Surface & Coatings Technology

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Surface & Coatings Technology 203 (2008) 730 735 Contents lists available at ScienceDirect Surface & Coatings Technology journal homepage: www.elsevier.

Thompson b a Mechanical Engineering Department, The University of Alabama, Tuscaloosa, Alabama, United States b Vista Engineering, Inc.

1 Surface & Coatings Technology 203 (2008) Contents lists available at ScienceDirect Surface & Coatings Technology journal homepage: Cohesive zone effects on coating failure evaluations of diamond-coated tools J. Hu a, Y.K. Chou a,, R.G. Thompson b a Mechanical Engineering Department, The University of Alabama, Tuscaloosa, Alabama, United States b Vista Engineering, Inc., Birmingham, Alabama, United States article info abstract Available online 20 August 2008 Keywords: Coating failure Diamond coating Finite element Interface delamination Diamond-coated cutting tools are economically attractive alternatives to polycrystalline diamond tools for machining applications. Despite the superior tribological and mechanical properties, the advantages of diamond-coated tools, however, have been largely compromised by the insufficient coating substrate adhesion. Interface characteristics are important in the failure and performance of diamond-coated tools. In this study, a cohesive zone model was incorporated to investigate diamond-coating tungsten carbide (WC) systems. The cohesive zone model is based on the traction separation law, represented by four parameters: the maximum normal and shear strength and the normal and shear characteristic lengths, whose values were determined from WC fracture properties. The cohesive zone model was implemented in finite element codes to simulate indentation on a coating substrate system. The model was applied to examine the interface behavior during the indentation, the role of the cohesive zone in the failure mechanism of coating systems, and the coating Young's modulus and thickness effects on different failure modes. The simulation results are summarized as follows. (1) The cohesive zone interface does not affect the critical load for coating surface tensile cracking, but affects the plastic strain during loading. (2) If the coating Young's modulus increases, the coating surface cracking will decrease, however, the interface delamination resistance will increase. (3) Increasing the coating thickness will generally increase the critical load for surface cracking, but will have an opposite effect when the coating exceeds a certain thickness. Moreover, thicker coatings typically reduce the interface delamination Elsevier B.V. All rights reserved. 1. Introduction Diamond coatings using advanced surface engineering technologies have been increasingly explored for tooling applications in machining. Diamond-coated tools are economically attractive alternatives to their polycrystalline diamond counterparts, offering an advantage in the fabrications of cutting tools with complex geometry such as drills. Despite the superior tribological and mechanical properties, the benefits of diamond-coated tools have been impacted by inadequate coating substrate adhesion, which can hardly withstand severe abrasive and adhesive wear during machining. The poor adhesion at the interface combined with interface stresses developed during machining leads to premature catastrophic tool failures. Though various techniques have been employed to evaluate the interface adhesion [1 4], indentation appears to be the mostly used technique and is widely employed in both research and industrial settings, however, the result is mostly interpreted in a qualitative fashion. Finite element (FE) methods have also been employed to study the failure of coated solids [5 9]. It is well known that concentrated tensile stresses are produced over the compliant substrate at the coating surface, which initiates coating surface Corresponding author. address: kchou@eng.ua.edu (Y.K. Chou). cracking, if the tensile stress exceeds the fracture strength of the coating material [10]. However, the critical load to initiate coating surface cracks seems to have little connection with the interface strength. Moreover, most studies were only concerned with the coating fracture and the substrate plastic deformation, while interface delamination was seldom discussed. The primary difficulty has been in modeling of interface behaviors. In most cases, researchers either assumed that the interface has infinite strengths [5,6] or some prespecified maximum interface stress as the failure criterion [11,12]. The concept of the cohesive zone model (CZM) was proposed decades ago [13,14]. In a pioneer work, Dugdale described the plastic deformation near the crack tip analytically and reported that the normal stress was limited by the yield strength of the elastic-perfectly-plastic materials [13]. Barenblatt formulated the fundamental idea of CZM as a traction separation law for decohesion of atomic lattices [14], according to which the traction across the interface first increases with the separation until it reaches a maximum value, then decreases and eventually vanishes. In recent years, a few researchers began to study the interface failure of coated solids under contact loading, although the material constants in their cohesive constitutive relations were often chosen on a broad basis, instead of a specific application [15 18]. In a previous study [19], an FE scheme of the indentation cycle on a coating substrate system, including a cohesive zone interface, was developed. The objective of this work is to examine the role of the /$ see front matter 2008 Elsevier B.V. All rights reserved. doi: /j.surfcoat

J. Hu et al. / Surface & Coatings Technology 203 (2008) 730 735 731 cohesive zone interface (vs.

2 J. Hu et al. / Surface & Coatings Technology 203 (2008) cohesive zone interface (vs. perfect interface) in coating substrate failure mechanisms, and to quantify coating Young's modulus and thickness effects on different coating failure modes. 2. Indentation simulations of diamond-coated tools with a cohesive zone interface Finite element codes were developed using ANSYS to incorporate a cohesive zone interface and applied to simulate the indentation of diamond coating on a WC Co substrate using a spherical diamond tip of 50-µm radius, details in [19]. The constitutive law of the cohesive zone model adopted is based on Xu and Needleman's approach [20]. The mechanical relations between the traction and displacement jump across the interface describe the interface behavior. The cohesive zone model is characterized by four parameters: σ max, τ max, δ n and δ t, which are the normal and shear strengths of the interface, and characteristic lengths for both the normal and shear modes, respectively. Currently, no effective experimental technique exists to directly measure such parameters. In this study, the cohesive zone parameters were idealized as material constants determined by the weaker component of the system the substrate. Such an approximation of cohesive properties on the weaker material of the adherent pair has been experimentally and theoretically proved [3, 21 22]. In diamond coating on a WC Co substrate, the cobalt phase at the surface must be etched off prior to depositions to prevent graphitization. Therefore, it is reasonable that the cohesive zone parameters were approximated solely by WC. From the relationship between the normal work of separation and Mode-I critical stress intensity (K IC ), σ max and τ max were determined to be 543 MPa and 314 MPa, and δ n and δ t were 0.26 µm and 1.05 µm, respectively [23].It needs to be pointed out that the interface properties are affected by the deposition process and substrate conditions, which may Fig. 1. Maximum principal stress contours in a coating system with two cases: (a) perfect interface and (b) cohesive zone interface (10-µm coating, 700-GPa Young's modulus).

732 J. Hu et al. / Surface & Coatings Technology 203 (2008) 730 735 Fig. 2. Shear stress evolution at increasing load: contours of shear stress (30 µm thick, 1200-GPa Young's modulus).

Quasistatic structural analysis was performed to simulate the loading unloading cycle during indentation.

3 732 J. Hu et al. / Surface & Coatings Technology 203 (2008) Fig. 2. Shear stress evolution at increasing load: contours of shear stress (30 µm thick, 1200-GPa Young's modulus). noticeably vary the model parameters. In the simulations, the material behaviors were perfect elastic for the diamond coating and elastic plastic with a hardening rule for the substrate, respectively. Quasistatic structural analysis was performed to simulate the loading unloading cycle during indentation. Though diamond WC indentation has been frequently reported, all data reported are crack and surface damage sizes at discrete loads (limits of Rockwell indentation testing), instead of continuous loadcontrolled (or displacement-controlled) indentation to monitor the failure. There is no data from diamond WC indentation available to directly validate the model. Since the model was developed without specific material requirements, it should be generic enough to be tested by other material systems. Thus, a study of ZnO films deposited on Si substrates with load-controlled indentation tests (Vickers indenter) was used to test the model [24]. The experiments from that study reported the critical load for the onset of coating delamination at various film thicknesses. The developed FE model was thus modified: the indenter shape and size, and the coating and substrate materials, to predict the critical load for interface delamination at different thicknesses, which were then compared with the experiments from [24]. The comparison shows that the relative difference is 170% in average [19]. Considering the complexity of the coating failure phenomena and uncertainty in material properties, the trend and order of magnitude comparisons indicate reasonable agreement. Once tested, the model was applied to examine the influences of the cohesive zone (vs. perfect interface) to critical loads for surface cracking, and interface delamination at a fixed load. In addition, coating Young's modulus and thickness effects on coating failure modes were evaluated. Fig. 3. Response of interface during unloading: normal traction at complete unloading (30-µm coating, 1200-GPa Young's modulus).

J. Hu et al. / Surface & Coatings Technology 203 (2008) 730 735 733 3. Results and discussion 3.1. Interface effects As an illustration example, Fig.

4 J. Hu et al. / Surface & Coatings Technology 203 (2008) Results and discussion 3.1. Interface effects As an illustration example, Fig. 1 compares first principal stresses during indentation of a diamond WC Co system (1200-GPa Young's modulus and 10-μm thickness) with two cases: (a) perfect interface (PI), i.e., infinite strength, and (b) cohesive zone interface (CZI). It can be noted that the maximum stress location is at the coating surface for the PI case, but at the interface for the CZI case. Thus, the PI assumption may incorrectly predict the failure location and mode. Moreover, the critical load to initiate the failure for the PI is greater than that for the CZI (5.8 N vs. 4.2 N), assuming 15 GPa of diamond fracture strength. Thus, the inclusion of the interface characteristics can better represent the coating system behavior and failure. It has also been obtained that the substrate yielding behavior is different as well; at a 50-N load, the PI case has a larger plastic strain than the CZI, vs The interface failure during indentation may occur in two modes: shear and normal delaminations. During the loading stage, the interface is under compression. Accordingly, the interface delamination can only be initiated in the shear mode. An example of shear stress evolutions under increasing load is shown in Fig. 2. With the current tested parameters, the shear mode delamination will not be produced even at the maximum applied load. If the substrate does not yield at the maximum load, the coating can recover to the undeformed shape once the indenter is completely withdrawn. However, if the substrate yielding occurs, a permanent plastic impression will be stored in the substrate and tensile traction is expected to develop at the interface. Therefore, the interface delamination in the normal mode may arise during the unloading stage if the normal separation is greater than its characteristic length and the corresponding normal traction exceeds the instantaneous strength. Fig. 3 presents the normal traction contours at the interface after the indenter has been completely withdrawn from the coating surface. The location of the maximum interface normal traction, which approaches the normal strength (543 MPa), is referred as the crack tip. In this case, the normal mode interface failure formed a circular delamination of about 13-μm radius. The interface properties can be affected by several factors associated with depositions and substrate conditions. To test the uncertainty of the interface properties, the cohesive zone parameters were modified, reduced to 50% and 10% of the original values, in the simulations. It was concluded that coating surface tensile cracking is Fig. 5. Examples of indentation impression on diamond-coated WC Co substrates to qualitatively illustrate coating failures: (a) Hertzian ring crack and (b) coating delamination. not sensitive to the interface strength. On the other hand, the delamination size is affected by the interface characteristics. Fig. 4 plots the interface delamination size for three levels of cohesive zone parameters. The result obtained is reasonably intuitive; the greater the interface strength, the smaller the delamination Coating Young's modulus effects Fig. 4. Cohesive zone property effects on interface delamination (30-µm coating, GPa Young's modulus, 50-N load). Diamond coatings produced by different deposition processes/ settings may have a wide range of properties, e.g., Young's modulus. It has been indicated that Young's modulus from 600 GPa to 1200 GPa can be obtained in diamond coatings [25]. Young's modulus significantly affects the mechanical behavior of the coating system and may impact the coating failure conditions. Thus, in indentation simulations, the coating Young's modulus was varied to investigate its effects. For comparison purpose, the tensile fracture strength of the diamond coating is assumed to be 15 GPa, noting that a wide range, 7 to 20 GPa, has been reported [3,6]. Coating surface cracking is one of the dominant failure modes in a brittle coating substrate system. For spherical indenters, it has often been observed that circular cracks always start near the edge of the contact circle, which is referred as the Hertzian ring crack. Fig. 5a shows an example of a ring crack from indentation of diamond coating on a carbide substrate. On the other hand, coating cracks may possibly originate at the interface, on the axis of symmetry, and propagate

5 734 J. Hu et al. / Surface & Coatings Technology 203 (2008) along the radial direction [10]. Moreover, delamination due to interface failure may lead to coating peeling-off, Fig. 5b. The effect of the coating Young's modulus on coating cracking and delamination is shown in Fig. 6 (30-µm thick coating). With such thick coatings, the critical tensile stress always occurs at the coating top surface, instead of the interface, which suggests that the ring crack is dominant. From the figure, it is indicated that increasing coating Young's modulus will lower the critical load, i.e., reduction of cracking resistance. On the other hand, with a fixed 50-N applied load, the delamination size decreases in a linear fashion with the increase of the coating Young's modulus. The coating with a greater Young's modulus is subject to smaller strains and less deformation, which also reduce the plastic deformation of the substrate, and hence a smaller delamination size. Fig. 7 plots the coating Young's modulus vs. critical load for the onset of substrate yielding. It is consistently shown that smaller coating Young's moduli lower the critical load to the onset of substrate yielding, which results in interface delamination. Fig. 7. Young's modulus effects on critical load for substrate yielding (30-µm coating) Coating thickness effects From the simulations, it was observed that 5-µm and 10-µm thick coatings result in radial cracks (i.e., maximum stress at the interface), while the rest (N10 µm) generates ring cracks (i.e., maximum stress at the coating surface). Fig. 7 evaluates both the critical load to initiate coating cracking as well as delamination sizes (at 50-N load). The results indicate that the critical load for coating surface cracking decreases with the increase of the coating thickness when the failure mode is Hertzian ring cracks (thickness greater 10 µm), while the opposite trend holds when the radial cracking is dominant. The contact between the indenter and the coating produces a high tensile stress right at the contact circle. On the other hand, the bending of the coating on a compliant substrate will introduce tensile stresses at the lower surface of the coating, but compressive stresses at the upper surface. These two mechanisms may affect failures in an opposite way at different coating thicknesses. The bending effect may vanish gradually with the increase of coating thickness, therefore, reducing the critical load for ring cracks. In contrast, for the radial crack at the lower surface of coating, the critical load will decrease with the decrease of the coating thickness. Chai and Lawn conducted indentation tests on various coatings deposited on polycarbonate substrates [10]. Their experiments indicated a transition of the coating failure modes as obtained from the FE simulations here. The coating thickness effect on interface delamination is also revealed in Fig. 8. For 40- and 50-μm thick coatings, delamination does Fig. 8. Coating thickness effects on critical load for coating cracks and interface delamination sizes (1200-GPa Young's modulus). not occur at a 50-N indentation load. As the coating thickness decreases, the delamination size increases noticeably due to the augmented plastic deformation. It is also interesting to note that when the coating thickness is further reduced to a certain extent, e.g., 5 μm in this test, excess loss of rigidity may exert an opposite effect. The interfacial traction may lead to a large amount of coating deflection, preventing the elastic recovery of the coating, and thereby reduce the size of delamination. However, in reality, coating tensile fracture may have already surpassed the interface delamination in coating failure. 4. Conclusions In this study, a cohesive zone model was implemented in finite element codes to simulate the indentation cycle, using a spherical indenter, on a diamond-coated WC Co substrate. The cohesive zone model is based on the traction separation law, represented by the maximum normal and shear strength, and the normal and shear characteristic lengths, determined from WC fracture properties. The FE simulations were then applied to investigate the role of the cohesive zone interface (vs. perfect interface) in coating substrate failure mechanisms, and to investigate the coating Young's modulus and thickness effects on different coating failure modes. The simulation results are summarized as follows. Fig. 6. Young's modulus effects on critical load for coating crack and interface delamination sizes (30-µm coating). (1) In general, for thin coatings, the maximum stress location and value are different between the perfect interface and cohesive zone interface conditions. However, for thick coatings (N10 µm)

6 J. Hu et al. / Surface & Coatings Technology 203 (2008) where the Hertzian ring crack is dominant, the cohesive zone interface does not affect the critical load to initiate coating surface tensile cracking. (2) If the diamond coating Young's modulus increases, the critical load for coating surface cracking will decrease. However, the interface delamination size will decrease with increasing Young's modulus. (3) For thick coatings, the critical load for coating failure (ring cracks) decreases with increasing coating thickness. However, such a trend is reversed for thin coatings, for which lateral cracking is the coating failure mode. Moreover, increasing the coating thickness will generally reduce the interface delamination size. Acknowledgement This research is supported by the National Science Foundation, Grant No.: CMMI References [1] V. Vohra, S.A. Catledge, Y.K. Vohra, Mater. Res. Soc. Symp. Proc. 791 (2004) Q [2] Q.H. Fan, J. Gracio, E. Pereira, J. Appl. Phys. 86 (1999) [3] R. Ikeda, M. Hayashi, A. Yonezu, T. Ogawa, M. Takemoto, Diamond and Related Materials 13 (2004) [4] T. Grogler, E. Zeiler, A. Horner, R.F. Singer, S.M. Rosiwal, Surf. Coat. Technol. 98 (1998) [5] H. Chai, Int. J. Fract. 119 (2003) 263. [6] J. Michler, E. Blank, Thin Solid Films 381 (2001) 119. [7] P. Miranda, A. Pajares, F. Guiberteau, F. Deng, B.R. Lawn, Acta Mater. 51 (2003) [8] E. Weppelmann, M.V. Swain, Thin Solid Films 286 (1996) 111. [9] R.M. Souza, G.G.W. Mustoe, J.J. Moore, Thin Solid Films 392 (2001) 65. [10] H. Chai, B.R. Lawn, J. Mater. Res. 19 (2004) [11] P.K. Gupta, J.A. Walowit, ASME J. Lubr. Technol. 94 (1974) 250. [12] J.M. Leroy, B. Villechaise, in: D. Dowson, C.M. Taylor, M. Godet (Eds.), Mechanics of Coatings, Elsevier, New York, [13] D.S. Dugdale, J Mech. Phys. Solids 8 (1960) 100. [14] G.I. Barenblatt, Advances in Applied Mechanics, Academic Press, New York, 1962, p. 55. [15] A. Abdul-Baqi, E.V. Giessen, Thin Solid Films 381 (2001) 143. [16] A. Abdul-Baqi, E.V. Giessen, J. Mater. Res. 16 (2001) [17] Y.W. Zhang, K.Y. Zeng, R. Thampurun, R. Mater. Sci. Eng. A (2001) 893. [18] S.M. Xia, Y.F. Gao, A.F. Bower, L.C. Lev, Y.T. Cheng, Int. J. Solids Struct. 44 (2007) [19] J. Hu, Y.K. Chou, R.G. Thompson, Trans. N. Am. Manuf. Res. Inst./Soc. Manuf. Eng. 36 (2008) 533. [20] X.P. Xu, A. Needleman, Solid State Phenom (1994) 287. [21] M.N. Cavalli, Cohesive zone modeling of structural joint failure, Ph.D. thesis, University of Michigan, Ann Arbor (2003). [22] J. Zhai, M. Zhou, Int. J. Fract. 101 (2000) 161. [23] M. Grujicic, G. Cao, G.M. Fadel, Proc. Inst. Mech. Eng., Part L: J. Mater.: Des. Appl. 215 (2001) 225. [24] B. Huang, M. Zhao, T. Zhang, Philos. Mag. 84 (2004) [25] J. Hu, Y.K. Chou, R.G. Thompson, Surf. Coat. Technol. 202 (2007) 1113.

Competing failure mechanisms in mixed-mode fracture of an adhesively bonded polymer-matrix composite

$Competing failure mechanisms in mixed-mode fracture of an adhesively bonded polymer-matrix composite$ International Journal of Adhesion & Adhesives 26 (26) 69 616 www.elsevier.com/locate/ijadhadh Competing failure mechanisms in mixed-mode fracture of an adhesively bonded polymer-matrix composite S. Li