated due to the difference in mechanical properties of the nitride layer with respect to the soft metal layer.

The subsurface damage in the coating is dominated (Fig. 3) by interfacial delamination ending in edge cracks (vertical cracks emanating from the ends of and linking the delaminations).

The load displacement curves of these coatings show slope changes at regular intervals. To get the origin of this slope change, indentations were observed at different points of the slope change as indicated in (Fig. 4(a)-(c)): after the slope change starts (Fig. 4(a)) then after the new slope stabilizes (Fig. 4(b)) and finally, after the slope changes for a second time (Fig. 4(c)). Fig. 4(a) shows some delamination, Fig. 4(b) shows delamination associated with microcracking while similar events take place after two slope change

ACCEPTED MANUSCRIPT sequences (Fig. 4(c)). These events suggest that the interfacial shear stress (which drives delamination) dominates the bending stress (S11) in the case of thin metal multilayers as

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compared to thick metal multilayers which display microcracking in the nitride at each

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interface [1]. After the first slope change, the cross section reveals presence of edge cracking accompanying the interfacial delamination (Fig. 4(b)). Thus, interfacial

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delamination precedes microcracking and not the other way around. Such a sequence can

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be more clearly understood from the example of a fiber reinforced ceramic in which a crack from the matrix deflects at the fiber and propagate along the matrix/fiber interface,

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leading to a high probability of fiber cracking at the point of interfacial crack termination, due to the presence of stress concentration. The center of the indent is free from any

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delamination due to the compressive stress field under the contact. TEM micrographs (Fig. 5) confirm that cracking occurs at the metal/nitride interface and

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as the metal nitride interfaces are curved, the sliding along the interface would give rise to openings, which are clearly visible in Fig. 5(b) (superimposed with a schematic to illustrate the sliding).

3.4. Stress State for Curved Interfaces All the FEM results display normal stress, as we are interested in the stresses leading to cracking. A clear difference may be seen in the stress field generated under the indent for planar and curved interfaces (Fig. 6-13) in S22, which is responsible for delamination, and in the principal stress, which is responsible for edge cracking and roughly follows the S11 contours. The tensile stress normal to interface is higher for curved interface multilayer compared to flat interface. Starting with lowest value for flat interface ~ 0.36 GPa then

ACCEPTED MANUSCRIPT for I (1000 nm) ~ 1.46 GPa then for III (250 nm) ~1.77 GPa and shows a relatively higher value for II (500 nm) ~2.69 GPa (Fig. 6-7). S22 shows the same trend is stress level

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for unloaded state of multilayer. The stress in the x2 direction responsible for

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delamination is present at the valley part of the curved interface in nitride layer for I (1000 nm) and II (500 nm) and in metal layer in case of III (250 nm), which further

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grows upon unloading as is seen in the FEM contours and stress profile (Fig. 8-9). All the

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enlarged views are taken from the edge of the contact near the middle of the coating, where maximum tensile stress is seen in all cases. Weighted average stress taken along

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each segment of curved interface show a similar stress magnitude among all curved interface multilayer but relatively higher value compared to flat interface multilayer (fig.

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10). It might be noted that the origin of the appearance of a stress normal to the interface is similar to the way in which such behavior is seen in residually stressed systems with

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thermal or oxidation-induced strain incompatibilities [7].

The radial stress is not greatly different in curved interface multilayer compared to the flat interface as the magnitude goes from 4.9 GPa for flat interface to 7.2 GPa for II (500 nm), 6.86 GPa for III (250 nm) and 5.77 GPa for I (1000 nm) (Fig. 11), with similar trends seen in unloaded stress state. The radial stress shows tensile stress concentration at the valley part of the curved interface, which remains similar even after unloading with slightly lower magnitude (Fig. 12-13). Enlarged views and profiles for all coatings are taken from near the edge and middle of coating, even though the maximum stress is present near the coating substrate interface, in order to understand the origin of edge cracking associated with delamination. As radial stress is responsible for radial and edge

ACCEPTED MANUSCRIPT cracking in the nitride, there is the possibility of generating an edge crack following delamination while loading. The presence of high principal tensile stress while unloading

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encourage edge cracks at the already present delamination.

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along with the S22 stress near the edge of the curve with a high tensile magnitude can

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Comparing the curved interfaces with different periodicity, fig. 6-13 clearly indicate that

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the stress levels are controlled by periodicity, but surprisingly in a non-monotonic manner such that the stresses are higher in case II with 500 nm wavelength compared to

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either III (250 nm) and I (1000 nm). Even though the stress magnitude changes with periodicity but the weighted average stress value is similar for all curved interfaces. The

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reason for this apparent maximum in stress at an intermediate wavelength is not known. The stress concentration location remains the same for curved interface, which is near the

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valley for all I, II and III 4. Summary

Curved interfaces in multilayered ZrN-Zr gives rise to an enhancement of tensile stresses in the loading direction, normal to the interface and which are responsible for promoting delamination. Such interfacial crack nuclei can then propagate under shear, leading to large delaminations and interfacial sliding. FEM is able to capture all the experimentally found features of deformation including the location of microcrack initiation at the valleys of interface perturbations. The magnitude of stress enhancement shows a smaller dependence on the wavelength of the interface.

ACCEPTED MANUSCRIPT Reference [1] Nisha Verma, V. Jayaram, Detailed investigation of contact deformation in ZrN/Zr

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multiplayer—understanding the role of volume fraction, bilayer spacing, and morphology

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of interfaces, J. Mater. Res. 28 (2013) 3146-3156.

[2] M.T. Vieira, A.S. Ramos, The influence of ductile interlayers on the mechanical

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performance of tungsten nitride coatings, J. Mater. Process. Technol. 92 (1999) 156-161.

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[3] G-H Song, X-P Yang, G-L Xiong, Z Lou, L-J Chen, The corrosive behavior of Cr/CrN multilayer coatings with different modulation periods, Vaccum. 89 (2013) 136–

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141.

[4] Nisha Verma, PhD thesis, Mechanism and modeling of contact damage in ZrN-Zr and

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TiAlN-TiN multilayer hard coatings, Indian Institute of Science, 2013. [5] G. Tang , Y.L. Shen , D.R.P. Singh , N. Chawla, Indentation behavior of metal–

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ceramic multilayers at the nanoscale: Numerical analysis and experimental verification, Acta. Materialia. 58 (2010) 2033–2044. [6] S. Lotfian, M. Rodríguez, K.E. Yazzie, N. Chawla, J. Llorca, J.M. Molina-Aldareguıa, High temperature micropillar compression of Al/SiC nanolaminates, Acta. Materialia. 61 (2013) 4439–4451. [7] D.S. Balint, J.W. Hutchinson, An analytical model of rumplining thermal barrier coatings, J. Mech. Phy. Solids. 53 (2005) 949. [8] C-H Hsueh, Edwin R. Fuller Jr, Residual stresses in thermal barrier coatings: effects of interface asperity curvature: height and oxide thickness, Mater. Sci. Eng A. 283 (2000) 46–55. [9] D. R. Clarke and W. Pompe, Critical radius for interface separation of a

ACCEPTED MANUSCRIPT compressively stressed film from a rough surface, Acta. Materialia. 47(6) (1999) 17491756.

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[10] R.D. Jamison, Y. L. Shen, Indentation Behavior of Multilayered Thin Films: Effects

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of Layer Undulation, Thin Solid Films (2014), doi:10.1016/j.tsf.2014.04.023. [11] G. S. Bales and A. Zangwill, Macroscopic model for columnar growth of amorphous

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films by sputter deposition, J. Vacuum. Sci. Tech. A. 9 (1991) 145.

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[12] L. Giannuzzi, F. Stevie, A review of focused ion beam milling techniques for TEM specimen preparation, Micron. 30 (1999) 197.

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[13] M. T. Tilbrook, D. J. Paton, Z. Xie, and M. Hoffman, Microstructural effects on

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Materialia. 55 (2007) 2489.

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indentation failure mechanisms in TiN coatings: Finite element simulations, Acta

[14] B.T. Wang, P. Zhang, H.Y. Liu, W. D Li, and P. Zhang, First-principals calculations

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of phase transition, elastic modulus, and superconductivity under pressure for zirconium, J. Appl. Phys. 109 (2011) 063514. [15] M. A. Auger, J. J. Araiza, C. Falcony, O. Sanchez, J. M. Albella, Hardness and tribology measurements on ZrN coatings deposited by reactive sputtering technique, Vacuum. 81 (2007) 1462.

[16] A. Singh, P. Kuppusami, R. Thirumurugesan, R. Ramaseshan, M. Kamruddin, S. Dash, V. Ganesan and E. Mohandas, Study of microstructure and nanomechanical properties of Zr films prepared by pulsed magnetron sputtering, Appl. Surf. Sci. 257 (2011) 9909.

Figure Captions

ACCEPTED MANUSCRIPT Figure 1: Schematic of loading for calculations of stresses for multilayers with curved interfaces. The loading direction is x2 and the outline of the indenter is shown.

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Figure 2: Bright field image of multilayer showing presence of both phases with the

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metal bright and the nitride dark. Waviness of the interface is clearly seen in the images.

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Figure 3: Cross section view of indent for 155/10 nm showing microcracking associated

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with interfacial sliding.

Figure 4: FIB cross section of indents for 150/10 nm with increasing loads from top (a) to

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bottom (c) with the corresponding load displacement curves.

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Figure 5: (a) Cross section view of indent showing interfacial delamination along with

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edge cracking. (b) Shows a magnified view in the vicinity of interfacial sliding where the

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openings are a signature of sliding of around of 200 nm. Schematic superimposed on image to show interfacial sliding under indent. (c) Shows that delamination occurs at the metal/nitride interface.

Figure 6: Tensile stress contour for S22 while loading for flat interface (a), I (b), II (c) and III (d). See the presence of significant tensile stress normal to interface even under contact in the S22 contours. Figure 7: Tensile stress profile for loading and unloading along the interface showing maximum S22 stress. Each curved segment show stress peak at the valley part of curve. Unloading increase the tensile stress magnitude and changes the stress to tensile which was compressive under contact.

ACCEPTED MANUSCRIPT Figure 8: Enlarged view of stress contour for S22 while loading for Flat (a), I (b), II (c) and III (d). See the stress enhancement near the edge of curve.

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Figure 9: Stress profile for all multilayers along the interface with maximum S22 stress

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(depth ~ 2.5 m). See the enhancement of tensile stress normal to interface for unloaded

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state.

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Figure 10: Averaged stress over each segment of curved interface for all multilayers along with average stress for flat interface. Multilayers with curved interfaces show

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higher magnitude of stress compared to flat interface.

Figure 11: Stress contour for SP,Max while loading for flat interface (a), I (b), II (c) and III

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(d). See the redistribution of stress due to curvature in multilayer.

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Figure 12: Enlarged view of stress contour for SP,Max while loading for flat (a), I (b), II (c) and III (d). See the stress enhancement near the edge of curve. Figure 13: Tensile stress profile for SP,Max for loaded and unloaded state along the interface showing maximum S22 stress. Each curved segment show stress peak at the valley part of curve. Unloading reduces the tensile stress slightly.

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(GPa)

Stainless steel

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0.675

ZrN

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0.33

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(GPa)

Poison ration

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Elastic modulus Yield stress

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0.25 0.33

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Table 1: Properties assigned to various materials for FEM model.

ACCEPTED MANUSCRIPT Highlights > We report the damage modes of metal/nitride multilayer coating with wavy interfaces.

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> The deformation is dominated by vertical cracking associated with interfacial delamination.

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> FEM analysis reveals that interface curvature leads to tensile stresses normal to interface.