Scientific Background

  • Haoyun TuEmail author
Part of the Springer Theses book series (Springer Theses)


Fracture is a problem which troubles structural engineers for centuries. People have been trying to answer when, where, and why the structures fail. Scientists have been trying to investigate the fracture mechanisms of complex components, e.g., the weldment, as the fracture behaviour of weldments influences the crack growth in structures which affects the lifetime and safety of the components.


  1. T. L. Anderson, Fracture Mechanics: Fundamentals and Applications. 3rd edn. (CRC Press, 2005)Google Scholar
  2. M. Anvari, I. Scheider, C. Thaulow, Simulation of dynamic ductile crack growth using strain-rate and triaxiality-dependent cohesive elements. Eng. Fract. Mech. 73, 2210–2228 (2006)CrossRefGoogle Scholar
  3. ARAMIS, User manual—software, ARAMIS V6.1, GOM mbH, 2008Google Scholar
  4. G.I. Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7, 55–129 (1962)CrossRefGoogle Scholar
  5. J. A. Begley, J. D. Landes, in Fracture Mechanics, The J-integral as a fracture criterion (ASTM STP 514 1972), pp. 1–23Google Scholar
  6. F.M. Beremin, A local criterion for cleavage fracture of a nuclear pressure vessel steel. Metall. Trans. A 14A, 2277–2287 (1983)CrossRefGoogle Scholar
  7. J. Bishop, R. Hill, A theoretical derivation of the plastic properties of a polycrystalline face-centred metal. Phil. Mag. 42, 1298–1307 (1951)CrossRefGoogle Scholar
  8. W. Brocks, Computational Fracture Mechanics, in Continuum Scale Simulation of Engineering Materials: Fundamentals—Microstructures—Process Applications, ed. by F. Roters, F. Barlat, L.Q. Chen (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2004)Google Scholar
  9. P. Cambrésy, Damage and fracture mechanisms investigations of an aluminium laser beam weld. Dissertation, GKSS-Forschungszentrum Geesthacht, (2006)Google Scholar
  10. G. Çam, M. Koçak, J.F. Dos Santos, Developments in laser welding of metallic materials and characterization of the joints. Weld. World 43, 13–26 (1999)Google Scholar
  11. O. Chabanet, D. Steglich, J. Besson, V. Heitmann, D. Hellmann, W. Brocks, Predicting crack growth resistance of aluminium sheets. Comp. Mater. Sci. 26, 1–12 (2003)CrossRefGoogle Scholar
  12. C.R. Chen, O. Kolednik, I. Scheider, T. Siegmund, A. Tatschl, F.D. Fischer, On the determination of the cohesive zone parameters for the modelling of microductile crack growth in thick specimens. Int. J. Fract. 120, 417–536 (2003)CrossRefGoogle Scholar
  13. Y. Cheng, V. Altapova, L. Helfen, F. Xu, T. dos Santos Rolo, P. Vagovič, M. Fiederle, T. Baumbach, Multi-contrast computed laminography at ANKA light source. J. Phys: Conf. Ser. 463, 012038 (2013)Google Scholar
  14. C.C. Chu, A. Needleman, Void nucleation effects in biaxially stretched sheets. J. Eng. Mater. Technol. 102, 249–256 (1980)CrossRefGoogle Scholar
  15. P. Cloetens, R. Barrett, J. Baruchel, J.P. Guigay, M. Schlenker, Phase objects in synchrotron radiation hard x-ray imaging. J. Phys. D: Appl. Phys. 29, 133–146 (1996)CrossRefGoogle Scholar
  16. A. Cornec, I. Scheider, K.-H. Schwalbe, On the practical application of the cohesive model. Eng. Fract. Mech. 70, 1963–1987 (2003)CrossRefGoogle Scholar
  17. D.S. Dugdale, Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8, 100–104 (1960)CrossRefGoogle Scholar
  18. A.G. Franklin, Comparison between a quantitative microscope and chemical methods for assessment of non-metallic inclusions. J. Iron Steel Inst. 207, 181–186 (1969)Google Scholar
  19. L. Graziani, M. Knećb, T. Sadowski, M.D. Orazio, S. Lenci, Measurement of R-curve in clay brick blocks using optical measuring technique. Eng. Fract. Mech. 121–122, 1–10 (2014)CrossRefGoogle Scholar
  20. A.A. Griffith, The phenomena of rupture and flow in solids. Philos. Trans. R. Soc. A 211, 163–198 (1920)Google Scholar
  21. J.R. Griffiths, An elastic-plastic stress analysis for a notched bar in plane strain bending. J. Mech. Phys. Solids 19, 419–431 (1971)CrossRefGoogle Scholar
  22. A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth, Part I—yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol. 99, 2–15 (1977)CrossRefGoogle Scholar
  23. L. Helfen, T. Baumbach, P. Pernot, P. Cloetens, H. Stanzick, K. Schladitz, J. Banhart, Investigation of pore initiation in metal foams by synchrotron-radiation tomography. Appl. Phys. Lett. 86, 231907-1–231907-3 (2005)Google Scholar
  24. L. Helfen, A. Myagotin, P. Mikulik, P. Pernot, A. Voropaev, M. Elyyan, M. DiMichiel, J. Baruchel, T. Baumbach, On the implementation of computed laminography using synchrotron radiation. Rev. Sci. Instrum. 82, 063702-1–063702-8 (2011)CrossRefGoogle Scholar
  25. A. Hillerborg, M. Modéer, P.-E. Petersson, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem. Conc. Res. 6, 773–782 (1976)CrossRefGoogle Scholar
  26. Y. Huang, Accurate dilatation rates for spherical voids in triaxial stress fields. J. Appl. Mech. Trans. ASME 58, 1084–1086 (1991)CrossRefGoogle Scholar
  27. J. Huang, S. Schmauder, U. Weber, S. Geier, Micromechanical modelling of the elastoplastic behaviour of nanodispersed elastomer particle-modified PA 6. Comp. Mater. Sci. 52, 107–111 (2011)CrossRefGoogle Scholar
  28. G.R. Irwin, Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. 24, 361–364 (1957)Google Scholar
  29. S. Kou, Welding metallurgy, 2nd edn. (John Wiley & Sons. Inc., Hoboken, New Jersey, 2003)Google Scholar
  30. K. Kussmaul, U. Eisele, M. Seidenfuss, in Fatigue & Fract Mech in Press Vess & Piping, ed. by Mehta, et al. On the Applicability of Local Approach Models for the Determination of the Failure Behaviour of Steels with Different Toughness, vol 304 (1995), pp. 17–25Google Scholar
  31. L. Laiarinandrasana, T.F. Morgeneyer, H. Proudhon, F. N’guyen, E. Maire, Effect of multiaxial stress state on morphology and spatial distribution of voids in deformed semicrystalline polymer assessed by x-ray tomography. Macromolecules 45, 4658–4668 (2012)CrossRefGoogle Scholar
  32. J. D. Landes, J. A. Begley, The J-Integral as a fracture criterion (ASTM STP 514, American Society for testing and Materials, Philadelphia, 1972), pp. 1–20Google Scholar
  33. W. Li, T. Siegmund, An analysis of crack growth in thin-sheet metal via a cohesive zone model. Eng. Fract. Mech. 69, 2073–2093 (2002)CrossRefGoogle Scholar
  34. G. Lin, A. Cornec, K.-H. Schwalbe, Three-dimensional finite element simulation of crack extension in aluminum alloy 2024-FC. Fatigue Fract. Eng. Mater. Struct. 21, 1159–1173 (1998)CrossRefGoogle Scholar
  35. G. Lin, Numerical investigation of crack growth behaviour using a cohesive zone model. Ph.D. thesis, TU Hamburg-Harburg, Geesthacht, (1998)Google Scholar
  36. G. Lin, X.-G. Meng, A. Cornec, K.-H. Schwalbe, The effect of strength mis-match on mechanical performance of weld joints. Int. J. Fract. 96, 37–54 (1999)CrossRefGoogle Scholar
  37. A. Mohanta, Numerical determination of failure curves. Master thesis, University of Stuttgart, (2003)Google Scholar
  38. T.F. Morgeneyer, J. Besson, H. Proudhon, M.J. Starink, I. Sinclair, Experimental and numerical analysis of toughness anisotropy in AA2139 Al-alloy sheet. Acta Mater. 57, 3902–3915 (2009)CrossRefGoogle Scholar
  39. T.F. Morgeneyer, L. Helfen, H. Mubarak, F. Hild, 3D Digital Volume Correlation of Synchrotron Radiation Laminography images of ductile crack initiation: An initial feasibility study. Exp. Mech. 53, 543–556 (2013)CrossRefGoogle Scholar
  40. A. Needleman, J. R, in Mechanics of Metal Sheet Forming, Rice, Limits to Ductility by Plastic Flow Localization, (1978), pp. 237–267Google Scholar
  41. A. Needleman, A continuum model for void nucleation by inclusion debonding. J. Appl. Mech. ASME 54, 525–531 (1987)CrossRefGoogle Scholar
  42. A. Needleman, An analysis of decohesion along an imperfect interface. I J Fract 42, 21–40 (1990)CrossRefGoogle Scholar
  43. A. Needleman, V. Tvergaard, A micromechanical analysis of ductile-brittle transition at a weld. Eng. Fract. Mech. 62, 317–338 (1999)CrossRefGoogle Scholar
  44. P. Nègre, D. Steglich, W. Brocks, Numerical simulation of crack extension in aluminium welds. Comput. Mater. Sci. 28, 723–731 (2003)CrossRefGoogle Scholar
  45. P. Nègre, D. Steglich, W. Brocks, Crack extension in aluminium welds: a numerical approach using the Gurson-Tvergaard-Needleman model. Eng. Fract. Mech. 71, 2365–2383 (2004)CrossRefGoogle Scholar
  46. K.L. Nielsen, Ductile damage development in friction stir welded aluminum (AA2024) joints. Eng. Fract. Mech. 71, 2795–2811 (2008)CrossRefGoogle Scholar
  47. A. Nonn, W. Dahl, W. Bleck, Numerical modelling of damage behaviour of laser-hybrid welds. Eng. Fract. Mech. 75, 3251–3263 (2008)CrossRefGoogle Scholar
  48. K.A. Nugent, T.E. Gureyev, D.F. Cookson, D. Paganin, Z. Barnea, Phys. Rev. Lett. 77, 2961–2964 (1996)CrossRefGoogle Scholar
  49. E. Østby, C. Thaulow, Z.L. Zhang, Numerical simulations of specimen size and mismatch effects in ductile crack growth—Part I: Tearing resistance and crack growth paths. Eng. Fract. Mech. 74, 1770–1792 (2007a)CrossRefGoogle Scholar
  50. E. Østby, C. Thaulow, Z.L. Zhang, Numerical simulations of specimen size and mismatch effects in ductile crack growth - Part II: Near-tip stress fields. Eng. Fract. Mech. 74, 1793–1809 (2007b)CrossRefGoogle Scholar
  51. D. Paganin, S.C. Mayo, T.E. Gureyev, P.R. Miller, S.W. Wilkins, Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object. J. Microsc. 206, 33–40 (2002)CrossRefGoogle Scholar
  52. J.R. Rice, A path independent integral and the approximate analysis of strain concentrations by notches and cracks. J. Appl. Mech. 35, 379–386 (1968)CrossRefGoogle Scholar
  53. J.R. Rice, D.M. Tracey, On the ductile enlargement of voids in triaxial stress fields. J. Mech. Phys. Solids 17, 201–217 (1969)CrossRefGoogle Scholar
  54. F. Rivalin, A. Pineau, M. Di Fant, J. Besson, Ductile tearing of pipeline-steel wide plates: I. Dynamic and quasi-static experiments, Eng. Fract. Mech. 68, 329–345 (2001)Google Scholar
  55. F. Rivalin, J. Besson, A. Pineau, M. Di Fant, Ductile tearing of pipeline-steel wide plates: II. Modeling of in-plane crack propagation. Eng. Fract. Mech. 68, 347–364 (2001)Google Scholar
  56. G. Rousselier, Ductile fracture models and their potential in local approach of fracture. Nucl. Eng. Des. 105, 97–111 (1987)CrossRefGoogle Scholar
  57. G. Rousselier, in Handbook of materials behaviour models, The Rousselier model for porous metal plasticity and ductile fracture. (2001), pp. 436–445Google Scholar
  58. T. Sadowski, M. Knec, P. Golewski, Experimental investigations and numerical modelling of steel adhesive joints reinforced by rivets. Int. J. Adhes. Adhes. 30, 338–346 (2010)CrossRefGoogle Scholar
  59. M.K. Samal, M. Seidenfuss, E. Roos, B.K. Dutta, H.S. Kushwaha, Finite element formulation of a new nonlocal damage model. Finite Elem. Anal. Des. 44, 358–371 (2008)CrossRefGoogle Scholar
  60. M.K. Samal, M. Seidenfuss, E. Roos, A new mesh-independent Rousselier’s damage model: Finite element implementation and experimental verification. Int. J. Mech. Sci. 51, 619–630 (2009)CrossRefGoogle Scholar
  61. J.F. Dos Santos, G. Çam, F. Torster, A. Insfran, S. Riekehr, V. Ventzke, Properties of power beam welded steel, Al-and Ti alloys: Significance of strength mismatch. Weld World 44, 42–64 (2000)Google Scholar
  62. S. Schmauder, D. Uhlmann, G. Zies, Experimental and numerical investigations of two material states of the material 15NiCuMoNb5 (WB 36). Comp. Mater. Sci. 25, 174–192 (2002)CrossRefGoogle Scholar
  63. S. Schmauder, L. J. Mishnaevsky, Micromechanics and Nanosimultion of Metals and Composites, ed. by S. Schmauder, L. J. Mishnaevsky (Springer-Verlag, Berlin, Heidelberg 2009), p. 420Google Scholar
  64. K.-H. Schwalbe, I. Scheider, A. Cornec, SIAM CM09—The SIAM method for application cohesive models of the damage behaviour of engineering materials and structures. GKSS report, 2009/1, GKSS-Forschungszentrum Geesthacht, (2009)Google Scholar
  65. I. Scheider, Bruchmechanische Bewertung von Laserschweißverbindungen durch numerische Rissfortschrittsimulation mit dem Kohäsivzonenmodell. Dissertation, TU Hamburg-Harburg, Geesthacht, (2001)Google Scholar
  66. I. Scheider, W. Brocks, The effect of the traction separation law on the results of cohesive zone crack propagation analyses. Key Eng. Mater. 251–252, 313–318 (2003)CrossRefGoogle Scholar
  67. Seib, Residual strength analysis of laser beam and friction stir welded aluminum panels for aerospace applications. Dissertation, TU Hamburg-Harburg, Geesthacht, (2006)Google Scholar
  68. H. P. Seebich, Mikromechanisch basierte Schädigungsmodelle zur Beschreibung des Versagensablaufs ferritischer Bauteile. Dissertation, Universität Stuttgart, (2007)Google Scholar
  69. M. Seidenfuss, Untersuchungen zur Beschreibung des Versagensverhaltens mit Hilfe von Schädigungsmodellen am Beispiel des Werkstoffs 20MnMoNi55. Dissertation, Universität Stuttgart, (1992)Google Scholar
  70. Y. Shen, T.F. Morgeneyer, J. Garnier, L. Allais, L. Helfen, J. Crépin, Three-dimensional quantitative in situ study of crack initiation and propagation in AA6061 aluminum alloy sheets via synchrotron laminography and finite-element simulations. Acta Mater. 61, 2571–2582 (2013)CrossRefGoogle Scholar
  71. T. Siegmund, A. Needleman, A numerical study of dynamic crack growth in elastic-viscoplastic solids. Int. J. Solids Struct. 34, 769–787 (1997)CrossRefGoogle Scholar
  72. M. Springmann, M. Kuna, Identification of material parameters of the Gurson—Tvergaard—Needleman model by combined experimental and numerical techniques. Comp. Mater. Sci. 32, 544–552 (2005)CrossRefGoogle Scholar
  73. B. Tanguy, T.T. Luu, G. Perrin, A. Pineau, J. Besson, Plastic and damage behaviour of a high strength X100 pipeline steel: Experiments and modeling. Int. J. Press. Vessels Piping 85, 322–335 (2008)CrossRefGoogle Scholar
  74. H.Y. Tu, S. Schmauder, U. Weber, Y. Rudnik, V. Ploshikhin, Numerical simulation and experimental investigation of the damage behavior on electron beam welded joints. Procedia Eng. 10, 875–880 (2011)CrossRefGoogle Scholar
  75. H.Y. Tu, S. Schmauder, U. Weber, Y. Rudnik, V. Ploshikhin, Simulation of the damage behavior of electron beam welded joints with the Rousselier model. Eng. Fract. Mech. 103, 153–161 (2013)CrossRefGoogle Scholar
  76. H.Y. Tu, S. Schmauder, U. Weber, Simulation of the fracture behavior of an S355 electron beam welded joint by cohesive zone modeling. Eng. Fract. Mech. 163, 303–312 (2016)CrossRefGoogle Scholar
  77. V. Tvergaard, On localization in ductile materials containing spherical voids. Int. J. Fract. 18, 237–252 (1982a)Google Scholar
  78. V. Tvergaard, Influence of void nucleation on ductile shear fracture at a free surface. J. Mech. Phys. Solids 30, 399–425 (1982b)CrossRefGoogle Scholar
  79. V. Tvergaard, A. Needleman, Analysis of the cup-cone fracture in a round tensile bar. Acta Metall. 38, 157–169 (1984)CrossRefGoogle Scholar
  80. V. Tvergaard, On the analysis of ductile fracture mechanisms. Proc. Int. Conf. Fracture, ICF7 (1989), 159–179Google Scholar
  81. V. Tvergaard, J.W. Hutchinson, The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. J. Mech. Phys. Solids 40, 1377–1397 (1992)CrossRefGoogle Scholar
  82. V. Tvergaard, A. Needleman, Analysis of the Charpy V-notch test for welds. Eng. Fract. Mech. 65, 627–643 (2000)CrossRefGoogle Scholar
  83. V. Tvergaard, A. Needleman, 3D analyses of the effect of weld orientation in Charpy specimens. Eng. Fract. Mech. 71, 2179–2195 (2004)CrossRefGoogle Scholar
  84. D. Uhlmann, Reactor Safety Research—Project No. 1501029: Material characterization of the material 15 NiCuMoNb 5 including the determination of the local approach parameter for the Rousselier model for two material states. Report-No: 878701004, MPA Stuttgart, (1999)Google Scholar
  85. U. Weber, A. Mohanta, S. Schmauder, Numerical determination of parameterised failure curves for ductile structural materials. Int. J. Mat. Res. 98, 1071–1080 (2007)CrossRefGoogle Scholar
  86. L. Xia, C.F. Shih, Ductile crack growth—III. Transition to cleavage fracture incorporating statistics. J. Mech. Phys. Solids 44, 603–639 (1996)CrossRefGoogle Scholar
  87. F. Xu, L. Helfen, A.J. Moffat, G. Johnson, I. Sinclair, T. Baumbach, J. Synchrotron Radiat. 17, 222–226 (2010)CrossRefGoogle Scholar
  88. H. Yuan, G. Lin, A. Cornec, Verification of a cohesive zone model for ductile fracture. J Eng. Mater. Technol. 118, 192–200 (1996)CrossRefGoogle Scholar
  89. Z. L. Zhang, C. Thaulow, J. Odegard, A complete Gurson model approach for ductile fracture. Eng. Fract. Mech. 67, 155–168 (2000)Google Scholar

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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.School of Aerospace Engineering and Applied MechanicsTongji UniversityShanghaiChina

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