Skip to main content
SpringerLink
Log in

A brief review of recent three-dimensional studies of brittle fracture

  • Published:
Physical Mesomechanics Aims and scope Submit manuscript

Abstract

3D crack problems are area where a further intensive research is required. 3D solutions can shed more light on fracture and fatigue phenomena, provide a more accurate evaluation of strength and fatigue life or justify the application of the classical solutions of plane theories of elasticity. These, in fact, are approximate theories even when the governing equations of these theories are solved exactly. The current paper aims to provide a brief summary of the latest investigations of 3D effects associated with crack geometries and brittle fracture. In particular, we present an overview of the coupled fracture modes and 3D vertex singularities, which are currently largely ignored in experimental and theoretical studies. We also describe a recently developed experimental method for the evaluation of the stress intensity factors. This review is concerned with the situation generally described in the literature as small scale plasticity. Large plastic deformations and other non-linear effects are beyond the scope of this article.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kotousov, A., Fracture in Plates of Finite Thickness, Int. J. Solids Struct., 2007, vol. 44, pp. 8259–8273.

    Article  MATH  Google Scholar 

  2. Kotousov, A. and Wang, C.H., Three-Dimensional Stress Constraint in an Elastic Plate with a Notch, Int. J. Solids Struct., 2002, vol. 39, pp. 4311–432I.

    Article  MATH  Google Scholar 

  3. Kotousov, A. and Wang, C.H., Three-Dimensional Solutions for Transversally Isotropic Composite Plates with a Notch, Compos. Struct., 2002, vol. 57, pp. 443–450.

    Article  Google Scholar 

  4. Kotousov, A., Effect of Plate Thickness on Stress State at Sharp Notches and the Strength Paradox of Thick Plate, Int. J. Solids Struct., 2010, vol. 47, pp. 1918–1923.

    Article  MATH  Google Scholar 

  5. Williams, M.L., Stress Singularities Resulting from Various Boundary Conditions in Angular Corners of Plates in Extension, J. Appl. Mech., 1952, vol. 19, pp. 526–528.

    Google Scholar 

  6. Williams, M.L., On the Stress Distribution at the Base of a Stationary Crack, J. Appl. Mech., 1957, vol. 24, pp. 109–114.

    MathSciNet  MATH  Google Scholar 

  7. Irwin, G.R., Analysis of Sresses and Strains near the End of a Crack Traversing a Plate, J. Appl. Mech., 1957, vol. 24, pp. 381–384.

    Google Scholar 

  8. Irwin, G.R., Fracture. Encylopedia of Physics. Vol. VI, Berlin: Springer, 1958, pp. 551–590.

    Google Scholar 

  9. Broek, D., Elementary Engineering Fracture Mechanics, The Hague: Martinus Nijhoff Publishers, 1982.

    Book  MATH  Google Scholar 

  10. Anderson, T.L., Fracture Mechanics: Fundamentals and Applications, Boca Raton: CRC Press, 1995.

    MATH  Google Scholar 

  11. Perez, N., Fracture Mechanics, Boston: Kluwer Academic Publishers, 2004.

    Google Scholar 

  12. Cotterell, B., The Past, Present, and Future of Fracture Mechanics, Eng. Fract. Mech., 2002, vol. 89, pp. 533553.

    Google Scholar 

  13. Kotousov, A., Effect of a Thin Plastic Adhesive Layer on the Stress Singularities in a Bi-Material Wedge, Int. J. Adhes. Adhes., 2007, vol. 27, pp. 847–852.

    Article  Google Scholar 

  14. Lazzarin, P. and Tovo, R., A Notch Intensity Approach to the Stress Analysis of Welds, Fatigue Fract. Eng. Mater. Struct., 1998, vol. 21, pp. 1089–1104.

    Article  Google Scholar 

  15. Lazzarin, P. and Livieri, P., Notch Stress Intensity Factors and Fatigue Strength of Aluminium and Steel Welded Joints, Int. J. Fatigue, 2001, vol. 23, pp. 225–232.

    Article  Google Scholar 

  16. Sinclair, G.B. and Chambers, A.E., Strength Size Effects and Fracture Mechanics: What Does the Physical Evidence Say? Eng. Fract. Mech., 1987, vol. 28, pp. 279–310.

    Article  Google Scholar 

  17. Li, J. and Zhang, X.B., A Criterion Study for Non-Singular Stress Concentrations in Brittle or Quasi-Brittle Materials, Eng. Fract. Mech., 2008, vol. 73, pp. 505–523.

    Article  Google Scholar 

  18. Smith, D.J., Ayatollahi, M.R., and Pavier, M.J., On the Consequences of T-Stress in Elastic Brittle Fracture, Proc. R. Soc. Lond. A, 2008, vol. 482, pp. 2415–2437.

    MATH  Google Scholar 

  19. Sun, C.T. and Qian, H.Y., Brittle Fracture Beyond the Stress Intensity Factor, J. Mech. Mater. Struct., 2009, vol. 4, pp. 743–753.

    Article  Google Scholar 

  20. Kumar, B., Chitsiriphanit, S., and Sun, C.T., Significance of K-Dominance Zone Size and Nonsingular Stress Field in Brittle Fracture, Eng. Fract. Mech., 2011, vol. 78, pp. 2042–2051.

    Article  Google Scholar 

  21. Szekrenyes, A., Interlaminar Stresses and Energy Release Rates in Delaminated Orthotropic Composite Plates, Int. J. Solids Struct., 2012, vol. 49, pp. 2480–2479.

    Article  Google Scholar 

  22. Yang, W. and Freund, L.B., Transverse Shear Effects for Through-Cracks in an Elastic Plate, Int. J. Solids Struct., 1985, vol. 9, pp. 977–994.

    Article  MathSciNet  MATH  Google Scholar 

  23. Burton, W.S., Sinclair, G.B., Solecki, J.S., and Swedlow, J.L., On the Implications for LEFM of the ThreeDimensional Aspects in Some Crack/Surface Intersection Problems, Int. J. Fract., 1984, vol. 25, pp. 3–32.

    Article  Google Scholar 

  24. Nakamura, T. and Parks, D.M., Antisymmetrical 3D Stress Field near the Crack Front of a Thin Elastic Plate, Int. J. Solids Struct., 1989, vol. 12, pp. 1411–142I.

    Article  Google Scholar 

  25. Nakamura, T. and Parks, D.M., Three-Dimensional Stress Field near the Crack Front of a Thin Elastic Plate, J. Appl. Mech., 1989, vol. 55, pp. 805–813.

    Article  Google Scholar 

  26. Omer, N. and Yosibash, Z., On the Path Independency of the Point-Wise J-Integral in Three-Dimensions, Int. J. Fract., 2005, vol. 136, pp. 1–36.

    Article  MATH  Google Scholar 

  27. Berto, F., Lazzarin, P., and Kotousov, A., On Higher Order Terms and Out of Plane Singular Mode, Mech. Mater., 2011, vol. 43, pp. 332–341.

    Article  MATH  Google Scholar 

  28. Berto, F., Lazzarin, P., and Kotousov, A., On the Presence of the Out-of-Plane Singular Mode Induced by Plane Loading with Kn = K = 0, Int. J. Fract., 2011, vol. 167, pp. 119–126.

    Article  MATH  Google Scholar 

  29. Kotousov, A., Lazzarin, P., Berto, F., and Pook, L.P., Three-Dimensional Stress States at Crack Tip Induced by Shear and Anti-Plane Loading, Eng. Fract. Mech., 2013, vol. 108, pp. 65–74.

    Article  Google Scholar 

  30. Kotousov, A., He, Z., and Gardeazabal, D., On Scaling of Brittle Fracture, Proc. 8th Int. Conf. on Structural Integrity and Fracture, 11-12 July 2013, Melbourne, Australia, pp. 93–98.

    Google Scholar 

  31. Nejati, M., Paluszny, A., and Zimmerman, R.W., A DiskShaped Domain Integral Method for the Computation of Stress Intensity Factors Using Tetrahedral Meshes, Int. J. Solids Struct., 2015, vol. 19, pp. 230–251.

    Article  Google Scholar 

  32. Hartranft, R.J. and Sih, G.C., The Use of Eigenfunction Expansions in the General Solution of Three-Dimensional Crack Problems, J. Math. Mech., 1989, vol. 19, pp. 123–138.

    MathSciNet  MATH  Google Scholar 

  33. Kong, X.M., Schluter, N., and Dahl, W., Effect of Triaxial Stress on Mixed-Mode Fracture, Eng. Fract. Mech., 1995, vol. 52, pp. 379–388.

    Article  Google Scholar 

  34. Yuan, H. and Brocks, W., Quantification of Constraint Effects in Elastic-Plastic, Crack Front Fields, J. Mech. Phys. Solids, 1998, vol. 48, pp. 219–241.

    Article  ADS  MATH  Google Scholar 

  35. Rosakis, A. and Ravi-Chandar, K., On Crack-Tip Stress State: An Experimental Evaluation of Three-Dimensional Effects, Int. J. Solids Struct., 1986, vol. 22, pp. 121134.

    Article  Google Scholar 

  36. Gregory, R.D. and Wan, F.Y.M., The Interior Solution for Linear Problems of Elastic Plates, J. Appl. Mech., 1988, vol. 55, pp. 551–559.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. She, C. and Guo, W., The Out-of-Plane Constraint of Mixed-Mode Cracks in Thin Elastic Plates, Int. J. Solids Struct., 2007, vol. 44, pp. 3021–3034.

    Article  MATH  Google Scholar 

  38. Harding, S., Kotousov, A., Lazzarin, P., and Berto, F., Transverse Singular Effects in V-Shaped Notches Stressed in Mode II, Int. J. Fract., 2010, vol. 164, pp. 1–14.

    Article  MATH  Google Scholar 

  39. Pook, L.P., A 50-Year Retrospective Review of ThreeDimensional Effects at Cracks and Sharp Notches, Fatigue Fract. Eng. Mater. Struct., 2013, vol. 36, pp. 699723.

    Article  Google Scholar 

  40. Pook, L.P., Five Decades of Crack Path Research, Eng. Fract. Mech., 2013, vol. 77, pp. 1619–1630.

    Article  Google Scholar 

  41. Berto, F., Lazzarin, P., Harding, S., and Kotousov, A., Out-of-Plane Singular Stress Fields in V-Notched Plates and Welded Lap Joints Induced by In-Plane Shear Load Conditions, Fatigue Fract. Eng. Mater. Struct., 2011, vol. 34, pp. 291–304.

    Article  Google Scholar 

  42. Berto, F., Lazzarin, P., Kotousov, A., and Pook, L.P., Induced Out-of-Plane Mode at the Tip of Blunt Lateral Notches and Holes under In-Plane Shear Loading, Fatigue Fract. Eng. Mater. Struct., 2012, vol. 35, pp. 538555.

    Article  Google Scholar 

  43. He, Z., Kotousov, A., and Branco, R., A Simplified Method for the Evaluation of Fatigue Crack Front Shapes under Mode I Loading, Int. J. Fract., 2014, vol. 188, pp. 203–211.

    Article  Google Scholar 

  44. He, Z., Kotousov, A., and Rose, L.R.F., Effect of Vertex Singularities on the Displacement and Strain Fields near a Crack Front, Recent Advances in Structural Integrity Analysis: Proc. Int. Congr. APCF/SIF-2014, pp. 12–16.

  45. He, Z., Kotousov, A., Fanciulli, A., Berto, F., and Nguyen, G., On the Evaluation of Stress Intensity Factor from Displacement Field Affected by 3D Corner Singularity, Int. J. Solids Struct., 2015, vol. 78-79, pp. 131–137.

    Article  Google Scholar 

  46. He, Z., Kotousov, A., Fanciulli, A., and Berto, F., An Experimental Method for Evaluating Mode II Stress Intensity Factor from near Crack Tip Field, Int. J. Fract., 2015, doi 10.1007/s10704-015-0062-x.

    Google Scholar 

  47. He, Z., Kotousov, A., and Berto, F., Effect of Vertex Singularities on Stress Intensities near Plate Free Surfaces, Fatigue Fract. Eng. Mater. Struct., 2015, vol. 38, no. 7, pp. 860–869.

    Article  Google Scholar 

  48. Sevcik, M., Hutar, P., Zouhar, M., and Nahlik, L., Numerical Estimation of the Fatigue Crack Front Shape for a Specimen with Finite Thickness, Int. J. Fatigue, 2012, vol. 39, pp. 75–80.

    Article  Google Scholar 

  49. Zheng, X., Cui, H., Engler-Pinto, C.C., Su, X., and Wen, W., Numerical Modelling of Fatigue Crack Propagation Based on the Theory of Critical Sistances: Effects of Overloads and Underloads, Eng. Fract. Mech., 2014, vol. 128, pp. 91–102.

    Article  Google Scholar 

  50. Dundar, H., and Ayhan, A.O., Three-Dimensional Fracture and Fatigue Crack Propagation Analysis in Structures with Multiple Cracks, Comput. Struct., 2015, vol. 158, pp. 259–273.

    Article  Google Scholar 

  51. Pathak, H., Singh, A., Singh, I.V., and Brahmankar, M., Three-Dimensional Stochastic Quasi-Static Fatigue Crack Growth Simulations Using Coupled FE-EFG Approach, Comput. Struct., 2015, vol. 110, pp. 1–19.

    Article  Google Scholar 

  52. Branco, R. and Antunes, F.V., Finite Element Modelling and Analysis of Crack Shape Evolution in Mode-I Fatigue Middle Cracked Tension Specimens, Eng. Fract. Mech., 2008, vol. 75, pp. 3020–3037.

    Article  Google Scholar 

  53. Smith, R.A. and Cooper, J.F., A Finite Element Model for the Shape Development of Irregular Planar Cracks, Int. J. Pres. Ves. Pip., 1989, vol. 36, pp. 315–328.

    Article  Google Scholar 

  54. Antunes, F.V., Branco, R., Costa, J.D., and Rodrigues, D.M., Plasticity Induced Crack Closure in Middle-Crack Tension Specimen: Numerical versus Experimental, Fatigue Fract. Eng. Mater. Struct., 2010, vol. 33, pp. 673–688.

    Article  Google Scholar 

  55. Branco, R., Antunes, F.V., and Costa, J.D., Extent of Surface Region in Notched Middle-Cracked Tension Specimens, Key Eng. Mater., 2013, vol. 560. P. 107–127.

    Article  Google Scholar 

  56. Branco, R., Antunes, F.V., and Costa, J.D., A Review on 3D-FE Adaptive Remeshing Techniques for Crack Growth Modeling, Eng. Fract. Mech., 2015, vol. 141, pp. 170–195.

    Article  Google Scholar 

  57. Wang, C., Wang, X., Ding, Z.Y., Xu, Y.J., and Gao, Z.L., Experimental Investigation and Numerical Prediction of Fatigue Crack Growth of2024-T4 Aluminum Alloy, Int. J. Fatigue, 2015, vol. 78, pp. 11–21.

    Article  Google Scholar 

  58. Chao, Y.J. and Liu, S., On the Failure of Cracks under Mixed-Mode Loads, Int. J. Fract., 1997, vol. 87, pp. 201–223.

    Article  Google Scholar 

  59. Pook, L.P., A Note on Corner Point Singularities, Int. J. Fract., 1992, vol. 53, pp. 3–8.

    Google Scholar 

  60. Pook, L.P., Some Implications of Corner Point Singularities, Eng. Fract. Mech., 1994, vol. 48, pp. 367–378.

    Article  ADS  Google Scholar 

  61. Pook, L.P., On Fatigue Crack Path, Int. J. Fract., 1995, vol. 17, pp. 5–13.

    Google Scholar 

  62. Pook, L.P., Finite Element Analysis of Corner Point Displacements and Stress Intensity Factors for Narrow Notches in Square Sheets and Plates, Fatigue Fract. Eng. Mater. Struct., 2000, vol. 23, pp. 979–992.

    Article  Google Scholar 

  63. Pook, L.P., Finite Element Analysis of Cracked Square Plates and Bars under Anti-Plane Loading, Proc. 6th Int. Conf. on Biaxial/Multi-Axial Fatigue and Fracture, Instituto Superior Tecnico, Lisbon, Portugal, Vol. II, 2001, pp. 701–708.

    Google Scholar 

  64. Pook, L.P., Crack Profiles and Corner Point Singularities, Fatigue Fract. Eng. Mater. Struct., 2001, vol. 23, pp. 141–150.

    Article  Google Scholar 

  65. Pook, L.P., Crack Paths, Southampton, UK: WIT Press, 2002.

    Google Scholar 

  66. Kotousov, A., Lazzarin, P., Berto, F., and Harding, S., Effect of the Thickness on Elastic Deformation and Quasi-Brittle Fracture of Plate Components, Eng. Fract. M ech, 2010, vol. 77, pp. 1665–1681.

    Article  Google Scholar 

  67. Manrique, J.G., Camas, D., Crespo, P.L., and Herrera, A.G., Stress Intensity Factor Analysis of through Thickness Effects, Int. J. Fatigue, 2012, vol. 44, pp. 41–50.

    Article  Google Scholar 

  68. Barsoum, R.S., On the Use of Isoparametric Finite Elements in Linear Fracture Mechanics, Int. J. Numer. Meth. Eng., 1976, vol. 10, pp. 25–37.

    Article  MATH  Google Scholar 

  69. Doquet, V., Abbadi, M., Bui, Q.H., and Pons, A., Influence of the Loading Path on Fatigue Crack Growth under Mixed-Mode Loading, Int. J. Fract., 2009, vol. 59, pp. 219–232.

    Article  Google Scholar 

  70. Doquet, V., Bui, Q.H., Bertolino, G., Merhy, E., Alves, L., 3D Shear-Mode Fatigue Crack Growth in Maraging Steel and Ti-6AL-4V, Int. J. Fract., 2010, vol. 165, pp. 6176.

    Article  Google Scholar 

  71. Seitl, S., Hutao, P., García, T.E., and Fernandez-Canteli, A., Experimental and Numerical Analysis of In-and Out-of Plane Constraint Effects on Fracture Parameters: Aluminium Alloy 2024, Appl. Comp. Mech., 2013, vol. 7, pp. 53–64.

    Google Scholar 

  72. Kotousov, A., On Stress Singularities at Angular Corners of Plates of Arbitrary Thickness under Tension, Int. J. Fract., 2005, vol. 132, pp. 29–36.

    Article  MATH  Google Scholar 

  73. Kotousov, A., Berto, F., Lazzarin, P., and Pegorin, F., Three Dimensional Finite Element Mixed Fracture Mode under Anti-Plane Loading of a Crack, Theor. Appl. Fract. Mech., 2012, vol. 62, pp. 26–33.

    Article  Google Scholar 

  74. Kotousov, A., He, Z., and Fanciulli, A., Application of Digital Image Correlation Technique for Investigation of the Displacement and Strain Fields within a Sharp Notch, Theor. Appl. Fract. Mech., 2015, vol. 79, pp. 5157.

    Article  Google Scholar 

  75. Berto, F., Kotousov, A., Lazzarin, P., and Pegorin, F., On a Coupled Mode at Sharp Notches Subjected to AntiPlane Loading, Eur. J. Mech. A. Solids, 2013, vol. 38, pp. 70–78.

    Article  ADS  Google Scholar 

  76. Sanford, R.J., Principles of Fracture Mechanics, New York: Pearson Education, 2005.

    Google Scholar 

  77. Hutar, P., Nahlik, L., and Knésl, Z., Quantification of the Influence of Vertex Singularities on Fatigue Crack Behavior, Comp. Mater. Sci., 2009, vol. 45, pp. 653–657.

    Article  Google Scholar 

  78. Hutar, P., Nahlik, L., and Knésl, Z., The Effect of a Free Surface on Fatigue Crack Behaviour, Int. J. Fatigue, 2010, vol. 32, pp. 1265–1269.

    Article  Google Scholar 

  79. Berto, F., A Review on Coupled Modes in V-Notched Plates of Finite Thickness: A Generalized Approach to the Problem, Phys. Mesomech., 2013, vol. 16, pp. 378390.

    Article  Google Scholar 

  80. Bazant, Z.P. and Estenssoro, L.F., Surface Singularity and Crack Propagation, Int. J. Solids Struct., 1979, vol. 15, pp. 405–426.

    Article  MathSciNet  MATH  Google Scholar 

  81. Benthem, J.P., State of Stress at the Vertex of a QuarterInfinite Crack in a Half-Space, Int. J. Solids Struct., 1977, vol. 13, pp. 479–492.

    Article  MATH  Google Scholar 

  82. Benthem, J.P., The Quarter-Infinite Crack in a Half-Space. Alternative and Additional Solutions, Int. J. Solids Struct., 1980, vol. 16, pp. 119–130.

    Article  MATH  Google Scholar 

  83. Huang, C.S., Corner Stress Singularities in a High-Order Plate Theory, Comput. Struct., 2004, vol. 82, pp. 1657–1669.

    Article  Google Scholar 

  84. Yu, P., She, C., and Guo, W., Equivalent Thickness Conception for Corner Cracks, Int. J. Solids Struct., 2010, vol. 47, pp. 2123–2130.

    Article  MATH  Google Scholar 

  85. Vu, M.N., Geniaut, S., Massin, P., and Marigo, J.J., Numerical Investigation on Corner Singularities in Cracked Plates Using the G-Theta Method with an Adapted 0 Field, Theor. Appl. Fract. Mech., 2015, vol. 77, pp. 59–68.

    Article  Google Scholar 

  86. Shivakumar, K.N. and Raju, I.S., Treatment of Singularities in Cracked Bodies, Int. J. Fract., 1990, vol. 45, pp. 159–178.

    Article  Google Scholar 

  87. de Matos, P.F.P. and Nowel, D., The Influence of the Poisson’s Ratio and Corner Point Singularities in ThreeDimensional Plasticity-Induced Fatigue Crack Closure: A Numerical Study, Int. J. Fatigue, 2008, vol. 30, pp. 1930–1943.

    Article  MATH  Google Scholar 

  88. Heyder, M., Kolk, K., and Kuhn, G., Numerical and Experimental Investigations of the Influence of Corner Singularities on 3D Fatigue Crack Propagation, Eng. Fract. Mech., 2005, vol. 72, pp. 2095–2105.

    Article  Google Scholar 

  89. Branco, R., Antunes, F.V., Ricardo, L.C.H., and Costa, J.D., Extent of Surface Regions near Corner Points of Notched Cracked Bodies Subjected to Mode-I Loading, Finite Elem. Anal. Des., 2012, vol. 50, pp. 147–1I0.

    Article  Google Scholar 

  90. Camas, D., Garcia-Manrique, J., and Gonzalez-Herrera, A., Crack Front Curvature: Influence and Effects on the Crack Tip Fields in Bidimensional Specimens, Int. J. Fatigue, 2012, vol. 44, pp. 41–50.

    Article  Google Scholar 

  91. Olaosebikan, L., On the Variation of Stress Along the Front of Cracks and Surface Flaws, Eng. Fract. Mech., 1990, vol. 37, pp. 221–235.

    Article  Google Scholar 

  92. Heyder, M. and Kuhn, G., 3D Fatigue Crack Propagation: Experimental Studies, Int. J. Fatigue, 2008, vol. 28, pp. 627–634.

    Article  MATH  Google Scholar 

  93. Dhondt, G., Cyclic Crack Propagation at Corners and Holes, Fatigue Fract. Eng. Mater. Struct., 2005, vol. 28, pp. 25–30.

    Article  Google Scholar 

  94. Dhondt, G., Application of the Finite Element Method to Mixed-Mode Cyclic Crack Propagation Calculations in Specimens, Int. J. Fatigue, 2014, vol. 58, pp. 2–11.

    Article  Google Scholar 

  95. Borrego, L.P.F., Fatigue Crack Growth under Variable Amplitude Load in an AlMgSi Alloy, PhD Thesis, Department of Mechanical Engineering, University of Coimbra, 2001.

    Google Scholar 

  96. Hosseini-Toudeshky, H., Sadeghi, G., and Daghyani, H.R., Experimental Fatigue Crack Growth and Crack-Front Shape Analysis of Asymmetric Repaired Aluminium Panels with Glass/Epoxy Composite Patches, Compos. Struct., 2005, vol. 71, pp. 401–406.

    Article  Google Scholar 

  97. Elber, W., The Significance of Fatigue Crack Closure. Damage Tolerance, Aircr. Struct. ASTM STP, 1971, vol. 485, pp. 230–242.

    Article  Google Scholar 

  98. Codrington, J. and Kotousov, A., A Crack Closure Model of Fatigue Crack Growth in Plates of Finite Thickness under Small-Scale Yielding Conditions, Mech. Mater., 2009, vol. 41, pp. 165–173.

    Article  Google Scholar 

  99. Kotousov, A. and Codrington, J., Application of Refined Plate Theory to Fracture and Fatigue, in Structural Failure Analysis and Prediction Methods for Aerospace Vehicles and Structures, Ho, S.Y., Ed., Bentham Science Publishers, 2010, pp. 90–103.

    Google Scholar 

  100. Machniewicz, T., Fatigue Crack Growth Prediction Models for Metallic Materials. Part II: Strip Yield Model-Choices and Decisions, Fatigue Fract. Eng. Mater. Struct., 2013, vol. 36, pp. 361–373.

    Article  Google Scholar 

  101. Hou, C.Y., Simulation of Surface Crack Shape Evolution Using the Finite Element Technique and Considering the Crack Closure Effects, Int. J. Fatigue, 2011, vol. 33, pp. 719–72I.

    Article  Google Scholar 

  102. Pfaff, R.D., Washabaugh, P.D., and Knauss, W.G., An Interpretation of Twyman-Green Interferograms from Static and Dynamic Fracture Experiments, Int. J. Solids Struct., 1995, vol. 32, pp. 939–955.

    Article  Google Scholar 

  103. Humbert, L., Valle, V., and Cottron, M., Experimental Determination and Empirical Representation of Out-ofPlane Displacements in a Cracked Elastic Plate Loaded in Mode I, Int. J. Solids Struct., 2000, vol. 37, pp. 54935504.

    Article  MATH  Google Scholar 

  104. Kotousov, A. and Tan, P.J., Effect of the Plate Thickness on the Out-of-Plane Displacement Field of a Cracked Elastic Plate Loaded in Mode I, Int. J. Fract., 2004, vol. 127, pp. 97–103.

    Article  MATH  Google Scholar 

  105. McNeill, S.R., Peters, W.H., and Sutton, M.A., Estimation of Stress Intensity Factor by Digital Image Correlation, Eng. Fract. Mech., 1987, vol. 28, pp. 101–112.

    Article  Google Scholar 

  106. Yoneyama, S., Morimoto, Y., and Takashi, M., Automatic Evaluation of Mixed-Mode Stress Intensity Factors Utilizing Digital Image Correlation, Strain, 2006, vol. 42, pp. 21–29.

    Article  Google Scholar 

  107. Brynk, T., Laptiev, A., Tolochyn, O., and Pakiela, Z., The Method of Fracture Toughness Measurements of High Speed Camera and DIC, Comp. Mater. Sci., 2012, vol. 64, pp. 221–224.

    Article  Google Scholar 

  108. Zhang, R. and He, L., Measurement of Mixed-Mode Stress Intensity Factors Using Digital Image Correlation Method, Opt. Lasers Eng, 2012, vol. 50, pp. 1001–1007.

    Article  Google Scholar 

  109. Sutton, A., Orteu, J.J., and Schreier, H.W., Image Correlation for Shape Motion and Deformation Measurements, Berlin: Springer, 2009.

    Google Scholar 

  110. Nevalainen, M. and Dodds, R.H., Numerical Investigation of 3D Constraint Effects on Brittle Fracture in SE(B) and C(T) Specimens, Int. J. Fract., 1995, vol. 74, pp. 131–161.

    Article  Google Scholar 

  111. Leung, A.Y.T. and Su, R.K.L., A Numerical Study of Singular Stress Field of 3D Cracks, Finite Elem. Anal. D es, 1995, vol. 18, pp. 389–401.

    Article  MATH  Google Scholar 

  112. Kwon, S.W. and Sun, C.T., Characteristics of ThreeDimensional Stress Field in Plates with a Through-the Thickness Crack, Int. J. Fract., 2000, vol. 104, pp. 291315.

    Article  Google Scholar 

  113. Codrington, J., Kotousov, A., and Ho, S.Y., Out-of-Plane Stress and Displacement for Through-the-Thickness Cracks in Plates of Finite Thickness, J. Mech. Mater. Struct., 2008, vol. 3, pp. 261–275.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, The University of Adelaide, Adelaide, SA, 5005, Australia

    Z. He & A. Kotousov

  2. Department of Management and Engineering, University of Padova, Vicenza, 36100, Italy

    F. Berto

  3. Department of Engineering Design and Materials, Norwegian University of Science and Technology, Trondheim, 7491, Norway

    F. Berto

  4. Department of Mechanical Engineering, Polytechnic Institute of Coimbra, Coimbra, 3045-601, Portugal

    R. Branco

Authors
  1. Z. He
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Kotousov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. Berto
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. Branco
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Z. He.

Additional information

Original text © Z. He, A. Kotousov, F. Berto, R. Branco, 2016, published in Fizicheskaya Mezomekhanika, 2016, Vol. 19, No. 1, pp. 89-101.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, Z., Kotousov, A., Berto, F. et al. A brief review of recent three-dimensional studies of brittle fracture. Phys Mesomech 19, 6–20 (2016). https://doi.org/10.1134/S1029959916010021

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1029959916010021

Keywords

Search

Navigation