Abstract
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.
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Notes
Departing from this rule, there might be cases such as weld craters or significant undermatching where the crack would be initiated at different positions.
Abbreviations
- a :
-
Crack length (crack depth for surface cracks)
- B :
-
Specimen thickness (fracture mechanics specimen)
- C:
-
Half crack length at surface (semi-elliptical crack)
- CTOD:
-
Crack tip opening displacement
- da/dN:
-
Fatigue crack propagation rate
- E :
-
Modulus of elasticity (Young’s modulus)
- f(Lr):
-
Plasticity correction function (monotonic loading)
- F(x):
-
Cumulative probability
- F Y :
-
Yield or limit loads
- H :
-
Width or half width of the weld strip (strength mismatch consideration)
- HV:
-
Hardness according to Vickers
- J :
-
J-Integral
- J mat :
-
Fracture resistance, monotonic loading (general term), Eq. (2)
- J 0.2;BL :
-
Resistance against stable crack initiation (monotonic loading)
- J 0.2 :
-
Resistance against stable crack initiation (alternative definition)
- K :
-
Stress intensity factor (K-factor)
- \( {K}_c^J \) :
-
Monotonic fracture resistance (formally derived from J-integral)
- K 0 :
-
Scale parameter in 3-parameter Weibull distribution
- K mat :
-
Fracture resistance, monotonic loading (general term), Eq. (2)
- K max :
-
Maximum K-factor in the loading cycle, cyclic loading
- K min :
-
Shift parameter in 3-parameter Weibull distribution
- K min :
-
Minimum K-factor in the loading cycle, cyclic loading
- K r :
-
Ordinate of the FAD diagram (= K/Kmat)
- L r :
-
Ligament yielding parameter (monotonic loading)
- L r max :
-
Maximum Lr (plastic collapse limit)
- m :
-
Shape parameter in 3-parameter Weibull distribution
- M :
-
Strength mismatch ratio (commonly σYW/σYB)
- N :
-
Number of loading cycles
- N :
-
Number of specimens in a statistical test set
- N c :
-
Number of loading cycles up to fracture
- P :
-
Failure probability
- R :
-
Loading ratio (= σmin/σmax or Kmin/Kmax)
- R eL :
-
Lower yield strength (materials showing a Lüders’ plateau)
- T p :
-
Peak temperature during welding
- U :
-
Energy dissipated in monotonic fracture mechanics test
- W :
-
Specimen width or half width (fracture mechanics specimen)
- Δa:
-
Crack extension
- δ 5 :
-
Definition of the CTOD
- ε a :
-
Strain amplitude (=½ Δε)
- ΔK:
-
K-Factor range (Kmax − Kmin), cyclic loading
- ν :
-
Poisson’s ratio
- σ a :
-
Stress amplitude (= ½ Δσ)
- σ app :
-
Applied stress
- σ max :
-
Maximum stress in the loading cycle, cyclic loading
- σ min :
-
Minimum stress in the loading cycle, cyclic loading
- σ ref :
-
Reference stress (reference stress approach, FAD)
- η p :
-
Geometry function in monotonic J-integral testing
- σ :
-
Stress
- σ 0 :
-
Reference yield stress
- σ Y :
-
Yield strength, general (either ReL or Rp0.2)
- σ m :
-
Hydrostatic stress
- \( {\sigma}_Y^{\prime } \) :
-
(Stabilized) Cyclic yield strength
- σ YB :
-
Yield strength of base metal
- σ YW :
-
Yield strength of weld metal
- ASTM:
-
American Society for Testing and Materials
- bcc:
-
Body-centered cubic (lattice)
- BM:
-
Base metal
- BS :
-
The British Standards Institution
- c :
-
Critical
- CG:
-
Coarse grain (HAZ)
- FAD:
-
Failure assessment diagram
- fcc:
-
Face-centered cubic (lattice)
- FG:
-
Fine grain (HAZ)
- h :
-
Stress triaxiality
- HAZ:
-
Heat-affected zone
- IIW:
-
International Institute of Welding
- ISO:
-
International Organization for Standardization
- M(T):
-
Middle crack tension (fracture mechanics specimen)
- NASGRO:
-
Computer program for fatigue crack propagation, provided by NASA
- OM:
-
Strength overmatching (σYW > σYB)
- R-curve:
-
Crack resistance curve
- TTT:
-
Temperature-time-transformation (diagram)
- UM:
-
Strength undermatching (σYW < σYB)
- WM:
-
Weld metal
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Zerbst, U. 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. Weld World 63, 1715–1732 (2019). https://doi.org/10.1007/s40194-019-00801-5
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DOI: https://doi.org/10.1007/s40194-019-00801-5