With the measured geometry morphologies of telephone cord blisters (TCBs), that is, the local blister width and height, and the global wavelength, a mechanical model is built to determine the residual compressive stress in thin films and interface adhesion toughness. This model is based on the hypothesis that pockets of energy concentration (PECs) drive the nucleation and growth of TCBs in thin films under the constant residual stress. The model is validated with independent experimental measurements and shows the strong potential to guide the fabrication of micro-patterns on thin films

Bo Yuan (1259997)

Christopher Harvey (1256223)

Gary Critchlow (1249479)

Rachel Thomson (1258278)

Simon Wang (1250952)

English

Loughborough University Institutional Repository

* Corresponding author, E-mail: s.wang@lboro.ac.uk (Simon Wang)  Thin film properties by blister tests Simon Wang1,2,*, Christopher M. Harvey1, Bo Yuan1, Gary W. Critchlow3 and Rachel C. Thomson3 1 Department of Aeronautical and Automotive Engineering,  Loughborough University, Loughborough, Leicestershire LE11 3TU, UK 2 College of Mechanical and Equipment Engineering,  Hebei University of Engineering, Handan 056038, China 3 Department of Materials Engineering,  Loughborough University, Loughborough, Leicestershire LE11 3TU, UK Abstract. With the measured geometry morphologies of telephone cord blisters (TCBs), that is, the local blister width and height, and the global wavelength, a mechanical model is built to determine the residual compressive stress in thin films and interface adhesion toughness. This model is based on the hypothesis that pockets of energy concentration (PECs) drive the nucleation and growth of TCBs in thin films under the constant residual stress. The model is validated with independent experimental measurements and shows the strong potential to guide the fabrication of micro-patterns on thin films. Keywords: Telephone cord blisters, Pockets of energy concentration, Residual stress, Interface adhesion toughness, Spallation 1 Introduction Thin solid films are built in engineering applications fulfilling various functions, such as confinement of electric charge in integrated electronic circuits, and in thermal insu-lation in thermal barrier coatings. Although these thin films are not primarily designed to withstand mechanical loads, their mechanical properties are usually major concerns since the desired functions may be lost as the result of the delamination of thin films driven by buckling [1–4] or pockets of energy concentration [5–9]. Under the residual stress, circular blisters, straight blisters, telephone cord blisters or more complex hex-agonal blisters are observed in thin films. It is however, difficult to accurately measure the mechanical properties in experiments, such as the residual compressive stress be-fore delamination and the interface adhesion toughness. The present work aims to de-velop a mechanical model to determine the residual compressive stress and fracture toughness in thin films with the measured TCB morphologies, that is, local blister width and height, and the global wavelength. The mechanical model is presented in Section 2, and the experimental validation is in Section3. Conclusions are drawn in Section 4. 2 2 Mechanical models The mechanical model to determine the film mechanical properties, i.e., residual com-pressive stress 0σ  and the interface adhesion toughness cG  is presented in this section. Fig. 1 shows a TCB in a film with the thickness h . The substrate thickness is assumed so large that its global deformations due to the residual stress in the film are neglected. The film material has Young’s modulus E  and Poisson’s ratio ν  and is assumed to be homogeneous and isotropic. In Fig. 1, the TCB geometry is described by the local si-nusoidal blister width 2R and blister height xA , and the global wavelength λ  and transverse amplitude yA . Note that in Fig. 1b, R  is perpendicular to the sinusoidal centreline of the TBC whilst R  in Fig 1c is in the direction of the global x.  Fig. 1. A telephone cord blister. (a): Top view. (b): 3D view of cut A. (c): 3D view of cut B. Based on the PECs theory in Ref. [5–7]. A TCB consists of a partial straight blister in fully-developed at some distance from the TCB tip, and a partial circular blister in non-fully-developed close to the TCB tip. The conditions for a TCB forms and propa-gates are: (1) 1.5Ω ≥  where Ω  represents the ratio between the in-plane residual strain energy density in films and the adhesion toughness at the film/substrate interface. The Ω  determines the blister growth and is given by,  ( )( )200 0 2c1 32 22 1hEGεε ϕνΩ = = ≥−  (1) where 0 0 ch Gϕ σ=  and ( )20 0 1 Eε σ ν= −  is the residual compressive plane strain in the plane strain condition. (2) For the partial circular blister, its blister energy denoting the net energy stored in the blister is required to reach the maximum level, called blister capacity before which is supplied by PECs. (3) For the partial straight blister, its half width is required to reach the level to trigger the secondary buckling, leading to the waviness of TCBs. The present work aims to obtain the mechanical properties, i.e., the in-plane residual compressive stress 0σ  before delamination and the interface adhesion toughness cG . Two methods are to calculate Ω first: (1) Based on the measured blister height xA , 3  238xxA hh A Ω = +    (2) (2) Based on the measured TCB wavelength-to-width ratio ( )2r Rλ= ,  1223 112 rνν− − Ω = −  +     (3) Then with the local TCB half width R , the ratio 0ϕ  can be obtained by  11 220 2 26 31 12Rhϕπ−  = + −  Ω     (4) Next, the residual strain 0 02ε ϕ= Ω , residual stress 0σ  and interface fracture tough-ness ( ) ( )2 2c 0 2 1G hE ε ν = − Ω   are evident to work out from Eq. (1). 3 Experimental validations The mechanical model is validated with two independent experimental measurements from Refs. [10,11]. The first comparison is against the measurements in Ref.[10] where the thin film is tantalum and the substrate is glass. The film thickness is 0.225 mμh = . The Young's modulus and Poisson's ratio of the film are 175 GPaE =  and 0.3ν = , respectively. With the measured TCB width, height, and the wavelength, the quantity Ω  is initially worked out from Eq. (2) then the mechanical properties are obtained from Eqs. (1) and (4). Comparisons between the predictions for the mechanical properties and the measurements are presented in Table 1, and the measurement locations are shown in Fig. 2.  Fig. 2. Telephone cord blister morphology measurement [10]. 4 Table 1. Comparisons between theoretical predictions and experimental measurements [10]. Experimental measurements  Theoretical predictions xA  [ ]μm  λ  [ ]μm  R  [ ]μm   Ω  Eq. (2) 0ε  Eq. (1) 0σ  [ ]GPa  cG  2J m−    Eq. (1) Section A 1.09 20.00 10.00  1.9779 0.49% 0.94 0.2641 Section B 1.01 20.20 10.10  1.8434 0.43% 0.83 0.2179 Section C 1.14 20.60 10.50  2.0702 0.48% 0.92 0.2376 Averaged 1.08 20.40 10.20  1.9602 0.47% 0.90 0.2395  From Table 1, the Ω  in all sections are larger than 1.5, and the predicted residual stresses have excellent agreement with the measurements, that is, 1 GPa reported in Ref. [10]. The measured interface fracture toughness is unavailable; however, the pre-dicted values at three locations are consistent with each other which is more expected. Hereby, taking the same definitions for the mode I and II critical interface adhesion toughness in Ref [12], that is, -1Ic 00.176 0.1584 N mG u= =  and -1IIc 028.5 25.6500 N mG u= = , respectively, where ( ) 20 01 /u h Eν σ= −  describes the residual train energy density. The fracture toughness cG  based on the mixed fracture mode partitions for classical plates, shear-deformable plates, and 2D elasticity theories are -10.1584 N m , -10.6221 N m  and -10.2534 N m . It is interesting to find the interface adhesion toughness from 2D partition theory agrees well with the results shown in Ta-ble 1 that based on the TCB morphologies. This demonstrates that the present PECs theory captures the real mechanics of TCBs. The second comparison is against the experimental measurements in Ref.[11] where the thin film is tungsten and the substrate is silica. There are four groups of specimens with different film thicknesses. The Young's modulus and Poisson's ratio are taken to be 411 GPaE =  and 0.28ν = , respectively. The quantity Ω  is firstly worked out from Eq. (3) then the mechanical properties are obtained from Eqs. (1) and (4) based on the measured R  and xA , at three locations (see Fig. 3). The theoretical results and comparisons are recorded in Table 2. 5  Fig. 3. Telephone cord blister morphology measurements at three different locations[11]. (a), Section A. (b), Section B, (c), Section C. A sketch of the cross-section is shown below each. Table 2. Comparison between theoretical predictions and experimental measurements [11]. Experimental measurements [11]  Theoretical predictions [ ] nmh  [ ] μmR  [ ] μmxA   Ω  Eq. (3) 0ε  Eq. (1) [ ]0  GPaσ  [ ]c  N mG  Eq. (1) 100        A 8.110 0.847  4.15 0.37% 1.67 [3.14] 0.08 [1.180±0.400] B 7.400 0.787  3.70 0.39% 1.76 [3.07] 0.09 [1.130±0.250] C 8.100 0.847  4.15 0.37% 1.67 [2.39] 0.08 [0.621±0.080] AVG 7.870 0.827  4.00 0.38% 1.70 [2.87] 0.08 [0.980±0.280]         200        A 5.400 0.670  1.54 0.75% 3.63 [4.75] 1.91 [6.010±0.900] B 5.160 0.633  1.52 0.83% 3.72 [4.70] 2.05 [5.960±0.900] C 5.400 0.670  1.54 0.81% 3.63 [3.74] 1.91 [2.930±0.420] AVG 5.320 0.658  1.53 0.82% 3.66 [4.40] 1.96 [4.970±0.770]         225        A 17.500 1.430  2.72 0.25% 1.10 [1.91] 0.11 [0.988±0.150] B 17.200 1.360  2.54 0.24% 1.05 [1.82] 0.11 [0.897±0.100] C 17.450 1.430  2.72 0.25% 1.11 [1.49] 0.11 [0.512±0.080] AVG 17.383 1.407  2.66 0.24% 1.09 [1.74] 0.11 [0.799±0.110]         300        A 20.000 1.730  2.40 0.29% 1.28 [2.14] 0.23 [1.670±0.200] B 18.800 1.470  2.00 0.25% 1.12 [2.18] 0.21 [1.800±0.200] C 20.000 1.730  2.40 0.29% 1.28 [1.64] 0.23 [0.862±0.120] AVG 19.600 1.643  2.26 0.27% 1.22 [1.99] 0.22 [1.444±0.180]  It is observed that all Ω  values in Table 2 are above 1.5, which gives the formation condition of TCBs, that is, 3 / 2Ω > . It is worth noting the values of Ω  for the second group of specimens rigorously obey the rule. The predictions for the residual stresses 6 0σ  and the fracture toughness cG  shown in brackets are according to the traditional buckling approach [13], and the corresponding results in sections A and C in each group are completely different with each other; however, those from the current PECs theory are very close to each other, which is expected in reality. This convincingly demon-strates that the present theory captures the real mechanics of TCBs. 4 Conclusion Telephone cord blisters are generated as an instability consequence under the constant residual stress in thin films. As per the hypothesis that pockets of energy concentration drive the nucleation and growth of TCBs, with the measured morphologies of TCBs, that is, the local blister width, height and the global wavelength, a mechanical model is built to effectively determine the mechanical properties of thin films, that is, the resid-ual compressive stress before blistering and the interface adhesion toughness. For the TCBs growth, it is also verified Ω  representing the ratio between the residual strain energy density and the interface adhesion toughness is required to be larger than 1.5. References 1. Chai H. Three-dimensional fracture analysis of thin-film debonding. Int. J. Fract. 46(4), 237–256 (1990). 2. Hutchinson JW, Thouless MD, Liniger EG. Growth and configurational stability of circular, buckling-driven film delaminations. Acta Metall. Mater. 40(2), 295–308 (1992). 3. Jensen HM, Sheinman I. Straight-sided, buckling-driven delamination of thin films at high stress levels. Int. J. Fract. 110(4), 371–385 (2001). 4. Moon MW, Jensen HM, Hutchinson JW, Oh KH, Evans AG. The characterization of telephone cord buckling of compressed thin films on substrates. J. Mech. Phys. Solids. 50(11), 2355–2377 (2002). 5. Wang S, Harvey CM, Wang B. Room temperature spallation of α-alumina films grown by oxidation. Eng. Fract. Mech. 178, 401–415 (2017). 6. Harvey CM, Wang B, Wang S. Spallation of thin films driven by pockets of energy concentration. Theor. Appl. Fract. Mech. 92, 1–12 (2017). 7. Yuan B, Harvey CM, Thomson RC, Critchlow GW, Wang S. Telephone cord blisters of thin films driven by pockets of energy concentration. , In review. 8. Tolpygo VK, Clarke DR. Spalling failure of α-alumina films grown by oxidation: I. Dependence on cooling rate and metal thickness. Mater. Sci. Eng. A. 278(1–2), 142–150 (2000). 9. Tolpygo VK, Clarke DR. Spalling failure of α-alumina films grown by oxidation. II. Decohesion nucleation and growth. Mater. Sci. Eng. A. 278(1–2), 151–161 (2000). 10. Ni Y, Yu S, He L, Jiang H. The shape of telephone cord blisters. Nat. Commun. 8, 1–6 (2017). 11. Cordill MJ, Bahr DF, Moody NR, Gerberich WW. Adhesion measurements using telephone cord buckles. Mater. Sci. Eng. A. 443(1–2), 150–155 (2007). 12. Faou J-Y, Parry G, Grachev S, Barthel E. How Does Adhesion Induce the Formation of Telephone Cord Buckles? Phys. Rev. Lett. 108(11), 116102 (2012). 13. Hutchinson JW, Suo Z. Mixed Mode Cracking in Layered Materials. In: Advances in Applied Mechanics. , 63–191 (1991).  

Thin film properties by blister tests

https://repository.lboro.ac.uk/articles/Thin_film_properties_by_blister_tests/9222995/files/16802339.pdf

Thin film properties by blister tests

Abstract

Similar works

Full text

Available Versions

Loughborough University Institutional Repository