International Journal of Fracture

, Volume 164, Issue 2, pp 231–252 | Cite as

An engineering methodology to assess effects of weld strength mismatch on cleavage fracture toughness using the Weibull stress approach

Original Paper


This work describes the development of an engineering approach based upon a toughness scaling methodology incorporating the effects of weld strength mismatch on crack-tip driving forces. The approach adopts a nondimensional Weibull stress, \({\bar{{\sigma}}_w}\), as a the near-tip driving force to correlate cleavage fracture across cracked weld configurations with different mismatch conditions even though the loading parameter (measured by J) may vary widely due to mismatch and constraint variations. Application of the procedure to predict the failure strain for an overmatch girth weld made of an API X80 pipeline steel demonstrates the effectiveness of the micromechanics approach. Overall, the results lend strong support to use a Weibull stress based procedure in defect assessments of structural welds.


Cleavage fracture Local approach Weibull stress Weld Strength mismatch 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. American Petroleum Institute (2005) Welding of pipelines and related facilities, 20th edn. API 1104Google Scholar
  2. American Petroleum Institute (2007a) Fitness-for-service. API RP-579-1/ASME FFS-1Google Scholar
  3. American Petroleum Institute (2007b) API specification for 5L line pipe, 44th ednGoogle Scholar
  4. American Society of Mechanical Engineers (2004) Boiler and pressure vessel code. New YorkGoogle Scholar
  5. American Society for Testing and Materials (2008a) Standard terminology relating to fatigue and fracture testing. ASTM E-1823, PhiladelphiaGoogle Scholar
  6. American Society for Testing and Materials (2008b) Standard test methods for determination of reference temperature, T0, for ferritic steels in the transition range. ASTM E-1921, PhiladelphiaGoogle Scholar
  7. American Welding Society (1987) Welding handbook: welding Technology, 8th edn, vol 1. MiamiGoogle Scholar
  8. Anderson TL (2005) Fracture mechanics: fundaments and applications. 3rd edn. CRC Press, New YorkGoogle Scholar
  9. Averbach BL (1965) Micro and macro formation. Int J Fract Mech 1: 272–290Google Scholar
  10. Bakker A, Koers RWJ (1991) Prediction of cleavage fracture events in the brittle–ductile transition region of a Ferritic steel. In: Blauel JG, Schwalbe KH (eds) Defect assessment in components—fundamentals and applications, ESIS/EG9. Mechanical Engineering Publications, London, pp 613–632Google Scholar
  11. Beremin FM (1983) A local criterion for cleavage fracture of a nuclear pressure vessel steel. Metall Trans 14: 2277–2287CrossRefGoogle Scholar
  12. Brindley BJ (1970) The effect of dynamic strain-aging on the ductile fracture process in mild steel. Acta Metall 18: 325–329CrossRefGoogle Scholar
  13. British Standard (1991) Fracture mechanics toughness tests. BS 7448Google Scholar
  14. British Standard Institution (2005) Guide on methods for assessing the acceptability of flaws in metallic structures, BS7910Google Scholar
  15. Cravero S, Ruggieri C (2005) Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens—part I: plane-strain analyses. Eng Fract Mech 72: 1344–1360CrossRefGoogle Scholar
  16. Det Norske Veritas (2007) Submarine pipeline systems. Offshore Standard OS-F101Google Scholar
  17. Dodds RH, Shih CF, Anderson TL (1993) Continuum and micro-mechanics treatment of constraint in fracture. Int J Fract 64: 101–133ADSGoogle Scholar
  18. Dodds RH, Ruggieri C, Koppenhoefer K (1997) 3-D constraint effects on models for transferability of cleavage fracture toughness. In: Underwood JH (eds) et al Fatigue and fracture mechanics: 28th Volume, ASTM STP 1321. American Society for Testing and Materials, Philadelphia, pp 179–197CrossRefGoogle Scholar
  19. Donato GHB, Magnabosco R, Ruggieri C (2009) Effects of weld strength mismatch on J and CTOD estimation procedure for SE(B) specimens. Int J Fract 159: 1–20CrossRefGoogle Scholar
  20. Evans AG, Langdon TG (1976) Structural ceramics. Prog Mater Sci 21: 171–441Google Scholar
  21. Feller W (1957) Introduction to probability theory and its application vol I. Wiley, New YorkGoogle Scholar
  22. Freudenthal AM (1968) Statistical approach to brittle fracture. In: Liebowitz H (eds) Fracture: an advanced treatise vol II. Academic Press, NY, pp 592–619Google Scholar
  23. Gao X, Ruggieri C, Dodds RH (1998) Calibration of Weibull stress parameters using fracture toughness data. Int J Fract 92: 175–200CrossRefGoogle Scholar
  24. Gao X, Dodds RH, Tregoning RL, Joyce JA, Link RE (1999) A Weibull stress model to predict cleavage fracture in plates containing surface cracks. Fatigue Fract Eng Mater Struct 22: 481–493CrossRefGoogle Scholar
  25. Gao X, Zhang G, Srivatsan TS (2005) Prediction of cleavage fracture in ferritic steels: a modified Weibull stress model. Mater Sci Eng A 394: 210–219CrossRefGoogle Scholar
  26. Glover AG, Hauser D, Metzbower EA (1986) Failures of weldments. In: Metals handbook, vol 11: failure analysis and prevention. American Society for Metals, pp 411–449Google Scholar
  27. Gurland J (1972) Observations on the fracture of cementite particles in a spheroidized 1.05% C steel deformed at room temperature. Acta Metall 20: 735–741CrossRefGoogle Scholar
  28. Gullerud A, Koppenhoefer K, Roy A, RoyChowdhury S, Walters M, Bichon B, Cochran K, Dodds R (2004) WARP3D: dynamic nonlinear fracture analysis of solids using a parallel computers and workstations. Structural Research Series (SRS) 607. UILU-ENG-95-2012. University of Illinois at Urbana-ChampaignGoogle Scholar
  29. Hughes TJ (1980) Generalization of selective integration procedures to anisotropic and nonlinear media. Int J Numer Methods Eng 15: 1413–1418MATHCrossRefGoogle Scholar
  30. Hutchinson JW (1983) Fundamentals of the phenomenological theory of nonlinear fracture mechanics. J Appl Mech 50: 1042–1051CrossRefGoogle Scholar
  31. Jutla T (1996) Fatigue and fracture control of weldments. In: ASM handbook, vol 19: fatigue and fracture. ASM International, pp 434–449Google Scholar
  32. Kendall MG, Stuart A (1967) The advanced theory of statistics. 2nd edn. Hafner, New YorkGoogle Scholar
  33. Kerr WH (1976) A review of factors affecting toughnness in welded steels. Int J Press Vessel Piping 4: 119–141CrossRefGoogle Scholar
  34. Lin T, Evans AG, Ritchie RO (1986) A statistical model of brittle fracture by transgranular cleavage. J Mech Phys Solids 21: 263–277Google Scholar
  35. Lindley TC, Oates G, Richards CE (1970) A critical appraisal of carbide cracking mechanism in ferride/carbide aggregates. Acta Metall 18: 1127–1136CrossRefGoogle Scholar
  36. Mann NR, Schafer RE, Singpurwalla ND (1974) Methods for statistical analysis of reliability and life data. Wiley, New YorkMATHGoogle Scholar
  37. Matsuo Y (1981) Statistical theory for multiaxial stress states using Weibull’s three-parameter function. Eng Fract Mech 14: 527–538CrossRefGoogle Scholar
  38. Minami F, Brückner-Foit A, Munz D, Trolldenier B (1992) Estimation procedure for the Weibull parameters used in the local approach. Int J Fract 54: 197–210Google Scholar
  39. Minami F, Ohata M, Toyoda M, Tanaka T, Arimochi K, Glover AG, North TH (1995) The effect of weld metal yield strength on the fracture behavior of girth welds in grade 550 pipe. Pipeline Technol 1: 441–461Google Scholar
  40. Moran B, Shih CF (1987) A general treatment of crack tip contour integrals. Int J Fract 35: 295–310CrossRefGoogle Scholar
  41. Nevalainen M, Dodds RH (1995) Numerical investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens. Int J Fract 74: 131–161CrossRefGoogle Scholar
  42. O’Dowd NP, Shih CF (1991) Family of crack-tip fields characterized by a triaxiality parameter: part I—structure of fields. J Mech Phys Solids 39(8): 989–1015CrossRefGoogle Scholar
  43. O’Dowd NP, Shih CF (1992) Family of crack-tip fields characterized by a triaxiality parameter: part II—fracture applications. J Mech Phys Solids 40: 939–963CrossRefGoogle Scholar
  44. Ruggieri C, Dodds RH (1996a) A transferability model for brittle fracture including constraint and ductile tearing effects: a probabilistic approach. Int J Fract 79: 309–340CrossRefGoogle Scholar
  45. Ruggieri C, Dodds RH (1996b) Probabilistic modeling of brittle fracture including 3-D effects on constraint loss and ductile tearing. J PhysGoogle Scholar
  46. Ruggieri C (2001) Influence of threshold parameters on cleavage fracture predictions using the Weibull stress model. Int J Fract 110: 281–304CrossRefGoogle Scholar
  47. Ruggieri C (2009a) WSTRESS release 3.0: numerical computation of probabilistic fracture parameters for 3-D cracked solids. EPUSP, University of São PauloGoogle Scholar
  48. Ruggieri C (2009b) FRACTUS2D: numerical computation of fracture mechanics parameters for 2-D cracked solids. EPUSP, University of São PauloGoogle Scholar
  49. 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
  50. Silva LAL, Cravero S, Ruggieri C (2006) Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens—part II: 3-D effects on constraint. Eng Fract Mech 73: 2123–2138CrossRefGoogle Scholar
  51. Tetelman AS, McEvily AJ (1967) Fracture of structural materials. Wiley, New YorkGoogle Scholar
  52. Thoman DR, Bain LJ, Antle CE (1969) Inferences on the parameters of the Weibull distribution. Technometrics 11: 445–460MATHCrossRefMathSciNetGoogle Scholar
  53. Wallin K (1984) The scatter in KIc results. Eng Fract Mech 19: 1085–1093CrossRefGoogle Scholar
  54. Wallin K (2002) Master curve analysis of the Euro fracture toughness dataset. Eng Fract Mech 69: 451–481CrossRefGoogle Scholar
  55. Weibull W (1939) The phenomenon of rupture in solids. Ingeniors Vetenskaps Akademien Handl 153: 55Google Scholar
  56. Weisstein EW (2009) “Ellipse” in mathWorld—a wolfram web resource.

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Naval Architecture and Ocean EngineeringUniversity of São PauloSão PauloBrazil

Personalised recommendations