Advertisement

Fracture Mechanics

  • Dominique François
  • André Pineau
  • André Zaoui
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 191)

Abstract

After an overlook about the aim of fracture mechanics, the strain energy release rate is defined in linear as well as in nonlinear elasticity. Perturbation to the stress field produced by the presence of an elliptical hole allows introducing the notion of stress intensity factor. Stress and strain fields at the tip of a crack are calculated. The relation between the strain energy release rate and the stress intensity factor is demonstrated. The presence of a crack produces displacements, which can be calculated. Various methods exist to determine the stress intensity factor: experimental, superposition, relation with the stress concentration factor, compliance, numerical methods. Consideration is given on three-dimensional cracks.

The plastic zones at the tip of cracks are different in plane stress and in plane strain. Various approximations give their dimensions as well as the crack opening displacement, in small scale yielding and also in large scale yielding. The way to measure fracture toughness is described. The “R” curve effect explains some of the standard procedures. In elastoplastic fracture mechanics, the “R6” method provides an assessment of the safety of a structure, while the measurement of the critical value of J, or of the CTOD is explained. Fracture mechanics of creeping solids follows the analysis of Riedel and Rice. It is shown how to determine the time to fracture.

The local approach to fracture mechanics is introduced. It leads to the use of cylindrical notched specimens. The ways to experiment and to analyse the results are presented.

Keywords

Fracture Toughness Stress Intensity Factor Crack Length Plastic Zone Plane Stress 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. ASTM standard E 1737 (1996) Standard test method for J-integral characterization of fracture thoughness. Annual book of ASTM standardsGoogle Scholar
  2. ASTM E 1921-02 (2002) Standard test method for determination of reference temperature, T0, for ferritic steels in the transition range. Annual book of ASTM standardsGoogle Scholar
  3. Azhdari A, Obata M, Nemat-Nasser S (2000) Alternative solution methods for crack problems in plane anisotropic elasticity, with examples. Int J Solids Struct 37:6433–6478MathSciNetzbMATHCrossRefGoogle Scholar
  4. Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7:55–129MathSciNetCrossRefGoogle Scholar
  5. Bensussan P, Piques R, Pineau A (1989) A critical assessment of global mechanical approaches to creep crack initiation and creep crack growth in 316L steel. In: Non linear fracture mechanics I – Time dependent fracture. ASTM STP 995. ASTM, Philadelphia, pp 27–54Google Scholar
  6. Berdin C, Besson J, Bugat S, Desmorat R, Feyel F, Forest S, Lorentz E, Maire E, Pardoen T, Pineau A, Tanguy B (2004) Local approach to fracture. Ecole des Mines de Paris, ParisGoogle Scholar
  7. Beremin FM (1980a) Calculs élastoplastiques par la méthode des éléments finis d’éprouvettes axisymétriques entaillées circulairement. Journal de Mécanique appliquée 4:307–325zbMATHGoogle Scholar
  8. Beremin FM (1980b) Influence de la triaxialité des contraintes sur la rupture par déchirement ductile et la rupture fragile par clivage d’un acier doux. Journal de Mécanique appliquée 4:327–342Google Scholar
  9. Beremin FM (1981) Cavity formation from inclusions in ductile fracture of A508 steel. Metall Trans 12A:723–731Google Scholar
  10. Beremin FM (1983) A local criterion for cleavage fracture of a nuclear pressure vessel steel. Metall Trans A14:2277–2287Google Scholar
  11. Besson J (2008) Notched axi-symmetric test pieces. In: François D (ed) Structural components. Wiley, Hoboken, pp 293–323CrossRefGoogle Scholar
  12. Betegon C, Hancock JW (1991) Two-parameter characterization of elastic-plastic crack-tip fields. J Appl Mech 58:104–110CrossRefGoogle Scholar
  13. Bilby BA, Cottrell AH, Swinden KH (1963) The spread of plastic yield from a notch. Proc R Soc A 272:304–314CrossRefGoogle Scholar
  14. Bridgman PW (1952) Studies in large plastic flow and fracture. Mc Graw Hill, New YorkzbMATHGoogle Scholar
  15. Buchalet CB, Bamford WH (1976) Stress intensity factors solutions for continuous surface flaws in reactor pressure vessel. In: Rice JR, Paris P (eds) Mechanics of crack growth. ASTM STP 590. ASTM, Philadelphia, pp 385–402Google Scholar
  16. Bui HD (1978) Mécanique de la rupture fragile. Masson, ParisGoogle Scholar
  17. Cherepanov GP (1974) Mechanics of brittle fracture. Nauka, MoscowGoogle Scholar
  18. Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100–104CrossRefGoogle Scholar
  19. ESIS P6-98 (1998) Procedure to measure and calculate material parameters for the local approach to fracture using notched tensile specimens. Procedure Document European Structural Integrity Society (ESIS)Google Scholar
  20. Gao X, Dodds RH (2001) An engineering approach to assess constraint effects on cleavage fracture toughness. Eng Fract Mech 68:263–283CrossRefGoogle Scholar
  21. Griffith AA (1921) The phenomenon of rupture and flow in solids. Philos Trans R Soc A221:163–198Google Scholar
  22. Harper MP, Ellison EG (1977) The use of the C* parameter in predicting creep crack propagation rates. J Strain Anal 12:167–199CrossRefGoogle Scholar
  23. Heerens J, Hellmann D (2002) Development of the Euro fracture toughness dataset. Eng Fract Mech 69:421–449CrossRefGoogle Scholar
  24. Hills DA, Kelly PA, Dai DN, Korsunsky AM (1996) Solutions of crack problems. The distributed dislocation technique. Kluwer Academic Publishers, DordrechtGoogle Scholar
  25. Hult JA, Mc Clintock FA (1956) Elastic-plastic stresses and strains distributions around sharp notches under repeated shear. In: Proceedings of 9th international congress on applied mechanics, University of Brussels, 8, pp 51–58Google Scholar
  26. Hutchinson JW (1968) Singular behavior at the end of a tensile crack in a hardening material. J Mech Phys Solids 16:13–31zbMATHCrossRefGoogle Scholar
  27. Irwin G (1958) Elasticity and plasticity. In: Flügge S (ed) Encyclopaedia of physics, vol 6. Springer, Berlin, pp 551–590Google Scholar
  28. ISO-27306 (2009) Method of loss correction of CTOD fracture toughness assessment of steel componentsGoogle Scholar
  29. Kachanov LM (1974) Fundamentals of the theory of plasticity. MIR Publishers, MoscowGoogle Scholar
  30. Kumar V (1980) Fully plastic crack solutions with application to creep crack growth. International conference on engineering aspects of creep. Mechanical Engineering Publications, London, 1, pp 211–214Google Scholar
  31. Labbens RC (1980) Introduction à la mécanique de la rupture. PluralisGoogle Scholar
  32. Labbens RC, Pelissier-Tanon A, Heliot J (1976) Practical methods of calculating stress intensity factors through weight functions. In: Rice JR, Paris P (eds) Mechanics of crack growth. ASTM STP 590. ASTM, Philadelphia, pp 368–384Google Scholar
  33. Landes JD, Begley JA (1976) A fracture mechanics approach to creep cracking. In: Rice JR, Paris P (eds) Mechanics of crack growth. ASTM STP 590. ASTM, Philadelphia, pp 128–148Google Scholar
  34. Lautridou JC, Pineau A (1981) Crack initiation and stable crack growth resistance in A508 steels in relation to inclusion distribution. Eng Fract Mech 15:55–71CrossRefGoogle Scholar
  35. Lawn BR, Wilshaw TR (1975) Fracture of brittle solids. Cambridge University Press, CambridgeGoogle Scholar
  36. Lin PC, Pan J (2008) Closed-form structural stress and stress intensity factor solutions for spot welds in commonly used specimens. Eng Fract Mech 75:5187–5206CrossRefGoogle Scholar
  37. Lin PC, Wang DA (2010) Geometric functions of stress intensity factor solutions for spot welds in U-shape specimens. Int J Solids Struct 47:691–704zbMATHCrossRefGoogle Scholar
  38. McMeeking RM (1977) Finite deformation analysis of crack tip opening in elastic-plastic materials and implication for fracture. J Mech Phys Solids 25:357–381CrossRefGoogle Scholar
  39. Mudry F (1982) Etude de la déchirure ductile et de la rupture par clivage d’aciers faiblement alliés. Ph.D. thesis, UTC, FranceGoogle Scholar
  40. Murakami Y et al (1987) Stress intensity factors handbook. Pergamon Press, New YorkGoogle Scholar
  41. O’Dowd NP, Shih CF (1991) Family of crack-tip fields characterized by a triaxiality parameter. I: Structure of fields. J Mech Phys Solids 39:989–1015CrossRefGoogle Scholar
  42. O’Dowd NP, Shih CF (1992) Family of crack-tip fields characterized by a triaxiality parameter. II: Fracture applications. J Mech Phys Solids 40:939–963CrossRefGoogle Scholar
  43. Parks DM (1974) A stiffness derivative finite element technique for determination of stress intensity factors. Int J Fract 10:487–502CrossRefGoogle Scholar
  44. Peterson RE (1974) Stress concentration factors. Wiley, New YorkGoogle Scholar
  45. Pineau A (1981) Review of fracture micromechanisms and a local approach to predicting crack resistance in low strength steels. In: François D et al (eds) Advanced in fracture research, 2. Proceedings of 5th international congress on fracture (ICF5). Pergamon, Oxford, pp 553–577Google Scholar
  46. Pineau A (1992a) Assessment procedures for defects in the creep range. In: Larsson LH (ed) High temperature structural design. ESIS 12. Mechanical Engineering Publications, London, pp355–396Google Scholar
  47. Pineau A (1992b) Global and local approaches of fracture – transferability of laboratory test results to components. In: Argon AS (ed) Topics in fatigue and fracture. Springer, New York, pp 197–234CrossRefGoogle Scholar
  48. Pineau A (1996) Defect assessment procedures in the creep range. In: Moura Branco C, Ritchie JR, Sklenicka V (eds) Mechanical behaviour of materials at high temperature. Kluwer Academic Publishers, Dordrecht/Boston/London, pp 59–82CrossRefGoogle Scholar
  49. Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35:379–386CrossRefGoogle Scholar
  50. Rice JR (1971) Mathematical analysis in the mechanics of fracture. In: Liebowitz H (ed) Fracture: an advanced treatise 2, 2nd edn. Academic, New York, pp 192–311Google Scholar
  51. Rice JR, Rosengren GR (1968) Plane strain deformation near a crack tip in power-law hardening material. J Mech Phys Solids 16:1–12zbMATHCrossRefGoogle Scholar
  52. Rice JR, Sorensen EP (1978) Continuing crack-tip deformation and fracture for plane-strain crack growth in elastic plastic solids. J Mech Phys Solids 16:1–12CrossRefGoogle Scholar
  53. Riedel H (1981) Creep deformation at crack tips in elastic-viscoplastic solids. J Mech Phys Solids 29:35–49zbMATHCrossRefGoogle Scholar
  54. Riedel H (1987) Fracture at high temperature. Springer, BerlinGoogle Scholar
  55. Ritchie RO, Knott JE, Rice JR (1973) On the relationship between critical tensile stress and fracture toughness in mild steel. J Mech Phys Solids 21:395–410CrossRefGoogle Scholar
  56. Ruggieri C, Dodds RH (1996) A transferability model for brittle failure including constraint and ductile tearing effects: A probilistic approach. Int J Fract 79:309–340CrossRefGoogle Scholar
  57. Ruggieri C, Dodds RH, Wallin K (1998) Constraint effects on reference temperature T 0 for ferritic steels in the transition region. Eng Fract Mech 60:19–36CrossRefGoogle Scholar
  58. Ruggieri C, Gao X, Dodds RH (2000) Transferability of elastic-plastic fracture toughness using the Weibull stress approach: significance of parameter calibration. Eng Fract Mech 67:101–117CrossRefGoogle Scholar
  59. Sherry AH, Wilkes MA, Beardmore DW, Lidbury DFG (2005) Material constraint parameters for the assessment of shallow defects in structural components. Part I: Parameters solutions. Eng Fract Mech 72:2373–2395CrossRefGoogle Scholar
  60. Shih CF (1976) J-integral estimates for strain hardening materials in antiplane shear using fully plastic solutions. In: Mechanics of crack growth. ASTM STP 590. American Society for Testing and Materials, Philadelphia, pp 3–22Google Scholar
  61. Shih CF, Hutchinson JW (1976) Fully plastic solutions and large scale yielding estimates for plane stress crack problems. J Eng Mater Technol 98:289–295CrossRefGoogle Scholar
  62. Standard ISO 12135 (2002) Metallic materials- Unified method of test for the determination of quasistatic fracture toughnessGoogle Scholar
  63. Standard ISO/TTA 5 (2007) Code of practice for creep fatigue testing of cracked componentsGoogle Scholar
  64. Tada H, Paris PC, Irwin GR (2000) The stress analysis of cracks handbook. Del Research Co., HellertonCrossRefGoogle Scholar
  65. Theocaris PS, Papadopoulos GA (1980) Elastodynamic forms of caustics for running cracks under constant velocity. Eng Fract Mech 13:683–698CrossRefGoogle Scholar
  66. Wilshaw RT, Rau CA, Tetelman AS (1968) A general model to predict elastic-plastic stress distribution and fracture strength of notched bars in plane strain bending. Eng Fract Mech 1:191–211CrossRefGoogle Scholar
  67. Zahoor K (1989) Ductile fracture handbook. Electric Power Research Institute NP-6301D and Novetech Corporation N14-1Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Dominique François
    • 1
  • André Pineau
    • 2
    • 3
  • André Zaoui
    • 3
    • 4
  1. 1.École Centrale de ParisParisFrance
  2. 2.École des Mines de Paris Paris Tech Centre des Matériaux UMR CNRSÉvry CedexFrance
  3. 3.Academy of EngineeringParisFrance
  4. 4.French Académie des SciencesParisFrance

Personalised recommendations