Fatigue overview
Introduction to fatigue analysis
• Fatigue is the failure of a component after
several repetitive load cycles.
• As a one-time occurrence, the load is not
dangerous in itself. Over time the alternating
load is able to break the structure anyway.
• It is estimated that between 50 and 90 % of
product failures is caused by fatigue, and
based on this fact, fatigue evaluation should
be a part of all product development.
What is fatigue?
In materials science, fatigue is the progressive and localized
structural damage that occurs when a material is subjected
to cyclic loading (material is stressed repeatedly).
Clients tous différents
Routes de qualités variables
Contraintes
Fatigue Design in
Automotive Industry
Conception fiable
PSA (Peugeot Citroën)
Résistances
3s
3s
Dispersion matériau
Dispersion de production
Fatigue
• Fracture mechanics can be divided into three
stages:
1. Crack nucleation
2. Crack-growth
3. Ultimate ductile failure
Introduction to fatigue analysis
• Fatigue is the failure of a component after
several repetitive load cycles.
• As a one-time occurrence, the load is not
dangerous in itself. Over time the alternating
load is able to break the structure anyway.
• It is estimated that between 50 and 90 % of
product failures is caused by fatigue, and
based on this fact, fatigue evaluation should
be a part of all product development.
Historical background
• In comparison to the classical stress analysis,
fatigue theory is a relative new phenomenon.
The need to understand fatigue arose after
the industrial revolution introduced steel
structures. Three areas were particularly
involved in early failures: Railway trains,
Mining equipment and Bridges.
Historical background
• 1837: Wilhelm Albert publishes the first article on fatigue. He devised a test
machine for conveyor chains used in the Clausthal mines.
• 1839: Jean-Victor Poncelet describes metals as being tired in his lectures at
the military school at Metz.
• 1870: Wöhler summarizes his work on railroad axles. He concludes that
cyclic stress range is more important than peak stress and introduces the
concept of endurance limit.
• 1910: O. H. Basquin proposes a log-log relationship for SN curves, using
Wöhler's test data.
• 1945: A. M. Miner popularizes A. Palmgren's (1924) linear damage
hypothesis as a practical design tool.
• 1954: L. F. Coffin and S. S. Manson explain fatigue crack-growth in terms of
plastic strain in the tip of cracks.
• 1968: Tatsuo Endo and M. Matsuiski devise the rainflow-counting algorithm
and enable the reliable application of Miner's rule to random loadings.
Historical background
• Fatigue theory is basically empirical. This means
that the process of initiation of micro cracks that
finally will form macroscopic cracks in the
material is not accounted for in detail in the
equations.
• Fatigue properties must be treated by statistical
means due to large variation during testing.
• Virtually all mathematical equations dealing
with fatigue are fitted to test results coming
from materials testing.
Fields of application & analysis
considerations
• Whenever a structure is subjected to time
varying loads, fatigue must be taken into
account. Typical structures subjected to time
varying loads are for example:
– Rotating machinery (pumps, turbines, fans, shafts)
– Pressure vessel equipment (vessels, pipes, valves)
– Land based vehicles, ships, air- and space crafts
– Bridges, lifting equipment, offshore structures
Fields of application & analysis
considerations
• In the design specification of the part there are
some questions that must be answered, for
example:
1. What is the expected number of cycles during the
expected life time?
2. Shall the individual components be designed for
infinite life or a specified life?
3. In case of a specified life time, what
service/inspection intervals are needed?
Fields of application & analysis
considerations
• Common Decisions for Fatigue Analysis
• There are 5 common input decision topics upon
which your fatigue results are dependent. These
fatigue decisions are grouped into the types listed
below:
1.
2.
3.
4.
5.
Fatigue Analysis Type
Loading Type
Mean Stress Effects
Multi-axial Stress Correction
Fatigue Modification Factor
Loading types
When minimum and maximum
stress levels are constant, this is
referred to as constant amplitude
loading. This is a much more simple
case and will be discussed first.
Otherwise, the loading is known as
variable amplitude or nonconstant amplitude and requires
special treatment
Loading types
The loading may be proportional or nonproportional: - Proportional loading means
that the ratio of the principal stresses is
constant, and the principal stress axes do
not change over time. This essentially means
that the response with an increase or
reversal of load can easily be calculated.
- Conversely, non-proportional loading means
that there is no implied relationship between
the stress components. Typical cases include
the following:
Alternating between two different load cases,
An alternating load superimposed on a static
load ,
Nonlinear boundary conditions .
Terminology
Consider the case of constant amplitude, proportional loading, with
min and max stress values σmin and σmax:
The stress range Δσ is defined as (σmax- σmin)
The mean stress σm is defined as (σmax+ σmin)/2
The stress amplitude or alternating stress σa is Δσ/2
The stress ratio R is σmin/σmax
Fully-reversed loading occurs when an equal and opposite load is
applied. This is a case of σm = 0 and R = -1.
Zero-based loading occurs when a load is applied and removed. This
is a case of σm = σmax/2 and R = 0.
Stress life theory
• General:
– The stress life (SN) analysis estimates the time spent to initiate and grow a
crack until the component breaks into parts.
– The model takes the stress variation and makes a look-up in a material
graph to find the corresponding number of cycles to failure.
– Historically this is the first mathematical model developed for lifetime
calculations, and the one with the most readily available material data.
– The analysis requires stress results from a linear static analysis as input.
• Suitability and limitations:
– The method is applicable for components failing after more than 10.000 to
100.000 cycles (HCF).
– For higher loadings with a shorter fatigue lifetime local plasticity is
probably considerable not only at the crack tip, but locally on the structure
as well.
– Such cases should be analysed using the Strain Life Method instead as the
stress life method gives overly conservative results here.
Stress life theory
Material data
– When doing test on stress range versus fatigue life and plotting
the results on two logarithmic axis, the results tends to be
linear.
– Gustaw Wöhler observed this when doing bending test on
railroad shafts, illustrated below.
– Later Basquin formulated this mathematically in a power law.
The curve may consist of several linear
pieces. Two parameters for each of the
curves in Basquin's law are needed as input:
Starting point Ss and slope b.
The properties are usually found for zero mean
stress and a uniaxial stress state on polished
specimens.
Stress life theory
• Metals typically experience infinite fatigue life for low
stress ranges.
• This is modelled as a flat curve at a cut-off stress ΔSe and
above Ne cycles.
• Ne is usually between 1 and 5 million cycles and Se is
typically half the ultimate strength Rm. The plateau
tendency may not be present for other metals, such as
aluminium or stainless steel.
• As explained, Basquin is not valid in
the low cycle fatigue region, so
caution should be used if the calculated life is low – as illustrated with
the dashed line in the figure below.
Stress life theory
• The material curve on previous page may
describe the fatigue strength of a base material,
but it may also be describing the fatigue strength
of a whole component, such as a welded T-joint.
• Alternatively the material curve to be used may
be dictated by a design standard, based not only
on the material but also as a function of
geometry, failure consequences and inspection
intervals for example.
Stress life theory
Basquin's law
Basquin's law calculates the number of cycles to fracture as:
Nf = ƒ (S, S0, N0, b)
Nf = Number of cycles to failure
S = Applied stress range = Δσ = 2σa
(N0, S0) = Point on the material curve
b = Fatigue strength exponent (Slope of material curve)
Basquin's law is usually presented as:
However, usually So = Se and No = Ne,
thus making Basquin's law:
Stress life theory
Basquin’s law
In lack of fatigue material data, the following guidelines
can be used (although other methods exist to predict
this):
Se=0.5×Su at Ne = 106
S =0.9×Su at N = 103
Su = Rm (ultimate tensile stress)
Stress life theory
Mean stress correction
Since the fatigue properties given are valid
for zero mean stress only, one must do
corrections if mean stresses are not equal to
zero in the actual load history. Compressive
mean stresses are good for fatigue life, while
mean tensile stresses are bad.
The three load histories to the right all have
equal stress amplitudes, but different mean
stresses. As such they will experience
different fatigue life also. This is not covered
by Basquin’s formulae. We will now look at a
method to account for this so that Basquin
still can be used.
Stress life theory
Mean stress correction
A number of models exist to compensate for mean stresses, four are
incorporated in ANSYS Fatigue module.
- Goodman (England 1899)
- Soderberg (USA 1930)
- Gerber (Germany 1870)
- Mean Stress Curves
The three first models work in the same manner: The stress
amplitude that is to be used in Basquin’s law is corrected according
to the mean stress σm and yield or tensile stress σy or σu. The three
models are shown graphically below:
Stress life theory
Mean stress correction
The last model does not use any correction formulae, but instead
have several material curves input - each corresponding to its own
Stress Ratio (R):
Tests yield results between that predicted by the Goodman and
Gerber models. Soderberg is usually over conservative and is
seldom used. In lack of any arguments what model to choose,
Goodman is a good choice if test data is not available for different
stress ratios. Soderberg is good for brittle materials
Stress life theory
Mean stress correction
For fatigue loadings that have small mean stress compared to the
alternating stress, the theories show little difference.
Goodman is presented as:
However, we are looking to calculate the corrected stress amplitude
σa’, so resolving for this gives the formulae actually used:
σa’ = Corrected stress amplitude
σa = Initial stress amplitude
σm = Mean stress
σu = Ultimate Tensile Strength, UTS
Stress life theory
Mean stress correction
Similarly, Gerber is presented as:
But it is used as:
Finally we have the same for Soderberg:
σy = Yield Strength
Stress life theory
Surface condition, volumetric dependency etc.
• Fatigue material property tests are usually
conducted under very specific and controlled
conditions (e.g. axial loading, polished specimens).
• If the service part conditions differ from as tested,
modification factors can be applied to account for the
difference.
• The fatigue alternating stress is usually divided by
this modification factor Kt and can be found in design
handbooks.
• Note that this factor is applied to the alternating
stress only and does not affect the mean stress.
Stress life theory
Surface condition, volumetric dependency etc.
The modification factor Kt is written as:
λ= technological volume dependency, l≤ 1.0
δ= geometrical (loading type) volume dependency, d≤ 1.0
κ= surface condition dependency (surface roughness), k≤ 1.0
ν= dependency due to coatings (zinc, chrome layer), n≤ 1.0
Ψ= mechanical or heat treatment of surface (shot peening, case
hardening), Y≥ 1.0
μ= Environmental influence (moisture, temperature, salt water), m≤ 1.0
Stress life theory
Performing a fatigue analysis is based on a linear static
analysis.
Although fatigue is related to cyclic or repetitive loading, the results
used are based on linear static, not harmonic analysis. Also,
although nonlinearities may be present in the model, this must be
handled with caution because a fatigue analysis assumes linear
behavior.
A component usually experiences a multiaxial state of stress. If the
fatigue data (S-N curve) is from a test reflecting a uniaxial state of
stress, care must be taken in evaluating life.
For welds the stresses perpendicular to or parallel with the weld
seam are treated or disregarded depending on the current
evaluation method.
Stress life theory
Performing a fatigue analysis is based on a linear static
analysis.
Mean stress affects fatigue life and is reflected in the shifting of
the S-N curve up or down (longer or shorter life at a given stress
amplitude).
• For welds the most important factor is the stress range, the
mean stress is normally of no or secondary importance.
Other factors mentioned earlier which affect fatigue life can be
accounted for with a correction factor in Simulation.
• For welds fatigue life time is improved by dressing, grinding,
deburring, TIG-treatment, shot peening and similar methods.
Strain life analysis, theory
Strain life (EN) analysis, LCF
The strain life (EN) analysis (a.k.a. Crack initiation analysis) estimates
the number of cycles needed to initiate a crack.
The remaining lifetime spent to grow the crack until the component
breaks into parts is not part of the calculated lifetime (this is
Fracture Mechanics Analysis).
The Strain Life analysis compensates for local plasticity and is valid
for fewer cycles than about 10.000. The strain life analysis requires
stress results from a linear static analysis as input.
Strain life analysis, theory
Suitability and limitations
•This analysis is better suited than a Stress Life analysis to cope with
higher stress ranges on the model because it contains an additional term
compared to the Stress-Life analysis and it also offers correction models
for local plasticity.
•The strain-life method is suitable in the lower cycle fatigue range,
involving less than about 1.000 to 10.000 cycles fatigue life and high local
stress. (So called low cycle fatigue, LCF).
•The model it is not suited for calculating fatigue life of welds, since it
must be assumed that welds already contain macroscopic cracks.
• The model is not suited for other materials than metals. Bear in mind
that depending on the crack propagation properties, the component may
have (but usually have not) significant fatigue life left after the crack has
developed.
•The model is not valid for loads resulting in multi-axial stresses, without
taking certain precautions.
Strain life analysis, theory
Material data
•The fatigue material properties in the Strain Life method are
modelled combining the strain-life models of Basquin and CoffinManson.
•The Basquin part is identical to that of the SN-analysis, but it is
solved in terms of strain rather than stress.
•The Coffin-Manson part is added to account for the plastic fatigue
properties. In addition to the data for Stress Life analysis, one needs
to two additional parameters:
•Fatigue ductility coefficient εf and fatigue ductility exponent c.
The curve describing the fatigue
strength as a function of strain
range is given to the right:
Strain life analysis, theory
Material data
Now the distinction between high versus low cycle fatigue can be
explained. It is not defined at some specific number of cycles, but
rather at the intersection point of the Coffin-Manson and Basquin
curves. At lower cycles, the plastic part dominates – while at higher
cycles, the elastic part.
Strain life analysis, theory
Basquin-Coffin-Mansons law
The B-C-M law calculates the number of cycles to fracture as:
Nf = ƒ (σf, b, εf, c)
σf = Fatigue strength coefficient
b = Fatigue strength exponent
εf = Fatigue ductility coefficient
c = Fatigue ductility exponent
E = Young’s modulus
Presented as:
Strain life analysis, theory
Mean stress correction
Since the fatigue properties given are valid for zero mean stress, one
must do corrections if mean stresses are present in the actual
loading. For the Strain Life Method, this could be done in accordance
with one of the two user-selected models incorporated in ANSYS:
- Smith-Topper-Watson
-Morrow
The program accounts for mean stresses by altering the fatigue
strength of the material, as can be remembered this approach is
different from the Stress Life method where the applied stress
amplitude is adjusted instead.
Strain life analysis, theory
The Morrow model accounts for mean stresses by
moving the elastic part of the material curve up and
down according to the mean stress of each cycle.
εa = Strain Amplitude
2Nf = Number of reversals to failure
En – None
En - Morrow
Strain life analysis, theory
Smith-Topper-Watson accounts for mean stresses by
using a damage parameter gathered from the maximum
stress at each cycle.
Smith-Topper-Watson should be used for loading involving tensile
stresses, whereas Morrow is best suited for compressive stresses.
En – None
EN – Smith-Watson-Topper
Strain life analysis, theory
Plasticity correction
Even though the strain life analysis has incorporated the CoffinManson term to better account for the low cycle fatigue region, further
corrections for local plasticity are available.
The linear elastic calculations done to acquire the stresses and strains
are usually done according to Hooke’s law of a linear stress-strain
relationship. This may erroneously give higher stresses than yield
stresses locally, not only at the crack tips, but also in small regions in
the model.
With the assumption that the higher-than-yield stresses are only local
occurrences, it is possible to correct for this somewhat - without
running a non-linear static analysis. Correction for plasticity can be
done by different versions of the Neuber formulae:
- Local or nominal
- Neuber (implemented in ANSYS fatigue module)
- Elastic Strain Energy Density (ESED)
Strain life analysis, theory
All adjust the stresses predicted by the linear curve described by Hooke
down to a lower stress at the nonlinear cyclic stress-strain curve described
by Ramberg-Osgood. This curve is the cyclic stress-strain curve derived
from a strain controlled cyclic test for a specified number of cycles.
•Using the Neuber rule σ×ε=constant will convert the calculated linear
elastic stress down to the nonlinear cyclic stress-strain curve as shown in
left figure.
•Elastic Strain Energy looks at the strain energy, and demands that the two
squares (green and blue) have the same area, as shown below to the right.
Strain life analysis, theory
In addition to the E-modulus, the Ramberg-Osgood material
model requires the input of a strength coefficient K and a
hardening exponent n to describe the curve. (The strength
coefficient K is not to be mixed with the fracture toughness K).
Hooke:
σ = ƒ (E, ε)
E = Young’s modulus
ε = Strain
Presented and used as:
and:
Ramberg-Osgood:
σ = ƒ ( E, ε, K, n)
K = Material strength coefficient
n = Material hardening exponent
Presented and used as:
and:
Strain life analysis, theory
Surface condition and treatment
Similarly to the Stress Life method, corrections for surface condition
and surface treatment are introduced via correction factors (Kf) that
modify the stress amplitude
Fatigue analysis, theory
BIAXIALITY
• When doing stress life or strain life fatigue analysis we have
done so based on the assumption that the stress state is pure
uni-axial tension-compression.
• If the stress is in shear, or the stress vector changes its
direction during the load, we have violated the basic
assumptions.
• This limitation is caused by the material data being collected
for a specimen loaded with a uni-axial stress state, as shown to
the right.
• If it turns out that this assumption is not valid, the fatigue
lives we calculated are not correct.
• In such cases we need to re-run the fatigue analysis and
include corrections for biaxiality.
Fatigue analysis, theory
Proportional – non proportional loading
A load may be proportional or non-proportional.
To explain the difference, consider the two models below. One
is loaded in moment and the other in torsion:
Each of the loads on their own result in a proportional load
since the stress vector is increasing in size but has a constant
direction.
Even if the two loads are applied simultaneously, the load is
still proportional.
Fatigue analysis, theory
However, if the load is applied in sequence (first one, then also
the other), then the load is non-proportional, since the vector
changes its direction, as illustrated below:
If the load is non-proportional, the critical fatigue location may
occur at a spatial location that is not easily identifiable by looking at
either of the base loading stress states (i.e. it may not be in the max
stress position for each of the load cases).
Normal cycle counting routines do not take into account the
sequence (order) of the respective part of the loads.
If the load is non-proportional and with a non-constant amplitude
load, a more advanced cycle counting is required such as path
independent peak methods or multiaxial critical plane methods.
Fatigue Analysis of Welded Connections
General:
• If the number of load cycles is larger than 1000 cycles a fatigue
analysis shall be performed.
• Watch out for structures that may come into resonance
(eigenfrequencies)
• If the base material is not welded, the fatigue strength is
proportional to the yield strength.
Fatigue Analysis of Welded Connections
General:
• Whenever plate material is cut using thermal methods (laser,
plasma or gas cutting), the fatigue strength is similar to a welded
component.
• High strength steel is NOT better than mild steel if the following
occur:
 Material is affected of weldments
 Material is cut using thermal cutting
 The environment is corrosive
• By placing weld joints in regions with low stresses admit use of
high strength steel material.
Fatigue Analysis of Welded Connections
General to fatique:
• The geometry of the welded joint is governing of the fatigue
strength.
• Both base material and filler material strength has no
influence on fatigue life of welded joints.
• The current stress level have minor influence on fatigue life.
• Most important factor for the weld fatigue life is the
stress range, Δσ.
Fatigue Analysis of Welded Connections
Geometry of weld joint
Heat affected zone (HAZ)
Fatigue Analysis of Welded Connections
Critical areas in welded joints:
Fatigue Analysis of Welded Connections
Influence of base material strength:
• For different quality of the base material the difference in
fatigue properties is the number of cycles to crack initiation.
• During the welding process a large number of “faults” is
introduced, i.e. the crack initiation phase has already passed.
Residual weld stresses
Influence of residual stresses of welded structures
• For a cantilever beam
subjected to a pulsating
load, the global stress
variation is linear bending.
• The residual stresses in weld
seam is equal to material yield
stress (Rp0.2)
• The governing factor for
fatigue is not the current stress,
only the stress range, Δσ.
Material properties
Material Properties
• Material testing is performed at constant amplitude loading for a
number of samples at each amplitude.
Material properties
Variants of the fatigue curves
Fatigue Classes
Fatigue Classes or weld joint classes, C or FAT
• The fatigue class is the stress range Δσ in MPa for a
corresponding fatigue life of N=2×106 load cycles.
• The fatigue class stress range is specified at an average fatigue life
time minus 2 σ of standard deviation, corresponding to n=2,3%
probability to failure.
• IIW-1823 and Eurocode 3 have the following fatigue strength
classes, FAT: 36, 40, 45, 50, 56, 63, 71, 80, 90, 100, 112, 125 and 160
• DNV RP C203 have the following fatigue strength classes, FAT: 36,
40, 45, 50, 56, 63, 71, 80, 90, 100, 112, 125, 140 and 160
Fatigue Classes
Fatigue Classes (FAT)
In the fatigue evaluation using nominal stress method or hot spot
method, the fatigue data used is depending on the current
geometry of the weld joint.
DNV-RP-C203, appendix A show the “Detail category” (FAT) with
corresponding “Construction detail”
Figure showing detail category for lap joint (W1) from DNV-RP-C203.
Fatigue Classes
Fatigue Classes (FAT)
IIW-1823, chapter 3-2 show the different classified details (joints)
and their FAT values.
Figure showing FAT category for lap joint (W1) from IIW-1823
Figure showing FAT category for lap joint (W1) from EN1991-1-9
Fatigue Classes
Fatigue Classes (FAT), comparison between different codes
Fatigue Classes
Fatigue Classes (FAT), comparison between different
codes, continued:
Design of weld connections
Fatigue curves for different fatigue classes according to
Eurocode 3
Design of weld connections
The calculation of the fatigue life time using the fatigue
curves is given by the following equation:
Design of weld connections
Fatigue modification factors:
• Eurocode 3 apply fatigue modification factor on size
effect for non welded components/areas.
• DNV RP C203 apply a modification factor on fatigue
life time based on plate thickness.
Design of weld connections
Load histories, non constant loading and partial damage:
The damage can be
calculated using
Palmgren- Miner
partial damage
theory:
Fatigue Evaluation Methods
Besides of hand book calculations there is a number of
different methods utilizing the FE-method available:
Fatigue Evaluation Methods
Nominal stress method:
This method includes the macroscopic geometric stress state
but does not include effects due to the welded joint itself.
Fatigue Evaluation Methods
The geometric stress state include effects due to the welded
joint itself but the current geometric shape of the weld
seam is not considered
Fatigue Evaluation Methods
Definition of notch stresses:
• The total stress in the notch is calculated using linear
elastic material properties.
• The total stress state (σln) can be divided into three
components:
 Membrane stress (σm)
 Equivalent linear bending stress (σb)
 Peak stress component (σnlp)
Total stress in notch σln = σm + σb + σnlp
Fatigue Evaluation Methods
There are a number of methods for fatigue assessment of
welded joints:
• Nominal stress method
• Hot Spot method (geometrical stresses)
• Effective Notch Method (notch stresses)
• CAB method (geometrical stresses)
• Fracture mechanics analysis
Fatigue Evaluation Methods
Nominal stress method:
• Find the nominal stress in FE-model and compare this with the
current fatigue strength class
• Traditional method, experience gathered over many years
• Works with stress either parallel or perpendicular to weld seam
• Method do include “normal” skewness, eccentricities and residual
weld stresses
• Verify that that weld type and load case is in accordance with
weld fatigue class.
• Difficulties may arise when other stress factor increase the stress
levels.
Fatigue Evaluation Methods
Hot spot method:
• Used when geometry or load case do not fit given fatigue
strength class
• Applicable when skewness, eccentricities are larger than
“normal”
• Has gathered experience, good reputation
• Stresses must be perpendicular to weld seam
• Do only consider stresses in the weld toe
• The method do not include skewness and eccentricities but do
include weld residual stresses.
• Each weld seam type have its specific fatigue strength class
Fatigue Evaluation Methods
CAB-method (geometric stresses):
• New method, not recognized outside Germany
• For use with solid models only
• Stresses must be perpendicular to weld seam
• Fillet welds only
• No evaluation at weld root, only fillet weld “toe” is considered
• The method is applicable for plate thicknesses from 8 to 80 mm
• Misalignment, skewness of plates or other geometric
imperfections must be modeled since it is not in the fatigue
strength class.
Fatigue Evaluation Methods
Effective notch stress method:
• Relatively new method, has not gathered much experience
• Misalignment, skewness of plates or other geometric
imperfections must be modeled since it is not in the fatigue
strength class
• Stresses must be perpendicular to weld seam
• Consider stress at root and toe of weld. Do not include embedded
cracks in weld
• Require very fine FE-models, submodelling techniques is a must in
most cases.
• Useful to compare different design/geometries of weldments
• In some cases not the best method to predict the absolute fatigue
life time?
Fatigue Evaluation Methods
Fracture mechanics:
• Used for complex details not specified in any fatigue strength class.
• Crack start in root or when there is other faults in weld seam
during welding
• A crack is assumed whose depth is based on the smallest crack size
that can be detected during non destructive testing.
•The stress intensity factor KI is calculated for the given geometry
and loading condition.
•Crack propagation is calculated by Paris Law:
•Fracture occur when the crack has grown to a size where KI > KIC.
Fatigue Evaluation Methods
The selection of which fatigue evaluation to be used is
governed by several factors:
• What is the goal with the fatigue evaluation?
 Calculate absolute life time
 Compare different designs
 Quick answer
• What types of stresses can be retrieved from the FE-model?
Type of FE-elements used (beam, shell or solid elements)
How much detail is included in FE-model
How good is the mesh
• What are the direction of the principal stresses relative to weld
seam
• Looking for the stresses in toe or root of weld?
Fatigue Evaluation Methods
Nominal stress method:
• Create a path perpendicular to weld seam starting at weld toe.
• Plot the principal stress on path, the straight line is the nominal
stress.
• Extrapolate the straight line portion of stress variation to the weld
toe.
•The linear stress at the intersection of the weld toe is the nominal
stress to be used in the weld fatigue evaluation (Δσ).
Fatigue Evaluation Methods
Nominal stress method:
• For the current weld joint geometry, find the corresponding fatigue
joint class.
• Calculate the fatigue life (if the stiffener has a length L=60 mm) as:
Fatigue Evaluation Methods
Hot Spot method:
• Origins from the offshore oil industry used for
pipe and tube connections
• The hot spot method was developed to evaluate
measurements from strain gages.
• The method is intended for evaluation of the
weld toe (figure a-d), not for the root (figure e-h)
Fatigue Evaluation Methods
Hot Spot method:
• Hot spot: The location where a crack will propagate from
• Hot spot stress: Value of the geometric stress in the “hot
spot”, i.e. The non linear stress peak in hot
spot is not included
• Extrapolation from predefined points close to hot spot is a
way to determine the hot spot stress
• Principal stress must be
perpendicular to weld
Fatigue Evaluation Methods
Extrapolation to get hot spot stress:
• Linear extrapolation:
 IIW-1823 and Eurocode 3 is using extrapolation
point at 0.4×t and 1.0 ×t.
 σhot spot= 1.67 ×σ(0.4t)-0.67 ×σ(1.0t)
Fatigue Evaluation Methods
Extrapolation to get hot spot stress:
• Linear extrapolation:
 DNV RCP-203 is using extrapolation point at 0.5×t and 1.5 ×t
 σhot spot= 1.5 ×σ(0.5t)-0.5 ×σ(1.5t)
 For pipe / tube connections the location of interpolation points is:
For extrapolation of stress along
the brace surface normal to the
weld toe
For extrapolation of stress along
the chord surface normal to the
weld toe at the crown position
For extrapolation of stress
along the chord surface normal
to the weld toe at the saddle
position
Fatigue Evaluation Methods
Extrapolation to get hot spot stress:
• Quadratic extrapolation:
 For a very non linear stress variation near web
plates or stiffeners a quadratic extrapolation may
be necessary
 IIW-1823 and Eurocode 3 is using extrapolation
point at 0.4×t, 0.9×t and 1.4 ×t.
 σhot spot= 2.52 ×σ(0.4t)-2.24 ×σ(0.9t) + 0.72 ×σ(1.4t)
Fatigue Evaluation Methods
Extrapolation to get hot spot stress:
• Example of geometry where extrapolation
rules does not apply since the plate thickness
is not relevant for this kind of geometry.
Fatigue Evaluation Methods
Tips and advice for FE-modelling:
• To reduce the influence of the geometric singularity at hot spot
location at the first interpolation point at 0.4×t, the element size must
be less than 0.4×t.
• As a rule of thumb, the influence of the singularity is almost
eliminated at about 2 or 3 elements away from the singularity.
• Use second order (quadratic) elements as first choice.
• Avoid large aspect ratios on the element sides, < 3 should be fine.
• Have a smooth transition between small and large elements size.
• For shell models consider the stiffening effect of the weld itself.
• Is skewness or misalignment within weld fatigue class or to be added?
• Remember that the hot spot method is applicable for stresses
perpendicular to weld.
Fatigue Evaluation Methods
Hot spot method fatigue evaluation:
IIW-1823, select the fatigue strength class
according to hot spot method:
Note: The tables do NOT include effects of misalignments.
For DNV RCP-203, the stress range at the hot spot of tubular joints
should be combined with the T-curve which corresponds to FAT=90
(D-curve). For other geometries than tubular joints use the D-curve.
Fatigue Evaluation Methods
Hot spot method fatigue evaluation:
Eurocode 3:
 Buttwelds details category (FAT) = 100
 Fillet welds details category (FAT) = 90
 Tables do not include skewness and imperfections in geometry!
Fatigue Evaluation Methods
Hot spot method fatigue evaluation:
Short notes on skewness and misalignements in geometry:
• Some weld fatigue strength classes are identical with nominal stress
method and in such cases the skewness is included (as specified in
nominal stress method).
• If the stresses are derived from measurements using strain gages,
imperfections are already included.
• Using FE-models imperfections / skewnesses can be accounted for by:
 Use a weld fatigue strength class that do include skewness
 Modify the geometry to conform with current skewness
 Adjust stresses using stress concentration factors
Fatigue Evaluation Methods
Fatigue Evaluation Methods
Fatigue Evaluation Methods
Fatigue Evaluation Methods
Methods for Improving Fatigue Life
• There are several methods to improve the
fatigue life for welded connections.
• All kinds of improvements do only apply for
the toe, so it assumed that the weld is
deigned in such a way that the toe is the
critical area and not the root of the weld joint.
• Both IIW-1823 and DNV RP-C203 give
guidelines for how to improve and how much
that will be gained by the different methods.
Methods for Improving Fatigue Life
The most commons way to improve weld fatigue life:
• Weld profiling
• Grinding of weld to eliminate undercut
• TIG, Laser or Plasma dressing
Methods for Improving Fatigue Life
The most commons way to improve weld fatigue life:
• Hammer-, needle-, shot-, brush-peening or
ultrasonic treatment
• Overstressing (proof stressing)
• Stress relief (post weld heat treatment)
• Painting or resin coating (environment
protection)