Fracture and Crack Propagation in Weldments. A Fracture Mechanics Perspective - Uwe Zerbst, BAM Berlin
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Fracture and Crack Propagation in Weldments.
A Fracture Mechanics Perspective
Uwe Zerbst, BAM BerlinOutline
Specific aspects of weldments
Determination of fracture toughness
Determination of the crack driving force
Shallow crack propagation and fatigue strengthOutline
Specific aspects of weldments
Determination of fracture toughness
Determination of the crack driving force
Shallow crack propagation and fatigue strengthFracture mechanics of weldments: Specific aspects
Susceptibility
Inhomogeneous to cracking Strength mismatch
microstructure
Residual stresses
MisalignmentFracture mechanics of weldments: Specific aspects
Susceptibility
to crackingWeld imperfections
Figure according to Gagg, 2005ISO 5817: Arc welded joints in steel - Guidance on quality levels
for imperfections
26 different types of weld imperfections
Can be assigned to distinct groups from the perspective of mechanical integrity
(a) Cracks and crack-like imperfections
have to be avoided or – if they occur – are immediately subject to
fracture mechanics analysis
(b) Material imperfections which act as crack initiation sites
of paramount importance for fatigue strength and fatigue life analyses
(c) Geometric discontinuities
increase the local stresses, affect crack initiation, propagation and final failure
(d) Imperfections which probably are of no effect on fracture or fatigue lifeFracture mechanics of weldments: Specific aspects
Susceptibility
Inhomogeneous to Cracking
microstructureMaterial inhomogeneity
Reason: Inhomogeneous cooling & TTT behaviour
HAZ regions Figure according to Toyoda, 1998Consequence
Toughness scatter
Specific requirements
on toughness testing
identification of
specific micro-
structure
number of test
specimens
Figure according to Toyoda, 1998Fracture mechanics of weldments: Specific aspects
Susceptibility
Inhomogeneous to cracking Strength mismatch
microstructureStrength mismatch
Unintended and intended
mismatch
Usually in steel:
moderate overmatching
Cases of undermatching:
aluminium, high strength steels
Pronounced mismatching:
laser & electron beam welding
M = σ YW σ YB
W = Weld metal
B = Base plateStrength mismatch
Effect on crack driving force
Effect on crack path deviation
UM
OM
Figures: Dos Santos et al., Koçak
Factors affecting the mismatch effect
Crack location (weld metal, fusion line etc.) Mismatch ratio (σYW /σYB)
Global constraint interdependency (W-a)/H
Residual stressesFracture mechanics of weldments: Specific aspects
Susceptibility
Inhomogeneous to cracking Strength mismatch
microstructure
Residual stressesWelding residual stresses
Reason: inhomogeneous cooling
constrained shrinking
solid state phase transformations
External restraint
macro-residual stresses (residual stresses of the
first kind); vary within the cross section over a
distance much larger than grain size
Internal forces and moments are in equilibrium with Figure according to
respect to any cross section and axis respectively Leggatt, 2008Welding residual stresses
Scatter and uncertainty in simulation and measurement
Figures according to
Bouchard, 2008Welding residual stresses
Dependency on location along the weld
Figures according to Hosseinzadeh and Bouchard,
2011; (b) Bouchard, 2008
Further effect: Stop-start featuresWelding residual stresses
Residual stress profiles
Individual determination
Compendia (upper bound curves
to literature data)
Membrane stress (as-welded:
max. value: yield strength)
Post weld treatment: σp + σr ≥ σY
Membrane stress (yield strength at
annealing temperature + correction
for ratio of E modules at room &
annealing temperatures
Mechanical post weld treatmentFracture mechanics of weldments: Specific aspects
Susceptibility
Inhomogeneous to cracking Strength mismatch
microstructure
Residual stresses
MisalignmentWelding residual stresses
Types of misalignment:
(a) Axial misalignment between flat plates
(b) Angular misalignment between flat plates
(c) Angular misalignment in a fillet welded joint
Consequence:
Notch effect/local bending stress
Strong effect of fatigue life and
shallow crack propagation
Effect on long crack fatigue
propagation and (sometimes)
on failure loadOutline
Specific aspects of weldments
Determination of fracture toughness
Determination of the crack driving force
Shallow crack propagation and fatigue strengthFracture toughness determination Modifications compared to testing of non-welded material Specimen geometries most appropriate for weldments, e.g., shallow cracked bend specimens Weldment specific aspects of specimen preparation such as the introduction of the notch, minimisation of residual stresses and misalignment Generation of a straight crack front Validity criteria ISO 15653 Required number of test specimens Strength mismatch effects for testing in the net section yielding range
Fracture toughness determination: Scheme
According to ISO 15653Fracture toughness determination
Adapted testing
Perform test as much as possible representative with respect to the component
in service. Relevant factors and parameters are:
Welding process including filler material
Base plate composition
Joint thickness
Preheat and interpass temperatures
Heat input
Detailed welding procedure
Joint configuration
Restraint Hydrogen release heat treatment
Postweld treatment prior to testing can be necessary
when the time between welding
Time between welding and testing
and the beginning of service is
Environment much longer than those between
Test temperature welding and testing.Fracture mechanics of weldments: Specific aspects
Susceptibility
Inhomogeneous to cracking
microstructureFracture toughness determination
Specific features because of inhomogeneous
microstructure, metallography
HAZ testing: Pre and post test
metallographic examination
In steel: crack tip no more distant
than 0.5 mm from target microstructure
Crack front should sample either 15%
or at least 7 mm of the HAZ microstructure
ISO 15653
Both within the central 75% of the specimen thicknessFracture toughness determination
Specific features due to inhomogeneous
microstructure: Weakest link approach (1)
Randomly distributed small regions of low toughness (“weak links”) across the ligament;
in weldments: HAZ brittle zones
During load increase, when stress peak is shifted into the ligament to the location of
the nearest “weak link” the whole specimen (or component) fails
Due to the random distribution of the “weak links”
in the ligament area the distance of the
first one from the crack tip varies from
specimen to specimen and so does the
work necessary to shift the stress peak
to the “right” position
fracture toughness scatterFracture toughness determination
Specific features due to inhomogeneous
microstructure: Weakest link approach (2)
The longer the crack front the higher the
probability of a “weak link” next to it
Toughness scatter becomes smaller
for longer crack fronts but lower bound
remains constant
Same lower bound toughness can be
determined by using few specimens
with large crack fronts or by using
many specimens with short crack fronts
Usually: 3-Parameter Weibull distribution; e.g., Stage 2 and 3 Options of SINTAP Master
Curve approachFracture toughness determination
Specific features due to inhomogeneous
microstructure: Weakest link approach (3)
BS 7910: Minimum of 12 valid HAZ tests for ductile-to-brittle transition
Figures according to Toyoda, 1998Fracture toughness determination
Pop-in behaviour
Pop-in: Discontinuity in the load versus displacement curve in the fracture mechanics test
displacement suddenly increases and
load decreases
Different reasons:
Limited cleavage fracture propagation + arrest
Out-of-plane slits
Other reasons Fig.: Dos Santos
et al., 2001
Criteria: > 4 (2) % of (W-a) crack propagartion
Load drop more than x %
Increase in compliance
Problem: When is a pop-in event
component relevant?Fracture mechanics of weldments: Specific aspects
Susceptibility
Inhomogeneous to cracking Strength mismatch
microstructureFracture toughness determination
Specific features because of strength mismatch
ISO 15653: Error in J integral or CTOD (standard equations) due to mismatch
less than 10% as long as
Weld metal testing:
CTOD tests: 0.5 < M < 1.5
J integral tests: 0.5 < M < 1.25
M > 1.5 or 1.25: overestimation of J or CTOD
M < 0.5 underestimation
HAZ testing: Error ± 5% for J and -20% to +10% for CTOD as long as
0.7 < M < 2.5
K2 U
Else mismatch specific ηpl function in J= + ηpl
E B (W − a)Fracture toughness determination
ηpl function for strength mismatch (EFAM , Schwalbe et al.)
Some additional solutions in the literatureFracture toughness determination
Definition of weld width H for other than prismatic welds
Proposals:
(a) H = average of 2H1 and 2H2
(b) equivalent H, Heq, on the basis of
the shortest distance between the
crack tip and the fusion line along
the slip lines emanating from the
crack tip
However: Systematic investigation
still missing.Fracture toughness determination
Effect of strength mismatch on constraint and toughness
According to Toyoda, 2002
Complex issue: Various constraint parameters
Damage mechanics simulation (e.g. GTN)
According to Kim (Schwalbe et al., 1996)Fracture toughness determination
Effect of strength mismatch on toughness
and crack path deviation
Electron beam weld, steel
Kocak et al., 1999
Probability of crack path deviation
decreases with longer crack front Laser beam weld, steel
Heerens & Hellmann, 2003Stress-strain curves
Micro tensile tests
e.g., Kocak et al., 1998
BS 7448: Estimation from hardness
Base plate : Rp0.2B = 3.28 HV − 221 for 160 < HV < 495
Weld metal : Rp0.2W = 3.15 HV − 168 for 150 < HV < 300Fracture mechanics of weldments: Specific aspects
Susceptibility
Inhomogeneous to cracking Strength mismatch
microstructure
Residual stressesFracture toughness determination
Specific features because of residual stresses
Considered at applied side
(crack driving force in component)
Specimen if possible residual
stress free (but not realistic)
Specimen preparation
in order to generate
straight crack front
From left to right:
- Local compression
- (Reverse
bending)
- High R ratio
testFracture mechanics of weldments: Specific aspects
Susceptibility
Inhomogeneous to cracking Strength mismatch
microstructure
Residual stresses
MisalignmentFracture toughness determination Specific features because of misalignment Deformation of specimen wings in order to avoid bending However, no plastic deformation within a distance B from weld
Outline
Specific aspects of weldments
Determination of fracture toughness
Determination of the crack driving force
Shallow crack propagation and fatigue strengthFracture mechanics of weldments: Specific aspects
Susceptibility
Inhomogeneous to cracking Strength mismatch
microstructureCrack driving force and
fracture assessment
Crack path simulation by damage
mechanics methods, e.g., GTN model
Local parameters for at least base plate,
weld metal and HAZ
Conventional fracture mechanics
(finite element based and analytical) Negre et al., 2004
Lower bound toughness or R curve
or probabilistic analysis
}
Effect of mismatch and residual stresses
on R curve or toughness scatter!
Mismatch corrected limit load
(crack path deviation)
Again: When are pop-in events component
relevant?Crack driving force: R6 type assessment
FAD approach CDF approach
-2
K r = f ( Lr ) J = Je ⋅ f (Lr )
K r = K K mat Je = K 2 E′
Example. Option 1B analysis (no Lüders‘ plateau)
-1 2
f (Lr ) = 1 + 0.5 ⋅ L2r ⋅ 0.3 + 0.7 ⋅ exp ( −µ ⋅ L6r ) 0 ≤ Lr ≤ 1
f (Lr ) = f (Lr = 1) ⋅ Lr (
N−1) 2N
1 ≤ Lr ≤ Lr max
Lr max = 0.5 ⋅ (Rp0.2 + Rm ) R eL
N = 0.3 ⋅ 1 − (Rp0.2 Rm ) Lr = F FY = σref σ Y
0.001(E Rp0.2 )
µ = min
0.6
Replace FY by FYMMismatch corrected limit load FYM
Example
Conservative option:
FYM determined as FY based on the lower yield
strength of base plate and weld metal
Individual determination
FYM solutions as functions of global geometry,
mismatch ratio M and (W-a)/H
Limit states:
long crack a and/or wide weld (large H) short crack and/or narrow weld (small H)
plastic zone mainly in weld metal plastic zone mainly in base plate
FY based on σYW gives good estimate FY based on σYB gives good estimate
(e.g. laser or electron beam weld)Mismatch corrected limit load FYM
Examples
UM OMFracture analyses including mismatch: Examples
Fc = 569 kN
M = 1.5
Fc = 589 kN
Fc (homogenous) = 550 kNFracture mechanics of weldments: Specific aspects
Susceptibility
Inhomogeneous to cracking Strength mismatch
microstructure
Residual stressesPrimary and secondary stresses
Primary stresses σp:
Arise from the applied mechanical contribute to
load, including dead weight or plastic collapse
inertia effects
Secondary stresses σs:
Result from suppressed local do not contribute
distortions, e.g., during the to plastic collapse
welding process, or are due
to thermal gradients
K factor determination is based
Self-equilibrating across the on both primary and secondary
structure, i.e., net force and stresses but only the primary
bending moment are zero stresses are taken into account
for the limit load FY,
However: Secondary stresses can act like primary stresses in the crack carrying section
Treatment as primary conservativCrack driving force due to primary
and secondary stresses
Primary stresses only
a
n
K = πa ⋅ ∑ σn ⋅ fn ⋅
n
T
x
σ ( x ) = ∑ σn ⋅
n }
n T
Primary + secondary stressesInteraction factor V
Small scale yielding:
K = Kp + Ks
However: because of rather high
σs in as-welded structures
K > Kp + Ks Lr ∼
1
Although secondary stresses don‘t
contribute to plastic collapse they
contribute to ligament yielding
KIp + V ⋅ KIs
FAD approach: K r =
K mat
p s
K = K + V ⋅K 2
1 KIp + V ⋅ KIs
CDF approach: J = ⋅
E′ f (Lr ) Determination of V
Plasticity corrected
„K factor“ for se-
condary stresses
Kps
V= s
⋅ξ
K
Fit function to finite
K factor for
element results
secondary
stresses
Different options for determining K s
p
(
Kps Kp Lr ) 0 0.02 0.04 …
e.g., plastic zone corrected K: Lr
0
K ps = ( aeff a ) ⋅ K s ( a ) 0.01
2 0.02
1 K (a)
s
3 plane strain
aeff =a+ ⋅ β= 0.03
2βπ σ Y 1 plane stress
……Fracture analyses including residual stresses
Example: Residual stress profile
Transverse residual stresses (compendium)
2 3
z z z
σRT σ*Y ( z t ) = 1 − 0.917 ⋅ − 14.533 ⋅ + 83.115 ⋅
t t t
4 5 6
z z z
−215.45 ⋅ + 244.16 ⋅ − 93.36 ⋅
t t tFracture analyses including residual stresses
Example: Critical load for stable crack initiation
Reduction in critical load: ca. 25%Fracture analyses including residual stresses
Example: Fatigue crack propagation and residual lifetime
No effect on ∆K
But on R = Kmin/Kmax
Effect on crack closure behaviour
Reduction in
residual lifetime:
ca. 25%
Simplified assumption:
R > 0.5 (BS 7910)Fracture analyses including residual stresses
Ongoing discussion on
less conservative deter-
mination of V factor
This workshop
Including solutions
Without elastic follow-up
Large elastic follow-up
for application to short crack propagation problemsFracture mechanics of weldments: Specific aspects
Susceptibility
Inhomogeneous to cracking Strength mismatch
microstructure
Residual stresses
MisalignmentFracture analyses including residual stresses
Misalignment
Example:
Angular distorsion
Butt weld
clamped
σs 3y tanh (β 2 ) 3 α ⋅ ℓ tanh (β 2 ) Solution for bending stress σs
= = ⋅
σm t β 2 2 t β 2 refered to membrane stress σm
12
2 ⋅ ℓ 3 σm Alternativ: Finite element stress distribution
β= (rad!)
t E Outline
Specific aspects of weldments
Determination of fracture toughness
Determination of the crack driving force
Shallow crack propagation and fatigue strengthInitial defects in engineering alloys
Frequently: Inclusions at or
close to surface are
crack initiaton sites
Further crack initiation sites:
Crack initiation at inclusions in steel (42CrMoS4)
Primary phases
(Figs. Pyttel)
Pores/cavities
Corrosion pits
Surface roughness
(scratches)
Welding defectsWeld discontinuities and defects
Distinguish between geometrical dis-
continuities (considered at applied
side) and material defects
Applied side Material
Initial crack size and
- Misalignment - Slag lines
geometry (multiple cracks)
- weldment geometry - Pores
- Undercuts - Lack of fusion
Usually excluded
- Overlap - Cracks
Specified by
weldment
quality Steel 350WT
system Crack initiation in WAZ
0.3 mm deep surfacerdefect
(Josi, 2010)Example: Weldment quality grades: VOLVO
Group Weld Quality Standard 181-0004, 2008
Discontinuity VD (normal quality) VC (high quality) VB (post weld treated)
Overlap < 0,5 mm < 0,1 mm not permissable
Lack of fusion not permissable not permissable not permissable
Transition > 0,25 mm > 1 mm > 4 mm
radius
Undecut < 0,05 t (max 1 mm) < 0,025 t (max 0,5 mm) not permissable
inadequate < - 0,2a (max 2 mm) smaller not permissable smaller not permissable
weld thickness
Misalignment < 0,1 t (max 2 mm) not permissable not permissable
Single Pore 0,4 t (max 4) 0,3 t (max 4) 0,2 t (max 2)
0,3 t (max 3) 0,2 t (max 2) 0,1 t (max 1)
Pores cluster 6% / 3% 4% / 2% 2% / 1%Contributions to fatigue life
Contribution to overall lifetime Nt:
- Crack initiation Ni
- short crack growth Ns
- long crack growth Nl
N t = Ni + N s + Nl
Polak (CSI, 2003):
Crack initiation stage Ni at smooth, nominally defect-free surfaces:
- less than 5-20% of overall lifetime Nt
- even less for existing initial defects
Allows to treat defects as initial cracks in a fracture mechanics modelSpecifica of mechanically short cracks
Long crack growth Short crack growth
(a > 0,5 mm, 2c > 1 mm)
∆K concept not applicable
Alternatives:
„plasticity corrected“ K
(e.g., plastic zone size corrected)
∆J-Integral
∆CTOD
Gradual built-up of plasticity-induced
crack closure effect:Fracture and Crack Propagation in Weldments.
A Fracture Mechanics Perspective
Specific aspects of weldments
Determination of fracture toughness
Determination of the crack driving force
Shallow crack propagation and fatigue strength
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