This article was published in an Elsevier journal. The attached copy is furnished to the author for non-commercial research and education use, including for instruction at the author s institution, sharing with colleagues and providing to institution administration. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier s archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright

Available online at www.sciencedirect.com Surface & Coatings Technology 202 (2007) 1098 1102 www.elsevier.com/locate/surfcoat Finite element analysis of peak stresses developed during indentation of ceramic coated steels T. Pachler a, R.M. Souza b, A.P. Tschiptschin a, a Metallurgical and Materials Engineering Department, Polytechnic School, University of São Paulo, Av. Prof. Mello Moraes, 2463, 05508-900, São Paulo, Brazil b Surface Phenomena Laboratory, Mechanical Engineering Department, Polytechnic School of the University of São Paulo, Av. Prof. Mello Moraes, 2231, 05508-900, São Paulo, Brazil Available online 1 August 2007 Abstract During Rockwell C indentation tests performed on TiN coated high-strength tool steels radial cracks were formed at the film surface and micrographs taken indicated that the cracks were generated after the unloading step of the indentation process, as they were only observed in the outer region of indentation mark. Finite Element Analysis simulating the penetration of Rockwell conical and spherical indenters were carried out to study the intensity of radial and circumferential stress peaks on the indentation edge during the loading and unloading steps of the indentation, aiming to determine the conditions where circumferential stress peaks overcome the radial stress peaks in the outer region of indentation mark, turning more easy the formation of this type of cracks. The behavior of the substrate and the ceramic film were considered to be elastic-plastic, the yield stress of the substrate being changed in each of the simulations. The results indicated that during loading the peak of radial stress in the indentation borders is higher than the peak of circumferential stress. During unloading, the peak of circumferential stress increases while the peak of radial stress decreases, inverting the stress pattern. It was found that this lower intensity of the radial stress peak is due to a change of the surface curvature when the system is unloaded. The peak (radial and circumferential) stresses increase more slowly for substrates having higher yield stresses. Substrates with higher yield stresses show a greater decrease of the radial stress peak during the unloading step. The results were similar for both indenters. 2007 Elsevier B.V. All rights reserved. Keywords: Indentation; Caoting; Radial Crack; FEM 1. Introduction The improvement of tribological properties in mechanical components can be done through the deposition of thin ceramic coatings, which are characterized by high hardness, low wear, and low friction coefficient. These coatings can be made of a wide variety of components and each combination of different coating and substrate will produce a system with a particular mechanical and tribological behavior. The main problem related to a coated component is the difference of mechanical properties between the film and the substrate. Usually the substrate is more ductile than the film, consequently when the system is deformed the substrate does not provide enough mechanical support for the film, leading to cracks and even to coating detachment. Corresponding author. Tel.: +55 11 3091 5656; fax: +55 11 3091 5243. E-mail address: antschip@usp.br (A.P. Tschiptschin). Fig. 1. Radial and circular cracks at the indentation edge, of a H13 steel nitrided for 3 h and coated with TiN. The black arrow indicates a radial crack, while the white one indicates a circular crack [2]. 0257-8972/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2007.07.041

T. Pachler et al. / Surface & Coatings Technology 202 (2007) 1098 1102 1099 Thus, a common method used to verify the resistance to detachment of a coated system is the Rockwell C Adhesion Test, which consists in performing a standard Rockwell C hardness test (maximum load of 1471 N) and comparing the micrographs (magnification of 100:1) of the indentation mark with a defined adhesion strength quality figure. The simplicity of this method makes it useful for quality control during the manufacture [1]. Previous works [2,3] used the Rockwell C adhesion test to study the resistance to detachment of titanium nitride (TiN) coatings deposited on AISI D2, H13, M2 and 4140 steels. Table 1 Assumptions and parameters used in the model Coating thickness (μm) 5 Maximum loads (N) 1100 and 200 Coefficient of friction 0.3 TiN coating properties (GPa) E=440, σ y =6.0 Substrate 1 properties (GPa) E=210, σ y =0.3 Substrate 2 properties (GPa) E=210, σ y =0.8 Substrate 3 properties (GPa) E=210, σ y =2.0 Rockwell C indenter dimension Tip radius=.2 mm angle=120 Rockwell F indenter dimension (inch) Radius=1/16 E: Young's modulus; σ y : yield strength. Circular and radial cracks were found together at the indentation border, as shown in Fig. 1. In both cases it was not explained the conditions under each one of the cracks tends to occur. At Piana's [3] study, finite element analysis was conducted to simulate the experimental testing and verify when the radial cracks occur. However the stress patterns at the film surface indicated that only circular cracks could propagate. In literature, it is found that circular crack propagation is caused by a radial stress peak, which is directly associated with film bending at the indentation border. This peak intensity is influenced by indentation's morphology (formation of pile-up or sink-in), which also determinates the amount of circular cracks that propagate at the indentation edge [4,5,6]. Radial cracks are more often observed at the edges of Vickers and Berkovich indentations marks. In these cases, radial crack propagation is prone too occur when three conditions are met [7]: a) a small Young modulus difference between the substrate and the film; b) a good adhesion of the film to the substrate; c) high toughness of both; Analyzing the micrographs of the Franco Jr an Piana's works, allowed creating a hypothesis that circular cracks occur first, and radial cracks propagate during unloading. This statement is based on two facts observed in Fig. 1: a) radial cracks are non-continuous. This discontinuity is caused by circular cracks that were already present when the radial cracks propagated; b) radial cracks do not penetrate into the indentation mark. Thus, the aim of this work is to analyze the intensity of tangential and radial stresses developed at the film surface, more precisely at the indentation borders, during the loading and unloading steps of a Rockwell C adhesion test. The study was carried out performing a series of finite element analysis simulating three different coated substrates, and verifying a possible difference in stress pattern when using conical or spherical indenters. 2. Model description Fig. 2. Top view of an indentation mark, definition of directions (z is the vertical direction, r is the radial direction and θ is tangential direction) and the axyssimetric finite element model. The model was developed using the FEA software ABAQUS/CAE 6.5. The model geometry, shown in Fig. 2, is

1100 T. Pachler et al. / Surface & Coatings Technology 202 (2007) 1098 1102 Fig. 3. Radial and tangential stresses at the film surface as a function of normalized radius (a is the contact radius). Substrate 3. Applied Load of 1100 N. axyssimetric and constituted of 64904 elements of four and three nodes. In the region where larger deformation and higher stresses develop a mesh refinement was made until the difference in the values of the stress peaks became insignificant. The applied boundary conditions were: encastre of the substrate basis; and allowance of indenter movements only in the vertical direction (z). The film-substrate interface was considered perfectly bonded (no separation allowed), and a friction coefficient of 0.3 was chosen for the contact at the film-indenter interface. For spherical indenters it is known that values equal or higher than 0.3 avoid that the indenter slips over the coating [8]; for the conical indenter, friction coefficients between 0 and 0.3 do not affect the indentation morphology [3]. The assumptions and parameters used in the model are described in Table 1. Three substrates were modeled. The yield strengths of the substrates were selected intending to enclose a wide range of steels' mechanical properties [9]. Substrate 1 represents a typical low-carbon strip steel; Substrate 2 represents a typical Quenched and Tempered Low-Alloy High Strength Steel and Substrate 3 represents a typical High Carbon Music Wire steel. All materials, including the coating, were modeled assuming the same plastic behavior: plastic modulus of 1 GPa until 20% of plastic deformation. The Young's modulus of the coating (440 GPa) is a common value found for TiN [10]. Usually [4 6,8,11] the mechanical behavior of the film is considered to be purely elastic, leading to stresses at the film surface, near the indentation border up to 70 GPa [3], much grater than the stresses the film can resist. So, to limit these stresses it was considered that the film had yield strength of 6 GPa, calculated trough a conversion of hardness to ultimate tensile strength. 3. Results and discussion Fig. 3 shows that the radial and tangential stress peaks are located out of the indentation mark. To study the formation of radial and circular cracks the intensities of radial and tangential stress peaks, as a function of the applied load, were analyzed. Fig. 4. Radial and tangential stress peak intensity as a function of applied load, for conical indenter. A) radial stress during loading, B) radial stress during unloading, C) tangential stress during loading, D) tangential stress during unloading.

T. Pachler et al. / Surface & Coatings Technology 202 (2007) 1098 1102 1101 Fig. 5. Radial and tangential stress peak intensity as a function of applied load, for spherical indenter. A) both stresses during loading, B) both stresses during unloading. In Fig. 4A, it can be seen that the peak of radial stress reaches a maximum even for lower loads; this behavior indicates that during loading circular cracks are prone to propagate. During unloading (Fig. 4B) it can be seen that the intensity of the peak of radial stresses decreases while the load is reduced, and the higher the yield strength of the substrate, the lower is the final intensity of this peak. Comparison between Fig. 4A and C permits to say that tangential stress peak's intensity increases more slowly than the peak of radial stress. Fig. 4C and d shows that, like the radial stress, the tangential stress reaches a maximum during loading, but differently from the first case, the intensity of the peak is maintained during unloading. In agreement with the experimental works, the tangential stress peak overcomes the radial stress peak during unloading, tending to form radial cracks at this step of the adhesion test. A similar result was observed during linear scratch tests, where the formation of cracks perpendicular to the movement of the indenter (transverse cracks) propagated behind the indenter [13,14]. In Li's work [14] it was found, through FEA that the stress that causes transverse cracks increases monotonically with the applied load. Fig. 4C also shows that the substrate 1 has a discontinuity of the rate of increase of the tangential stress peak, but this result could not be explained by the simulation results. With the exception of this case, the results shown in Figs. 4 and 5 indicate that, for substrates with lower yield strengths, the increase of radial and tangential stress peaks intensity is steeper. Fig. 5 shows that for spherical indenters the way how the intensity of stress peaks develop is the same found for conical indenters. Fig. 6 shows vertical displacements of the film when the system is fully loaded and when the load is released. It is worth noting that substrate 3 showed the biggest change of curvature during unloading, coincident with the biggest reduction in radial stress peak during unloading. This is in agreement with literature [5], which associates the radial stress peak with film bending. Substrate 3 has also the higher elastic recovery, thus, allowing stating that the higher the elastic recovery the lower the residual radial stress peak will be. A remarkable fact shown in Figs. 4 and 5 is the presence of a maximum in stress intensities, beyond which it remains constant. This behavior can be attributed to the elastic-plastic behavior assumed in the model. Indeed, when the stress reaches this maximum value, the region where the peak is located starts to deform plastically, holding the peak intensity constant. Fig. 7 shows the equivalent plastic deformation in the neighborhood of the indenter; the film shows greater plastic deformation, in regions where the stress peaks appear. Plastic deformation decreases with increasing radial distance. Scratch tests carried out by Ma [12] showed shear deformation and densification of the film, before macrocrack formation. Karimi's work [7] reported microcracks propagation before macrocrak formation. These results indicate that stress relief can occur through different mechanisms in regions where radial and tangential stresses are not maximum, and macrocrack formation is not the sole mechanism of stress relieving. Although secondary stress relieving mechanisms may be operating, it was observed that cracks occurred in places where the film was more intensely plastically deformed. 4. Conclusions (1) Finite element modeling, assuming elastic-plastic behavior of the pair TiN coating/substrate gave more reliable results, than those obtained assuming a pure elastic behavior of the ceramic film. Fig. 6. Vertical displacements when the system is fully loaded and when the load is released, for substrates 1 and 3 (a is the contact radius when the load is maximum).

1102 T. Pachler et al. / Surface & Coatings Technology 202 (2007) 1098 1102 Fig. 7. Equivalent plastic deformation (PEEQ), for substrate 2, at maximum load. (2) Circular cracks are prone to propagate during loading; radial cracks tend to propagate during unloading. (3) In most cases, the stress peaks increase more slowly for substrates with higher yield strength. It was also found that substrates with higher elastic recovery will have a lower intensity of the residual radial stress peak. (4) Spherical indenters presented the same behavior as conical indenters. Acknowledgements Thiago Pachler would like to acknowledge the São Paulo State Research Foundation-FAPESP for financial support through process 05/02160-9. The authors recognize the São Paulo State Research Foundation-FAPESP for financial support through project number 2003/10157-2. [3] L.A. Piana, E.A. Perez R., R.M. Souza, A.O. Kunrath, T.R. Strohaecker, Thin Solid Films 491 (2005) 197. [4] R.M. Souza, G.G.W. Mustoe, J.J. Moore, Thin Solid Films 355-356 (1999) 303. [5] E.A. Perez R., R.M. Souza, Surf. Coat. Technol. 188-189 (2004) 572. [6] E.A. Perez R., R.M. Souza, J. Metastable Nanocryst. Mater. 20-21 (2004) 763. [7] A. Karimi, Y. Wang, T. Cselle, M. Morstein, Thin Solid Films 420-421 (2002) 275. [8] M.R. Begley, A.G. Evans, J.W. Hutchinson, Int. J. Solids Struct. 36 (1999) 2773. [9] Metals Handbook, Properties and Selection: Irons, Steels and High- Perfomance Alloys, ASM International, vol. 1, 10th ed. [10] L. Hultman, and J.E. Sundgren, Handbook of Hard Coatings Deposition Technologies, Properties and Applications. ed. Bunshaw (New Jersey, 2001). [11] N.K. Fukumasu, R.M. Souza, Surf. Coat. Tech. 201 (2006) 4294. [12] K.J. Ma, A. Bloyce, T. Bell, Surf. Coat. Tech. 76-77 (1995) 297. [13] P. Hedenqvist, M. Olsson, S. Jacobson, Surf. Coat. Tech. 41 (1990) 31. [14] J. Li, W. Beres, Wear 260 (2006) 1232. References [1] W. Heinke, A. Leyland, A. Matthews, G. Berg, C. Friedrich, E. Broszeit, Thin Solid Films 270 (1995) 431. [2] A.F. Ribeiro Jr., Ph.D. theses - Duplex coatings on AISI H13 and AISI D2 tool steels by using plasma nitriding and TiN-PVD, São Paulo University (2003).