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Adhesion strength of Ni film on Ti substrate characterized by three-point bend test, peel test and theoretic calculation
Materials Science and Engineering A 419 (2006) 233–237
Adhesion strength of Ni film on Ti substrate characterized by three-point bend test, peel test and theoretic calculation F.Z. Ren ∗ , P. Liu, S.G. Jia, B.H. Tian, J.H. Su School of Materials Science and Engineering, Henan University of Science and Technology, Luoyang 471003, China Received in revised form 22 December 2005; accepted 22 December 2005
Abstract Electroplating was employed to fabricate the Ni film on the Ti substrate. Adhesion strength of Ni film on Ti substrate was determined using the three-point bend technique that was proposed in standard mechanics test. The experimental results demonstrate that the interface fracture energies obviously increase with the roughness of Ti substrates, and are independence with the thickness of Ni films. Moreover, the adhesion strength of Ni film on Ti substrate was also measured by peel test, and was evaluated by Miedema model of experiential electron theory. The intrinsic interface fracture energy measured by three-point bend test is reasonable agreement with that obtained by theoretical calculation of Miedema model, and is roughly comparable to that by peel test. © 2006 Elsevier B.V. All rights reserved. Keywords: Interface fracture energy; Fracture mechanics test; Peel test; Miedema model of experiential electron theory
1. Introduction The films are widely used in micro-electronic devices and structure components. Mechanical properties, which mainly include the elastic modulus of the film, residual stress in the film, yield stress of the film and adhesion strength of the film to the substrate, have a great influence upon the performance, the reliability and service life of the devices and the components. The adhesion strength between film and substrate is particularly of major concern because of the film-coated structure failure due to interfacial debonding. The intrinsic adhesion between two materials is associated with inter-atomic or intermolecular force, for which the quantitative assessment still remains as challenge [1]. Many mechanics testing methodologies have been designed to measure adhesion. For practical application, the adhesion properties of film/substrate system are usually characterized by the critical load measured in a scratch test or by micro-indenter data. The values obtained with both methods are a mixture of the adhesion strength and plastic and/or elastic properties of the substrate and the film materials [2]. Thus the interpretation of results is complex and is not well developed with respect to the
∗
Corresponding author. Tel.: +86 379 65318870; fax: +86 379 64230597. E-mail address: [email protected] (F.Z. Ren).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2005.12.024
determination of adhesion strength data. Since the blister test became known to the fracture community in 1961, many advantages have been realized, such as the avoidance of excessive plastic deformation due to the small contact angle at the crack front and no direct contact with loading grips or clamps. There are, however, some fundamental disadvantages which discourage investigators from adopting the technique. The blister crack propagates catastrophically once the applied pressure loaded by a constant liquid or gas pressure reaches a critical value. Fabrication of specimens with different initial crack size is both tedious and costly. In a peel test, since plastic deformation and high bend angle appear at the crack tip during peeling, the peel strength does not directly represent the actual interface fracture energy between film and substrate. Recently, Kim and Aravas [3], Moidu et al. [4,5] and Kinloch et al. [6] assumed strip or film as elastic-perfectly plastic or bilinear hardening materials, and assumed the attached part of the strip or film as an elasticplastic beam that was clamped on the elastic foundation. Then they analyzed the plastic deformation of the strip or film and calculated the energy dissipated during peeling in detail. But, the assumption is partly approximation to reality, and the obtained results are imprecision. Fracture mechanics tests provide data such as the fracture energy and the fracture toughness that are well-defined quantities for brittle materials. The adhesion strength of film/substrate system can also be characterized by fracture mechanics tests.
234
F.Z. Ren et al. / Materials Science and Engineering A 419 (2006) 233–237
However, few papers are concerned with the fracture mechanics tests such as the three-point bend test used to measure the adhesion of a specific film/substrate systems, especially with comparative studies among fracture mechanics tests and other methods. The three-point bend test specimens can yield data for the interface fracture energy, which provide information on the work of adhesion of a specific film/substrate system if a crack is propagated along the film/substrate interface. In the present work, the interface fracture energies of Ni films with different thickness on Ti substrates with different surface roughness were evaluated by the three-point bend technique. Moreover, comparative study of the intrinsic interface fracture energy of Ni film on Ti substrate by three-point bend test, peel test and Miedema model of experiential electron theory was conducted. 2. Experimental details 2.1. Films preparation and residual stress measurement Electronic depositing technique was employed to fabricate the Ni films on Ti substrates, the thickness of film was commanded by “Time Controlling” technique provided the electric current was stable with the relative fluctuation being less than 5%. The main compositions of electroplating solution are given in Table 1, and the temperature of the electronic plating solution was controlled at 50–55 ◦ C. A commercial tape was pasted on some parts of Ti substrate in order to prevent the corresponding parts from coating Ni films. X-ray diffractometer with Cr K␣ radiation was employed to measure the longitudinal and transverse components of the normal residual stress in Ni films. Reflection from (2 2 0) crystal planes was used. In order to fabricate three-point bend test specimen, Ti samples 8 mm × 16 mm × 35 mm with different surface roughness were coated by Ni films with different thickness on the top side 8 mm × 16 mm. The surface roughness of Ti substrates was 0.1, 0.5, 1.0 and 2.2 m, and the thickness of the Ni films was 8, 12 and 20 m. In peel test, the size of Ti substrate was 5 mm × 14 mm × 200 mm, and the roughness of electronic plating surface was 0.1 m. The length and width of Ni film were 170 and 10 mm, respectively, and the thickness 1 m. 2.2. Three-point bend specimens preparation and critical fracture loads measurement
Fig. 1. Specimen for three-point bend test.
35 mm) coated by Ni film on the top side (8 mm × 16 mm), the film was first peeled off about a half of the length of the Ni film acting as pre-crack. Then the peeling part of the Ni film and Ti substrate was colored in liquid in order to easily measure the length of the pre-crack after fracture. After the peeling and coloring processes, a similar piece of Ti was bonded by a strong adhesive as the counterpart on the top of Ni film. A schematic diagram of three-point bend test is shown in Fig. 2. The interface of Ni film and Ti substrate was in the middle of two supports, and application point of the load F was just on top of the interface. Test equipment was Instron 1195. A pressure transducer with the resolution of 1 N was employed to measure the load, a extensometer was used to measure the crack opening displacement. The distance between the supports L was 48 mm. For the three-point bend test, the critical loads of two kinds of specimens were measured. The first kind of specimens possesses identical surface roughness of the substrates and various thicknesses of the films, the second kind possesses various surface roughnesses of the substrates and identical thickness of the films. Because of the scatter of fracture mechanics data, a set of five identical specimens had to be tested. 2.3. Peel strength measurement Peeling measurement was carried out at a peel angle θ = 90◦ (see Fig. 3). The critical peel load per width (termed as peel strength) corresponding to the slow propagation of the interface crack at a rate of 1–4 mm/min during peeling was determined visually. Five specimens with thickness 1 m were tested.
Fig. 1 shows the design of the specimen used for the threepoint bend test. For Ti substrate sample (8 mm × 16 mm × Table 1 Main compositions of electroplating solution Na2 SO4 (g l−1 ) MgCl2 (g l−1 ) Ni2 CO3 (g l−1 ) NiCl (g l−1 ) HCl (ml l−1 ) H2 SO4 (ml l−1 ) H2 O
120 5 5 50 5 10 Other
Fig. 2. Schematic illustration for determining interface fracture energy.
F.Z. Ren et al. / Materials Science and Engineering A 419 (2006) 233–237
235
ual strain energy) stored as internal stress which facilitates the removal of the film from the substrate, i.e. G = Gc + Gr ,
(5)
If the longitudinal component of the normal residual stress is σ rl , while the transverse one is σ rt , for elastic material it also yields Gr =
h (σ 2 + σrl2 − 2νf σrt σrl ). 2Ef rt
(6)
Fig. 3. Peel test.
3. Theoretical model of experiment and Miedema model of experiential electron theory
where h is the film thickness. The value of residual strain energy (Gr ) is closely related to the values of the film thickness (h) and internal stress (σ rl , σ rt ).
3.1. Three-point bend test
3.2. Peel test
If a crack is propagated along the film/substrate interface, the fracture toughness of the interface (Kc ) can be calculated as [7] a Fc L Kc = (1 + α)Y , (1) Bw3/2 w
For slow peeling, the interface fracture energy G may be derived from an energy-balance argument [6,10], such that
where Fc is the maximum load (i.e. fracture load), L the distance between supports, B the specimen width, α one of the Dundur’s parameter, Y (a/w) a function of the ratio of the pre-crack length a to the specimen height w. This equation is an approximation derived from linear elastic fracture mechanics for materials in the limit of very thin joints. The measured interface fracture energy Gc is defined as [7] Gc =
(1 − β2 )Kc2 , E∗
G=
in which, β is the Young’s modulus of the interface and given by [8] 1 1 1 + (3 − 4νs ) 1 + (3 − 4νf ) = , (3) + E∗ 16 µs µf where µ is the shear modulus and ν is the Poisson ratio. The suffixes s and f denote the substrate and the film, respectively. For plane stress, the Dundur’s parameters can be expressed as [9] 1 (νs /Es ) − (νf /Ef ) (1/Es ) − (1/Ef ) , β= α− . α= (1/Es ) + (1/Ef ) 2 (1/Es ) + (1/Ef ) (4) For plane strain, E may be replaced by E/(1 − ν2 ), ν by ν/(1 − ν), E and ν are the elastic modulus and Poisson ratio, respectively. The width of the film is far greater than the thickness, the deformation state near interface is in plane strain. In fact there exists internal stress (i.e. residual stress) in film due to the difference of thermal expansion coefficient, as well as other physical properties, etc. So, the effect of internal stress on the interface fracture energy must be taken into consideration. The interface fracture energy G is the sum of the measured interface fracture energy Gc and the energy Gr (termed as resid-
(7)
where P is the critical peeling force, b the width of the film on the substrate, P/b peel strength, θ peel angle (see Fig. 3), Gdb the work expenditure per unit advance of the interface crack for per unit width of the film. If the plastic bend of the peel arm is too small to induce significant effect, the term concerning plastic bend is can be ignored, that is to say Gdb = 0, then
(2)
is the second Dundur’s parameter, E*
P (1 − cos θ) − Gdb + Gr , b
G=
P (1 − cos θ) + Gr . b
(8)
3.3. Miedema model of experiential electron theory According to Miedema model of experiential electron theory [11], for two kinds of the solid metals (A and B) clinging together closely, at zero temperature the intrinsic interface fracture energy G0 can be described by G0 = 0.85(γA0 + γB0 ) −
HA0 in B 2/3
c0 V A
,
(9)
where γA0 and γB0 are the surface energies of solid A and B at zero temperature, respectively, constant c0 equals 4.5 × 108 , VA is molar volume of the solid A. 2/3 HA0 in B /(c0 VA ) is far smaller than 0.85 (γA0 + γB0 ), G0 is mainly determined by 0.85 (γA0 + γB0 ) [11]. If the material keeps identical state, the intrinsic interface fracture energy varies weakly with temperature. So, the intrinsic interface fracture energy G at room temperature is nearly equal to that at zero temperature, i.e. G ≈ 0.85(γA0 + γB0 ).
(10)
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Table 2 Residual stress (σ rl , σ rt ) and residual strain energies Gr h (m) σ rt (MPa) σ rl (MPa) Gr (J m−2 )
8 −37 −121 0.25
12 −95 −140 0.59
20 −109 −154 1.22
Table 3 Mechanical properties of Ti substrate and Ni film Materials
Elastic modulus, E (GPa)
Shear modulus, µ (GPa)
Poisson ratio, ν
Ti Ni
116 210
44 73
0.3 0.3 Fig. 5. The relationships between the interface fracture energy and the thickness of Ni films.
4. Results and analysis 4.1. Interface fracture energies obtained by three-point bend test For Ni films with various thickness, measured residual stress (σ rl , σ rt ) and the calculated residual strain energies (Gr ) using Eq. (6) are listed in Table 2. It was found that crack propagation was along the film/substrate interface. Thus measured fracture toughness and measured fracture energy are just interface fracture toughness and interface fracture energy. In relation curve between the load F and the crack opening displacement δ, Fc is the maximum load (fracture load). F increases linearly with δ in the regime of 0 to Fc , and then decreases sharply. So, Fc can be used to calculate Kc . Mechanical properties of Ti substrate and Ni film are listed in Table 3. By the data in Table 3 and Fc , Gc and G were determined from formula (1) to (6). The interface fracture energies G of Ni films with the thickness h = 20 m on Ti substrates with the various the surface roughness Ra are shown in Fig. 4. Fig. 4 depicts that the interface fracture energies G are about the same and do not very scatter at identical substrate surface roughness and identical film thickness, especially at smaller surface roughness. The interface fracture energies G decrease with the surface roughness of Ti
Fig. 4. Variation of the interface fracture energy with the roughness of Ti substrate.
substrate and then tend to be stable values, which results from the decreasing of the imbedding action between Ni film and Ti substrate. Fig. 5 shows the relationships between the interface fracture energy and the thickness of Ni films for Ti substrates with the identical roughness Ra = 0.1 m. Within the studied range of the film thickness (8–20 m), the measured interface fracture energy Gc obviously varies with the film thickness h duo to the effect of the residual strain energy, but the interface fracture energy G is relatively stable. This shows that Gc is strongly affected by the film thickness h, and G not. The above experimental results reveal that the interface fracture energy G is not influenced by the film thickness, and is a small and stable value at smaller roughness of the substrates. That is to say that the interface fracture energy G is a stable value under deducting the influences of the internal stress in the film and the imbed between Ni film and Ti substrate. So, the interface fracture energy G at smaller roughness can be regarded as a proper “material parameter”, and is also called intrinsic interface fracture energy. It is G = 3.28–3.91 J m−2 . 4.2. Comparative study of the intrinsic interface fracture energy by three-point bend test, peel test and Miedema model In peel test, the peel strength decreases with an increase in the residual stress, and changes with the peel angle and film thickness. The interface fracture energy is relatively stable, which does not depend upon above mentioned parameters [6]. As to a given residual stress gradient, the total residual strain energy increases with the film thickness, which leads to a decrease of peel strength with the thickness of the film. The smaller peel strength results in a larger measurement error. Thus, smaller thickness of Ni film with h = 1 m was chosen in the peel test. The peeling samples showed a clear interface failure behavior, and Ni films were completely removed from Ti substrates. So the measured fracture energies were the interface fracture energies. The peel arm of Ni film was straight after peeling, which indicated that plastic bend deformation did not occur. So, Gdb = 0. The residual strain energy Gr is too small to induce significant effect on the interface fracture energy at smaller thick-
F.Z. Ren et al. / Materials Science and Engineering A 419 (2006) 233–237
ness, and then can be ignored [12]. In the peel test, at a smaller film thickness 1 m, Gr was ignored. At very small roughness value Ra = 0.1 m, the influence of imbed between Ni film and Ti substrate on the interface fracture energy could be ignored. Under above mentioned conditions, the interface fracture energy G obtained by peel test was roughly regarded as the intrinsic interface fracture energy, and about 2.30 ± 0.34 J m−2 . The interface between Ni film and Ti substrate should be clear because the diffusion in interface region is difficult at low electroplating temperature. This circumstance is consistent with the assuming precondition of Miedema model of experiential electron theory. The surface energies of solid Ti and Ni at zero temperature are 2.10 and 2.45 J m−2 , respectively [11]. Intrinsic interface fracture energy G was about 3.87 J m−2 evaluated by Miedema model. The intrinsic interface fracture energy measured by threepoint bend test is reasonable agreement with that obtained by Miedema model, and is comparable to that by peel test, roughly imparting validity to three approaches.
237
used to measure the interface fracture energy duo to crack propagation only through the interface. (2) The interface fracture energies obviously increase with the roughness of Ti substrates, and is independent of the thickness of Ni films. (3) The intrinsic interface fracture energy measured by threepoint bend test is reasonable agreement with that obtained by theoretical calculation of Miedema model, and is comparable to that by peel test, roughly imparting validity to three approaches. Acknowledgements The authors acknowledge the Natural Science Foundation of Henan Province for its kind support for the program under the research Grant No. 0411050100. They also would like to express their appreciation for financial support from the Program for Young Key Teacher in University of Henan Province (2005-461) and the Key Technologic Program of Henan Province through No. 0424290064.
5. Applicable conditions of three-point bend test References The results of three-point bend test can be well interpreted by fracture mechanics, but this kind of test has an upper detection limit for the adhesion strength. An upper limitation of this testing method is the adhesion strength of the film. If crack propagation is easier through the adhesive coating or the substrate than along the interface, then the fracture test fails. The stress field of crack tip will obviously change at smaller stiff of the adhesive coating and smaller thickness of the film. The detailed studies in this aspect should be carried out. In our fracture mechanics test, preparing pre-crack method only applies to the flexible film/rigid substrate system with weakening adhesion strength between the film and the substrate. For the film/substrate system with higher adhesion strength, a weakly bonded metal or carbon film or the oxide scale on one side of a coated surface of substrate can act as a notch or a pre-crack. 6. Conclusion (1) For Ni film on Ti substrate system produced by electronic depositing technique, the fracture mechanics test could be
[1] M. Zheng, Y.J. Su, L.Q. Chen, T.Y. Zhang, Theor. Appl. Fract. Mech. 32 (1999) 75–80. [2] P.J. Steinmann, Y. Tardy, H.E. Hintermann, Thin Solid Films 154 (1987) 339–349. [3] K.S. Kim, N. Aravas, Int. J. Solids Struct. 24 (1988) 417–435. [4] A.K. Moidu, A.N. Sinclair, J.K. Spelt, J. Test. Eval. 23 (1995) 241– 253. [5] A.K. Moidu, A.N. Sinclair, J.K. Spelt, J. Test. Eval. 26 (1998) 247– 254. [6] A.J. Kinloch, C.C. Lau, J.G. Williams, Int. J. Fract. 66 (1994) 45– 70. [7] T. Suga, G. Elsser, Z. Werkstofftech 16 (1985) 75–80. [8] D. Muller, Y.R. Cho, E. Fromm, Surf. Coat. Technol. 74–75 (1995) 849–856. [9] M. Charalambides, A.J. Kinloch, Y. Wang, J.G. Williams, Int. J. Fract. 54 (1992) 269–291. [10] F.Z. Ren, W.Z. Zhao, G.S. Zhou, X.H. Ju, M. Zheng, Met. Mater. Int. 8 (2002) 129–134. [11] F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema, A.K. Niessen, Cohesion in Metals, North-Holland Publishing Corporation, Amsterdam, 1988, pp. 655–693. [12] A.N. Gent, L.H. Lewandowski, J. Appl. Polym. Sci. 33 (1987) 1567–1577.
Adhesion strength of Ni film on Ti substrate characterized by three-point bend test, peel test and theoretic calculation F.Z. Ren ∗ , P. Liu, S.G. Jia, B.H. Tian, J.H. Su School of Materials Science and Engineering, Henan University of Science and Technology, Luoyang 471003, China Received in revised form 22 December 2005; accepted 22 December 2005
Abstract Electroplating was employed to fabricate the Ni film on the Ti substrate. Adhesion strength of Ni film on Ti substrate was determined using the three-point bend technique that was proposed in standard mechanics test. The experimental results demonstrate that the interface fracture energies obviously increase with the roughness of Ti substrates, and are independence with the thickness of Ni films. Moreover, the adhesion strength of Ni film on Ti substrate was also measured by peel test, and was evaluated by Miedema model of experiential electron theory. The intrinsic interface fracture energy measured by three-point bend test is reasonable agreement with that obtained by theoretical calculation of Miedema model, and is roughly comparable to that by peel test. © 2006 Elsevier B.V. All rights reserved. Keywords: Interface fracture energy; Fracture mechanics test; Peel test; Miedema model of experiential electron theory
1. Introduction The films are widely used in micro-electronic devices and structure components. Mechanical properties, which mainly include the elastic modulus of the film, residual stress in the film, yield stress of the film and adhesion strength of the film to the substrate, have a great influence upon the performance, the reliability and service life of the devices and the components. The adhesion strength between film and substrate is particularly of major concern because of the film-coated structure failure due to interfacial debonding. The intrinsic adhesion between two materials is associated with inter-atomic or intermolecular force, for which the quantitative assessment still remains as challenge [1]. Many mechanics testing methodologies have been designed to measure adhesion. For practical application, the adhesion properties of film/substrate system are usually characterized by the critical load measured in a scratch test or by micro-indenter data. The values obtained with both methods are a mixture of the adhesion strength and plastic and/or elastic properties of the substrate and the film materials [2]. Thus the interpretation of results is complex and is not well developed with respect to the
∗
Corresponding author. Tel.: +86 379 65318870; fax: +86 379 64230597. E-mail address: [email protected] (F.Z. Ren).
0921-5093/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2005.12.024
determination of adhesion strength data. Since the blister test became known to the fracture community in 1961, many advantages have been realized, such as the avoidance of excessive plastic deformation due to the small contact angle at the crack front and no direct contact with loading grips or clamps. There are, however, some fundamental disadvantages which discourage investigators from adopting the technique. The blister crack propagates catastrophically once the applied pressure loaded by a constant liquid or gas pressure reaches a critical value. Fabrication of specimens with different initial crack size is both tedious and costly. In a peel test, since plastic deformation and high bend angle appear at the crack tip during peeling, the peel strength does not directly represent the actual interface fracture energy between film and substrate. Recently, Kim and Aravas [3], Moidu et al. [4,5] and Kinloch et al. [6] assumed strip or film as elastic-perfectly plastic or bilinear hardening materials, and assumed the attached part of the strip or film as an elasticplastic beam that was clamped on the elastic foundation. Then they analyzed the plastic deformation of the strip or film and calculated the energy dissipated during peeling in detail. But, the assumption is partly approximation to reality, and the obtained results are imprecision. Fracture mechanics tests provide data such as the fracture energy and the fracture toughness that are well-defined quantities for brittle materials. The adhesion strength of film/substrate system can also be characterized by fracture mechanics tests.
234
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However, few papers are concerned with the fracture mechanics tests such as the three-point bend test used to measure the adhesion of a specific film/substrate systems, especially with comparative studies among fracture mechanics tests and other methods. The three-point bend test specimens can yield data for the interface fracture energy, which provide information on the work of adhesion of a specific film/substrate system if a crack is propagated along the film/substrate interface. In the present work, the interface fracture energies of Ni films with different thickness on Ti substrates with different surface roughness were evaluated by the three-point bend technique. Moreover, comparative study of the intrinsic interface fracture energy of Ni film on Ti substrate by three-point bend test, peel test and Miedema model of experiential electron theory was conducted. 2. Experimental details 2.1. Films preparation and residual stress measurement Electronic depositing technique was employed to fabricate the Ni films on Ti substrates, the thickness of film was commanded by “Time Controlling” technique provided the electric current was stable with the relative fluctuation being less than 5%. The main compositions of electroplating solution are given in Table 1, and the temperature of the electronic plating solution was controlled at 50–55 ◦ C. A commercial tape was pasted on some parts of Ti substrate in order to prevent the corresponding parts from coating Ni films. X-ray diffractometer with Cr K␣ radiation was employed to measure the longitudinal and transverse components of the normal residual stress in Ni films. Reflection from (2 2 0) crystal planes was used. In order to fabricate three-point bend test specimen, Ti samples 8 mm × 16 mm × 35 mm with different surface roughness were coated by Ni films with different thickness on the top side 8 mm × 16 mm. The surface roughness of Ti substrates was 0.1, 0.5, 1.0 and 2.2 m, and the thickness of the Ni films was 8, 12 and 20 m. In peel test, the size of Ti substrate was 5 mm × 14 mm × 200 mm, and the roughness of electronic plating surface was 0.1 m. The length and width of Ni film were 170 and 10 mm, respectively, and the thickness 1 m. 2.2. Three-point bend specimens preparation and critical fracture loads measurement
Fig. 1. Specimen for three-point bend test.
35 mm) coated by Ni film on the top side (8 mm × 16 mm), the film was first peeled off about a half of the length of the Ni film acting as pre-crack. Then the peeling part of the Ni film and Ti substrate was colored in liquid in order to easily measure the length of the pre-crack after fracture. After the peeling and coloring processes, a similar piece of Ti was bonded by a strong adhesive as the counterpart on the top of Ni film. A schematic diagram of three-point bend test is shown in Fig. 2. The interface of Ni film and Ti substrate was in the middle of two supports, and application point of the load F was just on top of the interface. Test equipment was Instron 1195. A pressure transducer with the resolution of 1 N was employed to measure the load, a extensometer was used to measure the crack opening displacement. The distance between the supports L was 48 mm. For the three-point bend test, the critical loads of two kinds of specimens were measured. The first kind of specimens possesses identical surface roughness of the substrates and various thicknesses of the films, the second kind possesses various surface roughnesses of the substrates and identical thickness of the films. Because of the scatter of fracture mechanics data, a set of five identical specimens had to be tested. 2.3. Peel strength measurement Peeling measurement was carried out at a peel angle θ = 90◦ (see Fig. 3). The critical peel load per width (termed as peel strength) corresponding to the slow propagation of the interface crack at a rate of 1–4 mm/min during peeling was determined visually. Five specimens with thickness 1 m were tested.
Fig. 1 shows the design of the specimen used for the threepoint bend test. For Ti substrate sample (8 mm × 16 mm × Table 1 Main compositions of electroplating solution Na2 SO4 (g l−1 ) MgCl2 (g l−1 ) Ni2 CO3 (g l−1 ) NiCl (g l−1 ) HCl (ml l−1 ) H2 SO4 (ml l−1 ) H2 O
120 5 5 50 5 10 Other
Fig. 2. Schematic illustration for determining interface fracture energy.
F.Z. Ren et al. / Materials Science and Engineering A 419 (2006) 233–237
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ual strain energy) stored as internal stress which facilitates the removal of the film from the substrate, i.e. G = Gc + Gr ,
(5)
If the longitudinal component of the normal residual stress is σ rl , while the transverse one is σ rt , for elastic material it also yields Gr =
h (σ 2 + σrl2 − 2νf σrt σrl ). 2Ef rt
(6)
Fig. 3. Peel test.
3. Theoretical model of experiment and Miedema model of experiential electron theory
where h is the film thickness. The value of residual strain energy (Gr ) is closely related to the values of the film thickness (h) and internal stress (σ rl , σ rt ).
3.1. Three-point bend test
3.2. Peel test
If a crack is propagated along the film/substrate interface, the fracture toughness of the interface (Kc ) can be calculated as [7] a Fc L Kc = (1 + α)Y , (1) Bw3/2 w
For slow peeling, the interface fracture energy G may be derived from an energy-balance argument [6,10], such that
where Fc is the maximum load (i.e. fracture load), L the distance between supports, B the specimen width, α one of the Dundur’s parameter, Y (a/w) a function of the ratio of the pre-crack length a to the specimen height w. This equation is an approximation derived from linear elastic fracture mechanics for materials in the limit of very thin joints. The measured interface fracture energy Gc is defined as [7] Gc =
(1 − β2 )Kc2 , E∗
G=
in which, β is the Young’s modulus of the interface and given by [8] 1 1 1 + (3 − 4νs ) 1 + (3 − 4νf ) = , (3) + E∗ 16 µs µf where µ is the shear modulus and ν is the Poisson ratio. The suffixes s and f denote the substrate and the film, respectively. For plane stress, the Dundur’s parameters can be expressed as [9] 1 (νs /Es ) − (νf /Ef ) (1/Es ) − (1/Ef ) , β= α− . α= (1/Es ) + (1/Ef ) 2 (1/Es ) + (1/Ef ) (4) For plane strain, E may be replaced by E/(1 − ν2 ), ν by ν/(1 − ν), E and ν are the elastic modulus and Poisson ratio, respectively. The width of the film is far greater than the thickness, the deformation state near interface is in plane strain. In fact there exists internal stress (i.e. residual stress) in film due to the difference of thermal expansion coefficient, as well as other physical properties, etc. So, the effect of internal stress on the interface fracture energy must be taken into consideration. The interface fracture energy G is the sum of the measured interface fracture energy Gc and the energy Gr (termed as resid-
(7)
where P is the critical peeling force, b the width of the film on the substrate, P/b peel strength, θ peel angle (see Fig. 3), Gdb the work expenditure per unit advance of the interface crack for per unit width of the film. If the plastic bend of the peel arm is too small to induce significant effect, the term concerning plastic bend is can be ignored, that is to say Gdb = 0, then
(2)
is the second Dundur’s parameter, E*
P (1 − cos θ) − Gdb + Gr , b
G=
P (1 − cos θ) + Gr . b
(8)
3.3. Miedema model of experiential electron theory According to Miedema model of experiential electron theory [11], for two kinds of the solid metals (A and B) clinging together closely, at zero temperature the intrinsic interface fracture energy G0 can be described by G0 = 0.85(γA0 + γB0 ) −
HA0 in B 2/3
c0 V A
,
(9)
where γA0 and γB0 are the surface energies of solid A and B at zero temperature, respectively, constant c0 equals 4.5 × 108 , VA is molar volume of the solid A. 2/3 HA0 in B /(c0 VA ) is far smaller than 0.85 (γA0 + γB0 ), G0 is mainly determined by 0.85 (γA0 + γB0 ) [11]. If the material keeps identical state, the intrinsic interface fracture energy varies weakly with temperature. So, the intrinsic interface fracture energy G at room temperature is nearly equal to that at zero temperature, i.e. G ≈ 0.85(γA0 + γB0 ).
(10)
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Table 2 Residual stress (σ rl , σ rt ) and residual strain energies Gr h (m) σ rt (MPa) σ rl (MPa) Gr (J m−2 )
8 −37 −121 0.25
12 −95 −140 0.59
20 −109 −154 1.22
Table 3 Mechanical properties of Ti substrate and Ni film Materials
Elastic modulus, E (GPa)
Shear modulus, µ (GPa)
Poisson ratio, ν
Ti Ni
116 210
44 73
0.3 0.3 Fig. 5. The relationships between the interface fracture energy and the thickness of Ni films.
4. Results and analysis 4.1. Interface fracture energies obtained by three-point bend test For Ni films with various thickness, measured residual stress (σ rl , σ rt ) and the calculated residual strain energies (Gr ) using Eq. (6) are listed in Table 2. It was found that crack propagation was along the film/substrate interface. Thus measured fracture toughness and measured fracture energy are just interface fracture toughness and interface fracture energy. In relation curve between the load F and the crack opening displacement δ, Fc is the maximum load (fracture load). F increases linearly with δ in the regime of 0 to Fc , and then decreases sharply. So, Fc can be used to calculate Kc . Mechanical properties of Ti substrate and Ni film are listed in Table 3. By the data in Table 3 and Fc , Gc and G were determined from formula (1) to (6). The interface fracture energies G of Ni films with the thickness h = 20 m on Ti substrates with the various the surface roughness Ra are shown in Fig. 4. Fig. 4 depicts that the interface fracture energies G are about the same and do not very scatter at identical substrate surface roughness and identical film thickness, especially at smaller surface roughness. The interface fracture energies G decrease with the surface roughness of Ti
Fig. 4. Variation of the interface fracture energy with the roughness of Ti substrate.
substrate and then tend to be stable values, which results from the decreasing of the imbedding action between Ni film and Ti substrate. Fig. 5 shows the relationships between the interface fracture energy and the thickness of Ni films for Ti substrates with the identical roughness Ra = 0.1 m. Within the studied range of the film thickness (8–20 m), the measured interface fracture energy Gc obviously varies with the film thickness h duo to the effect of the residual strain energy, but the interface fracture energy G is relatively stable. This shows that Gc is strongly affected by the film thickness h, and G not. The above experimental results reveal that the interface fracture energy G is not influenced by the film thickness, and is a small and stable value at smaller roughness of the substrates. That is to say that the interface fracture energy G is a stable value under deducting the influences of the internal stress in the film and the imbed between Ni film and Ti substrate. So, the interface fracture energy G at smaller roughness can be regarded as a proper “material parameter”, and is also called intrinsic interface fracture energy. It is G = 3.28–3.91 J m−2 . 4.2. Comparative study of the intrinsic interface fracture energy by three-point bend test, peel test and Miedema model In peel test, the peel strength decreases with an increase in the residual stress, and changes with the peel angle and film thickness. The interface fracture energy is relatively stable, which does not depend upon above mentioned parameters [6]. As to a given residual stress gradient, the total residual strain energy increases with the film thickness, which leads to a decrease of peel strength with the thickness of the film. The smaller peel strength results in a larger measurement error. Thus, smaller thickness of Ni film with h = 1 m was chosen in the peel test. The peeling samples showed a clear interface failure behavior, and Ni films were completely removed from Ti substrates. So the measured fracture energies were the interface fracture energies. The peel arm of Ni film was straight after peeling, which indicated that plastic bend deformation did not occur. So, Gdb = 0. The residual strain energy Gr is too small to induce significant effect on the interface fracture energy at smaller thick-
F.Z. Ren et al. / Materials Science and Engineering A 419 (2006) 233–237
ness, and then can be ignored [12]. In the peel test, at a smaller film thickness 1 m, Gr was ignored. At very small roughness value Ra = 0.1 m, the influence of imbed between Ni film and Ti substrate on the interface fracture energy could be ignored. Under above mentioned conditions, the interface fracture energy G obtained by peel test was roughly regarded as the intrinsic interface fracture energy, and about 2.30 ± 0.34 J m−2 . The interface between Ni film and Ti substrate should be clear because the diffusion in interface region is difficult at low electroplating temperature. This circumstance is consistent with the assuming precondition of Miedema model of experiential electron theory. The surface energies of solid Ti and Ni at zero temperature are 2.10 and 2.45 J m−2 , respectively [11]. Intrinsic interface fracture energy G was about 3.87 J m−2 evaluated by Miedema model. The intrinsic interface fracture energy measured by threepoint bend test is reasonable agreement with that obtained by Miedema model, and is comparable to that by peel test, roughly imparting validity to three approaches.
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used to measure the interface fracture energy duo to crack propagation only through the interface. (2) The interface fracture energies obviously increase with the roughness of Ti substrates, and is independent of the thickness of Ni films. (3) The intrinsic interface fracture energy measured by threepoint bend test is reasonable agreement with that obtained by theoretical calculation of Miedema model, and is comparable to that by peel test, roughly imparting validity to three approaches. Acknowledgements The authors acknowledge the Natural Science Foundation of Henan Province for its kind support for the program under the research Grant No. 0411050100. They also would like to express their appreciation for financial support from the Program for Young Key Teacher in University of Henan Province (2005-461) and the Key Technologic Program of Henan Province through No. 0424290064.
5. Applicable conditions of three-point bend test References The results of three-point bend test can be well interpreted by fracture mechanics, but this kind of test has an upper detection limit for the adhesion strength. An upper limitation of this testing method is the adhesion strength of the film. If crack propagation is easier through the adhesive coating or the substrate than along the interface, then the fracture test fails. The stress field of crack tip will obviously change at smaller stiff of the adhesive coating and smaller thickness of the film. The detailed studies in this aspect should be carried out. In our fracture mechanics test, preparing pre-crack method only applies to the flexible film/rigid substrate system with weakening adhesion strength between the film and the substrate. For the film/substrate system with higher adhesion strength, a weakly bonded metal or carbon film or the oxide scale on one side of a coated surface of substrate can act as a notch or a pre-crack. 6. Conclusion (1) For Ni film on Ti substrate system produced by electronic depositing technique, the fracture mechanics test could be
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