3.01 - Finite Element Methods for Linear Elastic Fracture Mechanics

Comprehensive Structural Integrity

Volumn 3, Issue , 2007, Pages 1-88

  Ingraffea, A R ^a   Wawrzynek, P A ^b  

^a Department of Obstetrics Gynecology   (United States)

^b Fracture Analysis Consultants Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; NUMERICAL METHODS;

LINEAR ELASTIC FRACTURE MECHANICS;

FRACTURE MECHANICS;

EID: 84903413345     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B0-08-043749-4/03007-X     Document Type: Chapter

References (156)

1. Al-Ani A., Hancock J.W. J-dominance of short cracks in tension and bending. J. Mech. Phys. Solids 1991, 39(1):23-43.
2. Atluri S.N., Kobayashi A.S., Nakagaki M. An assumed displacement hybrid finite element model for linear elastic fracture mechanics. Int. J. Fract. 1975, 11:257-271.
3. Banks-Sills L. Use of three-dimensional finite elements in linear elastic fracture mechanics. Anal. Num. Exp. Aspects Fract. Processes, ASME-AMD 1988, 91:89-97.
4. Banks-Sills L. Application of the finite element method to linear elastic fracture mechanics. Appl. Mech. Rev. 1991, 44:447-461.
5. Banks-Sills L., Bortman Y. Reappraisal of the quarter-point quadrilateral element in linear fracture mechanics. Int. J. Fract. 1984, 25:169-180.
6. Banks-Sills L., Bortman Y. Quarter-point singular elements revisited. Int. J. Fract. 1987, 34:R63-R69.
7. Banks-Sills L., Einav O. On singular, nine-noded, distorted, isoparametric elements in linear elastic fracture mechanics. Comp. Struct. 1987, 27:445-449.
8. Banks-Sills L., Sherman D. On quarter-point three-dimensional finite elements in elastic fracture mechanics. Int. J. Fract. 1989, 41:177-196.
9. Banks-Sills L., Sherman D. On the computation of stress intensity factors for three-dimensional geometries by means of the stiffness derivative and J-integral methods. Int. J. Fract. 1992, 53:1-20.
10. Barbero E.J., Reddy J.N. The jacobian derivative method for three-dimensional fracture mechanics. Comm. Appl. Num. Meth. 1990, 6:507-518.
11. Barsoum R.S. On the use of isoparametric finite elements in linear fracture mechanics. Int. J. Num. Meth. Eng. 1976, 10:25-37.
12. Barsoum R.S. Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements. Int. J. Num. Meth. Eng. 1977, 11:85-98.
13. Bazant Z.P. Scaling theories for quasibrittle fracture: recent advances and new directions. Proceedings of FRAMCOS-2, Zurich, 1995 1995, 515-534. AEDIFICATIO Publishers, Freiburg, Germany. F.H. Wittmann (Ed.).
14. Bazant Z.P., Ohtsubo H. Stability conditions for propagation of a system of cracks in a brittle solid. Mech. Res. Commun. 1977, 4(5):353-366.
15. Bazant Z.P., Ohtsubo H., Aho K. Stability and post-critical growth of a system of cooling or shrinkage cracks. Int. J. Fract. 1979, 15(5):443-456.
16. Bazant Z.P., Wahab A.B. Instability and spacing of cooling or shrinkage cracks. J. Eng. Mech. Division, ASCE 1979, 105(EM5):873-889.
17. Benzley S.F. Representations of singularities with isoparametric finite elements. Int. J. Num. Meth. Eng. 1974, 8:537-545.
18. Bittencourt T., Wawrzynek P., Sousa J., Ingraffea A. Quasi-automatic simulation of crack propagation for 2D LEFM problems. Eng. Fract. Mech. 1996, 55(2):321-334.
19. Bonnet M. Shape differentiation and boundary integral equations: application to energy methods in fracture mechanics. Proceedings of Boundary Element Method XVI, Southampton, 1994 1994, 373-380. Computational Mechanics Publications, Southampton, UK.
20. Buczek M.B., Herakovich C.T. A normal stress criterion for crack extension direction in orthotropic composite materials. J. Composite Mater. 1985, 19:544-553.
21. Budiansky B., Rice J. Conservation laws and energy release rates. J. Appl. Mech. 1973, 40:201-203.
22. Bui H.D. Associated path independent J-integral for separating mixed modes. J. Mech. Phys. Solids 1983, 31:439-448.
23. Bui H.D., Van K.D. Généralisation de la théorie de la rupture de Griffith. J. de Mécanique Appliquée 1979, 3(2):205-225.
24. Byskov E. The calculation of stress intensity factors using the finite element method with cracked elements. Int. J. Fract. 1970, 6:159-167.
25. Cardew G.E., Goldthorpe M.R., Howard I.C., Kfouri A.P. Fundamentals of Deformation and Fracture: Eshelby Memorial Symposium 1985, 465-476. Cambridge University Press, Cambridge, UK. B.A. Bilby, K.J. Miller, J.R. Willis (Eds.).
26. Ćervenka J., Saouma V.E. Numerical evaluation of 3D SIF for arbitrary finite element meshes. Eng. Fract. Mech. 1997, 57:541-563.
27. Chan S.K., Tuba I.S., Wilson W.K. On the finite element method in linear fracture mechanics. Eng. Fract. Mech. 1970, 2:1-17.
28. C.-S. Chen, 1999, Crack growth simulation and residual strength prediction in thin shell structures. Ph.D. dissertation, Cornell University. Ithaca, New York.
29. Chen C.-S., Krause R., Pettit R.G., Banks-Sills L., Ingraffea A.R. Numerical assessment of T-stress computation using a P-version finite element method. Int. J. Fract. 2001, 107(2):177-199.
30. Chen C.-S., Wawrzynek P.A., Ingraffea A.R. Methodology for fatigue crack growth and residual strength prediction with applications to aircraft fuselages. Comp. Mech. 1997, 19:527-532.
31. C.-S. Chen, P. A. Wawrzynek and A. R. Ingraffea, 2002, Prediction of residual strength and curvilinear crack growth in aircraft fuselages. AIAA J., accepted for publication.
32. G. P. Cherepanov, 1967, Crack propagation in continuous media. USSR J. Appl. Math. Mech., Translation, 31, 504.
33. Constable I., Williams J.G., Culver L.E. Notch root radii effects in the fatigue of polymers. Int. J. Fract. Mech. 1970, 6(3):279-285.
34. Cornell Fracture Group, 2002, FRANC2D and FRANC3-D,. http://www.cfg.cornell.edu.
35. Cotterell B., Rice J.R. Slightly curved or kinked cracks. Int. J. Fract. 1980, 16:155-169.
36. DeKoning A.U., Lof C.J. K-distributions extrapolated on the basis of stress intensity rates. Proceedings of the 3rd International Conference on Numerical Methods in Fracture Mechanics, Swansea, 1984 1984, 195-203. Pineridge Press, Swansea, UK. A.R. Luxmoore, D.R.J. Owen (Eds.).
37. deLorenzi H.G. On the energy release rate and the J-integral for 3-D crack configurations. Int. J. Fract. 1982, 19:183-193.
38. deLorenzi H.G. Energy release rate calculations by the finite element method. Eng. Fract. Mech. 1985, 21:129-143.
39. Destyunder D.L., Diaoua M., Lescure S. Quelques remarques sur la mécanique de la rupture élastique. J. Mécanique Théorique et Appliquée 1983, 2:113-135.
40. Dugdale D.S. Yielding in steel sheets containing slits. J. Mech. Phys. Solids 1960, 8:100-104.
41. Erdogan F., Sih G.C. On the extension of plates under plane loading and transverse shear. J. Basic Eng., ASME 1963, 85D(4):519-527.
42. Fett T. A Green's function for T-stresses in an edge-cracked rectangular plate. Eng. Fract. Mech. 1997, 57:365-373.
43. T. Fett, 1998, "A Compendium of T-stress Solutions." Institut für Materialforschung, Karlsruhe, Germany, Report FZKA 6057.
44. Finnie I., Saith A. A note on the angled crack problem and the directional stability of cracks. Int. J. Fract. 1973, 9:484-486.
45. Freese C.E., Tracey D.M. The natural triangle versus collapsed quadrilateral for elastic crack analysis. Int. J. Fract. 1976, 12:767-770.
46. Gao H., Rice J.R. Shear stress intensity factors for a planar crack with slightly curved front. J. Appl. Mech. 1986, 53:774-778.
47. Gao H., Rice J.R. Somewhat circular tensile cracks. Int. J. Fract. 1986, 33:155-174.
48. Gao H., Rice J.R. Nearly circular connections of elastic half spaces. J. Appl. Mech. 1987, 54:627-634.
49. Gao H., Rice J.R. A first-order perturbation analysis of crack trapping by arrays of obstacles. J. Appl. Mech. 1989, 56:828-836.
50. Goode R.J. Identification of fracture plane orientation. Mater. Res. Stand., (MIRSA), ASTM 1972, 12:9. (see also ASTM E1823).
51. B. Gross, J. E. Srawley and W. F. Brown, Jr., 1964, "Stress Intensity Factors for a Single-edge-notch Tension Specimen by Boundary Collocation of a Stress Function." NASA, Technical Note D-2395 NASA Lewis Research Center, Cleveland, OH.
52. M. L. Gruber, C. J. Mazur, K. E. Wilkins and R. E. Worden, 1996, "Investigation of Fuselage Structure Subject to Widespread Fatigue Damage." Technical Report DOT/FAA/AR95/47, Federal Aviation Administration, Washington DC.
53. Haber R.B., Koh M.K. Explicit expressions for energy-release rates using virtual crack extensions. Int. J. Num. Meth. Eng. 1985, 21:278-301.
54. Hartranft R.J., Sih G. Effect of plate thickness on the bending stress distribution around through cracks. J. Math. Phys. 1968, 47:276-291.
55. Hartranft R.J., Sih G.C. An approximate three-dimensional theory of plates with application to crack problems. Int. J. Eng. Sci. 1970, 8(8):711-729.
56. Hellen T.K. On the method of virtual crack extension. Int. J. Num. Meth. Eng. 1975, 9:187-207.
57. Henshell R.D., Shaw K.G. Crack tip finite elements are unnecessary. Int. J. Num. Meth. Eng. 1975, 9:495-507.
58. Hibbitt H.D. Some properties of singular isoparametric elements. Int. J. Num. Meth. Eng. 1977, 11:180-184.
59. Hoenig A. Near-tip behavior of a crack in a plane anisotropic elastic body. Eng. Fract. Mech. 1982, 16:393-403.
60. Hui C.Y., Zehnder A.T. A theory for the fracture of thin plates subjected to bending and twisting moments. Int. J. Fract. 1993, 61:211-229.
61. Hussain M.A., Coffin L.F., Zaleski K.A. Three-dimensional singular elements. Comp. Struct. 1981, 13:595-599.
62. Hussain M.A., Pu S.L., Underwood J.H. Strain energy release rate for a crack under combined mode I and mode II. Fracture Analysis, ASTM STP 560 1974, 2-28. ASTM, Philadelphia, PA.
63. Hwang C.G., Warwzynek P.A., Tayebi A.K., Ingraffea A.R. On the virtual crack extension method for calculating rates of energy release rate. Eng. Fract. Mech. 1998, 59(4):521-542.
64. Hwang C.G., Wawrzynek P.A., Ingraffea A.R. On the virtual crack extension method for calculating the derivatives of energy release rates for a 3D planar crack of arbitrary shape under mode I loading. Eng. Fract. Mech. 2001, 68(7):925-947.
65. Ingraffea A.R., Manu C. Stress-intensity factor computations in three dimensions. Int. J. Num. Meth. Eng. 1980, 15:1427-1445.
66. Irwin G.R. Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. 1957, 24:361-364.
67. Irwin G.R. Plastic zone near a crack and fracture toughness. Proceedings of the 7th Sagamore Ordnance Materials Conference on Mechanics & Metals Behavior of Sheet Materials, Racquette Lake, NY, 1960 1960, 463-478. Syracuse University, New York.
68. Irwin G.R. Crack extension force for a part-through crack in a plate. Trans. ASME. Ser. E, J. Appl. Mech. 1962, 29:651-654.
69. Ishikawa H. A finite element analysis of stress intensity factors for combined tensile and shear loading by only a virtual crack extension. Int. J. Fract. 1980, 16:243-246.
70. Ishikawa H., Kitagawa H., Okamura H. J-integral of a mixed mode crack and its application. Proceedings of the 3rd International Conference on Mechanical Behavior of Materials, Cambridge, England, 1979 1979, 447-455. Pergamon, Oxford, London. K.J. Miller, R.F. Smith (Eds.).
71. Isida M. Effect of width and length on stress intensity factors of internally cracked plates under various boundary conditions. Int. J. Fract. 1971, 7(3):301-316.
72. Isida M., Nishino T. Formulae of stress intensity factors at the tips of kinked cracks under various loadings. Eng. Fract. Mech. 1990, 36(5):697-711.
73. M. James, 1998, A plane stress finite element model for elastic plastic mode i/ii crack growth. Ph.D. dissertation, Kansas State University.
74. Joseph P.F., Erdogan F. Surface crack problems in plates. Int. J. Fract. 1989, 41:105-131.
75. Keer L.M., Nemat-Nasser S., Parthar K.S. Unstable growth of thermally induced interacting cracks in brittle solids: further results. Int. J. Solids Struct. 1978, 15:111-126.
76. Kfouri A.P. Some evaluations of the elastic T-term using Eshelby's method. Int. J. Fract. 1986, 30:301-315.
77. Kfouri A.P. Crack extension under mixed-mode loading in an anisotropic mode-asymmetric material in respect of resistance to fracture. Fatigue Fract. Eng. Mater. Struct. 1996, 19(1):27-38.
78. H. A. J. Knops, 1994, Numerical simulation of crack growth in pressurized fuselages. Ph.D. thesis, Delft University of Technology.
79. Knowles J.K., Wang N.M. On bending of an elastic plate containing a crack. J. Math. Phys. 1960, 39:223-236.
80. Koers R.W.J. Use of modified standard 20-node isoparametric brick elements for representing stress/strain fields at a crack tip for elastic and perfectly plastic material. Int. J. Fract. 1989, 40:79-110.
81. K. Koppenhoefer, A. S. Gullerund, C. Ruggieri, R. H. Dodds and B. E. Healy, 1994, "WARP3-D: Dynamic Nonlinear Analysis of Solids Using a Preconditioned Conjugate Gradient Software Architecture." Report number UILU-ENG-94-2017, Department of Civil Engineering, University of Illinois at Urbana-Champaign, Urbana, IL.
82. Kosai M., Kobayashi A.S., Ramulu M. Tear straps in aircraft fuselage. Proceedings of International Workshop on Structural Integrity of Aging Airplanes, Atlanta, 1992 1992, 443-457. Atlanta Technology Publications, Atlanta, GA. S. Atluri (Ed.).
83. Larsson S.G., Carlsson A.J. Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials. J. Mech. Phys. Solids 1973, 21:263-277.
84. Leevers P.S., Radon J.C. Inherent stress biaxiality in various fracture specimen geometries. Int. J. Fract. 1982, 19:311-325.
85. Lemant F., Pineau A. Mixed mode fracture of a brittle orthotropic material---example of strongly textured zinc sheets. Eng. Fract. Mech. 1981, 14:91-105.
86. Li F.Z., Shih C.F., Needleman A. A comparison of methods for calculating energy release rates. Eng. Fract. Mech. 1985, 21:405-421.
87. Lin S.C., Abel J.F. A variational approach for a new direct-integration form of the virtual crack extension methods. Int. J. Fract. 1988, 28:217-235.
88. Liu S.C. Crack growth and failure of aluminium plate under in-plane shear. AIAA J. 1974, 12:180-185.
89. Maccagno T.M., Knott J.F. The fracture behaviour of PMMA in mixed modes I and II. Eng. Fract. Mech. 1989, 34(1):65-86.
90. Maccagno T.M., Knott J.F. The low-temperature brittle fracture behaviour of steel in mixed modes I and II. Eng. Fract. Mech. 1991, 38(2/3):111-128.
91. Maiti S.K., Smith R.A. Comparison of criteria for mixed-mode brittle fracture based on the preinstability stress--strain field: Part I. Slit and elliptical cracks under uniaxial tensile loading. Int. J. Fract. 1983, 23:281-295.
92. Manu C. Quarter-point elements for curved crack fonts. Comp. Struct. 1983, 17:227-231.
93. Manu C. Complete quadratic isoparametric finite elements in fracture mechanics analysis. Int. J. Num. Meth. Eng. 1985, 21:1547-1553.
94. Meade K.P., Keer L.M. On the problem of a pair of point forces applied to the faces of a semi-infinite plane crack. J. Elasticity 1984, 14:3-14.
95. Meade K.P., Keer L.M. Stress intensity factors for semi-infinite plane crack with a wavy front. J. Elasticity 1984, 14:79-92.
96. Moran B., Shih C.F. A general treatment of crack tip contour integrals. Int. J. Fract. 1987, 35:295-310.
97. Narayana K.B. A general procedure for modified crack closure integral in 3-D problems with cracks. Eng. Fract. Mech. 1994, 48:167-176.
98. Nemat-Nasser S. Stability of a system of interacting cracks. Lett. Appl. Eng. Sci. 1978, 16:277-285.
99. Nemat-Nasser S., Keer L.M., Parihar K.S. Unstable growth of thermally induced interacting cracks in brittle solids. Int. J. Solids Struct. 1978, 14:409-430.
100. Nemat-Nasser S., Sumi Y., Keer L.M. Unstable growth of tension cracks in brittle solids: stable and unstable bifurcations, snap-through, and imperfection sensitivity. Int. J. Solids Struct. 1980, 16:1017-1035.
101. J. C. Newman, Jr. and I. S. Raju, 1981, "Stress Intensity Factors Equations for Cracks in Three-dimensional Finite Bodies." NASA Technical Memorandum 83200, NASA Langley Research Center, Hampton, VA, pp. 1-49.
102. Nguyen Q.S. Normal dissipativity and energy criteria in fracture. Proceedings of IUTAM. Symposium on Variational Methods in the Mechanics of Solids, Oxford, 1980 1980, 254-259. Pergamon. S. Nemat-Nasser (Ed.).
103. S. Nguyen, 1994, Bifurcation and stability in dissipative media (plasticity, friction, fracture). Appl. Mech. Rev., 47(1), part 1, 1-31.
104. Nguyen Q.S., Stolz C., Debruyne G. Energy methods in fracture mechanics: stability, bifurcation and second variations. Eur. J. Mech., A/Solids 1990, 9(2):157-173.
105. Nikishkov G.P., Atluri S.N. Calculation of fracture mechanics parameters for an arbitrary three-dimensional crack, by the 'equivalent domain integral' method. Int. J. Num. Meth. Eng. 1987, 24:1801-1827.
106. Papaioannou S.G., Hilton P.D., Lucas R.A. A finite element method for calculating stress intensity factors and its application to composites. Eng. Fract. Mech. 1974, 6:807-823.
107. Parks D.M. Stiffness derivative finite element technique for determination of crack-tip stress intensity factors. Int. J. Fract. 1974, 10:487-502.
108. Pettit R.G., Newman J.C., Domack M.S. Crack turning damage tolerance approach for integrally stiffened structure. Proceedings of the 19th Symposium of the International Committee on Aeronautical Fatigue, Vol. II, 1997, Edinburgh, Scotland 1997, 819-830. EMAS Publishing. R. Cook, P. Poole (Eds.).
109. Pook L.P. The effect of crack angle on fracture toughness. Eng. Fract. Mech. 1971, 3:205-218.
110. D.O. Potyondy, 1993, A methodology for simulation of curvilinear crack growth in pressurized shells. Ph.D. thesis, Cornell University, Ithaca, New York.
111. Potyondy D.O., Wawrzynek P.A., Ingraffea A.R. Discrete crack growth analysis methodology for through cracks in pressurized fuselage structures. Int. J. Num. Meth. Eng. 1995, 38:1611-1633.
112. Raju I.S. Calculation of strain-energy release rate with high order and singular finite elements. Eng. Fract. Mech. 1987, 28:251-274.
113. Ramamurthy T.S., Krishnamurthy T., Badari Narayana K., Vijayakumar K., Dattaguru B. Modified crack closure integral method with quarter point elements. Mech. Res. Commun. 1986, 13:179-186.
114. Ramulu M., Kobayashi A. Dynamic crack curving---a photoelastic evaluation. Exp. Mech. 1983, 23:1-9.
115. C. C. Rankin, F. A. Brogan, W. A. Loden and H. D. Cabiness, 1997, "STAGS User Manual Version 2.4." Lockheed Martin Missiles & Space Co., Advanced Technology Center, Palo, Alta, CA.
116. E. Reissner, 1947, On bending of elastic plates, Quarterly of Applied Math., 5, 55-68.
117. Rice J.R. A path-independent integral and the approximate analysis of strain concentrations by notches and cracks. J. Appl. Mech. 1968, 35:379-386.
118. Rice J.R. First-order variation in elastic fields due to variation in location of a planar crack front. J. Appl. Mech. 1985, 52:571-579.
119. Rice J.R., Johnson M.A. The role of large crack tip geometry changes in plain strain fracture. Inelastic Behavior of Solids 1969, 641-690. McGraw-Hill, New York.
120. Rybicki E.R., Kanninen M.F. A finite element calculation of stress intensity factors by a modified crack closure integral. Eng. Fract. Mech. 1977, 9:931-938.
121. Selvarathinam A.S., Goree J.G. T-stress based fracture model for cracks in isotropic materials. Eng. Fract. Mech. 1998, 60(5/6):543-561.
122. Sham T.-L. The determination of the elastic T-term using higher order weight functions. Int. J. Fract. 1991, 48:81-102.
123. Shih C.F., Delorenzi H.G., German M.D. Crack extension modeling with singular quadratic isoparametric elements. Int. J. Fract. 1976, 1:647-651.
124. M. Shirmohamadi, 1995, Stable crack growth trajectories and fracture due to interacting cracks, Ph. D. dissertation, University of California at Berkeley.
125. Sih G.C., Paris P.C., Irwin G.R. On cracks in rectilinearly anisotropic bodies. Int. J. Fract. Mech. 1965, 1:189-203.
126. Sih G.C. Strain-energy-density factor applied to mixed-mode crack problems, Int. J. Fract. 1974, 10:305-321.
127. Singh R., Carter B., Wawrzynek P., Ingraffea A. Universal crack closure integral for SIF estimation. Eng. Fract. Mech. 1998, 60:133-146.
128. Sneddon N. The distribution of stress in the neighborhood of a crack in an elastic solid. Proc. Roy. Soc. London, Ser. A, 1946, 187:229-250.
129. Saouma V.E., Schwemmer D. Numerical evaluation of the quarter-point crack tip element. Int. J. Num. Meth. Eng. 1984, 20:1629-1641.
130. J. Sousa, 1992, Three-dimensional simulation of near-wellbore phenomena related to hydraulic fracturing from a perforated wellbore. Ph.D. thesis, Cornell University, Ithaca, New York.
131. Spievak L., Lewicki D., Wawrzynek P., Ingraffea A. Simulating fatigue crack growth in spiral bevel gears. Eng. Fract. Mech. 2001, 68(1):53-76.
132. Stern M., Becker E.B., Dunham R.S. A contour integral computation of mixed-mode stress intensity factors. Int. J. Fract. 1976, 12:359-368.
133. Stone T.J., Babuška I. A numerical method with a posteriori error estimation for determining the path taken by a propagating crack. Comp. Meth. Appl. Mech. Eng. 1998, 160:245-271.
134. Streit R., Finnie I. An experimental investigation of crack-path directional stability. Exp. Mech. 1980, 20:17-23.
135. Sumi Y., Nemat-Nasser S., Keer L.M. A new combined analytical and finite-element solution method for stability analysis of the growth of interacting tension cracks in brittle solids. Int. J. Eng. Sci. 1980, 18:211-224.
136. Sumi Y., Nemat-Nasser S., Keer L.M. On crack path instability in a finite body. Eng. Fract. Mech. 1985, 22:759-771.
137. M.A. Sutton, X. Deng, F. Ma, J. C. Newman and M. James, 2000, Development and application of a COD-based mixed-mode fracture criterion. Int. J. Solids Struct., in press.
138. Sutton M.A., Zhao W., Boone M.L., Reynolds A.P., Dawicke D.S. Prediction of crack growth direction for mode I/II loading using small-scale yielding and void initiation/growth concepts. Int. J. Fract. 1997, 83:275-290.
139. Szabó B.A., Babuška I. Finite Element Analysis 1991, Wiley, New York.
140. Theocaris P.S. Variation on the theme of fracture criteria. Eng. Fract. Mech. 1989, 33:205-214.
141. Theocaris P.S., Andrianopoulos N.P. A modified strain energy density criterion applied to crack propagation. J. Appl. Mech. 1982, 49(1):81-86.
142. Timoshenkko S., Woinowsky-Krieger S. Theory of Plates and Shells 1959, McGraw-Hill, New York.
143. Tong P., Pian T.H.H., Lasry S.J. A hybrid element approach to crack problems in plane elasticity. Int. J. Num. Meth. Eng. 1973, 7:1031-1036.
144. Tracey D.M. Finite elements for determination of crack tip elastic stress intensity Factors. Eng. Fract. Mech. 1971, 3:255-256.
145. Tracey D.M. Discussion of "On the use of isoparametric finite elements in linear fracture mechanics," by R. S. Barsoum. Int. J. Num. Meth. Eng. 1977, 11:401-402.
146. A. Ural, A. R. Ingraffea, P. Wawrzynek and D. Lewicki, 2002, "Simulating Fatigue Crack Growth in Spiral Bevel Gears," NASA technical report, in press.
147. Viz M.J., Potyondy D.O., Zehnder A.T., Rankin C.C., Riks E. Computation of membrane and bending stress intensity factors for thin, cracked plates. Int. J. Fract. 1995, 72:21-38.
148. Wang N.M. Twisting of an elastic plate containing a crack. Int. J. Fract. Mech. 1970, 6:367-378.
149. Wawrzynek P.A., Ingraffea A.R. Interactive finite-element analysis of fracture processes: an integrated approach. Theor. Appl. Fract. Mech. 1987, 8:137-150.
150. A. A. Wells, 1961, Unstable crack propagation in metals: cleavage and fast fracture. In: "Proceedings of the Crack Propagation Symposium, 1961, Cranfield," College of Aeronautics, Cranfield, UK, vol. 1, paper 84.
151. Williams M.L. On the stress distribution at the base of a stationary crack. ASME Trans., J. Appl. Mech. 1957, 24:109-114.
152. Williams M.L. The bending stress distribution at the base of a stationary crack. ASME Trans., J. Appl. Mech. 1961, 28:78-82.
153. Williams M.L., Ewing P.D. Fracture under complex stress---the angled crack problem. Int. J Fract. Mech. 1972, 8:441-446.
154. Yau J.F., Wang S.S., Corten H.T. A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. J. Appl. Mech. 1980, 47:335-341.
155. Ying L.A. A note on the singularity and the strain energy of singular elements. Int. J. Num. Meth. Eng. 1982, 18:31-39.
156. F. G. Yuan and S. Yang, 1998, The application of fracture mechanics to stitched warpkit fabric composites. In: "Proceedings of the 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Long Beach, CA, April 1998." AIAA paper #98-2025 Reston, VA.