Influence of Disbond Defects on the Dispersion Properties of Adhesive. Bonding Structures

Transcription

1 Key Engineering Materials Online: ISSN: , Vols , pp doi: / Trans Tech Publications, Switzerland Influence of Disbond Defects on the Dispersion Properties of Adhesive Bonding Structures Xinlong Chang 1, a, Tao Ni 1,b, Chun an Ai 1,c 1 Xi an hi-tech institute, Xi an, Shanxi, PRC a xinlongch@sina.com.cn, b nitao_77@13.com, c ACA01@sina.com.cn Keywords: adhesive bonding, cohesive strength degradation, spring mode, disbond, dispersive curve Abstract. With increasing application of adhesive bonding structures, the quality assessment of adhesive bonding became critical. Ultrasonic approach was an acknowledged promising method in many Nondestructive testing (NDT) techniques. The research object was to use analytical models to develop a quantitative understanding of the affections in different situations on the dispersion properties. An improved global matrix method was introduced to compute the dispersive curves, which can effectively eliminate the instability for thicker layers and higher frequencies. In order to evaluate the disbond defect, the cohesive strength degradation mode and the spring mode were then adopted to describe the cohesive failure and the interface failure, respectively. In the paper, cohesive failure, interface failure and mixed failure were analyzed for the steel/adhesive layer/insulation layered structure. Interface failure induced the modes of multilayer structure to regress to the modes of single layers, while the cohesive failure made the dispersive curves move to the lower frequency direction, and changing the relative position of spring layer led the dispersive curves shift to the higher frequency direction. Among all the factors, the interface failure was dominant. Finally, the variety of the dispersive modes in a special frequency band (1~1.5MHz) was found that can be regarded as parameters of the adhesive bonding quality. Introduction Adhesive bonding structures were rapidly developing in aviation and aerospace sections because of its prominent merits including high specific strength, high specific modulus, good fatigue resistance etc., and those structures even exceeded 90% in some big passenger aircrafts [1]. So the quality of adhesive bonding structures was important and the NDT of the disbond defects became more critical. As we all know, ultrasonic method was an effective approach for detecting the disbond defects, Ultrasonic waves interacted with the interfaces in a complicated way on the propagation path, and the propagation properties could be changed by the interfaces. In order to research the influence of the disbond defects on the ultrasonic propagation property, the dispersion property must be studied. In this paper, an improved global matrix method was introduced, as well as the cohesive strength degradation mode and the spring mode, which developed a quantitative understanding of the affection. Matrix modeling theory The theories of researching the ultrasonic wave propagation the in multilayer structures had two important approaches: transfer matrix method and global matrix method. The transfer matrix method was presented by Thomson and Haskell [2], which used the boundary conditions of All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-03/03/1,23:39:29)

2 78 Damage Assessment of Structures VIII adjacent layers in order to cancel all the parameters of the middle layers, then the matrix formulation relating top layer with bottom layer was obtained, substituting the boundary conditions of those two layers, the dispersion curves were calculated finally. The advantage of the transfer matrix method was the matrix s rank wasn t depend on the number of the layers which determined the complex of computation, but the matrix asymptotically evolved into an ill-conditioned matrix with increasing of frequency and thickness, and the solutions were instable. To solve this problem, the global matrix method was introduced by Knopoff. This approach made use of a global matrix which included all the boundary conditions, and its solution gave the natures of waves in each layer. In this research, an improved global matrix method was adopted to calculate the dispersion modes in the multilayer structures. the first layer x1 the kth layer the (k+1)th layer the nth layer x3 Fig. 1 An nth layered structure and coordinate system Global matrix theory. Considering an nth layers structure shown in Fig. 1, the displacement vector in any layer could be written as the summation of six partial waves in components form: u, u, u 1, V, W U expi x x ct q q 1q 1 3 q (1) q 1 where q (q=1,2, ) denoted qth partial wave; c represented phase velocity; U 1 represented amplitude of u 1 ; V and W expressed the ratio of u 2 and u 3 to u 1,respectively; ξ was the wave vector in x 1 direction and α represented the ratio of wave vector in x 3 to x 1 directions, respectively. The coordinate system was selected so that the x 1, x 3 plane coincided with the incident plane and thus wave vector in x 2 direction was zero in Eq. 1. The stress vector also could be represented as the summation of six partial waves using Hooke s Law * * * 33, 13, 23 D1 q, D2 q, D3 q U 1q exp i x1 qx3 ct (2) q1 where /. Combining Eq. 1 with Eq. 2, the relation equation of displacement and stress ij ij i in single lamina could be written in matrix form P D A (3) k k k where P k, D k and A k were defined by T P u, u, u,,, (4) k T A U, U, U, U, U, U (5) k

3 Key Engineering Materials Vols E1 E2 E3 E4 E5 E V1 E1 V1 E2 V3E3 V3E4 V5E5 V5E W1 E1 W1 E2 W3E3 W3 E4 W5E5 W 5E Dk D11E1 D11E2 D13E3 D13E4 D15E5 D15E D21E1 D21E2 D23E3 D23E4 D25E5 D25E D 31E1 D31E2 D33E3 D33E4 D35E5 D35E where E q in the D k were given by 3 E exp i x, q 1,2,, (7) q q In Eq. 5, U 11, U 13 and U 15 represented three partial waves propagating along the -x 3 direction while U 12, U 14 and U 1 represented three partial waves propagating along the x 3 direction. Using the continuous conditions of displacement and stress for the interface between kth and k+1th, we had D D A k kb k1t A k 1 0 Then the local coordinate origin was modified at the top of the layer for waves propagating along the x 3 direction and the bottom of the layer for waves propagating along the -x 3 direction. Such a selection of the local coordinate system was very important for eliminating the numerical instability, which assured that the exponential terms were normalized decaying toward the opposite surface of the layer, and it s proved to be very useful for improving computational results. The square matrix D modified for the top and bottom of the lamina could be represented as 1 1/ E2 1 1/ E4 1 1/ E E1 1 E3 1 E5 1 V1 V1 / E2 V3 V3 / E4 V5 V5 / E V1E 1 V1 V3E3 V3 V5E5 V 5 W1 W1 / E2 W3 W3 / E4 W5 W 5 / E W1 E1 W1 W3E3 W3 W5E5 W 5 Dt Db D11 D11 / E2 D13 D13 / E4 D15 D15 / E D11E1 D11 D13E3 D13 D15E5 D15 D21 D21 / E2 D23 D23 / E4 D25 D25 / E D21E1 D21 D23E3 D23 D25E5 D 25 D 31 D31 / E2 D33 D33 / E4 D35 D35 / E D 31E1 D31 D33E3 D33 D35E5 D35 Consequently the global matrix for a n layered structure could be represented by arranging the Eq. 8 of all the layers in the matrix form D D A 1 1b 2t A D 2 2b D 3t 0 D D n2b n1t An 1 D n 1 D b nt An Eq. 10 had (n-1) equations while it had n arguments, so the boundary conditions of the top and bottom surface must be considered. Finally the global matrix adding the boundary conditions was given by D1 t D D A 1 1b 2t A D 2 2b D 3t 0 D n 2 D b n1t A n1 D n 1 D b nt An Dnb The characteristic equation could be determined as det(d)=0, then the dispersive curves were () (8) (9) (10) (11)

4 770 Damage Assessment of Structures VIII obtained by solving the characteristic equation. Modes of disbond failure. In order to calculate the influence of disbond defects on the adhesive bonded structures, the modes which describing the disbond failures must be introduced. There were three failure types in disbond failures: cohesive failure, interface failure and mixed failure. The layer with cohesive strength degraded could be seen as a lamina with lower elastic modular and lower density from the view of wave propagation [2], but it could not explain the interface failure yet. Aiming to the problem, lots of researchers had done many significant works [3,4,5], the most important mode was spring mode which was been developed from the multilayer media modes by dealing with the layer as a lamina of zero thickness and neglecting the coupling and inertial terms []. In this research, the two modes were adopted to describe the cohesive failure and interface failure, respectively. Cohesive strength degradation mode. According above stated, the layer with cohesive strength degraded could be described by the degradation of the ultrasonic velocity and density. The dispersion property in the condition of cohesive strength degradation then could be computed by substituting the modified parameters into the global matrix. In cohesive strength degradation mode, the variety of the cohesive strength was defined as change of the ratio of Young s modulus. For the undamaged adhesive lamina, the parameter was a group of mechanical and acoustic data written as (E 0, ρ 0, C T0 ), while the cohesive strength degraded adhesive lamina was (E, ρ, C T ). The ratio was defined as E / E C / C (12) T T0 0 where η was defined according to the quality of adhesive lamina, and the ultrasonic velocities and density could be derived from η. Spring mode. The displacement and stress could reflect the interface condition from the view of mechanics. The displacement and stress of all directions were continuous for the perfect interface, and were also continuous in normal direction for the slip interface (kissing disbond), but stress was zero and the displacement was discontinuous in tangential direction in slip interface situation. For air disbond interface, the stress was zero and the displacement was discontinuous in all directions. The spring mode used one normal directional coefficient k 33 and two tangential coefficients k 13, k 23 to describe the mechanical relationship between top and bottom of the spring layer. u u / k 1t 1b u u / k 2t 2b u u / k 3t 3b Matrices of the top and bottom could be written as 1 1/ k13 1 1/ k / k 33 Dt Db Diag[1,1,1,1,1,1] (15) From Eq. 13, let k 13, k 23, k 33, the spring mode showed a perfect interface; let k 13 0, k 23 0, k 33, the spring mode represented a slip interface (kissing disbond); when k 13 0, k 23 0, k 33 0, the spring mode denoted an air disbond interface. (13) (14)

5 Key Engineering Materials Vols Results and discussion In this paper, the steel/ adhesive layer/insulation structure was took as the object which was usually used in the rocket, the influence of all factors on the dispersion properties of adhesive bonding structures was computed which included interface failure, cohesive strength failure, mixed failure and other elements. Interface failure influence on the dispersion property of adhesive bonding. Before considering the affection of interface failure, the influence of adhesive layer on the dispersive curves should be investigated. The steel/insulation structure and the steel/adhesive layer/insulation structure were computed, respectively. Parameters of each layer were given in Table 1. Table 1. Parameters of each layer Layers Longitudinal wave velocity [Km/s] Shear wave velocity [Km/s] Density [g/cm 3 ] Thickness Steel Perfect adhesive layer insulation The dispersive curves had not obvious changing after adding the adhesive layer, which indicated that mode conversion didn t exist. Thus the affection of adhesive layer could be ignored for the situation that the thickness of adhesive layer far less than other layers. The affection of the spring layer on dispersion property was then considered on the basis of the steel/insulation structure. Fig. 2 showed the dispersion modes of perfect interface, slip interface and air disbond interface. Modes moved to the higher frequency direction coupled with shape shifting in the evolution course from perfect interface to slip interface which shown in Fig. 2(a), and magnitude of budging and shifting for the lower-order modes was less than which of the higher-order modes. When air disbond existed, the budging and shape shifting of dispersive curves represented further obvious as shown in Fig. 2(b) and Fig. 2(c). In order to investigate meanings of the variety of dispersive modes, dispersive curves of air disbond interface, single steel layer and insulation layer were compared, which had shown in Fig. 2(d). It s found that the modes of air disbond interface were the combination of modes of single steel layer and insulation layer. As for the literature [7, 8] which studied the anisotropy multilayer structures, it found that lower modes split into two branches which respectively trended toward the modes of perfect and air disbond conditions, and the phase velocities descended notably comparing with the perfect conditions. Obviously, the phenomena observed in this paper were contrary to the conclusions in the literatures. Thus the evolution regularity was strongly depended on the properties and plying manner, different materials and structures had different rules. Cohesive failure influence on the dispersion property of adhesive bonding. The cohesive failure influence on the dispersion property was investigated after adding adhesive layer on the basis of three layers mode of steel/spring layer/insulation. Firstly, the relative position of the spring layer to the adhesive layer was considered. Fig. 3 showed the effect of the relative position changing the spring layer from adhesive layer upside to downside, the dispersive modes shifted to the lower frequency direction. So it couldn t determine the position of disbond utilizing the shifting of dispersive curves since the place of disbond maybe any interface or both interfaces. Secondly, the cohesive strength degradation was studied. Calculating three cases when η was 100%, 35% and 10%, parameters in these situations were given in Table 2. As a result shown in Fig. 4, the shapes of dispersive modes weren t changed but moved to the lower frequency direction, lower-order modes had smaller shifting while higher-order modes had bigger shifting. [mm]

6 772 Damage Assessment of Structures VIII Fig.2(a) Fig.2(b) Fig.2(c) Fig.2(d) Fig.2 The interface failure influence on the dispersive modes Fig.3 The relative position influence on dispersive Fig.4 The cohesive strength degradation influence on modes dispersive modes According above stated, the dispersive curves moved to the higher frequency direction when spring lamina changed from adhesive layer upside to downside, while the dispersive curves moved to the opposite direction when the cohesive strength degraded. To considering the combination effect, the dispersive curves of steel/spring layer (slip interface)/adhesive layer (100%)/insulation and steel/ adhesive layer (10%)/spring layer (slip interface)/ insulation structures were calculated

7 Key Engineering Materials Vols shown in Fig. 5. The cohesive strength degradation effect was dominant for lower-order modes while the relative position of spring layer influence was major for higher-order modes, so cohesive strength maybe degraded when dispersive curves moved to the higher frequency direction, and the lower-order modes should be considered as the criterion of the cohesive strength assessment while the higher-order modes ought to be avoided. Table 2. Parameters of the adhesive layer Values of η Longitudinal wave velocity [Km/s] Shear wave velocity [Km/s] Density [g/cm 3 ] Thickness 100% % % [mm] Fig. 5 The integrated influence of cohesive strength degradation and the relative position on dispersive Fig. The mixed failure influence on dispersive modes modes Mixed failure Influence on the dispersion property of adhesive bonding. Finally the mixed pattern of cohesive failure and interface failure was considered. The dispersive curves of steel/spring layer (perfect)/adhesive layer (100%)/insulation structure and steel/spring layer (air disbond)/adhesive layer (10%)/insulation structure were given in Fig.. Generally, the mixed failure influence was combination of interface failure effect and the cohesive failure effect, and the interface failure influence was more notable than the other. With more detailed research, it s found that the dispersive curves in the 1~1.5MHz frequency band moved toward to the dispersive modes of single insulation layer, and this frequency band was slightly affected by the changing of cohesive strength, thus it could be used to assess the interface failure, and was also regarded as the evaluation criterion of cohesive strength when interface failure wasn t exist. So an approach was obtained for adhesive bonding assessment, firstly the dispersive modes of the experiments were got by time-frequency technique [9,10], then those were compared with the dispersive modes of single insulation layer, finally the adhesive bonding quality would be evaluated by utilizing the method discussed above. Conclusions In this paper, an improved global matrix method was introduced to calculate the dispersive curves of adhesive bonging structures, and the disbond defects were described by cohesive strength degradation mode and spring mode. By the way, cohesive failure, interface failure and mixed failure were discussed. The conclusions were as following:

8 774 Damage Assessment of Structures VIII 1. The interface failure made the dispersive modes regress to the single layers modes, and the dispersive modes changed into the combination of the single layers when air disbond existed, but it didn t lead to modes conversions. Comparing with the anisotropy layered structures, the phenomena of modes splitting and phase velocity descending weren t found. 2. The degradation of cohesive strength didn t change shape of dispersive curves but made it move to the lower frequency direction. The relative position of spring layer and adhesive layer made dispersive curves shift to the opposite directions when spring layer changing from adhesive layer upside to downside. Considering mixed effect, the cohesive strength degradation influence was dominant for lower-order modes while the relative position was primary for the higher-order modes. Thus the lower-order modes should be selected as the assessment criterion of the cohesive strength degradation. 3. The mixed failure influence was combination of interface failure and cohesive failure, and the interface failure effect was critical while the cohesive strength degradation affection was hardly observed. So the variety of cohesive strength was difficult to detect when interface failure existed. 4. The shifting of dispersive modes in 1~1.5MHz band could be considered as the parameters to evaluate adhesive bonding quality. It could assess the shifting of cohesive strength with no interface failure, which was most sensitive to the interface failure in other situations. References [1] Jiawei Li, Jimao Chen: Nondestructive Detecting Manuals (Mechanical Industry Press, Beijing 2002) [2] Joseph L.Rose: Ultrasonic Waves in Solid Media (Cambridge University Press, 1999) [3] P. P. Delsanto, M. Scalerandi: J. Acoust. Soc. Am. Vol.104 (1998), p.2584 [4] S.I. Rokhlin, Y. J. Wang: J. Acoust. Soc. Am. Vol.89 (1991), p.503 [5] Zhenqiang Cheng, A. K. Jemah, F. W. Williams: Journal of Applied Mechanics. Vol.3 (199), p.1019 [] S. I. Rokhlin, L. Wang: J. Acoust. Soc. Am. Vol.112 (2002), p.822 [7] Haiyan Zhang, Zhenqing Liu, Donghui Lu: Acta Materiae Compositae Sinica. Vol.21 (2004), p.111 [8] Haiyan Zhang, Zhenqing Liu, Xiaosong Ma: Acta Physica Sinica. Vol.52 (2003), p.2492 [9] Robert Seifried, Laurence J. Jacobs, Jianmin Qu: Nondestructive Evaluation. Vol.20 (2001), p.1074 [10] Robert Seifried, Laurence J. Jacobs, Jianmin Qu: NDT & E international Vol.35 (2002), p.317

9 Damage Assessment of Structures VIII / Influence of Disbond Defects on the Dispersion Properties of Adhesive Bonding Structures / DOI References [4] S.I. Rokhlin, Y. J. Wang: J. Acoust. Soc. Am. Vol.89 (1991), p /