Automatic 3-D crack propagation calculations: a pure hexahedral element approach versus a combined element approach

Original Paper


This article presents an evaluation of two different crack prediction approaches based on a comparison of the stress intensity factor distribution for three example problems. A single edge notch specimen and a quarter circular corner crack specimen subjected to shear displacements and a three point bend specimen with a crack inclined to the mid-plane are examined. The stress intensity factors are determined from the singular stress field close to the crack front. Two different fracture criteria are adopted for the calculation of an equivalent stress intensity factor and crack deflection angle. The stress intensity factor distributions for both numerical methods agree well to available reference solutions. Deviations are recorded at crack front locations near the free surface probably due to global contraction effects and the twisting behaviour of the crack front. Crack propagation calculations for the three point bending specimen give results that satisfy intuitive expectations. The outcome of the study encourages further pursuit of a crack propagation tool based on a combination of elements.


Linear elastic fracture mechanics Finite element method Crack growth Mixed mode Stress intensity factor 


  1. BEASY (2007) BEASY V10r7 Documentation. C.M. BEASY Limited, 2007Google Scholar
  2. Brebbia CA (1978) The boundary element method for engineers. Pentech Press, LondonGoogle Scholar
  3. Bremberg D, Dhondt G (2008) Automatic crack-insertion for arbitrary crack growth. Eng Frac Mech 75: 404–416CrossRefGoogle Scholar
  4. Chanel B, Dhondt G (2007) Verallgemeinerung des MTU 3-D Rissfortschrittskriteriums auf anisotrope materialien, 39. Tagung DVM-Arbeitskreis Bruchvorgnge, Dresden, 13–14 Feb 2007Google Scholar
  5. Cicilino AP, Aliabadi MH (1999) Three-dimensional boundary element analysis of fatigue crack growth in linear and non-linear fracture problems. Eng Frac Mech 63: 713–733CrossRefGoogle Scholar
  6. Citarella R, Buchholz FG (2008) Comparison of crack growth simulation by DBEM and FEM for SEN-specimens undergoing torsion or bending loading. Eng Frac Mech 72: 489–509CrossRefGoogle Scholar
  7. Dhondt G (1993) General behaviour of collapsed 8-node 2-D and 20-node 3-D isoparametric elements. Int J Num Meth Eng 36: 1223–1243MATHCrossRefGoogle Scholar
  8. Dhondt G (1998) Automatic 3-D mode I crack propagation calculation with finite elements. Int J Num Meth Eng 41: 739–757MATHCrossRefGoogle Scholar
  9. Dhondt G (1999) Automatic Three-dimensional cyclic crack propagation predictions with finite elements at the design stage of an aircraft engine. In: RTO AVT Symposium on design principles and methods for aircraft gas turbine engines. 11–15 May 1998. Toulouse, France, RTO MP-8, pp 33-1–33-8Google Scholar
  10. Dhondt G (2005) Cyclic crack propagation at corners and holes. Fatigue Frac Eng Mater Struct 28: 25–30CrossRefGoogle Scholar
  11. Dhondt G, Chergui A, Buchholz FG (2001) Computational fracture analysis of different specimens regarding 3D and mode coupling effects. Eng Frac Mech 68: 383–401CrossRefGoogle Scholar
  12. Forman RG et al (1988) Development of the NASA/FLAGRO computer program. In: Read DT, Read RP (eds) Fracture mechanics: eighteenth symposium, ASTM STP 945. American society for testing and materials. Philadelphia, PA, pp 781–803Google Scholar
  13. Mi Y, Aliabadi MH (1992) Dual boundary element method for three-dimensional fracture mechanics analysis. Eng anal Boundary Elem 1: 161–171CrossRefGoogle Scholar
  14. Murakami Y (ed) (1987) Stress intensity factors handbook. Pergamon Press, OxfordGoogle Scholar
  15. NASCRAC (1989) Theory manual. Failure analysis associates. Palo Alto, CAGoogle Scholar
  16. Paris PC, Erdogan F (1963) A critical analysis of crack propagation laws. J Basic Eng 85: 528–534Google Scholar
  17. Paris PC, Gomez MP, Anderson WE (1961) A rational analytical theory of fatigue. Trend Eng 13: 9–14Google Scholar
  18. Richard HA, Buchholz FG, Kullmer G, Schllmann M (2003) 2D- and 3D-mixed mode fracture criteria. Key Eng Mater 251–252: 251–260CrossRefGoogle Scholar
  19. Riddell WT, Ingraffea AR, Wawrzynek PA (1997) Experimental observations and numerical predictions of three-dimensional fatigue crack propagation. Eng Frac Mech 58: 293–310CrossRefGoogle Scholar
  20. Schöllmann M, Fulland M, Richard HA (2003) Development of a new software for adaptive crack growth simulations in 3D structures. Eng Frac Mech 70: 249–268CrossRefGoogle Scholar
  21. Schöberl J (1997) NETGEN—An advancing front 2D/3D-mesh generator based on abstract rules. Comp Vis Sci 1: 42–52Google Scholar
  22. Timbrell C, Cook G (1997) 3-D FE fracture mechanics analysis for industrial applications. Zentech International Limited, UK. Seminar: “Inelastic finite element analysis", Institute of Mechanical Engineering, London, October 14, 1997Google Scholar
  23. Wawrzynek PA, Martha LF and Ingraffea AR (1988) A computational environment for the simulation of fracture processes in three dimensions. In: Rosakis AJ et al (ed) Analytical, numerical and experimental aspects of three dimensional fracture processes. ASME AMD 91:321-327Google Scholar
  24. Zienkiewicz OC (1971) The finite element method in engineering science. McGraw Hill, LondonMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Solid MechanicsRoyal Institute of Technology (KTH)StockholmSweden
  2. 2.MTU Aero Engines GmbHMunichGermany

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