ADHESION MEASURES OF ELASTO-PLASTIC THIN FILM VIA BUCKLE-DRIVEN DELAMINATION

Transcription

1 ADHESION MEASURES OF ELASTO-PLASTIC THIN FILM VIA BUCKLE-DRIVEN DELAMINATION Yu Shouwen and Li Qunyang Department of Engineering Mehanis, Tsinghua University, Beijing 184, China Abstrat Indentation test is beoming inreasingly used to quantitatively assess the thin film interfaial adhesion for its simpliity and ability to mehanially probe the smallest of solids. The onventional tehnique is based on the analysis of Marshall and Evans whih is a ombination of Linear Elasti Frature Mehanis (LEFM) and simplified post-bukling theory. In this paper a full post-bukling response of elasto-plasti thin film is investigated by FEM alulation; the ontributions of double-bukling to the indentation test is disussed. The results show that double-bukling needs more energy than single-bukling ase thus lead to a greater value of strain energy release rate Key Words Indentation, interfaial strength, thin film, delamination, double-bukling 1 Introdution Thin films have a wide range of appliations in miroeletronis and magneti reording industries. Beause of the importane of thin film adhesion, it is not surprising that there are more than different methods [1] to measuring interfaial adhesion at present, suggesting them to be material, geometry and even industry speifi. This indentation tehnique is mainly based on the pioneer works of Marshall & Evans [7] and Evans & Huthinson [8] whih gave the theoretial analysis for the onial indentation-indued thin film delamination. Consider an indentation-indued interfae rak in a residually stressed film, shown in Fig.1. The film has a thikness t on a semi-infinite substrate, loaded by a hard angular indenter whih leaves a permanent impression, and the residual stress is assumed to be R. The strain energy release rate is obtained as follows by onsidering a few hypothetial operations [7,8] = ν { α R + + ν α } G t(1 ) (1 ) (1 ) / (1 )(1 / ) / E (1) ( ) 1 where α = 1 for + R < (no bukling) or α = (1 + ν) for + R > (bukling). After measuring the strain energy release rate G, the interfaial adhesion between the thin film and substrate an be alulated, whih needs the knowledge of the frature interfae and the phase angle to interpret the results orretly In many indentation tests, if the indenter is driven deep enough, so that the rak reahes its ritial bukling length, the film often double bukles during indentation, shown in Fig. [1].

2 R t Crak V Plasti Zone Film Fig.1 Shemati of indentation-indued delamination at the interfae of a thin film and substrate t z Film a (a) a t BC BC1 (b) Fig. 3(a) Cirular delamination at afilm/substrate interfae; (b) Model for FEM alutlation R r (a) (b) () Indenter Thin film Thin film Thin film Fig. (a) No bukling during indentation; (b) double-bukling during indentation; ()single-bukling after the indenter tip removal,see [6, 9] a a a V V V h h h with the plasti indentation volume V. But as what is mentioned above, the full analysis of double-bukling has not yet been done, whih is essential for the indentation tehnique. [9] Experiment of Kriese et al. found that during indentation the interfaial frature toughness was reproduibility high for shallow indents, 8 1J/m, but dropped to a fairly steady.7 1. J/m for deeper indents. It is hard to explain these experimental data via onventional analysis. As we know, the plastiity of materials will greatly affet the bukling proess; an it be a reason for this phenomenon. In the paper, we will emphasize on some aspets of thin film buking and their influenes to the indentation test. Based on FEM ode ABAUQS, the full post-bukling responses of thin films are obtained. Both the double-bukling and material plastiity are taken into onsideration and their ontributions are disussed. Large deformation bukling and double-bukling for thin film delamination.1 Model for FEM analysis The alulation is done by the ommerial FE-ode ABAQUS on a PC workstation. A irular delamination at a film/substrate interfae is onsidered, as shown in Fig.3(a), with a uniform biaxial ompression exiting in the film. For this axisymmetri problem, only one ross-setion of the bukled film (i.e. the bukled film dis) is modeled, shown in Fig.3(b). The film dis has a thikness t and a radius a, and is subjet to uniform biaxial ompression on the perimeter (BC). Boundary onditions are applied, suh that the

3 perimeter (BC) is always fixed in r diretion while the film enter (BC1) is fixed in r diretion for single-bukling ase but fixed in both r and z diretion for double-bukling ase.. FEM results of full single-bukling response The proedure of Eigenvalue Bukling Predition is used to obtain the ritial bukle stress. For various values of t/ a, using the non-dimensional stress = 1(1 ν ) / E, the relevant ritial load for the thin film is shown in Fig Critial stress of single-bukling 5 4 Single-bukling.8 = (t/a) / t /a Fig. 4 Critial bukle stress for film diss with different radius (single-bukling) / Fig.5 Plot of edge stress as a funtion of inward displaement ( and are the ritial stress and displaement for singlebukling) Fitting the above data, we get that the ritial stress follows the form ke t = 1(1 ν ) a with k = , whih oinides the theoretial Euler bukling stress k = very well. To alulate the film response when >, RIKS proedure is used to perform postbukling analyses: For the ase of t/ a = 1/, the edge stress as a funtion of displaement for this film dis is plotted in Fig.5. Fig.5 gives the full post-bukling response of the elasti thin film, from whih we an learly observe the whole proess of bukling and the stiffness of the film (i.e. the slope of the urve) is greatly redued after the ritial point of bukling. The initial slope α of the post-bukled load-displaement urve brunhes are drawn in Fig.6 for materials with different Poisson s ratio ν. (1)

4 Single-bukling 8 6 FEM Asymptoti solution α.4.4 G B 4.38 α = ( 1+1.7( 1+ν ) ) Fig.6 The initial slope α of bukled brunhes verse film Poisson s ratio ν for single-bukling ν / Fig.7 Energy release rate of FEM-based and asymptoti-solution-based results ( G = t E) B / The FEM results of the initial slope well fit the theoretial predition, whih is provided by Evans & Huthinson [8] 1 and assumed to be α = ( (1 + ν) ). But from Fig.5, it an be seen that the slope of the post-bukled brunh goes down as the inrease of inward displaement. To onsider the deviation from the initial slope value, we assume the slope α has the following form = α α β where α is the initial slop value and β is fitted from the FEM data to be around.1973 for different values of ν. Thus the equationfel! Hittar inte referenskälla. is modified as () t(1 ν ) β 1+ ν G = {(1 α ) R ( + R) + [ (1 α+ β)(1 ) ]} (3) E where α and β are determined by equation (). In the initial study we assume there is no pre-residual stress in the thin film, and the omparison of strain energy release rate between the result of equationfel! Hittar inte referenskälla. and equation(3) is shown in Fig.7. The omparison of Fig.7 shows that the relative error of the asymptoti solution is within 1% when < 3, but the results deviate a lot when large deformation is taken plae. For general indentation test of relatively low value of /, the asymptoti solution based results are satisfatory for engineering appliations..3 FEM results of double-bukling response The following will fous on the double-bukling responses, whih is shown in Fig.(b). First, we also alulate the ritial stress for different values of t/ a double-bukled, plot is shown in Fig.8 with = 1(1 ν ) /. E when the films

5 ..4.3 Critial stress of double-bukling 1.5 Double-bukling. =4.41 (t/a) / ' Fig.8 Critial bukle stress for film diss with different radius (double-bukling).4.4 t /a Double-bukling / ' Fig.9 Plot of edge stress as a funtion of inward displaement. ( and are the ritial stress and displaement for doublebukling) 1 8 Double-bukling Single-bukling α' G B 6 4 ν =.3.34 α' = ( ( 1+ν ) ) -1 = ' ν Fig.1 The initial slope α of bukled brunhes verse film Poisson s ratio ν for double-bukling ases / Fig.11 Comparison of energy release rate for the two bukling types Fitting the FEM data, we an get the ritial stress for double-bukling ke t = 1(1 ν ) a where k = 4.41, very lose to the Euler theoretial ritial value of k = For the ase of double-bukling, the full post-bukling response of the edge stress as a funtion of displaement for this film dis is plotted in Fig.9. While the initial slope α of the post-bukled load-displaement urve brunhes are drawn in Fig.1 for materials with different Poisson s ratio ν. The relationship between α and ν an also be fitted from the FEM results and expressed as (4) ( (1 )) 1 α = + + ν (5)

6 from equation(5) we an see that though the ritial stress value of double-bukling is muh larger than that of single-bukling. Considering the differene of the ritial bukled stress and its initial slope value of postbukled brunhes, the orresponding strain energy release rate of double-bukling will be larger. The omparison of the strain energy release rate for the two bukling types is shown in Fig.11, with the non-dimensional parameter G = t E and ν =.3. B / In Fig.11, it an be seen that the double-bukling ase has a muh larger strain energy release rate than single-bukling ase, so we must identify the bukling type in order to interpret the results orretly. 3 Conlusion An investigation on the post-bukling of thin film is arried out by FEM alulation. Some of the important fators, whih are often omitted before, suh as the double-bukling phenomenon and material plastiity, are disussed in this paper. The results show that for the ase of < 3, the asymptotial solution is satisfatory with a relative error less than 1%. For the double-bukling ases, the ritial stress and initial slope parameter are obtained, and the omparison of the energy release rate with the singlebukling ase shows that the different is obvious and need to be treated properly. The plastiity has signifiant influene on the post-bukling responses and should be onsidered in interpreting the indentation test results. The greater the value of /, the more ontributions of the plastiity. The abnormal experimental results of Keries [9] an be explained by this alulation. We an say that if the onventional method of indentation test is onsidered, the deeper indent the more preise of the results. Aknowledgement This projet is supported by NSFC (1175, 111) and SRFDP 364,Key grant proj-of Chinese MoE-No36. Referenes 1. Volinsky A A, Moody N R, Gerberih W W. Ata Materialia. vol. 5, ,. Jindal P C, Quinto D T, Wolfe G J. Thin Solid Films. vol. 154, , Rikerby D S. Surf. Coat. Teh. vol. 36, , Steinmann P A, Hintermann H E. J. Va. Si. Tehnol. A. vol. 7, 67-7, MCabe A R, Jones A M, Bull S J. Diamond and Related Tehnol. vol. 3, 5-9, Gerberih W W, Kramer D E, et al. Ata. Mater. vol. 47(15), , Marshall D B, Evans A G. J. Appl. Phys. vol. 56(1), , Evans A G, Huthinson J W. Int. J. Solids Strutures. vol. (5), , Krese M D, Boismier D A, Moody N R, Gerberih W W. Engineering Frature Mehanis. vol. 61, 1-, 1998 y