發光二極體具有低耗能、長壽命且高光電轉換效率的優點，因此已經被許多市售產品使用，如照明、號誌燈、顯示器之背光模組與汽車車燈等。在發光二極體晶片製造成上述產品之前，仍需透過封裝製程提高光取出率與電訊導通，目前發光二極體主要之封裝形式，仍是以打線封裝為主，然而打線封裝的製程參數極為敏感，常因不恰當之打線封裝參數造成發光二極體之晶片破壞進而導致金屬墊片脫離。

為了確保發光二極體在打線封裝良好的可靠度，本研究以單點負載試驗搭配離子聚焦束顯微鏡求得發光二極體之磊晶層之最大容許力量，並以此最大容許力量搭配有限單元分析求得不受接觸面積影響之最大容許應力，此最大應力發生於磊晶層且接近探頭之邊緣，如此即可得到有效的發光二極體極限強度確認工具，作為發光二極體晶片設計之參考。完成極限強度確認工具之後，先以參數化分析與新結構設計試圖降低接觸應力，其後並以實際結構進行實驗確認，結果顯示磊晶層之抗壓強度可透過數值分析有效的提高強度並阻止破壞發生。此外，為了解釋單點負載試驗中產生之橫向裂紋，本研究再以四點彎折脫層試驗搭配改良型虛擬裂紋閉合技術求得量子井介層之臨界應變能釋放率，模擬與實驗結果有良好的一致性，且顯示一旦有破壞發生，裂痕會很容易因外力負載而造成裂紋成長。

High-power light emitting diodes (LEDs) are found in a number of applications in high-volume consumer markets, such as illumination, signalling, screen backlights, automotives, and others, because of the numerous advantages of LEDs, including low power cost, long life span, and high efficiency. Wire bonding is one of the major processes in the LED packaging process that provide electrical interconnection between the bonding pad and the lead. However, due to bad parameter setup in a wire bonder, the LED will crack and the pad will peel after wire bonding.

In this study, the strength of LED is determined for the design requirement in order to ensure good reliability of wire bonding. Point-load test (PLT) and focused ion beam (FIB) are used to determine the maximum allowable force the epilayer can withstand, which is approximately 75 g. By combining the finite element method and experimental data, a useful design tool to confirm LED die strength is provided. The finite element result of contact analysis show that the stress concentration area is located on the edge of the pin and maximum stress (212 MPa) occurs in the epilayer. Parametric study and new structure design are employed to find ways to reduce stress in LED layer. The results indicate that the strength of epilayer can be enhanced to resist the crack initiation due to new structure design. Furthermore, the four-point bending (4PB) delamination test and modified virtual crack closure technique (MVCCT) is adopted to measure and predict the critical energy release rate near the interface of multiple quantum well. Simulation results have a good agreement with the experimental data and show a weak adhesion near the interface.

1. A. ZuKauskas, M. S. Shurand, and R. Gaska, Introduction
to Solid-State Lighting, John Wiley & Sons Inc, Canada,
2002.
2. E. Fred Schubert, Light–Emitting Diodes, second edition,
Cambridge University Press, 2006.
3. C. N. Han, T. L. Chou, C. F. Huang, and K. N. Chiang,
“Sappire-removed Induced the Deformation of High Power
InGaN Light Emitting Diodes,” 9th International on
Thermal, Mechanical and Multiphysics Simulation and
Experiments in Micro-Electronics and Micro-Systems, pp.1-
5, Freiburg, Germany, Apr., 20-23, 2008
4. H. A. Deng, S. Y. Yang, C. N. Han, T. L. Chou, and K. N.
Chiang “Warpage Analysis of High Power InGaN Light
Emitting Diodes after Laser Lift-off,” 11th International
Conference on Electronics Materials and Packaging, pp.1-
5, Penang, Malaysia, Dec 1-3, 2009.
5. W. H. Chi, T. L. Chou, C. N. Han, S. Y. Yang, K. N.
Chiang, “Analysis of Thermal and Luminous Performance of
MR-16 LED Lighting Module”, IEEE Transactions on
Components and Packaging Technologies, Vol. 33, Issue 4,
pp.713-721, 2010.
6. Y. F. Su, S. Y. Yang, T. Y. Hung, C. C. Lee, and K. N.
Chiang, “Light Degradation Test and Design of Thermal
Performance for High-power Light-emitting Diodes,”
Microelectronics Reliability, Vo. 52, Issue 5, pp.794-
803, 2012.
7. H. Sugawara, M. Ishikawa, and G. Hatakoshi, “High-
efficiency InGaAlP/GaAs Visible Light-emitting Diodes,”
Apply Physics Letters, Vol. 58, pp.1010, 1991.
8. H. Sugawara, K. Itaya, H. Nozaki, and G. Hatakoshi,
“High-brightness InGaAlP Green Light-emitting Diodes,”
Apply Physics Letters, Vol. 61, pp.1775-1777, 1992.
9. B. Saint-Cricq, A. Rudra, JD Ganiere, and M. Ilegems
“High-reflectance GaInP/GaAs Distributed Bragg
Reflector,” Electronics Letters, Vol. 29, No. 21,
pp.1854-5, 1993.
10.H. Sugawara, K. Itaya, and G. Hatakoshi “Hybrid-type
InGaAlP/GaAs Distributed Bragg Reflectors for InGaAlP
Light-emitting Diodes,” Japanese Journal of Applied
Physics, Vol. 33, No. 11, pp.6195-8, 1994.
11.S. W. Chiou, C. P. Lee, C. K. Huang, and C. W. Chen “Wide
Angle Distributed Bragg Reflectors for 590 nm Amber
AlGaInP Light-emitting Diodes,” Japanese Journal of
Applied Physics, Vol. 87, Issue 4, pp.2052, 2000.
12.F. A. Kish, F. M. Steranka, D. C. DeFevere, D. A.
Vanderwater, K. G. Park, C. P. Kuo, T. D. Osentowski, M.
J. Peanasky, J. G. Yu, R. M. Fletcher, D. A. Steigerwald,
and M. G. Craford, “Very High-efficiency Semiconductor
Wafer-bonded Transparent-substrate (AlxGa1−x)0.5
In0.5P/GaP Light-emitting Diodes,” Apply Physics Letters,
Vol. 64, pp.2839-2841, 1994.
13.F. A. Kish, D. A. Vanderwater, M. J. Peanasky, M. J.
Ludowse, S. G. Hummel, and S. J. Rosner, “Low-resistance
Ohmic Conduction across Compound Semiconductor Wafer-
bonded Interfaces,” Apply Physics Letters, Vol. 67,
pp.2060–2062, 1995.
14.G. E. Höfler, D. A. Vanderwater, D. C. DeFevere, F. A.
Kish, M. D. Camras, F. M. Steranka, and I.-H. Tan, “Wafer
Bonding of 50-mm Diameter GaP to AlGaInP-GaP Light-
emitting Diode Wafers,” Apply Physics Letters, Vol. 69,
pp.803-805, 1996.
15.D. A. Vanderwater, I. H. Tan, G. E. Hofler.,
D.C.Defevere, and F.A. Kish, “High-brightness AlGaInP
Light Emitting Diodes,” Proceedings of the IEEE, Vol.8,
No.11, pp.1752-64, 1997.
16.J. K. Sheu, Y. K. Su, S. J. Chang, M. J. Jou, C. C. Liu,
and G. C. Chi, “Investigation of Wafer-bonded (AlxGa1-
x)0.5In0.5P/GaP Light-emitting Diodes,” IEEE Proceedings
Optoelectronics, Vol. 145, No. 4, pp.248-52, 1998.
17.M. R. Krames, M. Ochinai-Holocomb, G. E. Höfler, C.
Carter-Coman, E. I. Chen, I.-H. Tan, P. Grillot, N. F.
Gardner, H. C. Chui, J.-W. Huang, S. A. Stockman, F. A.
Kish, and M. G. Craford, “High-power Truncated- inverted-
pyramid (AlxGa1-x)0.5In0.5P/GaP Light-emitting Diode
Exhibiting >50% External Quantum Efficiency,” Apply
Physics Letters, Vol. 75, pp.2365–2367, 1999.
18.Vanderwater DA, Kish FA, Peansky MJ, and Rosner SJ.
“Electrical Conduction through Compound Semiconductor
Wafer Bonded Interfaces.” Journal of Crystal Growth, Vol.
174, No. 1-4, pp.213-19, 1997.
19.R. H. Horng, D. S.Wuu, S. C.Wei, M. F. Huang, K. H.
Chang, P. H. Liu, and K. C. Lin, “AlGaInP/AuBe/glass
Light-emitting Diodes Fabricated by Wafer Bonding
Technology,” Apply Physics Letters, Vol. 75, Issue 2,
pp.154-156, 1999.
20.S. J. Chang, Y. K. Su, T. Yang, C. S. Chang, T. P. Chen,
and K. H. Huang, “AlGaInP-sapphire Glue Bonded Light-
emitting Diodes,” IEEE Journal of Quantum Electronics,
Vol. 38, Issue 10 ,pp.1390- 1394, 2002.
21.R. H. Horng, D. S. Wuu, S. C. Wei, C. Y. Tseng, M. F.
Huang, K. H. Chang, P. H. Liu, and K. C. Lin, “AlGaInP
Light-emitting Diodes with Mirror Substrates Fabricated
by Wafer Bonding,” Apply Physics Letters, Vol. 75,
pp.3054–3056, 1999.
22.R. H. Horng, D. S. Wuu, S. C. Wei, C. Y. Tseng, M. F.
Huang, K. H. Chang, P. H. Liu, and K. C. Lin, “Wafer-
Bonded AlGaInP/Au/AuBe /SiO2/Si Light-Emitting Diodes ,”
Japanese Journal of Applied Physics, Vol. 39, pp.2357-
2359, 2000.
23.K. H. Chang, K. C. Lin, R. H. Horng, M. F. Huang, D.S.
Wuu, S. C. Wei, and L. C. Chen, “Light Emitting Diode
with a Permanent Substrate of Transparent Glass or Quartz
and the Method for Manufacturing the same,” United States
Patent 6258699, 2001.
24.R. H. Horng and D. S. Wuu, “Wafer-Bonded 850-nm Vertical-
Cavity Surface-Emitting Lasers on Si Substrate with Metal
Mirror,” Japanese Journal of Applied Physics, Vol. 41,
pp.5849-5852, 2002.
25.R. H. Horng, S. H. Huang, D. S. Wuu, and C. Y. Chiu,
“AlGaInP/mirror/Si Light-emitting Diodes with Vertical
Electrodes by Wafer Bonding,” Apply Physics Letters, Vol.
82, 2003.
26.W. C. Peng and Y. S. Wu, “High-power AlGaInP Light-
emitting Diodes with Metal Substrates Fabricated by Wafer
Bonding” Apply Physics Letters, Vol. 84, No. 11, 2004.
27.C. Rooman, M. Kuijk, S. De Jonge, and P. Heremans, “High-
efficiency AlGaInP Thin-film LEDs using Surface-texturing
and Wafer Bonding with Conductive Epoxy,” IEEE Photonics
Technology Letters, Vol. 17, Issue 12, pp.2649- 2651,
2005.
28.Y. C. Lee, H. C. Kuo, C. E. Lee, T. C. Lu, S. C. Wang,
and S. W. Chiou, “High Temperature Stability of 650-nm
Resonant Cavity Light-emitting Diodes Fabricated Using
Wafer-Bonding Technique on Silicon Substrates,” IEEE
Photonics Technology Letters, Vol. 19, pp.1060-1062,
2007.
29.S. C. Hsu, D. S. Wuu, X. Zheng, , J. Y. Su, , M. F. Kuo,
P. Han, and R. H. Horng, “Power-enhanced ITO Omni-
directional Reflective AlGaInP LEDs by Two-dimensional
Wavelike Surface Texturing,” Semiconductor Science and
Technique, Vol. 23, pp.105013-105018, 2008.
30.T. L. Chou, C. F. Huang, C. N. Han, S. Y. Yang, and K. N.
Chiang, “Fabrication Process Simulation and Reliability
Improvement of High- brightness LEDs,” Microelectronics
Reliability, Vol. 49, Issue 9-11, pp.1244-1249, 2009.
31.A. Coucoulas, “Hot Work Ultrasonic Bonding? A Method of
Facilitating Metal Flow by Restoration Process,”
Proceedings 20th IEEE Electronic Components Conference,
pp.549-556, Washington, District of Columbia, USA, May,
1970.
32.G. Harman, Wire Bonding in Microelectronics, McGraw-Hill,
New York, 1997.
33.V. H. Winchell, “An Evaluation of Silicon Damage
Resulting from Ultrasonic Wire Bonding,” 14th Annual
Proceedings Reliability Physics, pp.211-219, Las Vegas,
Nevada, USA, Apr., 1976.
34.Y. S. Chen, and H. Fatemi, “Au Wire Bonding Evaluation by
Factional Factorial Designed Experiment,” The
International Journal for Hybrid Microelectronics, Vol.
10, No, 3, pp. 1-7, 1987.
35.T. C. Wei and A. R. Duad, “Cratering on Thermosonic
Copper Wire Ball Bonding,” Journal of Material
Engineering and Performance, Vol. 11, No.3, pp.283-287,
2002.
36.W. H. Lycette, E. R. Knight and S. W. Hinch, “Thermosonic
and Ultrasonic Wire Bonding to GaAs FETs,” International
Journal Hybrid Microelectronic, Vol. 5, , pp.512-517,
1982.
37.J. Hirota, K, Machida, T. Okuda, M. Shimotomai and R.
Kawanaka, “The Development of Copper Wire Bonding for
Plastic Molded Semiconductor Packages,” Proceedings 35th
Electronic Components Conference, pp.116-121, Washington,
District of Columbia, USA, May, 20-22, 1985.
38.K. V. Ravi and R White, “Reliability Improvement in 1-mil
Aluminum Wire Bonds for Semiconductors,” Final Report of
Motorola SPD, NASA Contract NAS8-26636, 1971.
39.V. S. Kale, “Control of Semiconductor Failure Caused by
Cratering of Bonding Pads,” Proceedings of the 1979
International Microelectronics Symposium, pp.311-318, Los
Angeles, California, USA, Nov., 13-15, 1979.
40.V. H. Winchell and H. M. Berg “Enhancing Ultrasonic Bond
Development,” IEEE Transactions on Components, Hybrids,
and Manufacturing Technology, Vol. CHMT-1, pp.211-219,
1978.
41.S. Mori, H. Yoshida and N Uchiyama, “The Development of
New Copper Ball bonding wire,” Proceedings 38h Electronic
Components Conference, pp.539-545, Los Angeles,
California, USA, May, 9-11, 1988.
42.N Srikanth, “Critical Study of Mircofoging Au Ball on Al
Coated Silicon Substrate using Finite Element Method,”
Materials Science and Technology , Vol. 13, pp.1199-1207,
2007.
43.N. Srikanth, S. Murali, Y. M. Wang and C. J. Vath,
“Critical Study of Thermosonic Copper Ball Bonding,” Thin
Solid Films , Vol. 1, pp.339-345, 2004.
44.G. Heinen, R. J. Stierman, D. Edwards and L. Nye, “Wire
Bonds over Active Circuits,” 44th Electronic Components
and Technology Conference, pp.922-928, Washington,
District of Columbia, USA, May, 1-4, 1994.
45.R. Mckenna, “High Impact Bonding to Improve Reliability
of VLSI Die in Plastic Packages,” 39th Proceedings of
IEEE Electronics Components Conference, pp.424-427,
Houston, Texas, May, 22-24, 1989.
46.V. S. Kale, “Control of Semiconductor Failure Caused by
Cratering of Bonding Pads,” Proceedings of the 1979
International Microelectronics Symposium, pp.311-318, Los
Angeles, California, USA, Nov., 13-15, 1979.
47.T. B. Ching and W. H. Schroen, “Bond Pad Structure
Reliability,” 24th Annual Proceedings, Reliability
Physics, pp.64-70, Monterey, California, Apr., 12-14,
1988.
48.I. Jeon and Q. Chung, “The Study on Failure Mechanisms of
Bond Pad Metal Peeling: Part A-Experimental
Investigation,” Microelectronics Reliability, Vol. 43,
pp.2047-2054, 2003.
49.I. Jeon, “The Study on Failure Mechanisms of Bond Pad
Metal Peeling: Part B-Numerical Analysis,”
Microelectronics Reliability, Vol. 43, pp.2055-2064,
2003.
50.K. C. Chang and K. N. Chiang, “Growth Analysis of
Interfacial Delamination of Plastic Ball Grid Array
Package during Solder Reflow using Global-local Finite
Element Method." Journal of Strain Analysis for
Engineering Design, Vol. 41, No. 1, pp.19-30, 2006.
51.M. C. Yew, C. C. Chiu, S. M. Chang and K. N. Chiang, “A
Novel Crack and Delamination Protection Mechanism for a
WLCSP Using Soft Joint Technology," Soldering & Surface
Mount Technology, Vol. 18, Issue 3, pp. 3-13, 2006.
52.C. C. Chiu, C. J. Huang, S. Y. Yang, C. C. Lee, and K. N.
Chiang, “Investigation of the Delamination Mechanism of
the Thin Film Dielectric Structure in Flip Chip
Packages,” Microelectronic Engineering, vol. 87, pp.496-
500, 2010.
53.C. J. Wu, M. C. Hsieh, C. C. Chiu, M. C. Yew, and K. N.
Chiang, “Interfacial Delamination Investigation between
Copper Bumps in 3D Chip Stacking Package by using the
Modified Virtual Crack Closure Technique,”
Microelectronic Engineering, Vol. 88, pp.739-744, 2011.
54.A. A. Volinsky, N. R. Moody, and W. W. Gerberich,
“Interfacial toughness measurements for thin films on
substrates,” Acta Materialia, Vol. 50, pp. 441-466, 2002.
55.M. Menningen, H. Weiss, and U. Fischer, “Metallic Wear-
Resistant Coatings for Carbon-Fiber Epoxy Composite
Rolls,” Surface & Coatings Technology, Vol. 71, pp. 208-
214, 1995.
56.Z. G. Suo and J. W. Hutchinson, “Sandwich Test Specimens
for Measuring Interface Crack Toughness,” Materials
Science and Engineering a-Structural Materials Properties
Microstructure and Processing, Vol. 107, pp. 135-143,
1989.
57.F. Aviles and L. A. Carlsson, “Analysis of the sandwich
DCB specimen for debond characterization,” Engineering
Fracture Mechanics, Vol. 75, pp. 153-168, 2008.
58.P. C. A. Lee, Z. X. Lima, N. Yantaraa, S. Loo, T. Y. Tee,
C. M. Tan, and Z. Chen, “Fracture Toughness Assessment of
a Solder Joint using Double Cantilever Beam Specimens,”
10th Electronics Packaging Technology Conference (EPTC),
pp.1066-1073, Singapore, Dec., 9-12, 2008.
59.C. Atkinson, R. E. Smelser, and J. Sanchez, “Combined
Mode Fracture Via the Cracked Brazilian Disk Test,”
International Journal of Fracture, Vol. 18, pp. 279-291,
1982.
60.J. S. Wang and Z. Suo, “Experimental-Determination of
Interfacial Toughness Curves Using Brazil-Nut-
Sandwiches,” Acta Metallurgica Et Materialia, Vol. 38,
pp. 1279-1290, 1990.
61.R. Dauskardt, M. Lane, Q. Ma, and N. Krishna, “Adhesion
and Debonding of Multi-layer Thin Film Structures,”
Engineering Fracture Mechanics, Vol. 61, pp. 141-162,
1998.
62.M. P. Hughey, D. J. Morris, R. F. Cook, S. P. Bozeman, B.
L. Kelly, S. L. N. Chakravarty, D. P. Harkens, and L. C.
Stearns, “Four-point Bend Adhesion Measurements of Copper
and Permalloy Systems,” Engineering Fracture Mechanics,
Vol. 71, pp. 245-261, 2004.
63.M. Lane, R. H. Dauskardt, N. Krishna, and I. Hashim,
“Adhesion and Reliability of Copper Interconnects with Ta
and TaN Barrier Layers,” Journal of Materials Research,
Vol. 15, pp. 203-211, 2000.
64.Q. Ma, “A Four-point Bending Technique for Studying
Subcritical Crack Growth in Thin Films and at
Interfaces,” Journal of Materials Research, Vol. 12, pp.
840-845, 1997.
65.Z. H. Gan, S. G. Mhaisalkar, Z. Chen, S. Zhang, Z. Chen,
and K. Prasad, “Study of Interfacial Adhesion Energy of
Multilayered ULSI Thin Film Structures using Four-point
Bending Test,” Surface & Coatings Technology, Vol. 198,
pp. 85-89, 2005.
66.M. Lane, R. H. Dauskardt, A. Vainchtein, and H. J. Gao,
“Plasticity Contributions to Interface Adhesion in Thin-
film Interconnect Structures,” Journal of Materials
Research, Vol. 15, pp. 2758-2769, 2000.
67.T. L. Chou, S. Y. Yang, C. J. Wu, C. N. Han, and K. N.
Chiang, “Measurement and Simulation of Interfacial
Adhesion Strength between SiO2 Thin Film and III-V
Material,” Microelectronics Reliability, Vol. 51, Issues
9-11, pp.1757-1761, 2011.
68.P. G. Charalambides, J. Lund, A. G. Evans, and R. M.
McMeeking, “A Test Specimen for Determining the Fracture
Resistarim of Bimaterial Interfaces,” Journal of Applied
Mechanics-Transactions of the Asme, Vol. 56, pp.77-82,
1989.
69.P. G. Charalambides, H. C. Cao, J. Lund, and A. G. Evans,
“Development of a Test Method for Measuring the Mixed-
Mode Fracture-Resistance of Bimaterial Interfaces,”
Mechanics of Materials, Vol. 8, pp.269-283, 1990.
70.E. P. Guyer, M. Patz, and R. H. Dauskardt, “Fracture of
Nanoporous Methyl Silsesquioxane Thin-film Glasses,”
Journal of Materials Research, Vol. 21, pp.882-894, 2006.
71.D. A. Maidenberg, W. Volksen, R. D. Miller, and R. H.
Dauskardt, “Toughening of Nanoporous Glasses using
Porogen Residuals,” Nature Materials, Vol. 3, pp.464-469,
2004.
72.Y. Kwon and J. Seok, “An Evaluation Process of Polymeric
Adhesive Wafer Bonding for Vertical System Integration,”
Japanese Journal of Applied Physics Part 1-Regular Papers
Brief Communications & Review Papers, Vol. 44, pp.3893-
3902, 2005.
73.Y. Kwon, J. Seok, J. Q. Lu, T. S. Cale, and R. J.
Gutmann, “Critical Adhesion Energy of Benzocyclobutene-
bonded Wafers,” Journal of the Electrochemical Society,
Vol. 153, pp.G347-G352, 2006.
74.W. S. Kwon, H. J. Kim, K. W. Paik, S. Y. Jang, and S. M.
Hong, “Mechanical Reliability and Bump Degradation of ACF
Flip Chip Packages using BCB (CycloteneTM) Bumping
Dielectrics under Temperature Cycling,” Journal of
Electronic Packaging, Vol. 126, pp.202-207, 2004.
75.Z. J. Cui, S. Ngo, and G. Dixit, “A Sample Preparation
Method for Four Point Bend Adhesion Studies,” Journal of
Materials Research, Vol. 19, pp.1324-1327, 2004.
76.R. Shaviv, S. Roham, and P. Woytowitz, “Optimizing the
Precision of the Four-point Bend Test for the Measurement
of Thin Film Adhesion,” Microelectronic Engineering, Vol.
82, pp.99-112, 2005.
77.D. M. Gage, K. Kim, C. S. Litteken, and R. H. Dauskard,
“Role of Friction and Loading Parameters in Four-point
Bend Adhesion Measurements,” Journal of Materials
Research, Vol. 23, pp.87-96, 2008.
78.B. Wang and T. Siegmund, “A Modified 4-point Bend
Delamination Test,” Microelectronic Engineering, Vol. 85,
pp.477-485, 2008.
79.I. Hofinger, M. Oechsner, H. A. Bahr, and M. V. Swain,
“Modified Four-point Bending Specimen for Determining the
Interface Fracture Energy for Thin, Brittle Layers,”
International Journal of Fracture, Vol. 92, pp.213-220,
1998.
80.H. Hertz, On the Contact of Elastic Solids, Macmillan &
Co., London, 1986.
81.K. L. Johnson, Contact Mechanics, Cambridge University
Press, Cambridge, 1985.
82.Z. H. Zhong, Finite Element Procedures for Contact-Impact
Problems,” Oxford University Press, New York, 1993.
83.R. D. Cook, D. S. Malkus, and M. E. Plesha, “Concepts and
Applications of Finite Element Analysis,” 4th edition,
Wiley, New York, 2002.
84.T. Belytschko, W. K. Liu, and B. Moran, “Nonlinear Finite
Elements for Continua and Structures,” John Wiley & Sons,
New York, 2000.
85.M. H. Aliabadi and C. A. Brebbia, Computational Methods
in Contact Mechanics, Computational Mechanics
Publications, Southampton, UK, 1993.
86.R. Glowinski, M. Vidrascu, and P. Letallec, “Augmented
Lagrangian Techniques for Solving Frictionless Contact
Problems in Finite Elasticity,” Proceedings of the
Europe-US Symposium on Finite Element Methods for
Nonlinear Problems, pp. 745-58, Trondheim, Norway, Aug.,
1985.
87.J. C. Simo and R. L. Taylor, “Quasi-Incompressible Finite
Elasticity in Principal Stretches. Continuum Basis and
Numerical Algorithms,” Computer Methods in Applied
Mechanics & Engineering, Vol. 85, pp. 273-310, 1991.
88.J. C. Simo and T. A. Laursen, “An Augmented Lagrangian
Treatment of Contact Problems Involving Friction,”
Computer & Structures, Vol. 42, pp. 97-116, 1992.
89.R. Glowinski, and P. L. Tallec, Augmented Lagrangian and
Operator-splitting Methods in Nonlinear Mechanics, SIAM
Studies in Applied Mathematics, Philadelphia, 1989.
90.A. A. Volinsky, N. R. Moody and W. W. Gerberich,
“Interfacial Toughness Measurements for Thin Films on
Substrates,” Acta Materialia, Vol. 50, pp. 441-466, 2002.
91.T. L. Anderson, Fracture Mechanics: Fundamentals and
Applications, second edition, CRC Press, 1994.
92.M. H. Aliabadi and C. A. Brebbia, Computational Methods
in Contact Mechanics, Computational Mechanics
Publications, Southampton, UK, 1993.
93.M. D. Drory, M. D. Thouless, and A. G. Evans, "On the
Decohesion of Residually Stressed Thin-Films," Acta
Metallurgica, Vol. 36, pp.2019-2028, 1988.
94.M. D. Thouless, A. G. Evans, M. F. Ashby, and J. W.
Hutchinson, "The Edge Cracking and Spalling of Brittle
Plates," Acta Metallurgica, Vol. 35, pp. 1333-1341, 1987.
95.P. G. Charalambides, J. Lund, A. G. Evans, and R. M.
McMeeking, “A Test Specimen for Determining the Fracture
Resistance of Bimaterial Interfaces,” Journal of Applied
Mechanics, Vol. 56, pp.77-82, 1989.
96.E. F. Rybicki, M. F. Kanninen “A Finite Element
Calculation of Stress Intensity Factors by a Modified
Crack Closure Integral,” Engineering Fracture Mechanics,
Vol. 9, Issue 4, pp.931-938, 1977.
97.I. S. Raju, "Calculation of Strain-Energy Release Rates
with Higher-Order and Singular Finite-Elements,"
Engineering Fracture Mechanics, Vol. 28, pp.251-274,
1987.
98.K. B. Narayana, B. Dattaguru, T. S. Ramamurthy, and K.
Vijayakumar, "Modified Crack Closure Integral using 6-
Noded Isoparametric Quadrilateral Singular Elements,"
Engineering Fracture Mechanics, Vol. 36, pp.945-955,
1990.
99.R. Sethuraman and S. K. Maiti, "Finite-Element Based
Computation of Strain-Energy Release Rate by Modified
Crack Closure Integral," Engineering Fracture Mechanics,
Vol. 30, pp.227-231, 1988.