- Email: [email protected]
Cracking investigation of W and W(C) films deposited by physical vapor deposition on steel substrates
Surface and Coatings Technology 111 (1999) 177–183
Cracking investigation of W and W(C ) films deposited by physical vapor deposition on steel substrates Emmanuelle Harry a,*, Michel Ignat b, Andre´ Rouzaud a, Pierre Juliet a a CEA/Grenoble, CEREM/DEM/SGM/LS2M, 17 rue des Martyrs, 38054 Grenoble, Cedex 9, France b INP/Grenoble, ENSEEG, BP 75, 38402 Saint Martin d’He`res, FRANCECEA/Grenoble, CEREM/DEM/SGM/LS2M, 17 rue des Martyrs, 38054 Grenoble, Cedex 9, France Received 23 March 1998; accepted 18 October 1998
Abstract This paper presents the investigation of the cracking of coatings deposited on steel substrates. The coating on substrate systems consisted on pure tungsten films ( W ) and films of solid solutions of carbon in tungsten [ W(C )], which were deposited by direct current reactive magnetron sputtering on stainless steel substrates. The systems were strained uniaxially with a microtensile device adapted to a scanning electron microscope. The mechanical response was analyzed from the experimental results: the straining of the samples showed an evolution of the density of cracks in the coating, which was described trough an empirical equation based on the Weibull distribution function. The density of cracks, which corresponds to the crack saturation of the coating, appeared to vary inversely with coating thickness. Critical parameters relative to their mechanical stability were also determined from the experimental results: the strain energy release rate for crack extension through the film, Gf , and the fracture toughness, Kf , of c Ic the coatings. These values are included between 0.2 and 14 J m−2, and between 0.1 and 2.5 MPa m−1/2. The fracture resistance of W and W(C ) coatings was found to be correlated to their thickness and microstructure. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Cracking; Tensile tests; Tungsten coatings
1. Introduction Multilayers are widely used in a broad range of technologies as different as microelectronic devices or wear and erosion protection. However, for their applications, the knowledge of their mechanical stability remains a critical aspect to analyze. For instance, because the elaboration techniques, residual stresses may remain in the layers after their production. When stresses reach high levels, they can induce spontaneous buckling or cracking of the layers [1]. Thus, one can expect that an external stress can be critical and cause significant damage. Therefore, to improve the properties of layered systems for intended mechanical applications, it seems obvious to investigate the coating failure mechanisms, when an external stress is applied to the system, and also to estimate relevant parameters for its mechanical stability. Uniaxial strain will cause layers failure before signifi* Corresponding author. Tel.: 33 4 72 44 83 06; Fax: 33 4 72 43 12 06; e-mail: [email protected]
cant extension of the substrate. The failure modes of the coatings are in general cohesive and sometimes adhesive with the peeling off the portions of the layer from the substrate. A large number of authors have studied this phenomenon [2–5]. The investigated coatings are pure tungsten ( W ) films and also solid solutions of carbon in tungsten [ W(C )] deposited by direct current reactive magnetron sputtering (DCRMS ) on stainless steel substrates. Basic properties of coatings of this type (morphology, microstructure, hardness, residual stresses) have been previously characterized [6–8], then permitting us to investigate and discuss the fracture resistance of these coatings, which can be considered as a key parameter when considering engineering applications. The objectives of this paper are: first to recall the theoretical approach of film cracking, previously described by Harry [6 ], which allows the estimation of the stress distribution in a cracked film. The second objective is to apply this theoretical approach to a system consisting of stiff coatings on ductile substrates, and then to investigate the mechanical response of these composites which were submitted to an elongation. This
0257-8972/99/$ – see front matter © 1999 Elsevier Science S.A. All rights reserved. PII S 02 5 7 -8 9 7 2 ( 9 8 ) 0 0 73 2 - 4
178
E. Harry et al. / Surface and Coatings Technology 111 (1999) 177–183
includes the determination of critical cracking stresses, fracture properties of the coatings that will be discussed through the Weibull analysis and in terms of the Griffith approach, and the examination of damage mechanisms with respect to the coatings structure.
2. Theoretical approach 2.1. Cracking of a deposited layer When considering the behavior of a tensile sample consisting of a brittle layer attached to a ductile substrate: when submitted to an elongation which follows a given direction (x) (see Fig. 1); both (the layer and the substrate), will first deform elastically. If we assume that Young’s modulus of the brittle layer is higher than that of the substrate, cracking of the layer is expected to start before plastic flow in the substrate. Then, by considering Young’s modulus of the layer (Ef) and the substrate (Es), and the critical cracking stress in the layer (sf ), that is experimentally accessible, the correxx,c sponding stress in the substrate (ss ) will be: 0 Es sf (1) ss = 0 Ef xx,c with ss
Fig. 1. (a) Schematic illustration of the cracking of a deposited layer and the plastic strain in the substrate at the crack tips. Stress redistribution in the substrate at the coating/substrate interface (b) and in the coating (c) at the crack vicinity. Each term is defined in the text.
free surfaces. The stress relaxation in the crack vicinity must indeed be limited to a zone extending over a distance d on both sides of the crack. The stress in the coating will then extend uniformly from zero at the crack surfaces to the critical cracking stress sf over the length d. On this distance, the xx,c coating stress is described by the following relation: x sf (x)= sf . xx d xx,c
(2)
The substrate stress can be expected to be the yield stress ss at the coating edges next to the crack. At the y crack vicinity, on the length d, the stress can be written: d−x (ss −ss ). ss (x)=ss + y 0 xx 0 d
(3)
Far from any crack surface (x>d), when increasing the elongation, the stress in the layer is supposed to raise up continuously, till reaching the critical value for opening new cracks (ssf ). The number of cracks xx,c which develop perpendicular to the tensile axis will increase. This crack evolution will redistribute the normal stresses acting in the layer and the stress level will be progressively lowered as the distance between two consecutive cracks tends to move closer. This process will develop until the saturation of cracks, which theoretically corresponds to a constant distance d among two consecutive cracks ( Fig. 2).
Fig. 2. (a) Schematic illustration of the cracking of a coating deposited on a substrate. The arrows indicate the direction of the applied tensile stress. Stress redistribution in the coating (b) at the crack vicinity; (c) between two consecutive cracks, the crack density being lower than the crack saturation density and the maximum stress in the coating corresponding to the critical cracking stress; (d) between two consecutive cracks, when the crack density reached the crack saturation density. The length among these cracks is minimal, and the global stress in the coating is lower than the critical cracking stress.
E. Harry et al. / Surface and Coatings Technology 111 (1999) 177–183
179
2.2. Strain energy release rate for crack extension The cracking of the layer will cause energy variations in the system. The net energy change DU can be determined from an energy balance for the system, when the film cracks, perfect adhesion between the layer and the substrate being assumed. This approach was used for Cr films on Al substrates [4], and has been previously described for W layers on stainless steel substrates [6,9]. The balance gives: (sf )2(tf)2 xx,c Ef
G A B
H
Ef
sf + xx,c (4) 앀3ss Es y F is a function of the elastic modulus ratio [4]. As the strain energy release rate for crack extension through the layer Gf is: c DU Gf = (5) c tf
DU=
pF
Fig. 3. Type of samples used for uniaxiale tensile tests. The arrows indicate the loading direction.
a microtensile device adapted to a scanning electron microscope (SEM ) [5]. Film surface is observed by SEM in order to detect the crack initiation and to follow the evolution of crack density versus the applied load or the system’s deformation. A measure of the average crack density D (cracks mm−1) is determined by counting the number of cracks in a given distance.
we obtain tf(sf )2 xx,c Gf = c Ef
C A B Ef
D
sf pF + xx,c . (6) 앀3ss Es y Assuming that the stress state in the layer, when it cracks, is tensile the mode I fracture toughness of the film can then be deduced: Kf =앀Gf Ef. c Ic
(7)
3. Experimental W and W(C ) coatings were deposited on stainless steel substrate by DCRMS. Their microstructural and basic mechanical properties were examined and in situ tensile experiments were performed on samples, consisting of W and W(C ) coatings on steel substrates to analyze the failure mechanisms. Parameters relative to the mechanical stability of the coatings, as the strain energy release rate [Eq. (6)] and the corresponding fracture toughness [Eq. (7)], were also determined. 3.1. Procedures Tungsten ( W ) and tungsten–carbon (14 at% C ) [ W(C )] coatings are deposited by DCRMS onto stainless steel substrates. The geometry of the systems is represented schematically in Fig. 3. Coating thickness extended from 2 to 16 mm and the substrate is 850 mm thick. Before coating deposition, the substrate surface is polished with diamond paste and cleaned. A detailed description of the deposition technique has been presented in a previous paper [6 ]. The beams are subjected to uniaxial tensile stress with
3.2. Results and discussion 3.2.1. Film properties Polycrystalline W sputtered coatings present a a-cubic phase, while the W(C ) coatings present a metastable interstitial solid solution of atoms of carbon in the same phase. Deposited on steel substrates, the W and W(C ) coatings generate high residual compressive stresses, of ca −3 GPa [6 ]. We may note that the corresponding residual stresses in the coatings remained similar for both of them (−3 GPa); showing no effect of the carbon content on this parameter. The hardness of the coatings was determined by Vickers indentation tests under 0.5 N contact load. It was of ca 12 GPa for the W coatings and 28 GPa for the W(C ) coatings, with increasing carbon content. With respect to the microstructure, the W coatings present a columnar structure with a grain diameter of ca 40 nm. Even though, the coatings rich in carbon showed a similar elongated texture of grains, the crystallites were smaller: of ca 6 nm in diameter, the diameter diminishing with the percent of added carbon. The hardness follows a Hall–Petch type relation, which gives semi empirically the increase of this parameter with the decrease of the grain size: H=H +kd−1/2. (8) 0 H and k are constant terms, H is the hardness 0 and d is the grain diameter. For the coatings, k=2.16 MPam−1/2 and H =11 MPa. 0 The Hall–Petch relation can also be related to the increase in hardness of W coatings (12 GPa) which present smaller grains as compared to the W bulk material presenting a grain size of 1 mm [10].
180
E. Harry et al. / Surface and Coatings Technology 111 (1999) 177–183
3.2.2. Failure of the coatings When the coating on substrate system is submitted to the tensile tests, the response of both the coating and the substrate is entirely elastic at the lower strains (<0.8%). As the coating is much stiffer and more brittle than the substrate, it cannot undergo significant extension. Then, at a critical deformation of the substrate es , the critical cracking stress sf is attained for the xx,c xx,c coating and failure occurs. The coating begins to crack, then the substrate’s deformation is still elastic. The critical cracking stress will be considered as the ‘‘crack onset’’. The critical cracking stress is determined experimentally, taking into account the residual stresses preexisting in the coating sf and the critical strain of the r substrate. Indeed, the critical cracking stress can be written: sf =Efes +sf . (9) xx,c xx,c r When considering the existence of defects in sputtered coatings, resulting from the growing process (structural imperfections) or previously existing on the substrate (roughness) [11], this stress may be associated to the presence of singularities pre-existing in the coatings. The resulting value of the critical cracking stress could then be lowered compared to that expected for a coating without defects. Taking into account the semi empirical common ratio between the hardness (H ) and the yield strength (s ) for y homogeneous and isotropic materials [12], applied to W and W(C ) films with hardness of 12 and 28 GPa, respectively: H=3s (10) y we may deduce that the tensile yield strength of any coatings we investigated are much higher than that of the corresponding stress in a bulk material. However, from our experiments ( Table 1) we detect a low critical cracking stress for both coatings, which is close to 500 MPa and lower than the values reported in the literature, for the W bulk material [12]. Besides, the
deduced fracture toughness values [Eq. (8)] are ranged from 1 to 2.5 MPa m−1/2 for W coatings and from 0.1 to 1 MPa m−1/2 for W(C ) films ( Table 1). These values appear to be lower than that of the tungsten bulk material of 10–20 MPa m−1/2 [12]. This tendency emphasizes the fact that our coatings are sensitive to pre-existing defects. For a non-homogeneous stress distribution, the value of the critical stress will be the fracture stress of the structure. Moreover, an earlier crack initiation is observed for the W(C ) coatings, which may not only depend on the already mentioned defects, but also on well known embrittlement effect induced by carbon segregation at the grain boundaries [13]. Then, assuming that cracking of the coatings initiates on defects (assumption that will be supported by a Weibull analysis), the size of these singularities can be estimated according to the Griffith approach. As a matter of fact, the fracture of materials can be described as a function of the defect size a: (11) Kf =sf 앀pa Ic xx,c The deduced values of the mean defect size are reported in Table 1. The results exhibit defect size as large as thickness of the films. It indicates that the defects may have grown from the substrate surface (from chemical impurities or asperities) during the coating deposition. Defects of this type are protruding conical features ( Fig. 4) and are called ‘‘growth defects’’. This defects, when emerging on the coating surface, can contribute to the surface roughness of the coating, resulting in dulllooking rough surface. For W(C ) coatings, the calculated values of the defect sizes are found to be slightly lower than the thickness of the coatings. This result may arise from the existence of both growth defects as large as the coating thickness and carbon segregation at grain boundaries.
Table 1 Experimental values of the critical strain applied to the substrate es when cracking the coating, the critical cracking stress for the xx,c coating sf [Eq. (9)], the fracture toughness Kf , [Eq. (7)] and the xx,c Ic defect size [Eq. (11)] with respect to the coating thickness tf tf (mm) W film 3.4 6.6 16.4 W(C) film 3.45 6.5 16
es xx,c
ss (MPa) xx,c
Kf (MPa m−1/2) Ic
a (mm)
0.85 0.867 0.87
400 404 348
1.350±6 1.860±6 2.470±5
3.6 6.7 16
0.78 0.81 0.54
120 240
0.350±2 1±0.2
2.7 5.53
Fig. 4. SEM micrograph of a growth defect through the thickness of a sputtered film.
181
E. Harry et al. / Surface and Coatings Technology 111 (1999) 177–183
From Eq. (6) values of the strain energy release rate for crack extension through the coating, Gf , can be c calculated. They are ranged from 2.5 to 14 J m−2 for the W films and from 0.07 to 1.2 J m−2 for the W(C ) coatings. According to the Griffith criterium (U=2), and the tungsten surface energy ca 3.3 J m−2 [14], we may note that the experimentally determined values for the W coatings remain in the order of magnitude of a thermodynamically predicted value, 6.6 J m−2. Generally, mechanically deduced values of rupture energies, when compared to thermodynamically surface free energy value, present discrepancies which sometimes are higher than an order of magnitude [15]. In our case the results seem to validate the experimental procedure we followed. The cracking phenomenon can be described in successive stages (Fig. 5). At the crack onset, the coating will then develop series of regular and parallel spaced cracks, perpendicular to the loading direction. These initial cracks will multiply rapidly after the crack onset. Their edges are sharp and well defined [6 ]. When increasing the composite deformation further, additional cracks progressively appear and the distance separating two consecutive cracks decreases. This evolution can be followed by the crack density parameter D which is defined as the number of cracks over a given length. Continuing the strain, this parameter which grows at the beginning of the deformation, will reach a constant value: the crack saturation density D , corresponding sat to a minimal length between two cracks. The vicinity of the crack free surfaces lowered the global stress level in the coating under the critical cracking stress sf . xx,c When the saturation of cracks is reached, if the deformation continues, no new cracks appear; but the existing ones will continue to open, with increasing plastic deformation in the substrate, concentrated at the crack tip. The experimental evolution of crack density is plotted versus the applied strain for W and W(C ) coatings in Fig. 6. An empirical relation, based on a Weibull type
(a)
(b) Fig. 6. Transverse crack density of W coatings (a) and W(C ) coatings (b) of thickness: &, 3.5 mm; $, 6.5 mm; and +, 16 mm versus longitudinal strain.
distribution function, was applied to describe the crack density as a function of the applied strain in the substrate es [16,17]: xx D(es )=D {1−exp[−A(es −es )a]}. (12) xx sat xx xx,c A and a are constant parameters which will depend on the film/substrate system. For our coatings, we noted that at the saturation, the corresponding crack densities, D , decreased with the sat coating thickness, showing an average intercrack spacing larger for thicker films. This dependence can be explained when considering the analytical approach of Mezin describing the stress distribution in a cracked film [17]: 2tf ss sf = 0 +sf − r pK xx K
Fig. 5. Typical evolution of the transverse crack density versus the substrate’s longitudinal strain. The different stages of damage are indicated. D is the saturation of crack density. sat
P
+L/2
∂sf (u) xx du. x−u ∂u 1
(13) −L/2 K is Young’s moduli ratio of the film and the substrate, tf the thickness of the film and L the distance separating two consecutive cracks. In this relation, the first term is relative to the uncracked film. The integral term represents the interaction induced by the proximity of the cracks and
182
E. Harry et al. / Surface and Coatings Technology 111 (1999) 177–183
lowering the stress level in the film. Thus, this relation shows that an increase in thickness should result in a more significant stress release in the coating, preventing any further crack propagation. Hence, the saturation crack density is lowered. The empirical equation which describes the dependence between the crack density at saturation and the coating thickness is in our case: B D = sat (tf)n
(14)
For our systems, the parameters B and n obtained from the experiments are: B=43.9, n=0.33 for W coatings and B=93.6, n=0.4 for W(C ) coatings. Therefore, in the empirical relation which describes the evolution of the crack density with respect to the applied strain to the substrate can be rewritten as: B {1−exp[−A(es −es )a]}. D(es )= xx xx,c xx (tf)n
(15)
Notice that the constant A and the exponent a, known as the Weibull modulus, are determined experimentally. They are respectively the ordinate at zero point and the slope of the line obtained from the plot of ln{−ln [1−(D/D )]} versus ln(es −es ). Experimental plots sat xx xx,c are reported in Fig. 7, for W and W(C ) coatings with different thickness. The values of the Weibull modulus are ranged from 0.923 to 1.021 for W layers, and from 0.686 to 0.767 for W(C ) layers, depending on the coating thickness. We may recall that the Weibull modulus expresses the statistical scatter of events: a high Weibull modulus indicates a low scatter [18]. The Weibull analysis gives a mathematical tool for predicting the fracture probability of one structure. In our case, the Weibull modulus appears to be small, reflecting a high probability of cracking of the coating and then the presence of numerous defects. As a comparison, soda-lime glass
Fig. 7. Experimental plots of ln{−ln[1−(D/D )]} versus sat ln(es −es ) for W films of thickness: &, 3.5 mm; $, 6.5 mm; +, xx xx,c 16 mm and for W(C ) films of thickness: %, 3.5 mm; #, 6.5 mm; 6, 16 mm. Each term is defined in the text.
has a Weibull modulus of 2–3 and polysilicon films have a value of 7–11 [18]. The Weibull modulus tells nothing on the severity of the defects or their location. However, the difference in Weibull modulus obtained for W and W(C ) films may indicate the existence of different types and/or densities of defects. When increasing the substrate strain to 20%, other types of cracks may appear, between the transverse cracks. These new cracking systems are activated by local complex stress fields, induced for example by defects, emerging on the substrate surface, as deformation bands or grain boundary displacements. However, even though these effects of singularities are activated only when reaching high strains, and develop a new cracking pattern in the coating, no debonding was observed. This revealed that the adhesion between the coatings and the substrate was good. We may recall that several authors reported qualitative relationship between adhesion and cracking phenomena. Some noted that an improved adhesion of a film is generally associated with an increase of crack density at saturation and no debonding even after being submitted to significant elongations [5,19]. In films, with poor adhesion, in particular those exhibiting buckling, a lower crack saturation density is generally reported [6 ]. In our study, it was not possible to characterize the interfacial adhesion, since no decohesion of the coatings from the substrate occurred even at the highest strains. However, scratch test experiments have been performed on coatings of this type to investigate the mechanical behavior of the films [20]. This method permitted to clarify the failure mechanisms and to rank coatings to delamination resistance.
4. Conclusion We performed in situ microtensile tests on systems consisting of W and W(C ) coatings deposited by DCRMS on steel substrates. The analysis of the mechanical response of the coatings was focused on their rupture properties. This was studied through the energy balance of the cracked system. The parameters which correspond to the rupture properties of the coatings were deduced: the strain energy release rate and the fracture toughness. The coatings were also characterized by the evolution of the crack densities with respect to the imposed deformation to the system, and the cracking probability was analyzed through the Weibull analysis. The calculated values of the Weibull modulus revealed a high probability of cracking for both coatings, supported by the low measured values of the fracture toughness, and the existence of different types and/or density of defects when considering pure metal coatings or carbon containing films with different thickness. Assuming defects as crack nucleation centers, an approximate value of the
E. Harry et al. / Surface and Coatings Technology 111 (1999) 177–183
defect size was determined in terms of the Griffith approach. This analysis reveals defects as large as coating thickness located at the coating/substrate interface and emerging at the coating surface. The analysis showed that the coatings rupture properties depended on both the type, the size and the density of structural defects. These intrinsic parameters modified the rupture properties, decreasing the fracture toughness when compared to bulk materials. Despite the identification of these embrittlement effects, and even though the substrate was deformed up to 20% in tension and the coatings cracked, our coatings remained attached to the substrate, proving a rather good interfacial adhesion in these systems.
References [1] E. Klokholm, IBM J. Res. Dev. 31 (1987) 5. [2] P.H. Wojciechowski, M.S. Mendolia, J. Vac. Sci. Technol. A 7 (3) (1989) 1282. [3] T.S. Chow, C.A. Liu, R.C. penwell, J. Polym. Sci. 14 (1976) 1305. [4] M.S. Hu, A.G. Evans, Acta Metall. 37 (3) (1989) 917. [5] M. Ignat, Key Eng. Mater. 116117 (1996) 279.
183
[6 ] E. Harry, International Conference on Metallurgical Coatings and Thin Films, Materials Research Society, 1998. [7] P. Juliet, A. Rouzaud, K. Aabadi, P. Monge-Cadet, Y. Pauleau, Thin Solid Films 290291 (1996) 232. [8] A. Rouzaud, E. Barbier, J. Ernoult, E. Quesnel, Thin Solid Films 270/271 (1995) 270. [9] E.Harry, Stabilite´ me´canique et modes d’endommagements de reveˆtements multicouches a` base de tungste`ne et de tungste`ne– carbone e´labore´s par PVD. Thesis, National Polytechnic Institute of Grenoble, Grenoble, France, 1998. [10] H.J. Frost, M.F. Ashby, Deformation–Mechanism Maps, 1st edn, Pergamon Press, New York, 1982. [11] D.M. Mattox, Surface Coat. Technol. 81 (1996) 8. [12] M.F. Asbhy, D.R.H. Jones, Mate´riaux, vol. 1, Dunod, Paris, 1991. [13] J.Y. Liu, S.C. Chang, J. Mater. Sci. 31 (1966) 4159. [14] J. Gerkema, A.R. Miedema, Surf. Sci. 124 (1983) 351. [15] J.H. Selvarian, D. O’Neil, Thin Solid Films 235 (1993) 129. [16 ] W. Weibull, J. Appl. Mech. September (1951) 293. [17] A. Mezin, J.-P. Chambard, J. Lepage, M. Nivoit, Thin Solid Films 185 (1990) 57. [18] S. Greek, F. Ericson, S. Johansson, J.-A. Schweitz, Thin Solid Films 292 (1997) 247. [19] M. Ignat, P. Scafidi, E. Duloisy, J.Dijon, in: P. Borgesen, J.C. Coburn, J.E. Sanchez, K.P. Rodbell, W.F. Filter (Eds.), Materials Reliability in Microelectronics IV, vol. 338, Material Research Society, Pittsburgh, 1994, p. 135. [20] E. Harry et al., Conference on Plasma Surface Engineering, Garmisch-Partenkirschen, 1998.
Cracking investigation of W and W(C ) films deposited by physical vapor deposition on steel substrates Emmanuelle Harry a,*, Michel Ignat b, Andre´ Rouzaud a, Pierre Juliet a a CEA/Grenoble, CEREM/DEM/SGM/LS2M, 17 rue des Martyrs, 38054 Grenoble, Cedex 9, France b INP/Grenoble, ENSEEG, BP 75, 38402 Saint Martin d’He`res, FRANCECEA/Grenoble, CEREM/DEM/SGM/LS2M, 17 rue des Martyrs, 38054 Grenoble, Cedex 9, France Received 23 March 1998; accepted 18 October 1998
Abstract This paper presents the investigation of the cracking of coatings deposited on steel substrates. The coating on substrate systems consisted on pure tungsten films ( W ) and films of solid solutions of carbon in tungsten [ W(C )], which were deposited by direct current reactive magnetron sputtering on stainless steel substrates. The systems were strained uniaxially with a microtensile device adapted to a scanning electron microscope. The mechanical response was analyzed from the experimental results: the straining of the samples showed an evolution of the density of cracks in the coating, which was described trough an empirical equation based on the Weibull distribution function. The density of cracks, which corresponds to the crack saturation of the coating, appeared to vary inversely with coating thickness. Critical parameters relative to their mechanical stability were also determined from the experimental results: the strain energy release rate for crack extension through the film, Gf , and the fracture toughness, Kf , of c Ic the coatings. These values are included between 0.2 and 14 J m−2, and between 0.1 and 2.5 MPa m−1/2. The fracture resistance of W and W(C ) coatings was found to be correlated to their thickness and microstructure. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Cracking; Tensile tests; Tungsten coatings
1. Introduction Multilayers are widely used in a broad range of technologies as different as microelectronic devices or wear and erosion protection. However, for their applications, the knowledge of their mechanical stability remains a critical aspect to analyze. For instance, because the elaboration techniques, residual stresses may remain in the layers after their production. When stresses reach high levels, they can induce spontaneous buckling or cracking of the layers [1]. Thus, one can expect that an external stress can be critical and cause significant damage. Therefore, to improve the properties of layered systems for intended mechanical applications, it seems obvious to investigate the coating failure mechanisms, when an external stress is applied to the system, and also to estimate relevant parameters for its mechanical stability. Uniaxial strain will cause layers failure before signifi* Corresponding author. Tel.: 33 4 72 44 83 06; Fax: 33 4 72 43 12 06; e-mail: [email protected]
cant extension of the substrate. The failure modes of the coatings are in general cohesive and sometimes adhesive with the peeling off the portions of the layer from the substrate. A large number of authors have studied this phenomenon [2–5]. The investigated coatings are pure tungsten ( W ) films and also solid solutions of carbon in tungsten [ W(C )] deposited by direct current reactive magnetron sputtering (DCRMS ) on stainless steel substrates. Basic properties of coatings of this type (morphology, microstructure, hardness, residual stresses) have been previously characterized [6–8], then permitting us to investigate and discuss the fracture resistance of these coatings, which can be considered as a key parameter when considering engineering applications. The objectives of this paper are: first to recall the theoretical approach of film cracking, previously described by Harry [6 ], which allows the estimation of the stress distribution in a cracked film. The second objective is to apply this theoretical approach to a system consisting of stiff coatings on ductile substrates, and then to investigate the mechanical response of these composites which were submitted to an elongation. This
0257-8972/99/$ – see front matter © 1999 Elsevier Science S.A. All rights reserved. PII S 02 5 7 -8 9 7 2 ( 9 8 ) 0 0 73 2 - 4
178
E. Harry et al. / Surface and Coatings Technology 111 (1999) 177–183
includes the determination of critical cracking stresses, fracture properties of the coatings that will be discussed through the Weibull analysis and in terms of the Griffith approach, and the examination of damage mechanisms with respect to the coatings structure.
2. Theoretical approach 2.1. Cracking of a deposited layer When considering the behavior of a tensile sample consisting of a brittle layer attached to a ductile substrate: when submitted to an elongation which follows a given direction (x) (see Fig. 1); both (the layer and the substrate), will first deform elastically. If we assume that Young’s modulus of the brittle layer is higher than that of the substrate, cracking of the layer is expected to start before plastic flow in the substrate. Then, by considering Young’s modulus of the layer (Ef) and the substrate (Es), and the critical cracking stress in the layer (sf ), that is experimentally accessible, the correxx,c sponding stress in the substrate (ss ) will be: 0 Es sf (1) ss = 0 Ef xx,c with ss
Fig. 1. (a) Schematic illustration of the cracking of a deposited layer and the plastic strain in the substrate at the crack tips. Stress redistribution in the substrate at the coating/substrate interface (b) and in the coating (c) at the crack vicinity. Each term is defined in the text.
free surfaces. The stress relaxation in the crack vicinity must indeed be limited to a zone extending over a distance d on both sides of the crack. The stress in the coating will then extend uniformly from zero at the crack surfaces to the critical cracking stress sf over the length d. On this distance, the xx,c coating stress is described by the following relation: x sf (x)= sf . xx d xx,c
(2)
The substrate stress can be expected to be the yield stress ss at the coating edges next to the crack. At the y crack vicinity, on the length d, the stress can be written: d−x (ss −ss ). ss (x)=ss + y 0 xx 0 d
(3)
Far from any crack surface (x>d), when increasing the elongation, the stress in the layer is supposed to raise up continuously, till reaching the critical value for opening new cracks (ssf ). The number of cracks xx,c which develop perpendicular to the tensile axis will increase. This crack evolution will redistribute the normal stresses acting in the layer and the stress level will be progressively lowered as the distance between two consecutive cracks tends to move closer. This process will develop until the saturation of cracks, which theoretically corresponds to a constant distance d among two consecutive cracks ( Fig. 2).
Fig. 2. (a) Schematic illustration of the cracking of a coating deposited on a substrate. The arrows indicate the direction of the applied tensile stress. Stress redistribution in the coating (b) at the crack vicinity; (c) between two consecutive cracks, the crack density being lower than the crack saturation density and the maximum stress in the coating corresponding to the critical cracking stress; (d) between two consecutive cracks, when the crack density reached the crack saturation density. The length among these cracks is minimal, and the global stress in the coating is lower than the critical cracking stress.
E. Harry et al. / Surface and Coatings Technology 111 (1999) 177–183
179
2.2. Strain energy release rate for crack extension The cracking of the layer will cause energy variations in the system. The net energy change DU can be determined from an energy balance for the system, when the film cracks, perfect adhesion between the layer and the substrate being assumed. This approach was used for Cr films on Al substrates [4], and has been previously described for W layers on stainless steel substrates [6,9]. The balance gives: (sf )2(tf)2 xx,c Ef
G A B
H
Ef
sf + xx,c (4) 앀3ss Es y F is a function of the elastic modulus ratio [4]. As the strain energy release rate for crack extension through the layer Gf is: c DU Gf = (5) c tf
DU=
pF
Fig. 3. Type of samples used for uniaxiale tensile tests. The arrows indicate the loading direction.
a microtensile device adapted to a scanning electron microscope (SEM ) [5]. Film surface is observed by SEM in order to detect the crack initiation and to follow the evolution of crack density versus the applied load or the system’s deformation. A measure of the average crack density D (cracks mm−1) is determined by counting the number of cracks in a given distance.
we obtain tf(sf )2 xx,c Gf = c Ef
C A B Ef
D
sf pF + xx,c . (6) 앀3ss Es y Assuming that the stress state in the layer, when it cracks, is tensile the mode I fracture toughness of the film can then be deduced: Kf =앀Gf Ef. c Ic
(7)
3. Experimental W and W(C ) coatings were deposited on stainless steel substrate by DCRMS. Their microstructural and basic mechanical properties were examined and in situ tensile experiments were performed on samples, consisting of W and W(C ) coatings on steel substrates to analyze the failure mechanisms. Parameters relative to the mechanical stability of the coatings, as the strain energy release rate [Eq. (6)] and the corresponding fracture toughness [Eq. (7)], were also determined. 3.1. Procedures Tungsten ( W ) and tungsten–carbon (14 at% C ) [ W(C )] coatings are deposited by DCRMS onto stainless steel substrates. The geometry of the systems is represented schematically in Fig. 3. Coating thickness extended from 2 to 16 mm and the substrate is 850 mm thick. Before coating deposition, the substrate surface is polished with diamond paste and cleaned. A detailed description of the deposition technique has been presented in a previous paper [6 ]. The beams are subjected to uniaxial tensile stress with
3.2. Results and discussion 3.2.1. Film properties Polycrystalline W sputtered coatings present a a-cubic phase, while the W(C ) coatings present a metastable interstitial solid solution of atoms of carbon in the same phase. Deposited on steel substrates, the W and W(C ) coatings generate high residual compressive stresses, of ca −3 GPa [6 ]. We may note that the corresponding residual stresses in the coatings remained similar for both of them (−3 GPa); showing no effect of the carbon content on this parameter. The hardness of the coatings was determined by Vickers indentation tests under 0.5 N contact load. It was of ca 12 GPa for the W coatings and 28 GPa for the W(C ) coatings, with increasing carbon content. With respect to the microstructure, the W coatings present a columnar structure with a grain diameter of ca 40 nm. Even though, the coatings rich in carbon showed a similar elongated texture of grains, the crystallites were smaller: of ca 6 nm in diameter, the diameter diminishing with the percent of added carbon. The hardness follows a Hall–Petch type relation, which gives semi empirically the increase of this parameter with the decrease of the grain size: H=H +kd−1/2. (8) 0 H and k are constant terms, H is the hardness 0 and d is the grain diameter. For the coatings, k=2.16 MPam−1/2 and H =11 MPa. 0 The Hall–Petch relation can also be related to the increase in hardness of W coatings (12 GPa) which present smaller grains as compared to the W bulk material presenting a grain size of 1 mm [10].
180
E. Harry et al. / Surface and Coatings Technology 111 (1999) 177–183
3.2.2. Failure of the coatings When the coating on substrate system is submitted to the tensile tests, the response of both the coating and the substrate is entirely elastic at the lower strains (<0.8%). As the coating is much stiffer and more brittle than the substrate, it cannot undergo significant extension. Then, at a critical deformation of the substrate es , the critical cracking stress sf is attained for the xx,c xx,c coating and failure occurs. The coating begins to crack, then the substrate’s deformation is still elastic. The critical cracking stress will be considered as the ‘‘crack onset’’. The critical cracking stress is determined experimentally, taking into account the residual stresses preexisting in the coating sf and the critical strain of the r substrate. Indeed, the critical cracking stress can be written: sf =Efes +sf . (9) xx,c xx,c r When considering the existence of defects in sputtered coatings, resulting from the growing process (structural imperfections) or previously existing on the substrate (roughness) [11], this stress may be associated to the presence of singularities pre-existing in the coatings. The resulting value of the critical cracking stress could then be lowered compared to that expected for a coating without defects. Taking into account the semi empirical common ratio between the hardness (H ) and the yield strength (s ) for y homogeneous and isotropic materials [12], applied to W and W(C ) films with hardness of 12 and 28 GPa, respectively: H=3s (10) y we may deduce that the tensile yield strength of any coatings we investigated are much higher than that of the corresponding stress in a bulk material. However, from our experiments ( Table 1) we detect a low critical cracking stress for both coatings, which is close to 500 MPa and lower than the values reported in the literature, for the W bulk material [12]. Besides, the
deduced fracture toughness values [Eq. (8)] are ranged from 1 to 2.5 MPa m−1/2 for W coatings and from 0.1 to 1 MPa m−1/2 for W(C ) films ( Table 1). These values appear to be lower than that of the tungsten bulk material of 10–20 MPa m−1/2 [12]. This tendency emphasizes the fact that our coatings are sensitive to pre-existing defects. For a non-homogeneous stress distribution, the value of the critical stress will be the fracture stress of the structure. Moreover, an earlier crack initiation is observed for the W(C ) coatings, which may not only depend on the already mentioned defects, but also on well known embrittlement effect induced by carbon segregation at the grain boundaries [13]. Then, assuming that cracking of the coatings initiates on defects (assumption that will be supported by a Weibull analysis), the size of these singularities can be estimated according to the Griffith approach. As a matter of fact, the fracture of materials can be described as a function of the defect size a: (11) Kf =sf 앀pa Ic xx,c The deduced values of the mean defect size are reported in Table 1. The results exhibit defect size as large as thickness of the films. It indicates that the defects may have grown from the substrate surface (from chemical impurities or asperities) during the coating deposition. Defects of this type are protruding conical features ( Fig. 4) and are called ‘‘growth defects’’. This defects, when emerging on the coating surface, can contribute to the surface roughness of the coating, resulting in dulllooking rough surface. For W(C ) coatings, the calculated values of the defect sizes are found to be slightly lower than the thickness of the coatings. This result may arise from the existence of both growth defects as large as the coating thickness and carbon segregation at grain boundaries.
Table 1 Experimental values of the critical strain applied to the substrate es when cracking the coating, the critical cracking stress for the xx,c coating sf [Eq. (9)], the fracture toughness Kf , [Eq. (7)] and the xx,c Ic defect size [Eq. (11)] with respect to the coating thickness tf tf (mm) W film 3.4 6.6 16.4 W(C) film 3.45 6.5 16
es xx,c
ss (MPa) xx,c
Kf (MPa m−1/2) Ic
a (mm)
0.85 0.867 0.87
400 404 348
1.350±6 1.860±6 2.470±5
3.6 6.7 16
0.78 0.81 0.54
120 240
0.350±2 1±0.2
2.7 5.53
Fig. 4. SEM micrograph of a growth defect through the thickness of a sputtered film.
181
E. Harry et al. / Surface and Coatings Technology 111 (1999) 177–183
From Eq. (6) values of the strain energy release rate for crack extension through the coating, Gf , can be c calculated. They are ranged from 2.5 to 14 J m−2 for the W films and from 0.07 to 1.2 J m−2 for the W(C ) coatings. According to the Griffith criterium (U=2), and the tungsten surface energy ca 3.3 J m−2 [14], we may note that the experimentally determined values for the W coatings remain in the order of magnitude of a thermodynamically predicted value, 6.6 J m−2. Generally, mechanically deduced values of rupture energies, when compared to thermodynamically surface free energy value, present discrepancies which sometimes are higher than an order of magnitude [15]. In our case the results seem to validate the experimental procedure we followed. The cracking phenomenon can be described in successive stages (Fig. 5). At the crack onset, the coating will then develop series of regular and parallel spaced cracks, perpendicular to the loading direction. These initial cracks will multiply rapidly after the crack onset. Their edges are sharp and well defined [6 ]. When increasing the composite deformation further, additional cracks progressively appear and the distance separating two consecutive cracks decreases. This evolution can be followed by the crack density parameter D which is defined as the number of cracks over a given length. Continuing the strain, this parameter which grows at the beginning of the deformation, will reach a constant value: the crack saturation density D , corresponding sat to a minimal length between two cracks. The vicinity of the crack free surfaces lowered the global stress level in the coating under the critical cracking stress sf . xx,c When the saturation of cracks is reached, if the deformation continues, no new cracks appear; but the existing ones will continue to open, with increasing plastic deformation in the substrate, concentrated at the crack tip. The experimental evolution of crack density is plotted versus the applied strain for W and W(C ) coatings in Fig. 6. An empirical relation, based on a Weibull type
(a)
(b) Fig. 6. Transverse crack density of W coatings (a) and W(C ) coatings (b) of thickness: &, 3.5 mm; $, 6.5 mm; and +, 16 mm versus longitudinal strain.
distribution function, was applied to describe the crack density as a function of the applied strain in the substrate es [16,17]: xx D(es )=D {1−exp[−A(es −es )a]}. (12) xx sat xx xx,c A and a are constant parameters which will depend on the film/substrate system. For our coatings, we noted that at the saturation, the corresponding crack densities, D , decreased with the sat coating thickness, showing an average intercrack spacing larger for thicker films. This dependence can be explained when considering the analytical approach of Mezin describing the stress distribution in a cracked film [17]: 2tf ss sf = 0 +sf − r pK xx K
Fig. 5. Typical evolution of the transverse crack density versus the substrate’s longitudinal strain. The different stages of damage are indicated. D is the saturation of crack density. sat
P
+L/2
∂sf (u) xx du. x−u ∂u 1
(13) −L/2 K is Young’s moduli ratio of the film and the substrate, tf the thickness of the film and L the distance separating two consecutive cracks. In this relation, the first term is relative to the uncracked film. The integral term represents the interaction induced by the proximity of the cracks and
182
E. Harry et al. / Surface and Coatings Technology 111 (1999) 177–183
lowering the stress level in the film. Thus, this relation shows that an increase in thickness should result in a more significant stress release in the coating, preventing any further crack propagation. Hence, the saturation crack density is lowered. The empirical equation which describes the dependence between the crack density at saturation and the coating thickness is in our case: B D = sat (tf)n
(14)
For our systems, the parameters B and n obtained from the experiments are: B=43.9, n=0.33 for W coatings and B=93.6, n=0.4 for W(C ) coatings. Therefore, in the empirical relation which describes the evolution of the crack density with respect to the applied strain to the substrate can be rewritten as: B {1−exp[−A(es −es )a]}. D(es )= xx xx,c xx (tf)n
(15)
Notice that the constant A and the exponent a, known as the Weibull modulus, are determined experimentally. They are respectively the ordinate at zero point and the slope of the line obtained from the plot of ln{−ln [1−(D/D )]} versus ln(es −es ). Experimental plots sat xx xx,c are reported in Fig. 7, for W and W(C ) coatings with different thickness. The values of the Weibull modulus are ranged from 0.923 to 1.021 for W layers, and from 0.686 to 0.767 for W(C ) layers, depending on the coating thickness. We may recall that the Weibull modulus expresses the statistical scatter of events: a high Weibull modulus indicates a low scatter [18]. The Weibull analysis gives a mathematical tool for predicting the fracture probability of one structure. In our case, the Weibull modulus appears to be small, reflecting a high probability of cracking of the coating and then the presence of numerous defects. As a comparison, soda-lime glass
Fig. 7. Experimental plots of ln{−ln[1−(D/D )]} versus sat ln(es −es ) for W films of thickness: &, 3.5 mm; $, 6.5 mm; +, xx xx,c 16 mm and for W(C ) films of thickness: %, 3.5 mm; #, 6.5 mm; 6, 16 mm. Each term is defined in the text.
has a Weibull modulus of 2–3 and polysilicon films have a value of 7–11 [18]. The Weibull modulus tells nothing on the severity of the defects or their location. However, the difference in Weibull modulus obtained for W and W(C ) films may indicate the existence of different types and/or densities of defects. When increasing the substrate strain to 20%, other types of cracks may appear, between the transverse cracks. These new cracking systems are activated by local complex stress fields, induced for example by defects, emerging on the substrate surface, as deformation bands or grain boundary displacements. However, even though these effects of singularities are activated only when reaching high strains, and develop a new cracking pattern in the coating, no debonding was observed. This revealed that the adhesion between the coatings and the substrate was good. We may recall that several authors reported qualitative relationship between adhesion and cracking phenomena. Some noted that an improved adhesion of a film is generally associated with an increase of crack density at saturation and no debonding even after being submitted to significant elongations [5,19]. In films, with poor adhesion, in particular those exhibiting buckling, a lower crack saturation density is generally reported [6 ]. In our study, it was not possible to characterize the interfacial adhesion, since no decohesion of the coatings from the substrate occurred even at the highest strains. However, scratch test experiments have been performed on coatings of this type to investigate the mechanical behavior of the films [20]. This method permitted to clarify the failure mechanisms and to rank coatings to delamination resistance.
4. Conclusion We performed in situ microtensile tests on systems consisting of W and W(C ) coatings deposited by DCRMS on steel substrates. The analysis of the mechanical response of the coatings was focused on their rupture properties. This was studied through the energy balance of the cracked system. The parameters which correspond to the rupture properties of the coatings were deduced: the strain energy release rate and the fracture toughness. The coatings were also characterized by the evolution of the crack densities with respect to the imposed deformation to the system, and the cracking probability was analyzed through the Weibull analysis. The calculated values of the Weibull modulus revealed a high probability of cracking for both coatings, supported by the low measured values of the fracture toughness, and the existence of different types and/or density of defects when considering pure metal coatings or carbon containing films with different thickness. Assuming defects as crack nucleation centers, an approximate value of the
E. Harry et al. / Surface and Coatings Technology 111 (1999) 177–183
defect size was determined in terms of the Griffith approach. This analysis reveals defects as large as coating thickness located at the coating/substrate interface and emerging at the coating surface. The analysis showed that the coatings rupture properties depended on both the type, the size and the density of structural defects. These intrinsic parameters modified the rupture properties, decreasing the fracture toughness when compared to bulk materials. Despite the identification of these embrittlement effects, and even though the substrate was deformed up to 20% in tension and the coatings cracked, our coatings remained attached to the substrate, proving a rather good interfacial adhesion in these systems.
References [1] E. Klokholm, IBM J. Res. Dev. 31 (1987) 5. [2] P.H. Wojciechowski, M.S. Mendolia, J. Vac. Sci. Technol. A 7 (3) (1989) 1282. [3] T.S. Chow, C.A. Liu, R.C. penwell, J. Polym. Sci. 14 (1976) 1305. [4] M.S. Hu, A.G. Evans, Acta Metall. 37 (3) (1989) 917. [5] M. Ignat, Key Eng. Mater. 116117 (1996) 279.
183
[6 ] E. Harry, International Conference on Metallurgical Coatings and Thin Films, Materials Research Society, 1998. [7] P. Juliet, A. Rouzaud, K. Aabadi, P. Monge-Cadet, Y. Pauleau, Thin Solid Films 290291 (1996) 232. [8] A. Rouzaud, E. Barbier, J. Ernoult, E. Quesnel, Thin Solid Films 270/271 (1995) 270. [9] E.Harry, Stabilite´ me´canique et modes d’endommagements de reveˆtements multicouches a` base de tungste`ne et de tungste`ne– carbone e´labore´s par PVD. Thesis, National Polytechnic Institute of Grenoble, Grenoble, France, 1998. [10] H.J. Frost, M.F. Ashby, Deformation–Mechanism Maps, 1st edn, Pergamon Press, New York, 1982. [11] D.M. Mattox, Surface Coat. Technol. 81 (1996) 8. [12] M.F. Asbhy, D.R.H. Jones, Mate´riaux, vol. 1, Dunod, Paris, 1991. [13] J.Y. Liu, S.C. Chang, J. Mater. Sci. 31 (1966) 4159. [14] J. Gerkema, A.R. Miedema, Surf. Sci. 124 (1983) 351. [15] J.H. Selvarian, D. O’Neil, Thin Solid Films 235 (1993) 129. [16 ] W. Weibull, J. Appl. Mech. September (1951) 293. [17] A. Mezin, J.-P. Chambard, J. Lepage, M. Nivoit, Thin Solid Films 185 (1990) 57. [18] S. Greek, F. Ericson, S. Johansson, J.-A. Schweitz, Thin Solid Films 292 (1997) 247. [19] M. Ignat, P. Scafidi, E. Duloisy, J.Dijon, in: P. Borgesen, J.C. Coburn, J.E. Sanchez, K.P. Rodbell, W.F. Filter (Eds.), Materials Reliability in Microelectronics IV, vol. 338, Material Research Society, Pittsburgh, 1994, p. 135. [20] E. Harry et al., Conference on Plasma Surface Engineering, Garmisch-Partenkirschen, 1998.