Fracture initiation at geometric and material discontinuities: Criteria based on critical stress intensities of linear elasticity

Journal of Mechanics

Volumn 19, Issue 1, 2003, Pages 15-29

  Dunn, Martin L ^a  

^a UCB 450   (United States)

Author keywords

Fracture initiation; Interface corner; Sharp notch; Singular stresses

Indexed keywords

CRACKS; ELASTICITY; INTERFACES (MATERIALS); MATERIALS HANDLING; STRESSES;

LINEAR ELASTICITY;

FRACTURE MECHANICS;

EID: 0041781743     PISSN: 17277191     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (85)

1. Rice, J. R., "Elastic Fracture Mechanics Concepts for Interfacial Cracks," J. Appl. Mech., 55, pp. 98-103 (1988).
2. Hutchinson, J. W. and Suo, Z., "Mixed-Mode Cracking in Layered Materials," Advances in Applied Mechanics, 29, pp. 63-191 (1991).
3. Ting, T. C. T. and Chou, S. C., "Edge Singularities in Anisotropic Composites," Int. J. Solids Structures, 17, pp. 1057-1068 (1981).
4. Ting, T. C. T., "Explicit Solution and Invariance of the Singularities at an Interface Crack in Anisotropic Composites," Int. J. Solids Structures, 22, pp. 965-983 (1986).
5. Ting, T. C. T., "Generalized Dundurs Constants for Anisotropic Bimaterials," Int. J. Solids Structures, 32, pp. 483-500 (1985).
6. Ting, T. C. T., Anisotropic Elasticity: Theory and Applications, Oxford Science Publications (1996).
7. Ting, T. C. T., "Stress Singularities at the Tip of Interfaces in Polycrystals," Damage and Failure of Interfaces, Rossmanith (ed.), Balkema, Rotterdam, pp. 75-82 (1998).
8. Somaratna, N. and Ting, T. C. T., "Three-Dimensional Stress Singularities in Anisotropic Materials and Composites," Int. J. Engng. Sci., 24, pp. 1115-1134 (1986).
9. Leguillon, D., "Strength or Toughness? A Criterion for Crack Onset at a Notch," European Journal of Mechanics A - Solids, 21, pp. 61-72 (2002).
10. Walsh, P. F., "Crack Initiation in Plain Concrete," Mag. Concrete Res., 28, pp. 37-41 (1976).
11. Carpinteri, A., "Stress-Singularity and Generalized Fracture Toughness at the Vertex of Re-Entrant Corners," Engineering Fracture Mechanics, 26, pp. 143-155 (1987).
12. Seweryn, A., "Brittle Fracture Criterion for Structures with Sharp Notches," Engineering Fracture Mechanics, 47, pp. 673-681 (1994).
13. Dunn, M. L., Suwito, W. and Cunningham, S. J., "Fracture Initiation at Sharp Notches: Correlation Using Critical Stress Intensities," International Journal of Solids and Structures, 34, pp. 3873-3883 (1997).
14. Dunn, M. L., Suwito, W. and Cunningham, S. J., "Fracture Initiation at Sharp Notches under Mode I, Mode II, and Mild Mixed-Mode Loading," International Journal of Fracture, 84, pp. 367-381 (1997).
15. Lefebvre, D. R. and Dillard, D. A., "A Stress Singularity Approach for the Prediction of Fatigue Crack Initiation in Adhesive Bonds, Part 2: Experimental," Journal of Adhesion, 70, pp. 139-154 (1999).
16. Seweryn, A. and Lukaszewicz, A., "Verification of Brittle Fracture Criteria for Elements with V-Shaped Notches," Engineering Fracture Mechanics, 69, pp. 1487-1510 (2002).
17. Lazzarin, P. and Livieri, P., "Notch Stress Intensity Factors and Fatigue Strength of Aluminium and Steel Welded Joints," International Journal of Fatigue, 23, pp. 225-232 (2001).
18. Suwito, W., Dunn, M. L. and Cunningham, S. J., "Fracture Initiation at Sharp Notches in Single Crystal Silicon" Journal of Applied Physics, 83, pp. 3574-3582 (1998).
19. Suwito, W., Dunn, M. L., Cunningham, S. J. and Read, D. T., "Elastic Moduli, Strength, and Fracture Initiation at Sharp Notches in Etched Single Crystal Silicon Microstructures," Journal of Applied Physics, 85, pp. 3519-3534 (1999).
20. Mason, W., Physical Acoustics and Properties of Solids, Van Nostrand (1958).
21. Hattori, T., Sakata, S., Hatsuda, T. and Murakami, G., Journal of Electronic Packaging, 111, pp. 243-248 (1989).
22. Qian, Z. and Akisanya, A. R., "An Experimental Investigation of Failure Initiation in Bonded Joints," Acta Materialia, 46, pp. 4895-4904 (1998).
23. Mazza, E. and Dual, J., "Mechanical Behavior of a μm-Sized Single Crystal Silicon Structure with Sharp Notches," Journal of the Mechanics and Physics of Solids, 47, pp. 1795-1821 (1999).
24. Dunn, M. L., Cunningham, S. J. and Labossiere, P. E. W., "Initiation Toughness of Silicon/Glass Anodic Bonds," Acta Materialia, 48, pp. 735-744 (2000).
25. Reedy, E. D. and Guess, T. R., "Rigid Square Inclusion Embedded within an Epoxy Disk: Asymptotic Stress Analysis," Int. J. Solids Structures, 38, pp. 1281-1293 (2001).
26. Labossiere, P. E. W. and Dunn, M. L., "Fracture Initiation at Three-Dimensional Bimaterial Interface Corners," Journal of the Mechanics and Physics of Solids, 49, pp. 609-634 (2001).
27. Akisanya, A. R. and Meng, C. S., "Initiation of Fracture at the Interface Corner of Bi-material Joints," Journal of the Mechanics and Physics of Solids, 51, pp. 272-346 (2003).
28. Reedy, Jr., E. D. and Guess, T. R., "Comparison of Butt Tensile Strength Data With Interface Corner Stress Intensity Factor Prediction," Int. J. Solids Structures, 30, pp. 2929-2936 (1993).
29. Reedy, Jr., E. D. and Guess, T. R., "Butt Tensile Joint Strength: Interface Corner Stress Intensity Factor Prediction," J. Adhesion Sci. Technol., 9, pp. 237-251 (1995).
30. Reedy, Jr., E. D. and Guess, T. R., "Interface Corner Failure Analysis of Joint Strength: Effect of Adherent Stiffness," Int. J. Fracture, 88, pp. 305-314 (1998).
31. Reedy, Jr., E. D. and Guess, T. R., "Additional Interface Corner Toughness Data for an Adhesively-Bonded Butt Joint," Int. J. of Fracture, 98, pp. L3-L8 (1999).
32. Reedy, Jr., E. D. and Guess, T. R., "Butt Joint Strength: Effects of Residual Stress and Stress Relaxation," J. Adhesion Sci. Technol., 10, pp. 33-45 (1996).
33. Reedy, E. D. and Guess, T. R., "Nucleation and Propagation of an Edge Crack in a Uniformly Cooled Epoxy/Glass Bimaterial," Int. J. Solids Structures, 39, pp. 325-340 (2002).
34. Su, B., Lee, Y. C. and Dunn, M. L., "Die Cracking at Solder (In60-Pb40) Joints on Brittle (GaAs) Chips: Fracture Correlation Using Critical Interface Corner Stress Intensities," Journal of Electronic Packaging, in press (2003).
35. Labossiere, P. E. W. and Dunn, M. L., "Stress Intensities at Interface Corners in Anisotropic Bimaterials," Engineering Fracture Mechanics, 62, pp. 555-575 (1999).
36. Labossiere, P. E. W., Dunn, M. L., and Cunningham, S. J., "Application of Bimaterial Interface Corner Failure Mechanics to Silicon/Glass Anodic Bonds," Journal of the Mechanics and Physics of Solids, 50, pp. 405-433 (2002).
37. Lazzarin, P. and Zambardi, R., "The Equivalent Strain Energy Density Approach Re-Formulated and Applied to Sharp V-Shaped Notches Under Localized and Generalized Plasticity," Fatigue and Fracture of Engineering Materials, 10, pp. 917-928 (2002).
38. Lefebvre, D. R. and Dillard, D. A., "A Stress Singularity Approach for the Prediction of Fatigue Crack Initiation in Adhesive Bonds, Part 1: Theory," Journal of Adhesion, 70, pp. 119-138 (1999).
39. Atzori, B., Lazzarin, P. and Tovo, R., "Stress Field Parameters to Predict the Fatigue Strength of Notched Components," Journal of Strain Analysis in Engineering, 34, pp. 437-453 (1999).
40. Klingbeil, N. W. and Beuth, J. L., "On the Design of Debond-Resistant Bimaterials - Part I: Free-Edge Singularity Approach," Engineering Fracture Mechanics, 66, pp. 93-110 (2000).
41. Klingbeil, N. W. and Beuth, J. L., "On the Design of Debond-Resistant Bimaterials - Part II: A Comparison of Free-edge and Interface Crack Approaches," Engineering Fracture Mechanics, 66, pp. 111-128 (2000).
42. Tovo, R. and Lazzarin, P., "Relationships between Local and Structural Stress in the Evaluation of the Weld Toe Stress Distribution," International Journal of Fatigue, 21, pp. 1063-1078 (1999).
43. Reedy, Jr., E. D., "Connection Between Interface Corner and Interfacial Fracture Analyses of an Adhesively Bonded Butt Joint," Int. J. Solids Structures, 37, pp. 2443-2471 (2000).
44. Dunn, M. L., Hui, C. Y., Labossiere, P. E. W. and Lin, Y. Y., "Small Scale Geometric and Material Features at Geometric Discontinuities and Their Role in Fracture Analysis," International Journal of Fracture, 110, pp. 101-121 (2001).
45. Williams, M. L., "Stress Singularities Resulting from Various Boundary Conditions in Angular Corners of Plates in Extension," J. Appl. Mech., 19, pp. 526-528 (1952).
46. Bogy, D. B. and Wang, K. C., "Stress Singularities at Interface Corners in Bonded Dissimilar Materials," Int. J. Solids Struct., 1, pp. 993-1005 (1971).
47. Hein, V. L. and Erdogan, F., "Stress Singularities in a Two Material Wedge," International Journal of Fracture Mechanics, 1, pp. 317-330 (1971).
48. Dempsey, J. P. and Sinclair, G. B., "On the Stress Singularities in the Plane Elasticity of the Composite Wedge," Journal of Elasticity, 9, pp. 373-391 (1979).
49. Dempsey, J. P. and Sinclair, G. B., "On the Singular Behavior at the Vertex of a Bimaterial Wedge," Journal of Elasticity, 11, pp. 317-327 (1981).
50. Cho, S. B. and Lee, K. R., "Determination of Stress Intensity Factors and Boundary Element Analysis for Interface Cracks in Dissimilar Anisotropic Materials," Engineering Fracture Mechanics, 43, pp. 603-614 (1992).
51. Pageau, S. S., Joseph, P. F. and Biggers, S. B., "Finite Element Analysis of Anisotropic Materials with Singular Inplane Stress Fields," Int. J. Solids Structures, 32, pp. 571-591 (1995).
52. Yang, Y. Y. and Munz, D., "Stress Intensity Factor and Stress Distribution in a Joint with an Interface Corner under Thermal and Mechanical Loading," Computers & Structures, 57, pp. 461-476 (1995).
53. Yosibash, Z. and Szabo, B., "Numerical Analysis of Singularities in Two-Dimensions, Part 1: Computation of Eigenpairs," International Journal for Numerical Methods in Engineering, 38, pp. 2055-2082 (1995).
54. Szabo, B. and Yosibash, Z., "Numerical Analysis of Singularities in Two-Dimensions, Part 2: Computation of Generalized Flux/Stress Intensity Factors," International Journal for Numerical Methods in Engineering, 39, pp. 409-434 (1996).
55. Bazant, Z. P., "Three-Dimensional Harmonic Functions Near Termination or Intersection of Gradient Singularity Lines: A General Numerical Method," Int. J. Engng Sci., 12, pp. 221-243 (1974).
56. Benthem, J. P., "State of Stress at the Vertex of a Quarter Infinite Crack in a Half Space," Int. J. Solids Struct., 13, pp. 479-492 (1977).
57. Bazant, Z. P. and Estensoro, L. F., "Surface Singularity and Crack Propagation," Int. J. Solids Struct., 15, pp. 405-426 (1979).
58. Ghahremani, F., "A Numerical Variational Method for Extracting 3D Singularities," Int. J. Solids Structures, 27, pp. 1371-1386 (1991).
59. Ghahremani, F. and Shih, C. F., "Corner Singularities of Three-Dimensional Planar Interface Cracks," J. Appl. Mech., 59, pp. 61-68 (1992).
60. Picu, C. R. and Gupta, V., "Three-Dimensional Stress Singularities at the Tip of a Grain Triple Junction Line Intersecting the Free Surface," J. Mech. Phys. Solids, 45, pp. 1495-1520 (1997).
61. Koguchi, H., Muramoto, T. and Ihara, I, "Analysis for Stress Singularity Field at a Vertex in Three-Dimensional Bonded Structures," JSME Int. J., 42, pp. 80-89 (1999).
62. Glushkov, E., Glushkova, N. and Lapina, O., "3-D Elastic Stress Singularity at Polyhedral Corner Points," Int. J. Solids Structures, 36, pp. 1105-1128 (1999).
63. Carpenter, W. C., "A Collocation Procedure for Determining Fracture Mechanics Parameters at a Corner," International Journal of Fracture, 24, pp. 255-266 (1984).
64. Sinclair, G. B., Okajima, M. and Griffen, J. H., "Path Independent Integrals for Computing Stress Intensity Factors at Sharp Notches in Elastic Plates," International Journal for Numerical Methods in Engineering, 20, pp. 999-1008 (1984).
65. Carpenter, W. C. and Byers, C., "A Path Independent Integral for Computing Stress Intensities for V-Notched Cracks in a Bi- Material," International Journal of Fracture, 35, pp. 245-268 (1987).
66. Kuo, M. C. and Bogy, D. B., "Plane Solutions for Displacement and Traction-Displacement Problems for Anisotropic Elastic Wedges," J. Appl. Mech., 41, pp. 197-203 (1974).
67. Im, S. and Kim, K.-S., "An Application of Two-State M-Integral for Computing the Intensity of the Singular Near-Tip Field for a Generic Wedge," J. Mech. Phys. Solids, 48, pp. 129-151 (2001).
68. Akisanya, A. R. and Fleck, N. A., "Interfacial Cracking from the Free Edge of a Long Bimaterial Strip," Int. J. Solids Structures, 34, pp. 1645-1665 (1997).
69. Hui, C. Y. and Ruina, A., "Why K? High Order Singularities and Small Scale Yielding," International Journal of Fracture, 72, pp. 97-120 (1995).
70. Genestedt, J. L., and Hallstrom, S., "Crack Initiation from Homogeneous and Bimaterial Corners," J. Appl. Mech., 64, pp. 811-818 (1997).
71. Mohammed, H. and Liechti, K. M., "Cohesive Zone Modeling of Crack Nucleation at Bimaterial Corners," J. Mech. Phys. Solids, 48, pp. 735-764 (2000).
72. Munz, D., Fett, T. and Yang, Y. Y., "The Regular Stress Term in Bonded Dissimilar Materials after a Change in Temperature," Engineering Fracture Mechanics, 44, pp. 185-194 (1993).
73. Joseph, P. F. and Zhang, N., "Multiple Root Solutions, Wedge Paradoxes and Singular Stress States that are not Variable-Separable," Composites Science and Technology, 58, pp. 1839-1859 (1998).
74. Munz, D. and Yang, Y. Y., "Stresses Near the Edge of Bonded Dissimilar Materials Described by Two Stress Intensity Factors," International Journal of Fracture, 60, pp. 169-177 (1993).
75. Yang, Y. Y. and Munz, D., "Stress Intensity Factor and Stress Distribution in a Joint with an Interface Corner under Thermal and Mechanical Loading," Engineering Fracture Mechanics, 56, pp. 691-710 (1997).
76. Leicester, R. H., "Effect of Size on the Strength of Structures," CSIRO Forest Products Laboratory, Division of Building Research, Paper No. 71 (1973).
77. Stroh, A. N., "Dislocations and Cracks in Anisotropic Elasticity," Phil. Mag., 3, pp. 625-646 (1958).
78. Barnett, D. M. and Lothe, J., "Synthesis of the Sextic and the Integral Formalism for Dislocations, Green's Function and Surface Waves in Anisotropic Elastic Solids," Phys. Norv., 7, pp. 13-19 (1973).
79. Wu, K. C. and Chang, F. T., "Near-Tip Fields in a Notched Body with Dislocations and Body Forces," J. Appl. Mech., 60, pp. 936-941 (1993).
80. Stern, M., Becker, E. B. and Dunham, R. S., "A Contour Integral Computation of Mixed-Mode Stress Intensity Factors," International Journal of Fracture, 12, pp. 359-368 (1976).
81. Liu, X. H., Suo, Z. and Ma, Q., "Split Singularities: Stress Field near the Edge of a Silicon Die on a Polymer Substrate," Acta Mater., 47, pp. 67-76 (1998).
82. Koguchi, H., "Stress Singularity Analysis in Three-Dimensional Bonded Structures," Int. J. Solids Structures, 34, pp. 461-480 (1997).
83. Frankle, M., Munz, D. and Yang, Y. Y., "Stress Singularities in a Bimaterial Joint with Inhomogeneous Temperature Distribution," Int. J. Solids Structures, 33, pp. 2039-2054 (1996).
84. Glushkov, E. V., Glushkova, N. V., Munz, D. and Yang, Y. Y., "Analytical Solution for Bonded Wedges under Thermal Stresses," Int. J. Fracture, 106, pp. 321-339 (2000).
85. Su, B., Labossiere, P. E. W., Dunn, M. L. and Lee, Y. C., "Gallium Arsenide/Gold Flip-Chip Connection Stress Fields," in EEP-Advances in Electronic Packaging, 26-2, pp. 2037-2045 (1999).