塑膠球柵陣列封裝與覆晶技術已經廣泛應用於電子工業，然而，在製造及使用過程當中，濕氣與熱將導致封裝體內部應力之產生，因此，可靠度仍是一重要且深受關切之主題。其中，各相關界面熱-機械行為變化所造成之效應，更是舉足輕重。本文首先探討儲存條件與迴焊參數對塑膠球柵陣列封裝晶片翹曲產生之影響，結果顯示塑膠球柵陣列封裝晶片吸濕程度和迴焊參數之交互作用相對於翹曲值變化，二者之間具有極為密切之關係。此外，當相對吸濕量達到0.25%至0.30%之臨界吸濕量時，迴焊過程中塑膠球柵陣列封裝晶片之翹曲值將急劇增加。其後，作者規劃一實驗流程，應用突鈕剪力試驗方法探討環氧基封膠、防焊漆與底板黏結接頭於承受溫度循環時，界面強度劣化之相關特性。同時，防焊漆厚度對界面強度變化之影響亦將一併探討。再者，利用掃瞄式電子顯微鏡進行試片破壞表面觀察以分析其界面劣化特性與破壞型態。其結果顯示防焊漆與底板界面強度明顯受到熱疲勞影響而降低，並且具有較大防焊漆厚度之試片具有較高之界面強度。最後，作者應用單搭接接頭試驗、非線性有限元素分析及疊紋干涉術探討防焊漆與底板界面之相關應力/應變分佈，並分別導出其與防焊漆厚度及搭接長度之關係。本研究所得之結果可提供對塑膠球柵陣列封裝晶片吸濕特性、翹曲特性與界面黏結特性之進一步了解，並且提供改善考靠度設計之參考。

The Plastic Ball Grid Array (PBGA) package and flip-chip technology have been widely used in the microelectronics industry. However, due to the effect of hygroscopic and thermal stresses, the reliability is still of concern during manufacturing and operation, especially for the thermal-mechanical behavior of its corresponding interfaces. Influences of the storage conditions and reflow parameters on the warpage of the PBGA package are investigated in this study first. As the results, the warpage reflected the interaction of the extent of moisture absorption and the change in reflow parameters significantly. Furthermore, a critical relative moisture absorption between 0.25% and 0.30% is found for a considerable warpage response. Next, this study presents an experimental investigation of the adhesion strength of epoxy-based encapsulant material to solder mask coated FR-4 substrate under thermal cycling. Effects of the number of thermal cycles on the interfacial strength are investigated by using button shear test. The relationship between the interfacial strength and thickness of solder mask is also examined. Moreover, to characterize the degradation and fracture behavior, the morphologies of fractured surfaces of the test specimens are analyzed by scanning electron microscopy. The results of this experiment show that the interfacial strength of the epoxy-based encapsulant/solder mask/substrate joint is apparently reduced by thermal fatigue. And, the test specimen with larger solder mask thickness has higher interfacial strength. Finally, the single-lap joint test, nonlinear finite element analysis and Moiré interferometry are employed to obtain strain/stress distributions on the interface of solder mask and substrate. The effects of solder mask thickness and overlap length are then determined, separately. The results of this study can afford important information for characterizing the features of moisture absorption, warpage and interfacial adhesion of PBGA packages. Furthermore, it can be helpful to identify improvements required in reliability of the package design.

TABLE OF CONTENTS / i
LIST OF TABLES / v
LIST OF FIGURES / vi
LIST OF SYMBOLS / ix
ABSTRACT / xii

CHAPTER 1 INTRODUCTION / 1
1.1 Background / 1
1.2 Review of Literature / 3
1.2.1 PBGA Technologies / 3
1.2.2 Thermal and Moisture Effects on PBGA Packages / 6
1.2.3 Adhesion Strength of PBGA Package’s Interfaces / 8
1.3 Objectives of Dissertation / 12
1.4 Scopes of Dissertation / 12
FIGURES / 14

CHAPTER 2 EXPERIMENTAL PROGRAM / 16
2.1 Experimental Framework / 16
2.2 Shadow Moiré / 17
2.3 Button Shear Test / 18
2.4 Lap Shear Test / 18
2.5 Moiré Interferometry / 19
FIGURES / 21

CHAPTER 3 INFLUENCES OF THE MOISTURE ABSORPTION ON PBGA
PACKAGE'S WARPAGE DURING IR REFLOW PROCESS / 24
3.1 Introduction / 24
3.2 Taguchi's Orthogonal Array Analysis / 25
3.3 Experimental Analysis / 26
3.3.1 Moisture Sensitivity Test / 27
3.3.2 Warpage Measurement of the PBGA Package / 28
3.4 Results and Discussions / 29
3.4.1 Relationships of the Relative Moisture Absorption and Storage
Conditions / 29
3.4.2 Effects of the Relative Moisture Content on the Warpage During IR Reflow
Process / 30
3.4.3 Effects of Temperature Profile Parameters on the Warpage During IR Reflow
Process / 31
TABLES / 34
FIGURES / 38

CHAPTER 4 THERMO-MECHANICAL BEHAVIOR OF UNDERFILL/SOLDER
MASK/SUBSTRATE INTERFACE UNDER THERMAL CYCLING / 43
4.1 Introduction / 43
4.2 Experimental Analysis / 43
4.2.1 Materials and Specimens / 43
4.2.2 Thermal Cycling Program / 44
4.2.3 Interfacial Shear Test / 44
4.2.4 SEM Analysis / 45
4.3 Finite Element Modeling / 45
4.4 Results and Discussions / 46
4.4.1 Interfacial Stress Distributions / 46
4.4.2 Effect of Thermal Cycling on the Interfacial Adhesion Strength / 47
4.4.3 Fracture Surface Analysis / 49
TABLES / 51
FIGURES / 52

CHAPTER 5 THE DEFORMATION MECHANISM OF UNDERFILL/SOLDER MASK/SUBSTRATE
ADHESIVE JOINTS / 60
5.1 Introduction / 60
5.2 Experimental Analysis / 60
5.2.1 Materials and Specimens / 60
5.2.2 Lap Shear Strength Test / 61
5.2.3 Moiré Interferometry Measurement / 61
5.3 Finite Element Modeling / 62
5.4 Results and Discussions / 64
5.4.1 Fracture Strength Analysis / 64
5.4.2 Adhesive Stress Analysis / 65
5.4.3 Adhesive Strain Analysis / 66
FIGURES / 69

CHAPTER 6 SUMMARY / 81
6.1 Conclusions of the Study / 81
6.2 Future Work and Recommendations / 82
REFERENCES / 84

1.Suhir, E.,“The Future of Microelectronics and Photonics and the Role of Mechanics and Materials,”ASME, J. Electron. Packag., Vol. 120, pp. 1-11, 1998.
2.Chong, T.O., Ong, S.H., and Yew, T.G.,“Low Cost Flip Chip Package Design Concepts for High Density I/O,”IEEE Electronic Components and Technology Conference, 2001.
3.Pecht M.G.,“Moisture Sensitivity Characterization of Build-up Ball Grid Array Substrates,”IEEE Transactions on Advanced Packaging, Vol. 22, pp. 515-523, 1999.
4.Shook, R.L. and Sastry, V.S.,“Influence of Preheat and Maximum Temperature of the Solder-reflow Profile on Moisture Sensitive IC’s," IEEE Electronic Components and Technology Conference, pp. 1041-1048, 1997.
5.Guo, Y.,“Applications of Shadow Moiré Method in Determination of Thermal Deformations in Electronic Packaging,”In: Proceedings of the 1995 SEM Spring Conference, Grand Rapids, MI, 1995.
6.Stitelar, M.R. and Ume, I.C.,“System for Real-time Measurement of Thermally Induced PWB/PWA Warpage,”ASME Journal of Electronic Packaging, Vol. 119, pp. 1-7, 1997.
7.Leung, S.Y., Lam, D.C. and Wong, C.P.,“Experimental Investigation of Time Dependent Degradation of Coupling Agent Bonded Interfaces,”IEEE Electronic Components and Technology Conference, 2001.
8.Hutt, D.A., Webb, D.P., Hung, K.C., Tang, C.W., Conway, P.P., Whalley, D.C. and Chan, Y.C.,“Scanning Acoustic Microscopy Investigation of Engineered Flip-chip Delamination,”IEEE/CPMT Int’l Electronics Manufacturing Technology Symposium, pp. 191-199, 2000.
9.Palm, P., Puhakka K., Moaattanen, J., Heimonen, T. and Tuominen, A., “Applicability of No-flow Fluxing Encapsulants and Flip Chip Technology in Volume Production,”IEEE, pp. 163-167, 2000.
10.Cheng, Z.N., Chen, L., Wang, G.Z., Xie, X.M. and Zhang, Q.,“The Effects of Underfill and Its Material Models on Thermomechanical Behaviors of Flip Chip Package,”IEEE Int’l Symp on Electronic Materials & Packaging, pp. 232-239, 2000.
11.Luo, S. and Wong, C.P.,“Environmental Influence on Adhesion of Underfill with Passivation Materials,”IEEE Int’l Symp on Advanced Materials Packaging, pp. 305-311, 2001.
12.Lau, J.H. and Pao, Y.H.,“Solder Joint Reliability of BGA, CSP, Flip Chip, and Fine Pitch SMT Assemblies," McGraw-Hill, p. 4, 1997.
13.AN-1126, “Ball Grid Array,” National Semiconductor Corporation, 2000.
14.William, K.S., “PBGA Wire Bonding Development,” IEEE Electronic Components and Technology Conference, pp. 219-265, 1996.
15.Jianjun, Li and Sung, Y., “Studies on Thermal and Mechanical Properties of PBGA Substrate and Material Construction,” IEEE Electronic Components and Technology Conference, pp. 1595-1604, 2002.
16.Evans, T.C., “Practical Considerations for the Design, Performance, and Applications of Plastic BGA Packages,” IEEE Electronic Components and Technology Conference, pp. 875-883, 1996.
17.Mihelcic, S., “Advanced Packaging: Flexible Flip Chip,” PennWell Corporation, 2002.
18.Suzuki, H., Nakashima, H., Ito, S., Sudo, S., Fukushima, T., Noro, H. and Mizutani, M., “The Trend of Organic Resin Systems for High End IC Encapsulating Packages,” Nitto Denko Corporation, 2002.
19.Liu, J.J., Berg, H., Wen, Y., Mulgaonker, S., Bowlby, R. and Mawer, A., “Plastic Ball Grid Array,” Materials Chemistry and Physics, Vol. 40, pp. 236-244, 1995.
20.Calata, J.N., Lu, G.Q. and Luechinger, C., “Evaluation of Interconnect Technologies for Power Semiconductor Devices,” Inter Society Conference on Thermal Phenomena, IEEE, pp.1089-1096, 2002.
21.Hvims, H.L., “The Nordic Electronics Packaging Guideline,” DELTA, Danish Electronics, Lights & Acoustics, 2002.
22.Bulumulla, S.B., Caggiano, M.F., Lischner, D.J. and Wolf, R.K., “A Comparison of Large I/O Flip Chip and Wire Bonded Packages,” IEEE Electronic Components and Technology Conference, 2001.
23.Ishida, Y., Katoh, T., Ishiwata, S., Omura, A. and Oohara, T., “High Reliable FC-PBGA,” IEEE/CPMT Int’l Electronics Manufacturing Technology Symposium, pp. 104-108, 1996.
24.Pecht, M.G., Nguyen, L.T. and Hakim, E.B., “Plastic-encapsulated Microelectronics,” John Wiely & Sons, Inc., 1995.
25.Hong, B.Z. and Su, L.S., “On Thermal Stresses and Reliability of a PBGA Chip Scale Package,” IEEE Electronic Components and Technology Conference, pp. 503-510, 1998.
26.Matsuda, Y., Woosley, A., Koschmieder, T., Teh, G.K. and Ibrahim, R., “Development of Environmentally Preferred Plastic Ball Array, PBGA, Components,” IEEE, pp. 946-951, 2001.
27.Yip, L., Massingill, T. and Naini, H., “Moisture Sensitivity Evaluation of Ball Grid Array Packages,” IEEE Electronic Components and Technology Conference, pp. 829-835, 1996.
28.Suhir, E., “Predicted Bow of Plastic Package of Integrated Circuit Derives,” J. of Reinforced Plastic and Composites, Vol. 12, pp. 951-972, 1993.
29.Kelly, G., Lyden, C., Lawton, W., Barrett, J., Sabou, A., Page, H. and Peters, H., “The Importance of Molding Compound Chemical Shrinkage in the Stress and Warpage Analysis of PQFPs,” IEEE Conference of Electronic Component and Technology, pp. 977-981, 1995.
30.Liang, D., “Warpage Study of Glob Top Cavity-up EPBGA Package,” IEEE Conference of Electronic Components and Technology, pp. 694-701, 1996.
31.Polsky, Y., Sutherlin, W. and Ume, IC., “A Comparison of PWB Warpage Due to Simulated Infrared and Wave Soldering Process,” IEEE Transactions on Electronics Packaging Manufacturing, Vol. 23, pp.191-199, 2000.
32.Fai, L.T., “FEA Simulation on Moisture Absorption in PBGA Packages under Various Moisture Pre-conditioning,” IEEE Conference of Electronic Components and Technology, pp. 1078-1082, 2000.
33.Wong, E.H., Chan, K.C., Rajoo, R. and Lim, T.B., “The Mechanics and Impact of Hygroscopic Swelling of Polymeric Materials in Electronic Packaging,” IEEE Conference of Electronic Components and Technology, pp. 576-580, 2000.
34.Ilyas, Q.S.M. and Poborets, B., “Evaluation of Moisture Sensitivity of Surface Mount Plastic Packages,” In: Proceedings of the ASME Conference, pp. 145-156, 1993.
35.Shook, R.L., Conrad, T.R., Sastry, S. and Steele, D.B., “Diffusion Model to Derate Moisture Sensitive Surface Mount IC’s for Factory Use Condition,” IEEE Transactions on Components﹐Packaging﹐and Manufacturing Technology-Part C, Vol. 19, No. 2, pp. 110-118, April 1996.
36.Shook, R.L. and Goodelle, J.P., “Handling of Highly-moisture Sensitive Components- An Analysis of Low-humidity Containment and Baking Schedules,” IEEE Transactions on Electronics Packaging Manufacturing, Vol. 23, No. 2, pp. 81-86, April 2000.
37.Huang, Y.E., Hagen, D., Dody, G. and Burnette, T., “Effect of Solder Reflow Temperature Profile on Plastic Package Delamination,” IEEE/CPMT Int’l Electronics Manufacturing Technology Symposium, pp. 105-111, 1998.
38.Galloway, J.E. and Miles, B.M., “Moisture Absorption and Desorption Predictions for Plastic Ball Grid Array Packages,” In: Inter Society Conference on Thermal Phenomena, IEEE, pp. 180–186, 1996.
39.Sawada, Y., Yamaguchi, A., Oka, S. and Fujioka, H., “The Reliability of Plastic Ball Grid Array Package,” IEMT/IMC Proceedings, pp. 35-39, 1998.
40.Egan, E., Kelly, G. and Herard, L., “PBGA Warpage and Stress Prediction for Efficient Creation of the Thermomechanical Design Space for Package-Level Reliability,” IEEE Conference of Electronic Components and Technology, pp. 1217-1223, 1999.
41.Qi, Q., “Reliability Studies of Two Flip-chip BGA Packages Using Power Cycling Test,” Microelectronics Reliability, Vol. 41, pp. 553-562, 2001.
42.Fan, L., Moon, K.S. and Wong, C.P., “Adhesion Study on Underfill Encapsulant Affected by Flip Chip Assembly Variables,” IEEE Int’l Symp on Advanced Packaging Materials, pp. 213-217, 2001.
43.Ferguson, T.P. and Qu, J., “Moisture Absorption in No-flow Underfill Materials and Its Effect on Interfacial Adhesion to Solder Mask Coated FR4 Printed Wiring Board,” IEEE Int’l Symp on Advanced Packaging Materials, pp. 327-332, 2001.
44.Tong, Q., Ma, B., Xiao, A., Savoca, A., Luo, S. and Wong, C.P., “Fundamental Adhesion Issues for Advanced Flip Chip Packages,” IEEE Electronic Components and Technology Conference, pp. 1373-1379, 2002.
45.Bressers, H., Beris, P., Cacrs, J. and Wondegem, J., “Influence of Chemistry and Processing of Flip Chip Underfills on Reliability,” in Proc. 2nd Int. Conf. Adhesive Joining Coating Technol. Electron. Manufact., Sweden, 1996.
46.Ume, I.C., Martin, C., and Gatro, J.T., “Finite Element Analysis of PWB Warpage Due to the Solder Masking Process,” IEEE Trans. on Compoents, Packaging, and Manufacturing Technology, Part A, Vol. 20, pp. 295-306, 1997.
47.Zhu, H., Guo, Y., Li, W.Y., Tseng, A.A. and Martin, B., “Micro-mechanical Characterization of Solder Mask Materials,” IEEE Electronics Packaging Technology Conference, pp. 148-153, 2000.
48.Royce, B.H., “Differential Thermal Expansion in Microelectronic Systems,” IEEE Complete manuscript reviewed by I-THERM Program Committee, pp. 171-180, 1988.
49.Kinloch, A.J., “Adhesion and Adhesives-science and Technology,” Chapman and Hall, 1990.
50.Costlow, T., “Focus on conductive epoxies,” Electronic design, Vol. 34, No. 11, pp. 181-186, May 1986.
51.Yamagochi, Y. and Kato, M., "Some Progress in Anisotropic Conductive Film," Proceedings from Nepcon west 1991, Feb. pp. 24-28, 1991.
52.Dassele, M.A., "EPO-TEK H20E Conductive Epoxy: the Effects of Mix Ratio and Potage on Electrical and Mechanical Performance," Epoxy Technology Inc., 2000.
53.Dorbath, B. and Mieskes, H.D., "Development and Application of Conductive Adhesives for New Interconnection Technologies in Electronics," Demetron, Preceedings from "Verbindungstechnik in der Elektronik/Interconnection technology in electronics", DVS 129, Feb. 1990.
54.Stone, B., Czarnowski, J.M., and Guajardo, J.R., “High Performance Flip Chip PBGA Development,” IEEE Electronic Components and Technology Conference, 2001.
55.Shi, X.Q., Wang, Z.P., Pang, H.J., and Zhang, X.R., “Investigation of Effect of Temperature and Strain Rate on Mechanical Properties of Underfill Material by Use of Microtensile Specimens,” Polymer Testing, Vol. 21, pp. 725-733, 2002.
56.Pyland, J., Pucha, R.V., and Sitaraman, S.K., “Thermalmechanical Reliability of Underfilled BGA Packages,” IEEE Trans. on Electronics Packaging Manufacturing, Vol. 25, No. 2, pp. 100-106, 2002.
57.Schubert, A., Dudek, R., Michel, B., Reichl, H., “Materials Mechanics and Mechanical Reliability of Flip Chip Assemblies on Organic Substrates,” IEEE Int’l Symp on Advanced Materials Packaging, pp. 106-109, 1997.
58.Cheng, Z., Xu, B., Zhang, Q., Cai, X., Huang, W. and Xie, X., “Underfill Delamination Analysis of Flip Chip on Low-cost Board,” IEEE Int’l Symp on Electronic Materials & Packaging, pp. 280-285, 2001.
59.Chung, W.K., Chan, S.K., Yuen, M.F., Lam, C.C. and Teng, A., “Energy Based Failure Criterion for Interfacial Delamination,” IEEE Int’l Symp on Electronic Materials & Packaging, pp. 201-205, 2000.
60.Szeto, W.K., Xie, M.Y., Kim, J.K., Yuen, M.F., Tong, P. and Yi, S., “Interface Failure Criterion of Button Shear Test as a Means of Interface Adhesion Measurement in Plastic Packages,” IEEE Int’l Symp on Electronic Materials & Packaging, pp. 263-268, 2000.
61.Her, S.C., “Stress Analysis of Adhesively-bonded Lap Joints,” Composite Structures, 1999.
62.Lang, T.P. and Mallick, P.K., “The Effect of Recessing on the Stresses in Adhesively Bonded Single-lap Joint,” International Journal of Adhesion & Adhesives, pp. 257-271, 1999.
63.Hu, N., Wang, B., Sekine, H., Yao, Z. and Tan, G., “Shape-optimum Design of a Bi-material Sing-lap Joint,” Composite Structures, pp. 315-350, 1998.
64.Li, G. and Pear, L.S., “Finite Element and Experimental Studies on Single-lap Balanced Joints in Tension,” International Journal of Adhesion & Adhesives, pp. 211-220, 2001.
65.Cheikh, M., Coorevits, P. and Loredo, A., “Modelling the Stress Vector Continuity at the Interface of Bonded Joints,” International Journal of Adhesion & Adhesives, Vol. 21, pp.249-257, 2001.
66.Tsai, M.Y., “The Effect of a Spew Fillet on Adhesive Stress Distributions in Laminated Composite Single-lap Joint,” Composite Structures, pp. 123-131, 1995.
67.Tsai, M.Y., Oplinger, D.W. and Morton, J., “Improved Theoretical Solutions for Adhesive Lap Joints,” Int. J. Solids Structures, Vol. 35, No. 12, pp. 1163-1185, 1998.
68.Yilan, K., Laermann, K.H. and Youquan, J., “Experiment Analysis for Bonded Biomaterial Beam under Bending Load,” Measurement, pp. 85-90, 1995.
69.Kafkalidis, M.S. and Thouless, M.D., “The Effects of Geometry and Material Properties on the Fracture of Single Lap-shear Joints,” International Journal of Solids and Structures, Vol. 39, pp. 4367-4383, 2002.
70.Owens, F.P. and Pearl, L.S., “Stiffness Behavior Due to Fracture in Adhesively Bonded Composite-to-aluminum Joints: 1. Theoretical Model,” International Journal of Solids and Structures, Vol. 20, pp. 39-45, 2000.
71.Belingardi, G., Goglio, L. and Tarditi, A., “Investigating the Effect of Spew and Chamfer Size on the Stresses in Metal/Plastics Adhesive Joints,” International Journal of Adhesion & Adhesives, Vol. 22, pp.273-282, 2002.
72.Hibbeler, R. C., ”Mechanics of Materials,“ Prentice Hall International, 1997.
73.Post, D., Han, B. and Ifju, P., “High Sensitivity Moiré,” Springer-Verlag, 1994.
74.Kawamura, N., Hirohata, K., Kawakami, T., Sawada, K., Mino, T., Kurosu, A., Takano, E. and Yeoul, Y.H., “Adhesion Integrity Evaluation of Plastic Encapsulated Semiconductor Package,” IEEE Electronic Components and Technology Conference, pp. 1132-1139, 2001.
75.Kim, S., “The Role of Plastic Package Adhesion in IC Performance,” Proc 41st Electronic Components and Technology Conference, pp. 750-758, 1991.
76.Ohsuga, H., Suzuki, H., Aihara, T. and Hamano, T., “Development of Molding Compounds Suited for Copper Leadframes,” Proc 44st Electronic Components and Technology Conference, pp. 141-146, 1994.
77.Cui, C.Q., Tay, H.L., Chai, T.C., Gopalakrishan, R. and Lim, T.B. ”Surface Treatment of Copper for the Adhesion Improvement to Epoxy Mold Compounds,” IEEE, 1998.
78.Suhir, E., “Interfacial Stresses in Bi-metal thermostats,” Journal of Applied Mechanics, Vol. 56, pp. 595-600, 1989.
79.Suhir, E., “Approximate Evaluation of the Interfacial Shearing Stress in Cylindrical Double Lap Shear Joints with Application to Dual-coated Optical Fibers,” International Journal of Solid and Structures, Vol. 31, pp. 3261-3283, 1994.
80.Tsai, M.Y. and Morton, J., “An Experimental Investigation of Nonlinear Deformations in Single-lap Joint,” Mechanics of Materials, pp.183-194, 1995.
81.“D3164 Standard Test Method for Strength Properties of Adhesively Bonded Plastic Lap-Shear Sandwich Joints in Shear by Tension Loading,” ASTM, 1997.
82.Rao, C.R., “Factorial Experiments Derivable From Combinational Arrangements of Arrays,” Journal of Royal Statistical Society Series B, Vol. 9, pp. 128-139, 1947.
83.Taguchi G., “Off-line and On-line Quality Control System,” Internatinal Conference on Quality Control, 1978.
84.JESD22-A104-B, “Temperature Cycling”, JEDEC Solid State Technology Association, July 2000.
85.Li, G., Pearl, L.S. and Thring, R.W., “Nonlinear Finite Elements Analysis of Stress and Strain Distributions Across the Adhesive Thickness in Composite Single-lap Joints,” Composite Structures, Vol. 46, pp. 395-403, 1999.
86.Andruet, R.H., Dillard D.A. and Holzer, S.M., “Two- and Three-dimensional Geometrical Nonlinear Finite Elements for Analysis of Adhesive Joints,” International Journal of Adhesion & Adhesives, Vol. 21, pp.17-34, 2001.