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A concise review about fracture assessments of brittle solids with V-notches

  • Hsien-Yang YehEmail author
  • Bin Yang
Review
  • 17 Downloads

Abstract

A concise review of recent studies about the fracture assessments of elastic brittle solid materials containing V-notches is presented. In this preliminary and brief survey, elastic stress distributions in V-notched solids are discussed first. The concept of notch stress intensity factor is introduced. Combine the digital image correlation method with numerical computation techniques to analyze the stress distribution near the notches. Fracture criteria such as strain energy density, J-integral, theory of critical distance are used.

However, various new materials are developed in different engineering fields, thus, the establishment of reliable and accurate material strength theory or failure criterion is imperative. Therefore, predicting fracture for various modern materials would require more experiments to infer material dependent parameters in the local fracture model.

Keywords

fracture assessment brittle solids V-notches review 

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Notes

Acknowledgements

The support of literature search provided by the Tongji University Library is deeply appreciated.

References

  1. 1.
    Kanninen M F, Popelar C H. Advanced Fracture Mechanics. Oxford: Oxford University Press, 1985zbMATHGoogle Scholar
  2. 2.
    Broek D. The Practical Use of Fracture Mechanics. Netherlands: Kluwer Academic Publishers, 1989CrossRefGoogle Scholar
  3. 3.
    Taylor D. The Theory of Critical Distances. Amsterdam: Elsevier, 2007Google Scholar
  4. 4.
    Anderson T L. Fracture Mechanics. London: Taylor & Francis, 2005zbMATHCrossRefGoogle Scholar
  5. 5.
    Savruk M P, Kazberuk A. Two-dimensional fracture mechanics problems for solids with sharp and rounded V-notches. International Journal of Fracture, 2010, 161(1): 79–95zbMATHCrossRefGoogle Scholar
  6. 6.
    Wieghardt K. Uber das Spalten und Zerreiben elastischer Koper. Mathematics and Physics, 1907, 55(2): 60–103zbMATHGoogle Scholar
  7. 7.
    Brahtz J H A. Stress distribution in a reentrant corner. Trans ASME, 1933a,55: 31–37Google Scholar
  8. 8.
    Brehtz J H A. Stress distribution in wedges with arbitrary boundary forces. Journal of Applied Physics, 1933b,4(2): 56–65Google Scholar
  9. 9.
    Williams M L. Stress singularities resulting from various boundary conditions in angular corners of plates in extension. Journal of Applied Mechanics, 1952, 19(4): 526–530Google Scholar
  10. 10.
    Karal F C J, Karp S N. The elastic field behavior in the neighborhood of a crack of arbitrary angle. Communications on Pure and Applied Mathematics, 1962, 15(4): 413–421MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Kalandiya A I. Remarks on the singularity of elastic solutions near corners. Journal of Applied Mathematics and Mechanics, 1969, 33 (1): 127–131zbMATHCrossRefGoogle Scholar
  12. 12.
    Rösel R. On the wedge/notch eigenvalue. International Journal of Fracture, 1987, 33(1): 61–71CrossRefGoogle Scholar
  13. 13.
    Vasilopoulos D. On the determination of higher order terms of singular elastic stress fields near corner. Numerische Mathematik, 1988, 53(1-2): 51–95MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Savruk M P, Osiv P N, Prokopchuk I V. Numerical Analysis in Plane Problems of the Crack Theory. Russia: Naukova Dumka Kiev, 1989Google Scholar
  15. 15.
    Seweryn A, Molski K. Elastic stress singularities and corresponding generalized stress intensity factors for angular corners under various boundary conditions. Engineering Fracture Mechanics, 1996, 55(4): 529–556CrossRefGoogle Scholar
  16. 16.
    Mori K. Tension of a semi-infinite plate with a circular hole connected to the straight edge by a slit. Bulletin of the JSME, 1964, 7(26): 272–277CrossRefGoogle Scholar
  17. 17.
    Zappalorto M, Lazzarin P. In-plane and out-of-plane stress field solutions for V-notches with end holes. International Journal of Fracture, 2011, 168(2): 167–180zbMATHCrossRefGoogle Scholar
  18. 18.
    Neuber H. Finite element analysis of corner point displacements and stress intensity factors for narrow notches in square sheets and plates. Fatigue & Fracture of Engineering Materials & Structures, 1985, 24: 979–992Google Scholar
  19. 19.
    Kullmer G. Elastic stress fields in the vicinity of a narrow notch with circular root. In: Reliability and structural integrity of advanced materials, Proceedings of the 9th biennial European conference on fracture. Varna: Bulgaria, 1992,905–910Google Scholar
  20. 20.
    Radaj D, Lehrke H P, Greuling S. Theoretical fatigue-effective notch stresses at spot welds. Fatigue & Fracture of Engineering Materials & Structures, 2001, 24(5): 293–308CrossRefGoogle Scholar
  21. 21.
    Smith E. The mode-III elastic stress distribution near the root of (a) an intrusion-type notch and (b) a keyhole notch. Int J Engng Sci, 44: 340–344Google Scholar
  22. 22.
    Kullmer G, Richard H A. Influence of the root radius of crack-like notches on the fracture load of brittle components. Archive of Applied Mechanics, 2006, 76(11–12): 711–723zbMATHCrossRefGoogle Scholar
  23. 23.
    Creager M, Paris P C. Elastic field equations for blunt cracks with reference to stress corrosion cracking. International Journal of Fracture, 1967, 3: 247–252Google Scholar
  24. 24.
    Muskhelishvili N I. Some Basic Problems of the Mathematical Theory of Elasticity. 4th ed. Leyden: Noordhoff International Publishing, 1977CrossRefGoogle Scholar
  25. 25.
    Benthem J P. Stresses in the region of rounded corners. International Journal of Solids and Structures, 1987, 23(2): 239–252CrossRefGoogle Scholar
  26. 26.
    Lazzarin P, Zappalorto M, Berto F. Generalised stress intensity factors for rounded notches in plates under in-plane shear loading. International Journal of Fracture, 2011, 170(2): 123–144zbMATHCrossRefGoogle Scholar
  27. 27.
    Gross R, Mendelson A. Plane elastostatic analysis of V-notched plates. International Journal of Fracture, 1972, 8(3): 267–276CrossRefGoogle Scholar
  28. 28.
    Zhao Z, Hahn H G. Determining the SIF of a V-notch from the results of a mixed-mode crack. Engineering Fracture Mechanics, 1992, 43(4): 511–518CrossRefGoogle Scholar
  29. 29.
    Chen D H. Stress intensity factors for V-notched strip under tension or in-plane bending. International Journal of Fracture, 1995, 70(1): 81–97CrossRefGoogle Scholar
  30. 30.
    Dunn M L, Suwito W, Cunningham S. Fracture initiation at sharp notches: correlation using critical stress intensities. International Journal of Fracture, 1997, 34: 3873–3883zbMATHGoogle Scholar
  31. 31.
    Dunn M L, Suwito W, Cunningham S, May C W. Fracture initiation at sharp notches under mode-I, mode-II, and mild mixed mode loading. International Journal of Fracture, 1997, 84(4): 367–381CrossRefGoogle Scholar
  32. 32.
    Lazzarin P, Tovo R. A notch intensity approach to the stress analysis of welds. Fatigue & Fracture of Engineering Materials & Structures, 1998, 21(9): 1089–1103CrossRefGoogle Scholar
  33. 33.
    Strandberg M. A numerical study of the elastic stress field arising from sharp and blunt V-notches in a SENT-specimen. International Journal of Fracture, 2000, 100(4): 329–342CrossRefGoogle Scholar
  34. 34.
    Strandberg M. Upper bounds for the notch intensity factor for some geometries and their use in general interpolation formulae. Engineering Fracture Mechanics, 2001, 68(5): 577–585CrossRefGoogle Scholar
  35. 35.
    Noda N, Takase Y. Generalized stress intensity factors for Vshaped notch in a round bar under torsion, tension and bending. Engineering Fracture Mechanics, 2003, 70(11): 1447–1466CrossRefGoogle Scholar
  36. 36.
    Zappalorto M, Lazzarin P, Berto F. Elastic notch stress intensity factors for sharply V-notched rounded bars under torsion. Engineering Fracture Mechanics, 2009, 76(3): 439–453CrossRefGoogle Scholar
  37. 37.
    Knésl Z. A criterion of V-notch stability. International Journal of Fracture, 1991, 48: 79–83CrossRefGoogle Scholar
  38. 38.
    Nui L S, Chehimi C, Pluvinage G. Stress field near a large blunted tip V-notch and application of the concept of the critical notch stress intensity factor (NSIF) to the fracture toughness of very brittle materials. Engineering Fracture Mechanics, 1994, 49(3): 325–335CrossRefGoogle Scholar
  39. 39.
    Gogotsi G A. Fracture toughness of ceramics and ceramic composites. Ceramics International, 2003, 29(7): 777–784CrossRefGoogle Scholar
  40. 40.
    Gómez F J, Elices M. A fracture criterion for sharp V-notched samples. International Journal of Fracture, 2003, 123(3-4): 163–175CrossRefGoogle Scholar
  41. 41.
    Gómez F J, Elices M. A fracture criterion for blunted V-notched samples. International Journal of Fracture, 2004, 127(3): 239–264zbMATHCrossRefGoogle Scholar
  42. 42.
    Gómez F J, Elices M, Berto F, Lazzarin P. A generalised notch stress intensity factor for U-notched components loaded under mixed mode. Engineering Fracture Mechanics, 2008, 75(16): 4819–4833CrossRefGoogle Scholar
  43. 43.
    Gómez F J, Elices M, Berto F, Lazzarin P. Fracture of V-notched specimens under mixed mode (I + II) loading in brittle materials. International Journal of Fracture, 2009, 159(2): 121–135CrossRefGoogle Scholar
  44. 44.
    Boukharouba T, Tamine T, Nui L L, Chehimi C, Pluvinage G. The use of notch stress intensity factor as a fatigue crack initiation parameter. Engineering Fracture Mechanics, 1995, 52(3): 503–513CrossRefGoogle Scholar
  45. 45.
    Verreman Y, Nie B. Early development of fatigue cracking at manual fillet welds. Fatigue & Fracture of Engineering Materials & Structures, 1996, 19(6): 669–681CrossRefGoogle Scholar
  46. 46.
    Gómez F J, Elices M. Fracture loads for ceramic samples with rounded notches. Engineering Fracture Mechanics, 2006, 73(7): 880–894CrossRefGoogle Scholar
  47. 47.
    Ayatollahi M R, Torabi A R. Investigation of mixed mode brittle failure in rounded-tip V-notches components. Engineering Fracture Mechanics, 2010, 77(16): 3087–3104CrossRefGoogle Scholar
  48. 48.
    Lazzarin P, Filippi S. A generalized stress intensity factor to be applied to rounded V-shaped notches. International Journal of Solids and Structures, 2006, 43(9): 2461–2478zbMATHCrossRefGoogle Scholar
  49. 49.
    Ayatollahi M R, Torabi A R, Azizi P. Experimental and theoretical assessment of brittle fracture in engineering components containing a sharp V-notch. Experimental Mechanics, 2011, 51(6): 919–932CrossRefGoogle Scholar
  50. 50.
    Carpinteri A. Stress-singularity and generalized fracture toughness at the vertex of re-entrant corners. Engineering Fracture Mechanics, 1987, 26(1): 143–155CrossRefGoogle Scholar
  51. 51.
    Dini D, Hills D. Asymptotic characterization of nearly sharp notch root stress fields. International Journal of Fracture, 2004, 130(3): 651–666zbMATHCrossRefGoogle Scholar
  52. 52.
    Taylor D. Predicting the fracture strength of ceramic materials using the theory of critical distances. Engineering Fracture Mechanics, 2004, 71(16–17): 2407–2416CrossRefGoogle Scholar
  53. 53.
    Seweryn A. Brittle fracture criterion for structures with sharp notches. Engineering Fracture Mechanics, 1994, 47(5): 673–681CrossRefGoogle Scholar
  54. 54.
    Dunn M L, Suwito W, Cunningham S. Stress intensities at notch singularities. Engineering Fracture Mechanics, 1997, 57(4): 417–430zbMATHCrossRefGoogle Scholar
  55. 55.
    Lazzarin P, Zambardi R. A finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp Vshaped notches. International Journal of Fracture, 2001, 112(3): 275–298CrossRefGoogle Scholar
  56. 56.
    Livieri P. A new path independent integral applied to notched components under mode I loadings. International Journal of Fracture, 2003, 123(3-4): 107–125CrossRefGoogle Scholar
  57. 57.
    Leguillon D, Yosibash Z. Crack onset at a V-notch influence of the notch tip radius. International Journal of Fracture, 2003, 122(1-2): 1–21CrossRefGoogle Scholar
  58. 58.
    Ayatollahi M R, Torabi A R. Brittle fracture in rounded-tip Vshaped notches. Materials & Design, 2010, 31(1): 60–67CrossRefGoogle Scholar
  59. 59.
    Dunn M L, Suwito W, Cunningham S, May C. Fracture initiation at sharp notches under mode-I, mode-II, and mild mixed mode loading. International Journal of Fracture, 1997, 84(4): 367–381CrossRefGoogle Scholar
  60. 60.
    Seweryn A, Mróz Z. A non-local stress failure condition for structural elements under multiaxial loading. Engineering Fracture Mechanics, 1995, 51(6): 955–973CrossRefGoogle Scholar
  61. 61.
    Seweryn A, Lukaszewicz A. Verification of brittle fracture criteria for elements with V-shaped notches. Engineering Fracture Mechanics, 2002, 69(13): 1487–1510CrossRefGoogle Scholar
  62. 62.
    Priel E, Bussiba A, Gilad A, Yosibash Z. Mixed mode failure criteria for brittle elastic V-notched structures. International Journal of Fracture, 2007, 144(4): 247–265zbMATHCrossRefGoogle Scholar
  63. 63.
    Hutchinson J W, Suo Z. Advances in Experimental Mechanics. San Diego: Academic, 1996,64–187Google Scholar
  64. 64.
    Erdogan F, Sih G. On the crack extension in plates under plane loading and transverse shear. J Basic Eng, 1963, 85(4): 519–525CrossRefGoogle Scholar
  65. 65.
    Papadopoulos G A, Paniridis P I. Crack initiation from blunt notches under biaxial loading. Engineering Fracture Mechanics, 1988, 31(1): 65–78CrossRefGoogle Scholar
  66. 66.
    Leguillon D. Strength or toughness? A criterion for crack onset at a notch. European Journal of Mechanics/A Solids, 2002, 21: 61–72zbMATHCrossRefGoogle Scholar
  67. 67.
    Berto F, Lazzarin P, Radaj D. Fictitious notch rounding concept applied to sharp V-notches: evaluation of the microstructural support factor for different failure hypotheses. Engineering Fracture Mechanics, 2009, 76(9): 1151–1175CrossRefGoogle Scholar
  68. 68.
    Sih G C, Ho J W. Sharp notch fracture strength characterized by critical energy density. Theoretical and Applied Fracture Mechanics, 1991, 16(3): 179–214CrossRefGoogle Scholar
  69. 69.
    Berto F, Lazzarin P, Matvienko Y G. J-integral evaluation for Uand V-blunt notches under Mode I loading and materials obeying a power hardening law. International Journal of Fracture, 2007, 146 (1–2): 33–51zbMATHCrossRefGoogle Scholar
  70. 70.
    Elices M, Guinea G V, Gomez F J, Planas J. The cohesive zone model: advantages, limitations and challenges. Engineering Fracture Mechanics, 2002, 69(2): 137–163CrossRefGoogle Scholar
  71. 71.
    Gómez F J, Guinea G V, Elices M. Failure criteria for linear elastic materials with U-notches. International Journal of Fracture, 2006, 141(1–2): 99–113zbMATHCrossRefGoogle Scholar
  72. 72.
    Atzori B, Lazzarin P, Meneghetti G. Fracture mechanics and notch sensitivity. Fatigue & Fracture of Engineering Materials & Structures, 2003, 26(3): 257–267CrossRefGoogle Scholar
  73. 73.
    Ayatollahi M R, Torabi A R. Determination of mode II fracture toughness for U-shaped notches using Brazilian disc specimen. International Journal of Solids and Structures, 2010, 47(3–4): 454–465zbMATHCrossRefGoogle Scholar
  74. 74.
    Berto F, Elices M, Lazzarin P, Zappalorto M. Fracture behavior of notched round bars made of PMMA subjected to torsion at room temperature. Engineering Fracture Mechanics, 2012, 90: 143–160CrossRefGoogle Scholar
  75. 75.
    Berto F, Cendon D A, Lazzarin P, Elices M. Fracture behaviour of notched round bars made of PMMA subjected to torsion at–60°C. Engineering Fracture Mechanics, 2013, 102: 271–287CrossRefGoogle Scholar
  76. 76.
    Lomakin E V, Zobnin A I, Berezin A V. Finding the fracture toughness characteristics of graphite materials in plane strain. Strength of Materials, 1975, 7(4): 484–487CrossRefGoogle Scholar
  77. 77.
    Sato S, Kawamata K, Awaji H, Osawa M, Manaka M. Thermal shock resistance and fracture toughness during the graphitization process. Carbon, 1981, 19(2): 111–118CrossRefGoogle Scholar
  78. 78.
    Yamauchi Y, Nakano M, Kishida K, Okabe T. Measurement of mixed mode fracture toughness for brittle materials using edgenotched half-disk specimen. J of the Society of Material Science, 2001, 50: 224–229.CrossRefGoogle Scholar
  79. 79.
    Nakhodchi S, Smith D J, Flewitt P E J. The formation of fracture process zones in polygranular graphite as a precursor to fracture. Journal of Materials Science, 2013, 48(2): 720–732CrossRefGoogle Scholar
  80. 80.
    Bazaj D K, Cox E E. Stress concentration factors and notch sensitivity of graphite. Carbon, 1969, 7(6): 689–697CrossRefGoogle Scholar
  81. 81.
    Kawakami H. Notch sensitivity of graphite materials for VHTR. The Atomic Energy Society of Japan, 1985, 27 (4): 357–364.CrossRefGoogle Scholar
  82. 82.
    Ayatollahi M R, Torabi A R. Tensile fracture in notched polycrystalline graphite specimens. Carbon, 2010, 48(8): 2255–2265CrossRefGoogle Scholar
  83. 83.
    Torabi A R, Berto F. Strain energy density to assess Mode-II fracture in U-notched disk-type graphite plates. International Journal of Damage Mechanics, 2014, 23(7): 917–930CrossRefGoogle Scholar
  84. 84.
    Torabi A R, Pirhadi E. Stress based criteria for brittle fracture in key-hole notches under mixed mode loading. European Journal of Mechanics/A Solids, 2015, 49: 1–12zbMATHCrossRefGoogle Scholar
  85. 85.
    Torabi A R, Amininejad S H. Brittle fracture in V-notches with end holes. International Journal of Damage Mechanics, 2015, 24(4): 529–545CrossRefGoogle Scholar
  86. 86.
    Torabi A R, Campagnolo A, Berto F. Experimental and theoretical investigation of brittle fracture in key-hole notches under mixed mode I/II loading. Acta Mechanica, 2015, 226(7): 2313–2322CrossRefGoogle Scholar
  87. 87.
    Neuber H. Theory of Notch Stresses: Principles for Exact Calculation of Strength with Reference to Structural Form and Material. Berlin: Springer-Verlag, 1958Google Scholar
  88. 88.
    Rice J R. A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics, 1968, 35(2): 379–386CrossRefGoogle Scholar
  89. 89.
    Atluri S N. Computational Methods in the Mechanics of Fracture. Amsterdam: North Holland, 1986Google Scholar
  90. 90.
    Berto F, Lazzarin P. Relationships between J-integral and the strain energy evaluated in a finite volume surrounding the tip of sharp and blunt V-notches. International Journal of Solids and Structures, 2007, 44(14–15): 4621–4645zbMATHCrossRefGoogle Scholar
  91. 91.
    Barati E, Alizadeh Y, Aghazadeh J, Berto F. Some new practical equations for rapid calculation of J-integral in plates weakened by U-notches under bending. Materials & Design, 2010, 31(6): 2964–2971CrossRefGoogle Scholar
  92. 92.
    Sutton M, Wolters W, Peters W, Ranson W, McNeill S. Determination of displacements using an improved digital correlation method. Image and Vision Computing, 1983, 1(3): 133–139CrossRefGoogle Scholar
  93. 93.
    Wells A A. Unstable crack propagation in metals: cleavage and fast fracture. Crack Propag Symp, 1961, 1: 210–230Google Scholar
  94. 94.
    Williams M L. On the stress distribution at the base of stationary crack. Journal of Applied Mechanics, 1957, 24: 109–114MathSciNetzbMATHGoogle Scholar
  95. 95.
    Becker T H, Mostafavi M, Tait R B, Marrow T J. An approach to calculate the J-integral by digital image correlation displacement field measurment. Fatigue & Fracture of Engineering Materials & Structures, 2012, 35(10): 971–984CrossRefGoogle Scholar
  96. 96.
    Meneghetti G, Campagnolo A, Berto F, Atzori B. Averaged strain energy density evaluated rapidly from the singular peak stresses by FEM: cracked components under mixed-mode (I + II) loading. Theoretical and Applied Fracture Mechanics, 2015, 79: 113–124CrossRefGoogle Scholar
  97. 97.
    Akin J E. The generation of elements with singularities. International Journal for Numerical Methods in Engineering, 1976, 10(6): 1249–1259MathSciNetzbMATHCrossRefGoogle Scholar
  98. 98.
    Portela A, Aliabadi M H, Rooke D P. Efficient boundary element analysis of sharp notched plates. International Journal for Numerical Methods in Engineering, 1991, 32(3): 445–470zbMATHCrossRefGoogle Scholar
  99. 99.
    Tracey D M. Finite element for determination of crack tip elastic stress intensity factors. Engineering Fracture Mechanics, 1971, 3 (3): 255–265CrossRefGoogle Scholar
  100. 100.
    Pu S L, Hussain M A, Lorensen W E. The collapsed cubic isoparametric element as a singular element for crack problems. International Journal for Numerical Methods in Engineering, 1978, 12(11): 1727–1742zbMATHCrossRefGoogle Scholar
  101. 101.
    Benzley S E. Representation of singularities with iso-parametric finite elements. International Journal for Numerical Methods in Engineering, 1974, 8(3): 537–545zbMATHCrossRefGoogle Scholar
  102. 102.
    Heyliger P R, Kriz R D. Stress intensity factors by enriched mixed finite elements. International Journal for Numerical Methods in Engineering, 1989, 28(6): 1461–1473zbMATHCrossRefGoogle Scholar
  103. 103.
    Givoli D, Rivkin L. The DtN finite element method for elastic domains with cracks and re-entrant corners. Computers & Structures, 1993, 49(4): 633–642zbMATHCrossRefGoogle Scholar
  104. 104.
    Sheppard S D. Field effects in fatigue crack initiation: long life fatigue strength. Journal of Mechanical Design, 1991, 113(2): 188CrossRefGoogle Scholar
  105. 105.
    Sih G C. Strain-energy-density factor applied to mixed mode crack problems. International Journal of Fracture, 1974, 10(3): 305–321CrossRefGoogle Scholar
  106. 106.
    Sih G C. Mechanics of Fracture Initiation and Propagation. Dordrecht: Springer, 1991CrossRefGoogle Scholar
  107. 107.
    Gdoutos E E. Fracture Mechanics Criteria and Applications. Dordrecht: Springer, 1990zbMATHCrossRefGoogle Scholar
  108. 108.
    Hensel J, Nitschke-Pagel T, Tchoffo Ngoula D, Beier H T, Tchuindjang D, Zerbst U. Welding residual stresses as needed for the prediction of fatigue crack propagation and fatigue strength. Engineering Fracture Mechanics, 2018, 198: 123–141CrossRefGoogle Scholar
  109. 109.
    Song S, Dong P. Residual stresses at weld repairs and effects of repair geometry. Science and Technology of Welding and Joining, 2017, 22(4): 265–277CrossRefGoogle Scholar
  110. 110.
    Martínez-Pañeda E, Niordson C F. On fracture in finite strain gradient plasticity. International Journal of Plasticity, 2016, 80: 154–167CrossRefGoogle Scholar
  111. 111.
    Pluvinage G. Fatigue and fracture emanating from notch: the use of the notch stress intensity factio. Nuclear Engineering and Design, 1998, 185(2–3): 173–184CrossRefGoogle Scholar
  112. 112.
    Peterson R E. Notch sensitivity. In: Sines G, Waisman JL, eds. Metal Fatigue. New York: McGraw Hill, 1959,293–306Google Scholar
  113. 113.
    Ibáñez-Gutiérrez F T, Cicero S. Fracture assessment of notched short glass fiber reinforced polyamide 6: an approach from failure assessment diagrams and the theory of critical distances. Composites Part B: Engineering, 2017, 111: 124–133CrossRefGoogle Scholar
  114. 114.
    Jones R M. Mechanics of Composite Materials. New York: Hemisphere, 1975Google Scholar
  115. 115.
    Tsai S W, Wu E M. A general theory of strength for anisotropic materials. Journal of Composite Materials, 1971, 5(1): 58–80CrossRefGoogle Scholar
  116. 116.
    Kim C H, Yeh H Y. Development of a new yielding criterion: the Yeh-Stratton criterion. Engineering Fracture Mechanics, 1994, 47 (4): 569–582CrossRefGoogle Scholar
  117. 117.
    Yeh H Y, Kim C H. The Yeh-Stratton criterion for composite materials. Journal of Composite Materials, 1994, 28(10): 926–939CrossRefGoogle Scholar
  118. 118.
    Zhang R, Wang Z H, Zhang Q. Biaxial strength of glass fabric reinforced polyester. In: Proc Eighth Int Conf Compoite materials. 1991Google Scholar
  119. 119.
    Andreev G E. Brittle Failure of Rock Materials: Test Results and Constitutive Models. Rotterdam: Balkema, 1995Google Scholar
  120. 120.
    Hoek E, Brown E T. Underground Excavations in Rock. London: Institute of Mining and Metallurgy, 1980Google Scholar
  121. 121.
    Hoek E, Brown E T. Empirical strength criterion for rock mass. J Geotech Eng, 1980, 106: 1013–1035Google Scholar
  122. 122.
    Zuo J P, Li H T, Xie H P, Yang J, Peng S P. A nonlinear strength criterion for rock-like materials based on fracture mechanics. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(4): 594–599CrossRefGoogle Scholar
  123. 123.
    Peterson M S, Wong T F. Experimental Rock Deformation - The Brittle Field. Berlin: Springer, 2005Google Scholar
  124. 124.
    Jaeger J C, Cook N G W, Zimmerman R W. Fundamentals of Rock Mechanics, 4th ed. Oxford: Blackwell, 2007Google Scholar
  125. 125.
    Zuo J P, Liu H H, Li H T. A theoretical derivation of the Hoek-Brown failure criterion for rock. Journal of Rock Mechanics and Geotechnical Engineering, 2015, 7(4): 361–366CrossRefGoogle Scholar
  126. 126.
    Berto F, Campagnolo A, Pook L P. Three-dimensional effects on cracked components under anti-plane loading. Frattura Ed Integrità Strutturale, 2015, 33: 17–24CrossRefGoogle Scholar
  127. 127.
    Campagnolo A, Berto F, Pook L P, Three-dimensional effects on cracked discs and plates under nominal Mode-III loading. Frattura Ed Integrità Strutturale, 2015, 34: 190–199Google Scholar
  128. 128.
    Kotousov A, Lazzarin P, Berto F, Pook L P. Three-dimensional stress states at crack tip induced by shear and anti-plane loading. Engineering Fracture Mechanics, 2013, 108: 65–74CrossRefGoogle Scholar
  129. 129.
    Pook L P. A 50-year retrospective review of three-dimensional effects at cracks and sharp notches. Fatigue & Fracture of Engineering Materials & Structures, 2013, 36(8): 699–723CrossRefGoogle Scholar
  130. 130.
    Lazzarin P, Campagnolo A, Berto F. A comparison among some recent energy- and stress-based criteria for the fracture assessment of sharp V-notched components under Mode-I loading. Theoretical and Applied Fracture Mechanics, 2014, 71: 21–30CrossRefGoogle Scholar
  131. 131.
    Carpinteri A, Cornetti P, Pugno N, Sapora A, Taylor D. A finite fracture mechanics approach to structures with sharp V-notches. Engineering Fracture Mechanics, 2008, 75(7): 1736–1752CrossRefGoogle Scholar
  132. 132.
    Goyal R, Glinka G. Fracture mechanics-based estimation of fatigue lives of welded joints. Welding in the World, 2013, 57(5): 625–634CrossRefGoogle Scholar
  133. 133.
    Lindroth P, Marquis G, Glinka G. Fatigue crack growth of arbitrary planar cracks in welded components. Welding in the World, 2013, 57: 425–435Google Scholar
  134. 134.
    Mikheevskiy S, Glinka G, Cordes T. Total life approach for fatigue life estimation of welded structures. Procedia Engineering, 2015, 101: 177–184CrossRefGoogle Scholar
  135. 135.
    Correia J A F O, Huffman P J, De Jesus A M P, Cicero S, Fernandez-Canteli A, Berto F, Glinka G. Unified two-stage fatigue methodology based on a probabilistic damage model applied to structural details. Theoretical and Applied Fracture Mechanics, 2017, 92: 252–265CrossRefGoogle Scholar
  136. 136.
    Goyal R, Bogdanov S, El-zein M, Glinka G. Fracture mechanics based estimation of fatigue lives of laser welded joints. Engineering Failure Analysis, 2018, 93: 340–355CrossRefGoogle Scholar
  137. 137.
    Irwin G R. Fracture mechanics. In: Goodier J N, Hoff N J, eds. Structural Mechanics. New York: Pergamon Press, 1960, 557–591Google Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringCalifornia State UniversityLong BeachUSA
  2. 2.Department of Chemical EngineeringShanghai Jiao Tong UniversityShanghaiChina

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