Application of fracture mechanics to welds with crack origin at the weld toe: a review Part 1: Consequences of inhomogeneous microstructure for materials testing and failure assessment

  • U ZerbstEmail author
Research Paper


This two-part paper provides an overview on the state-of-the-art in the application of engineering fracture mechanics to weldments. This, of course, cannot be exhaustive but is limited to butt and fillet welds with crack initiation at weld toes. In the present first part, the authors briefly focus on the susceptibility of welds to cracks and other defects. Following this, they discuss in more detail the consequences of material inhomogeneity across the weld for fracture mechanics. Inhomogeneity causes scatter in fracture toughness and strength mismatch effects both of which have to be considered in fracture toughness testing, crack driving force determination, and fracture assessment of welded components. Part 2 of the paper series will add a discussion on welding residual stresses and questions of applying fracture mechanics to residual as well as total lifetime estimation of welds under cyclic loading.


Fracture toughness Crack driving force Material inhomogeneity Strength mismatch 



Crack length (crack depth for surface cracks)


Specimen thickness (fracture mechanics specimen)


Half crack length at surface (semi-elliptical crack)


Crack tip opening displacement


Fatigue crack propagation rate


Modulus of elasticity (Young’s modulus)


Plasticity correction function (monotonic loading)


Cumulative probability


Yield or limit loads


Width or half width of the weld strip (strength mismatch consideration)


Hardness according to Vickers




Fracture resistance, monotonic loading (general term), Eq. (2)


Resistance against stable crack initiation (monotonic loading)


Resistance against stable crack initiation (alternative definition)


Stress intensity factor (K-factor)

\( {K}_c^J \)

Monotonic fracture resistance (formally derived from J-integral)


Scale parameter in 3-parameter Weibull distribution


Fracture resistance, monotonic loading (general term), Eq. (2)


Maximum K-factor in the loading cycle, cyclic loading


Shift parameter in 3-parameter Weibull distribution


Minimum K-factor in the loading cycle, cyclic loading


Ordinate of the FAD diagram (= K/Kmat)


Ligament yielding parameter (monotonic loading)


Maximum Lr (plastic collapse limit)


Shape parameter in 3-parameter Weibull distribution


Strength mismatch ratio (commonly σYW/σYB)


Number of loading cycles


Number of specimens in a statistical test set


Number of loading cycles up to fracture


Failure probability


Loading ratio (= σmin/σmax or Kmin/Kmax)


Lower yield strength (materials showing a Lüders’ plateau)


Peak temperature during welding


Energy dissipated in monotonic fracture mechanics test


Specimen width or half width (fracture mechanics specimen)


Crack extension


Definition of the CTOD


Strain amplitude (=½ Δε)


K-Factor range (Kmax − Kmin), cyclic loading


Poisson’s ratio


Stress amplitude (= ½ Δσ)


Applied stress


Maximum stress in the loading cycle, cyclic loading


Minimum stress in the loading cycle, cyclic loading


Reference stress (reference stress approach, FAD)


Geometry function in monotonic J-integral testing




Reference yield stress


Yield strength, general (either ReL or Rp0.2)


Hydrostatic stress

\( {\sigma}_Y^{\prime } \)

(Stabilized) Cyclic yield strength


Yield strength of base metal


Yield strength of weld metal



American Society for Testing and Materials


Body-centered cubic (lattice)


Base metal


The British Standards Institution




Coarse grain (HAZ)


Failure assessment diagram


Face-centered cubic (lattice)


Fine grain (HAZ)


Stress triaxiality


Heat-affected zone


International Institute of Welding


International Organization for Standardization


Middle crack tension (fracture mechanics specimen)


Computer program for fatigue crack propagation, provided by NASA


Strength overmatching (σYW > σYB)


Crack resistance curve


Temperature-time-transformation (diagram)


Strength undermatching (σYW < σYB)


Weld metal



  1. 1.
    Zerbst U (2019) Application of fracture mechanics to fusion welds with crack origin at the weld toe – a review. Part 2: welding residual stresses. Residual and total live assessment. Subm to Weld World this issueGoogle Scholar
  2. 2.
    Schulze G, Krafka H, Neumann P (1992) Schweißtechnik. Werkstoffe – Konstruieren – Prüfen. VDI Verl., Düsseldorf, in German Google Scholar
  3. 3.
    Otegui JL, Kerr HW, Burns DJ, Mohaupt UH (1989) Fatigue crack initiation from defects at weld toes in steel. Int J Press Vess Piping 38:385–417. CrossRefGoogle Scholar
  4. 4.
    Schork B, Kucharczyk P, Madia M, Zerbst U, Hensel J, Bernhard J, Tchuindjang D, Kaffenberger M, Oechsner M (2018) The effect of the local and global weld geometry as well as material defects on crack initiation and fatigue strength. Eng Fract Mech 198:103–122CrossRefGoogle Scholar
  5. 5.
    Verreman Y, Nie B (1991) Short crack growth and coalescence along the toe of a manual fillet weld. Fatigue Fracture Engng Mat Struct 14:337–349. CrossRefGoogle Scholar
  6. 6.
    Madia M, Zerbst U, Beier HT, Schork B (2018) The IBESS model – elements, realisation and validation. Eng Fract Mech 198:171–208CrossRefGoogle Scholar
  7. 7.
    Signes EG, Baker RG, Harrison JD, Burdekin FM (1967) Factors affecting the fatigue strength of welded high strength steels. Br Weld J, March 1967:108–116Google Scholar
  8. 8.
    Zerbst U, Ainsworth RA, Beier HT, Pisarski H, Zhang ZL, Nikbin K, Nitschke-Pagel T, Münstermann S, Kucharczyk P, Klingbeil D (2014) Review on the fracture and crack propagation in weldments – a fracture mechanics perspective. Eng Fract Mech 132:200–276CrossRefGoogle Scholar
  9. 9.
    Zerbst U, Madia M, Klinger C, Bettge D (2019) Defects as a root cause of fatigue failure of metallic components. Part I: basic aspects; part II: types of defects – non-metallic inclusions; part III: types of defects – cavities, dents, corrosion pits, scratches. Engng Failure Anal 97:772–792, 98:228–239 and 97:759–776Google Scholar
  10. 10.
    Toyoda M (1989) Significance of procedure/evaluation of CTOD test of weldments. International Institute of Welding (IIW); Document X-1192-89, DOI:
  11. 11.
    Kucharczyk P, Madia M, Zerbst U, Schork B, Gerwin P, Münstermann S (2018) Fracture-mechanics based prediction of the fatigue strength of weldments. Material aspects. Eng Fract Mech 198:79–102CrossRefGoogle Scholar
  12. 12.
    BS 7448 (1997) Fracture mechanics toughness tests. Part 2: method for determination of KIc, critical CTOD and critical J values of welds in metallic materials, British Standards Institution, LondonGoogle Scholar
  13. 13.
    ISO 15653 (2010) Metallic materials – method for the determination of quasistatic fracture toughness of welds, International Organisation for Standardization (ISO), DOI:
  14. 14.
    Landes JD, Shaffer GH (1980) Statistical characterisation of fracture in the transition regime. ASTM STP 700:368–383, American Society for Testing and Materials (ASTM)Google Scholar
  15. 15.
    BS 7910 (2005) Guide to methods for assessing the acceptability of flaws in metallic structures. The British Standards Institution (BSI) Standards Publ, LondonGoogle Scholar
  16. 16.
    BS 7910 (2013) Guide to methods for assessing the acceptability of flaws in metallic structures. Including Amendment (2015) and Corrigenda I-2. The British Standards Institution (BSI) Standards Publ, LondonGoogle Scholar
  17. 17.
    ASTM E 1921-10 (2010) Standard test method for determination of reference temperature, T0, for ferritic steels in the transition range. American Society for Testing and Materials, West Conshohocken, PAGoogle Scholar
  18. 18.
    Wallin K (2002) Master curve analysis of the “Euro” fracture toughness dataset. Eng Fract Mech 69:451–481CrossRefGoogle Scholar
  19. 19.
    Romano S, Maneti D, Beretta S, Zerbst U (2016) Semi-probabilistic method for residual lifetime of aluminothermic welded rails with foot cracks. Theoretical Appl Fracture Mech 85, Part B:398–411. CrossRefGoogle Scholar
  20. 20.
    Wallin K, Nevasmaa P, Laukkanen A, Planman T (2004) Master curve analysis of inhomogeneous ferritic steels. Eng Fract Mech 71:2329–2346CrossRefGoogle Scholar
  21. 21.
    Zerbst U, Schödel M, Webster S, Ainsworth RA (2007) Fitness-for-service fracture assessment of structures containing cracks. A workbook based on the European SINTAP/FITNET procedure. Elsevier. Amsterdam et al Google Scholar
  22. 22.
    Jutla T, Garwood SJ (1987) Interpretation of fracture toughness data. Metal Construction 19:276R–281RGoogle Scholar
  23. 23.
    Pisarski H (2017) Treatment of fracture toughness data for engineering critical assessment (ECA). Weld World 61:723–732. CrossRefGoogle Scholar
  24. 24.
    BS PD 6493 (1980) Guidance on some methods for the derivation of acceptance levels for defects in fusion welded joints. British Standards Institution (BSI), LondonGoogle Scholar
  25. 25.
    Zerbst U, Madia M (2018) Analytical flaw assessment. Eng Fract Mech 187:316–367CrossRefGoogle Scholar
  26. 26.
    Dawes, MG, Pisarski HG, Squirrell SJ (1989) Fracture mechanics tests on welded joints. ASTM STP 995:191–213, American Society for Testing and Materials (ASTM), PhiladelphiaGoogle Scholar
  27. 27.
    Dos Santos J, Çam G, Torster F, Isfan A, Riekehr S, Ventzke V, Koçak M (2000) Properties of power beam welded steels, Al- and Ti-alloys: significance of strength mismatch. Weld World 44:42–64Google Scholar
  28. 28.
    Çam G, Koçak M, Dos Santos J (1999) Developments in laser welding of metallic materials and characterization of the joints. Weld World 43:13–25Google Scholar
  29. 29.
    Schwalbe KH, Kim YJ, Hao S, Cornec A, Koçak M (1997) EFAM ETM-MM 96 – the ETM method for assessing the significance of crack-like defects in jiints with mechanical heterogeneity (strength mismatch). GKSS Research Centre, Report GKSS 97/E/9, Geesthacht, GermanyGoogle Scholar
  30. 30.
    Schwalbe KH, Heerens J, Zerbst U, Pisarski H, Koçak M (2002) EFAM GTP 02 – the GKSS test procedure for determining the fracture behaviour of materials. GKSS Research Centre, Report GKSS 2002/24, Geesthacht, GermanyGoogle Scholar
  31. 31.
    Junghans E (1998) Anwendung des Engineering Treatment Model für Mismatch (ETM-MM) auf Schweißverbindungen mit Berücksichtigung von Schweißnahtgeometrie und Werkstoffverfestigung, PhD Thesis, TU Hamburg; in GermanGoogle Scholar
  32. 32.
    R6, Revision 4 (2014) Assessment of the integrity of structures containing defects. EDF Energy, Barnwood, Gloucester, DOI:
  33. 33.
    Kim YJ, Kim JS, Schwalbe KH, Kim JY (2003) Numerical investigation on J-integral testing of heterogeneous fracture toughness testing specimens: part I – weld metal cracks. Fatigue Fracture Engng Mat Struct 26:683–694. CrossRefGoogle Scholar
  34. 34.
    Paredes M, Ruggieri C (2012) Further results in J and CTOD estimation procedures for SE(T) fracture specimens – part II: weld centreline cracks. Eng Fract Mech 89:24–39CrossRefGoogle Scholar
  35. 35.
    Koo JM, Huh Y, Seok CS (2012) Plastic h factor considering strength mismatch and crack location in narrow gap weldments. Nuclear Engng Des 247:34–41CrossRefGoogle Scholar
  36. 36.
    Kim YJ (2002) Experimental J estimation equations for single-cracked bars in four-point bend: homogeneous and bi-material specimens. Eng Fract Mech 69:793–811CrossRefGoogle Scholar
  37. 37.
    Heerens J, Hellmann D (2003) Application of the master curve method and the engineering lower bound toughness method to laser beam welded steel. J Test Eval 31:215–221Google Scholar
  38. 38.
    Sumpter JDG (1999) Fracture toughness evaluation of laser welds in ship steels, in European Symposium on Assessment of Power Beam Welds (ASPOW), Geesthacht, Germany, GKSS Reserarch Centre Geesthacht, Paper 8, DOI:
  39. 39.
    Koçak M, Kim YJ, Çam G, dos Santos J, Cardinal N, Webster S, Kristensen J, Borggre K (1999) Recommendations on tensile and fracture toughness testing procedures for power beam welds. in European Symposium on Assessment of Power Beam Welds (ASPOW), Geesthacht, Germany, GKSS Research Centre, Paper 9Google Scholar
  40. 40.
    Toyoda M (2002) Transferability of fracture mechanics parameters to fracture performance evaluation of welds with mismatching. Prog Struct Eng Mater 4:117–125. CrossRefGoogle Scholar
  41. 41.
    Thaulow C, Hauge M, Zhang ZL, Ranesta O, Fattorini F (1999) On the interrelationship between fracture toughness and material mismatch for cracks located at the fusion line of weldments. Eng Fract Mech 64:369–382CrossRefGoogle Scholar
  42. 42.
    Koçak M, Çam G, Riekehr S, Torster F, Dos Santos G (1998) Micro tensile test technique for weldments. IIW Document SC X-F-079-98Google Scholar
  43. 43.
    Oeser S, Fehrenbach C, Burget W (2000) Ermittlung lokaler Werkstoffkennwerte in Schweißverbindungen als Grundlage für numerische Bauteilanalysen. Proc. Werkstoffprüfung 2000, Bad Nauheim, Germany, DVM: 189–194, in GermanGoogle Scholar
  44. 44.
    Zhang ZL, Hauge M, Thaulow C, Ødegård J (2002) A notched cross weld tensile testing method for determining true stress strain curves for weldments. Eng Fract Mech 69:353–366CrossRefGoogle Scholar
  45. 45.
    Tu S, Ren X, Nyhus B, Akselsen OM, He J, Zhang Z (2017) A special notched tensile specimen to determine the flow stress-strain curve of hardening materials without applying the Bridgman correction. Eng Fract Mech 179:225–239CrossRefGoogle Scholar
  46. 46.
    Scheider I (2000) Bruchmechanische Bewertung von Laserschweißverbindungen durch numerische Rissfortschrittssimulation mit dem Kohäsivzonenmodell, PhD Thesis, Univ. Hamburg-Harburg: GKSS-Report GKSS 2001/3Google Scholar

Copyright information

© International Institute of Welding 2019

Authors and Affiliations

  1. 1.Bundesanstalt für Materialforschung und -prüfung (BAM)BerlinGermany

Personalised recommendations