J. Cent. South Univ. (2012) 19: 1175-1181

DOI: 10.1007/s11771-012-1125-z

Finite element and experimental analysis of Vickers indentation testing on Al₂O₃ with diamond-like carbon coating

ZHAI Jian-guang¹, WANG Yi-qi¹, KIM Tae-gyu², SONG Jung-il¹

1. Department of Mechanical Engineering, Changwon National University, Changwon 641-773, Korea;

2. Department of Nanosystem and Nanoprocess Engineering, Pusan National University, Pusan 609-735, Korea

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: Numerical simulation and experimental study of the Vickers indentation testing of the Al₂O₃ ceramic coated by diamond-like carbon (DLC) layer were conducted. The numerical analysis was implemented by a two-dimensional finite element (FE) axis symmetry model. FE analysis results gave insight into the fracture mechanism of DLC films coated on brittle ceramic (Al₂O₃) substrates. The maximum principal stress field was used to locate the most expected area for crack formation and propagation during the Vickers indentation testing. The results show that the median crack initiates in the interface under indenter, before ring crack occurs as the indenter presses down. Finally, the plastic deformation appears when the indenter penetrates into the substrate. The thicker DLC coating increases the Vickers hardness and fracture toughness.

Key words: Vickers indentation testing; finite element; diamond-like carbon; Al₂O₃; fracture toughness

1 Introduction

Diamond-like carbon (DLC) layers are usually used as protective coatings on metal substrates, such as steel or hard metal. In recent years, DLC films have attracted more and more interest due to their excellent physical and chemical properties, such as very high elastic modulus, high electric resistivity, high dielectric constant, and chemical and thermal stability. When applied in pure form, they are as hard as natural diamond or even harder. In pure form, these diamond coatings offer extraordinary protection against abrasive wear and attack from atmospheric moisture and chemical vapors. In certain applications, there is a need for thin coatings to improve friction and wear performance. However, very little is understood on their fracture toughness. Fracture toughness is the ability of a material to resist the growth of a preexisting crack. Toughness encompasses the energy required both to create the crack and to enable the crack to propagate until fracture, whereas fracture toughness takes only account of the energy required to facilitate the crack propagation to fracture. These are two different concepts and should not be confused and interchangeably used. For bulk materials and some thick films, fracture toughness is easily measured according to ASTM standards [1]. Numerous literatures have been reported on the studying of fracture mechanism [2-5]. Apparently it seems that a crack propagates due to the applied load only. Therefore, when only the applied load is taken into account to evaluate stress intensity or fracture mechanism, its critical value gives the apparent fracture toughness. Important factor that controls interactions between coating and substrate and have pronounced effect on coating adhesion and durability of coated component is the level of residual stresses that are frequently present in the coating [6-7]. Physical vapor deposited (PVD) and chemical vapor deposited (CVD) coatings possess high hardness and may be in a state of tensile or compressive stress, depending on the choice of material and process used. In most cases, a compressive stress acts in the coating. Such combination of hard surfaces and compressive stresses can be expected to have a profound influence on the fatigue properties of surface coated material system [8-9].

Various coated system configurations containing cracks were reported to differ in some assumptions concerning substrate and coating properties, residual stress state, loading mode and crack geometry.

SMITH et al [10] stated that the typical failure mode of the coating–substrate system is often a two stage process. At the first stage, when a coating–substrate system is under sufficient tensile stress, through- thickness cracks usually develop in the brittle coating. At the second stage, when the crack tip reaches the interface, the crack may stop at the interface or propagate along the interface or into the substrate. Whether the crack stops  or propagates depends on many factors, such as the load conditions, mechanical properties of the coating and the substrate and interfacial adhesion properties between the coating and the substrate [11].

The behavior of the crack perpendicular to the interface was studied by ROMEO and BALLARINI [12] and most relevant conclusions are:

1) Local stress intensity decreases and reaches zero at the interface when crack approaches the interface from an elastically weaker material to a stiffer one.

2) Local stress intensity increases and reaches infinity at the interface when crack approaches the interface from a stiffer material to a weaker one.

CHAKRAVARTHY et al [13] calculated energy release rate for the crack perpendicular to the interface between the coating and the substrate with its tip in the homogeneous substrate.

YANG et al [14] studied the fracture behavior of material system composed of laser pre-quenched steel substrate and elastic coating. The case of a crack perpendicular to the interface between the coating and the hardened layer with the crack tip in the substrate was analyzed and yield properties of the substrate were taken into account.

In the case when material undergoes both elastic and plastic deformation, J-integral can be used instead of stress intensity factor to characterize the fracture behavior of the material containing crack of a certain length. The value of J integral is related to strain energy in the vicinity of the crack and can be used to predict stress and strain conditions for crack initiation under monotonic loading.

It has been shown previously that the effect of microcracks developed in the elastic coating on localization of plastic deformation in the substrate material is sensitive to certain properties of the coating and substrate materials, i.e. the ratio of elastic moduli of both coating and substrate materials, coating thickness and distribution of yield strength in the diffusion strengthened layer [15].

Large number of parameters that characterize the surface layer and have significant effect on its properties and performance make it difficult for the process of optimization of the microstructure and properties of surface layer. Beside the experimental trial-and-error methods, some numerical tools like finite element method, can be effectively used to predict the particular properties of hard coatings, e.g. residual stresses resulted from the deposition process, and to analyze the effect of individual parameter of the surface layer on coating performance and durability of coated components.

And many researchers have taken experimental or finite element analysis (FEA) on the failure mechanism of such coating system [16-17]. The elastic-plastic and elastic-plastic-cracking constitutive models are usually used to investigate the indentation induced cracking behavior in brittle materials.

In this work, DLC films were coated on the surfaces of Al₂O₃ ceramics with different thicknesses. Fracture mechanism of these coating materials was investigated. By comparing to experimental results, the finite element method (FEM) was used to give insight into the role of the loads and materials.

2 Methodology

2.1 Vickers indentation testing

The microstructures of Al₂O₃ and thickness of DLC coating were observed with scanning electron microscope (SEM) of model JSM-5610 (JEOL, JAPAN). Prior to the test, the samples were coated with a thin layer of platinum to avoid sample charging under the electron beam. The observation was performed in high vacuum mode with secondary electron detector and accelerating voltage between 5 kV and 10 kV.

The Vickers indentation method is capable of testing the softest and the hardest materials under varying loads. Therefore, in this work, Vickers indentation method was employed for investigating fracture toughness.

Al₂O₃ ceramic substrates were machined into a width of 10 mm, a thickness of 10 mm, and a length of 50 mm. Load of 29.4 N was applied on the Al₂O₃ ceramic. Two kinds of loads (19.6 N and 49 N) were applied on the Al₂O₃ with DLC coating. The coating had thickness of 6.4, 40 and 50 μm deposited on the surfaces of machined Al₂O₃ ceramics. The average crack lengths were used for calculating the fracture toughness. During the loading step, the indenter is moved downwards in the vertical direction by applying force and during unloading the indenter is back to the same position.

The Vickers indenter is applied onto the surface and cracks can be generated at the extremities of the indent. Since it is impossible to compare Vickers indentation fracture (VIF) toughness to K_IC, it is simply suggested to calculate a mean value for K_C by using the average equation. For the Palmqvist crack pattern, the crack equation according to expression is [18-19]

               (1)

                               (2)

where E is the elastic modulus; H_v is the Vickers hardness; a is the half diagonal distance of indentation; l is the crack median length; F is the load; Φ is a constant which usually equals 3. Figure 1 shows the Palmqvist crack, in which the cracks are only generated at the extremities of the indent. The Vickers hardness test method consists of indenting the test material with a diamond indenter, in the form of a pyramid with a square base and an angle of 136° (shown in Fig. 2) between opposite faces subjected to a test force. The two diagonals of the indentation left on the surface of the material after removal of the load are measured using a microscope and their averages are calculated. The area of the sloping surfaces of the indentation is calculated. The Vickers hardness is the quotient obtained by dividing the load by the area of indentation.

Fig. 1 Schematic Vickers indentation crack morphology

Fig. 2 Schematic drawing of Vickers indentation

Figure 2 shows the details of the Vickers indenter. Moreover, the micro-meter thick DLC coatings were deposited on one face (10 mm×55 mm) of the ceramic materials by plasma enhanced chemical vapor deposition (PECVD) method at 200 °C. The DLC films were deposited onto ceramic substrates using a standard capacitively coupled parallel plate electrode reaction chamber, powered by a 13.56 MHz radio frequency power source. The substrates were placed onto the lower electrode, which was maintained at 20 °C by a feedback-controlled cooling system. All samples were chemically pre-cleaned using firstly an acid dip followed by a selection of solvent and deionised water, in an ultra-sonic bath. They were then subjected to a 1 min in-situ Ar sputter clean prior to admission of the process gases and deposition. Figure 3 shows the coating devices used in this work.

Fig. 3 Experimental setup of PECVD process

2.2 Finite element implementation

The geometric and loading symmetry simplifies the simulation and saves computation time.

The coating was assumed to be isotropic, linear elastic material with elastic modulus of 150 GPa, as reported in Ref. [20]. The coating thickness was set to be 6.4, 40 and 50 μm according to the measurement of samples.

The ceramic substrate was modeled as an isotropic, rate-independent solid with bilinear elastic-plastic constitutive relation, assuming kinematic strain- hardening and von Mises yield criterion. It was assumed that compared with the significantly higher elastic modulus of the potential coating materials and wide range of these values, the variation in elastic modulus of Al₂O₃ ceramic that depends on its chemical composition and microstructure on the deformation process is negligible. So, constant values of elastic modulus E=300 GPa and Poisson ratio υ=0.21 were assigned to the substrate in all analyses. Tangent (hardening) modulus E_h=0.414 GPa was set. For the substrate, yield stress of 0.255 GPa was assumed in all analyses in which diffusion layer was not accounted for (Table 1).

Table 1 Material properties used in FE simulations

Finite element analysis was performed using the commercial software ANSYS 12.0. The Vickers indenter shows a four-fold symmetry; therefore only half of the indented area and geometric was modeled. SOILD 82 type elements were used in this work. This type of element uses 8-node brick elements and is specifically formulated to model large deformation with plastic behavior. For the surface of contact, CONTA175 surface to surface contact elements were used for the deformable material while a TARGE169 element provided the diamond face, which was assumed to be perfectly rigid. The contact friction was assumed to be zero, which has been shown to be a reasonable assumption for the high-load test regime. The indentation was applied to the model by driving the target element (representing the face of the diamond) vertically into the mesh. The indentation procedure was simulated using two alternating steps, namely loading and unloading.

Because of symmetry, only the half of the segment was modeled, as shown in Fig. 4. On the symmetry axis, all nodal displacements were set to be zero. These reflect the fact that, in reality, the region being simulated would be constrained by large sections of matrix. The bottom was fixed in all directions as shown in Fig. 4(a). Plane strain conditions were assumed in all analyses. Significant mesh refinement around the indenter has been done in the FE modeling in order to get more precision results, as shown in Fig. 4(b). The ratio of largest to smallest element area was 0.0639/0.00833≈ 7.67. Such mesh conditions are helpful enough to manifest the real stress distribution and deformation by the finite element method.

Fig. 4 Model of Vickers indentation: (a) Geometry and boundary conditions; (b) FE mesh of DLC coated Al₂O₃

3 Results and discussion

3.1 Indentation test of substrate material

Figure 5 shows the indentation test result of Al₂O₃ ceramic under 29.4 N. The Al₂O₃ ceramic exhibited elastic-plastic-cracking property. During the loading process, the ceramic firstly behaved with a linear-elastic response. Upon reaching the maximum tensile fracture stress, cracks initiated and the plastic deformation zone was clear even after the load was removed. The tensile cracking and compressive yielding behavior is typical of brittle materials during indentation experiments. The plasticity associated with compressive stresses induced during the loading phase of the Vickers indentation cycle is mainly responsible for subsequent lateral cracking during the unloading phase of the indentation cycle.

Fig. 5 Topography of Vickers diamond indentation on Al₂O₃ surface produced by 29.4 N

The finite element mode was made according to such property. The stress analysis result is shown in   Fig. 6, which indicates the distribution of the maximum principal stress predicted by the model by the end of the test. The predicted maximum principal stress attains the maximum value near the indenter, which usually induces the crack, as shown in Fig. 5. It was noted that there was another stress concentration area under the position of indenter. This area would induce median crack if only the stress value exceeded the tensile strength of ceramic material.

Figure 7 shows the distribution of the equivalent stress (von Mises stress) which is a representation of “severity” of the stress condition in solids. It is clear that when the equivalent stress attains the yield stress of Al₂O₃ ceramic, the equivalent stress concentration area looks like a “flask”. The stress distribution area deep under the indenter is larger than the area in the lateral direction. This means that the plastic deformation in longitude would easily be induced rather than in lateral direction. The plastic deformation in indentation test is shown in Fig. 5. We can see the FEM analysis results agree well with the indentation test.

Fig. 6 Distribution of maximum principal stress (MPa) in indentation testing by 29.4 N load

Fig. 7 Distribution of equivalent stress (MPa) in indentation testing by 294 N load

The distribution of the maximum principal stress by 49 N load is shown in Fig. 8. The maximum tensile stress is located at the interface and the surface with a distance about 100 μm from the centre. The DLC layer is considered to have small elastic-plastic behavior in this work. However, the maximum principal stress was still used to estimate the fracture of the material because of the brittle property. From the FEM analysis result, we can see that the maximum value of the first principal stress attained 4.346 GPa under the load of 49 N, which is much lower than the value of 20 GPa reported in Ref. [10].

Fig. 8 Distribution of maximum principal stress (MPa) in indentation testing by 49 N load

Compared to the indentation test result as shown in Fig. 9, we can see that the DLC layer under the indenter splits away from the substrate. And the shape of fracture area does not perfectly match with the indenter shape, which means that the fracture type is ring crack. This phenomenon agrees well with the FEM analysis result. The first principal stress must exceed tensile strength of DLC in that area, and ring cracks are induced. The reason that stress value is too low when crack arises is because of the roughness of substrate. The formation of radial cracks precedes ring cracks in DLC coatings on the rougher substrate, and the ring crack happens at higher loads for the rougher samples, due to the early formation of the radial cracks at the coating/substrate interface, coupled with the plastic deformation of asperities on the surface of the coating [23]. The radial cracks could not be observed in Fig. 9; however, it was predicted by the maximum principal stress in the FEM analysis.

Fig. 9 Topography of Vickers indentation on Al₂O₃/DLC surface produced by 49 N

3.2 Indentation test of Al₂O₃ coated by DLC

Usually, for an elastic-plastic substrate, the composite of substrate coated by DLC is assumed to fail by plastic deformation of the substrate and/or coating fracture [11]. In this work, the substrate is a brittle ceramic, and the maximum principal stress is the main factor to induce fracture of the composite. However, there are still two fracture patterns for the DLC layer: the ring crack and the median crack.

Figure 10 shows the distribution of the maximum principal stress under 19.6 N load. We can see that the maximum stress value is located in the centre of the interface, which will induce median crack. The median crack is sure to initiate preceding to ring crack in loading process according to the FEM analysis result. Figure 11 shows the result of indentation test under 19.6 N.

Fig. 10 Distribution of maximum principal stress (MPa) in indentation testing with 19.6 N load

Fig. 11 Topography of Vickers diamond indentation on Al₂O₃/DLC surface produced by 19.6 N

By comparing Figs. 8, 9, 10 and 11, we can deduce the fracture mechanism that during loading process, the median crack firstly initiates in the interface under indenter, then ring crack occurs as the indenter presses down, and finally, the plastic deformation happens when the indenter penetrates into the substrate. The substrate will impossibly exhibit plastic deformation before coating layer fails.

3.3 Indentation test of fracture toughness

From applying a 49 N load, it was found that the Vickers hardness increased from 18 to 22. The average fracture toughness value was found to increase from 8 to 12 MPa·m^1/2 by using Al₂O₃/DLC-6.4 μm, Al₂O₃/DLC- 40.4 μm, and Al₂O₃/DLC-53.2 μm coatings, as shown in Fig. 12.

Fig. 12 Average fracture toughness values on Al₂O₃ and DLC coated Al₂O₃ of various thicknesses under applied load 19.6 N

Even on the same substrate, the in situ toughness of coatings depends on the coating thickness. Based on constraint arguments, we expect that the coating toughness will increase as the coatings get thicker. This expectation agrees with experimental results for DLC coating on Al₂O₃ substrates. Paradoxically, even though the toughness increases as the coatings get thicker, thicker coatings may still crack sooner than thinner coatings. Such behavior can be explained by the theoretical result that the total energy released due to formation of a single crack also increases as the coating thickness increases [24]. Whenever the increase in energy release rate due to thickness is larger than the increase in toughness due to thickness, thicker coatings will crack sooner than thinner coatings.

4 Conclusions

Vickers indentation test and FEM analysis were carried out on the brittle Al₂O₃ ceramic with DLC coating. Finite element method gives better understanding of critical elastic-plastic fracture behavior of ceramic with coating materials during Vickers indentation test. The fracture mechanism was found to be a little different from the previous studying. Even though the Al₂O₃ is considered to have elastic-plastic property, the substrate will not exhibit plastic deformation before DLC coating fails. The median crack will initiate in the interface under indenter, before ring crack occurs as the indenter presses down, and finally, the plastic deformation appears when the indenter penetrates into the substrate. The thicker coating layer helped to increase fracture toughness. The effect is related to the phenomenon that the total energy released due to formation of a single crack also increases as the coating thickness increases. The future research will be focused on the coating layer effect on the brittle substrate.

References

[1] American Society for Testing and Materials. Standard test for plane strain fracture toughness of metallic materials, ASTME-399 [S]. Philadelphia, PA, 1987.

[2] JOHNSON K L. Contact mechanics [M]. Cambridge University, 1989.

[3] CHEN Y F, ERDOGAN F. The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate [J]. Journal of the Mechanics and Physics of Solids, 1996, 44(5): 771-787.

[4] AFSAR A M, ANISUZZAMAN M, SONG J I. Inverse problem of material distribution for desired fracture characteristics in a thick-walled functionally graded material cylinder with two diametrically-opposed edge cracks [J]. Engineering Fracture Mechanics, 2009 76(7): 845-855.

[5] AFSAR A M, RASEL S M, SONG J I. Analysis of apparent fracture toughness of a thick-walled cylinder with an FGM coating at the inner surface containing a radial edge crack [J]. The Korean Society for Composite Materials, 2010, 23(2): 1-9.

[6] CLAPA M, BATORY D. Improving adhesion and wear resistance of carbon coatings using Ti:C gradient layers [J]. Journal of Achievements in Materials and Manufacturing Engineering, 2007, 20(1/2): 415-418.

[7] MIKULA J, DOBRZANSKI L A. PVD and CVD coating systems on oxide tool ceramics [J]. Journal of Achievements in Materials and Manufacturing Engineering, 2007, 24(2): 75-78.

[8] HETRMANCZYK M, SWADZBA L, MENDALA B. Advanced materials and protective coatings in aero-engines application [J]. Journal of Achievements in Materials and Manufacturing Engineering, 2007, 24(1): 372-381.

[9] ZALOUNINA A, ANDREASEN J H. Theoretical analysis of fatigue crack growth in a coated substrate [J]. International Journal of Fracture, 2005, 133(1): 3-10.

[10] SMITH G A, JENNETT N, HOUSDEN J. Adhesion of thin coatings—The VAMAS (TWA 22-2) interlaboratory exercise [J]. Surface and Coatings Technology, 2005, 197(2/3): 336-344.

[11] XIE Chang-jin, TONG Wei. Cracking and decohesion of a thin Al₂O₃ film on a ductile Al-5%Mg substrate [J]. Acta Materialia, 2005, 53(2): 477-485.

[12] ROMEO A, BALLARINI R. A crack very close to a bimaterial interface [J]. Journal of Applied Mechanics, 1995, 62(3): 614-619.

[13] CHAKRAVARTHY S S, JORDAN E H, CHIU W K S. Thin film and substrate cracking under the influence of externally applied loads [J]. Engineering Fracture Mechanics, 2005, 72(8): 1286-1298.

[14] YANG Ban-quan, ZHANG Kun, CHEN Guang-nan, LUO Geng-xing, XIAO Jing-hua. Effect of a laser pre-quenched steel substrate surface on the crack driving force in a coating-steel substrate system [J]. Acta Materialia, 2007, 55(13): 4349-4358.

[15] ZIAJA W, SIENIAWSKI J. Tensile deformation behaviour of the titanium alloy with hard elastic coating [J]. Advanced Engineering Materials, 2006, 8(3): 205-208.

[16] ZHAO Xiao-li, XIE Zong-han. Nanoindentation of hard multilayer coatings: Finite element modeling [J]. Material Science and Engineering A, 2011, 528(3): 1111-1116.

[17] ZHANG W, SUBHASH G. Finite element analysis of interacting Vickers indentations on brittle materials [J]. Acta Materialia, 2001, 49(15): 2961-2974.

[18] NIIHARA K, MORENA R. Evaluation of KIC of brittle solid by the indentation method with low crack-to-indent ratios [J]. Journal of Material Science, 1982, 1(1): 13-16.

[19] Vicker’s hardness calculation [EB/OL]. [2012-02-06]. http://invsee.asu.edu/nmodules/carbonmod/vicker.html

[20] XIE Zong-han, SINGH R, BENDAVID A, MARTIN P J, MUNROE P R, HOFFMAN M. Contact damage evolution in a diamond-like carbon (DLC) coating on a stainless steel substrate [J]. Thin Solid Films, 2007, 515(6): 3196-3201.

[21] MEMSnet. Aluminum oxide (Al₂O₃) property [EB/OL]. [2012-02-06]. http://www.memsnet.org/material/aluminumoxi-deAl2O3bulk/

[22] KODALI P, WALTER K C. Investigation of mechanical and tribological properties of amorphous diamond-like carbon coatings [J]. Tribology International, 1997, 30(8): 591-598.

[23] SINGH R K, ZHOU Zhi-feng, KWOK L, LI Yan, MUNROE P, HOFFMAN M, XIE Zong-han. Design of functionally gradient carbon coatings against contact damage [J]. Thin Solids Films, 2010, 518(20): 5769-5776.

[24] MICHLER J, BLANK E. Analysis of coating fracture and substrate plasticity induces by spherical indenters: Diamond and diamond-like carbon layers on steel substrates [J]. Thin Solids Films, 2001, 381(1): 119-341.

(Edited by YANG Bing)

Received date: 2011-05-29; Accepted date: 2011-08-15

Corresponding author: SONG Jung-il, Professor; Tel: +82-55-213-3606; E-mail: jisong@changwon.ac.kr