Fatigue Analysis Notes
From Grasp Engineering –
https://www.graspengineering.com/what-is-fatigue-analysis-stages-of-fatigue-analysis/
What is Fatigue Analysis? Stages of Fatigue Analysis
Fatigue is the Initiation, formation and propagation of cracks in a material due to cyclic
loads. The failure occurs due to the cyclic nature of the load which causes microscopic
material imperfections to grow into a macroscopic crack. This phenomenon mainly
happens but due to multiple load cycles which causes components to lose their strength
and get tired, hence it is called fatigue.
Once a fatigue crack has initiated, it grows a small amount with each loading cycle and it
will continue to grow until it reaches a critical size, which occurs when the stress intensity
factor of the crack exceeds the fracture toughness of the material, producing rapid
propagation and typically complete fracture of the structure.
Figure 1: Helical gear and Pedal Crank Failure
Fatigue cracks normally initiate at stress concentrations, structural discontinuities.
Fatigue cracks can also propagate from existing macroscopic cracks, such
as weld defects. Almost all structural components are subjected to fluctuating loads at
one time or another.
Fatigue Life:
It is defined as the number of cycles that a component can withstand before fatigue
failure occurs. Figure 2 depicts the various fatigue life stages.
There are three stages of fatigue fracture: Crack initiation, Crack propagation and Final
rupture. Fatigue failures, both for high and low cycles follows the same basic step
process of Crack initiation stage I, stage II Crack Propagation, and step III finally ultimate
failure. Refer figure 3 for stages of fatigue failure on plate with hole in central under pull
force on both end.
Figure 2: Graph for Stages of Fatigue failure
Crack Initiation:
This phase includes crack nucleation and small crack growth. This is the beginning
process, in which cracks initiate at very small material microstructures or at areas with
high void density. At these tiny locations, the cracks lead to persistent slip bands that
propagate along the maximum shear plane (45 degree from the direction of the applied
load) under cyclic loads (alternating stress). These locations are undetectable with naked
eyes and result in highly localized stress concentrations.
Crack Propagation:
In this stage, once cracks reach a critical size, micro cracks grow and transverse 2-3 grain
boundaries large compared to material microstructure. The stress concentration at these
locations results in plastic stresses at the crack tip locations. These cyclic plastic
stresses start orienting perpendicular to maximum principal stress and thus micro-crack
slowly grows over an indefinable area of fatigue fracture.
Fatigue Failure:
In this stage, the crack which developed in the second stage, if continues to grow due to
existing sufficient energy will continue until tensile failure occurs.
For example if the test specimen went under crack nucleation and growth stage and
propagation of crack continues, it gradually reduces of the cross-sectional area of test
specimen and eventually weakens the part so that final, complete fracture can occur with
only one more load application. The fracture mode may be either ductile or brittle or any
combination depending upon the metal concerned, the stress level, the environment, etc.
Figure 3: Stages of Fatigue Failure
Fatigue Life Estimation Methods:
There are various methods to determine the fatigue life of a material.
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Stress-life method,
Strain-life method,
Vibration (Frequency based) fatigue method,
Crack growth method and
Probabilistic methods, which can be based on either life or crack growth
methods.
Whichever method is used by engineers to find out fatigue life, the complex fatigue
loadings (completely random or variable) is reduced to a series of fatigue equivalent
simple cyclic loadings by cycle counting methods such as rainflow counting algorithm.
Stress-Life (SN) Method:
Stress life methods also known as Nominal stress method or S-N method uses elastically
calculated stresses for total life calculations. It assumes that the structure is fully elastic
and stress drives the crack growth while initiation & crack growing phase is not
considered. It is applicable to low stress/high cycle fatigue problems (whereas low load
and long life is involved); usually more than 100,000 cycles to failure of ductile metals.
Key features of Stress-Life methods:
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Rainflow cycle counting is used to simplify the complex fatigue cycle loads.
Simple computational techniques even hand calculations can be used.
Fatigue life is based on Wholers curve (alternating stress range and SN curve).
Goodmon, Gerber, soderberg, ASME Elliptical mean stress correction theories are
used.
The S-N curve is commonly used to estimate the degree of fatigue damage to materials.
This curve is also called the Wholer curve, which is the oldest diagram which allows one
to visualize the resistance of the part or the materials in the field of fatigue. This curve
defines a relation between the applied stress σ ( sigma sometimes noted S) and the
number of cycles to failure. Mathematical description of the material S-N curve is shown
in figure 4.
Figure 4: S-N Curves (Wholers Curve)
Strain-Life Method:
Strain Life method is also known as local stress-strain, critical location approach, E-N or
crack initiation which uses plastic strain to predict the fatigue damage. It is commonly
referred to as the low-cycle-fatigue (LCF) method but it can also be used in the high cycle
(HCF) domain. In the presence of stress concentration, when strain is no longer elastic,
the total stain can be used instead of stress to predict fatigue life, this is known as strain
life method.
Strain-life design method is based on the assumption that the behavior (fatigue life) of
notched part at a notch root is similar to small test specimen under strain controlled
conditions. Figure 5 shows components under pull force along with small test specimen.
Here, the overall body remains elastic while the localized plasticity (critical zone) can be
simulated using smooth test specimens.
Figure 5: Small Test Specimen under Strain Controlled Condition
When strains are no longer elastic, such as in the presence of stress concentrations, the
total strain can be used instead of stress as a similitude parameter. This is known as the
strain-life method.
The figure 6 shows the strain amplitude vs reversal of failures (2Nf). The total strain is
obtained from the equation shown in figure.
Figure 6: Strain Amplitude vs Reversal of Failure
Key features of Strain-Life methods:
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It uses elastic-plastic strains estimated from elastic results or even calculated
directly.
Best suited for low cycle fatigue and can be used for high cycle fatigue too.
It is difficult to apply with hand calculations hence generally implemented using
numerical methods like CAE.
Rainflow cycle counting can be used to simplify the complex fatigue cycle loads.
Predicts crack initiation and stress amplitude of local strain at the crack initiation
phase
Vibration Fatigue (Frequency Based Fatigue):
As we know, fatigue is the initiation and propagation of cracks in a material due to cyclic
loading. These cyclic loads may happen in vibrations too, due to its own natural frequency
or other external excitation such as random vibration, harmonic vibrations, etc. This
forced vibrations of random or harmonic natures causes material fatigue, called vibration
fatigue. The structure responds to its natural dynamic modes due applied excitations,
resulting in dynamic stress in the material points. The process of vibration fatigue is thus
governed largely by the shape of the excitation profile analyzed in frequency domain,
power spectral density (PSD).
The vibration fatigue analysis is mainly based on the modal analysis response as natural
modes and frequencies of vibrating structure which enables accurate prediction of the
local stress responses for the given excitation. Thus, when stress responses are known,
the vibration fatigue is said to be successfully characterized.
There are few classical approaches which are used to calculate the fatigue evaluation; in
this rainflow algorithm is used to simplify cycle counting & palmgren miner damage
hypothesis is used to sum damages of respective cycles. In combination with classical
approaches, FEM is being used nowadays to calculate fatigue damage. FEM performs
the frequency domain dynamic analysis for given fatigue loads. There are various
commercial software which provides frequency based fatigue calculations such as
ANSYS Fatigue, Ncode, Abaqus, Nastran, etc. ANSYS mechanical fatigue tool supports
fatigue analysis for random vibration and harmonic response analysis.
Applications:
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Automobiles traveling on roadway
The wind blowing on the wind turbine
Waves hitting offshore structures and marine vessels
Space vehicles during launch
Crack Growth Methods:
In this method, the fatigue life is estimated based on the developed crack growth for each
loading cycle; the crack growth equations are used to sum the width of each increment
of crack. Paris Erdogan equations are used to predict the fatigue life of components
which are useful to predict the growth of crack from 10 micro M to failure. The ASTM
international has developed standard methods for measuring crack growth.
The crack growth methods predict the intermediate size of cracks which are used to
schedule inspections to ensure safety of components whereas strain life/stress life only
give life until component fails. FEM software’s also used to predict crack growth through
fracture mechanics parameters.
Furthermore, refer fatigue Design philosophy blogpost for more insights on fatigue
analysis.
Summary
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Fatigue is the Initiation, formation and propagation of cracks in a material due to
cyclic loads.
There are three stages of fatigue fracture: Crack initiation, Crack propagation and
Final rupture.
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There are two major methods to predict fatigue life the first one is stress (S-N)
life and second one is Strain (E-N) life. In addition to this, frequency based or
vibration fatigue & crack growth (crack-life) methods are used to predict fatigue
life.
https://www.graspengineering.com/fatigue-design-philosophy/
Fatigue Design Philosophy
Posted on September 10, 2021 by graspengineering
As we know fatigue is very important term in engineering and which if not studied will
leads to failure of structure and causes fatal accident. Hence, design In this blog, we
will going to discuss about the design philosophy of fatigue. Before understanding
design philosophy you should aware of What is fatigue and its various stages.
Fatigue Design Philosophies:
There are three primary design philosophies used with respect to fatigue and durability
of structure. These are Safe Life, Fail Safe and Damage Tolerance. These design
philosophies are used even before attempting to carry out fatigue calculations or even
before deciding the calculation method of fatigue. These design philosophies are mainly
used in aerospace industries such as aircraft & helicopter structure. This fatigue design
philosophies methods are also used other industries such as automotive, industrial
products, static equipment’s, the practical examples are discussed below:
The safe-life approach is used for planning and envisaging the toughness of the
mechanisms in the automotive industry,
The fail safe design in Roller-shutter fire doors that are activated by building alarm
systems or local smoke detectors must close automatically when signaled regardless of
power,
Isolation valves, and control valves, that are used for example in systems containing
hazardous substances, can be designed to close upon loss of power, for example by
spring force. This is known as fail-closed upon loss of power.
Safe Life:
In the safe life design approach, the products are designed to survive specific design life,
meaning products are intended to be removed from service at a specific design life. This
method is used in critical systems components whose failure may cause severe damage
to life and which are very difficult to repair and hence these systems are designed to work
for years without any repairs.
As the components were designed to perform for intended design life, this may also lead
to huge disadvantages of the system. In order to satisfy this design philosophy, serious
assumptions were made about alternating loads regardless of whether it will perform for
design life or not and if cracks were introduced due to alternating loads before their
service life, it may lead to huge accidents of the whole system. For example, De havilland
comet accident (1950): During the comet era, the aircraft design used was predominantly
using Safe-Life approach, which means the aircraft structure was designed to sustain the
required fatigue life with no initial damage or crack and no accumulation of damage
during service. But the Comet accidents showed that around stress concentration cracks
would initiate and propagate much earlier than expected, such that safety could not be
universally guaranteed in the SAFE-LIFE approach without uneconomically short aircraft.
Refer figure 1 showing failure origin of comet G-ALYU around window.
Figure 1: Failure origin of Comet G-ALYU around square windows
To counter this disadvantage, alternative design philosophies like fail-safe
design and fault-tolerant design were developed.
Fail- Safe Approach:
Fail safe approach is a design feature which incorporates various techniques in the event
of failure to mitigate the losses so that the failure will cause minimal or no harm to the
equipment, environment or people. The system design with a fail safe approach does not
mean that the failure will not happen, but rather than the system design mitigates the
unsafe consequences of the system failure, meaning if the system fails, it will fail in a
safe manner.
In case of aircraft design, Fail-safe is the characteristics of the structure that permits it
to retain required residual strength for a period of un-repaired use after failure or partial
failure of a principal structural element. The design principle emphasis on using multiple
load paths means multiple elements carrying the loads. This approach developed in 1950,
limited service life of critical components, failure of primary members does not risk safety
of aircraft because other components still carry the loads resulting in a more robust
design of the structure. The issue with this approach is that it does not anticipate all
failure modes & it is ineffective in multiple site damage.
Examples:
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The control valves and isolation valves that are used for example in systems containing
hazardous substances are closed by spring force when loss of power may happen. This
is known as fail-closed upon loss of power.
A railway semaphore signal is specially designed so that, should the cable controlling
the signal break, the arm returns to the “danger” position, preventing any trains passing
the inoperative signal.
Many nuclear reactor designs have neutron absorbing control rods suspended by
electromagnets. If the power fails, they drop under gravity into the core and shut down
the chain reaction in seconds by absorbing the neutrons needed for fission to continue.
Damage Tolerance:
Damage Tolerance is the ability of the structure to resist failure due to presence of
defects, cracks, or other damage for a time period sufficient to enable their
detection. This approach is based on the assumption that the flaws can exist in any
structure and such flaws can propagate with their uses.
Damage tolerance, or safety by inspection, was developed as a design philosophy in the
1970s as an improvement on the fail-safe principle for structural deterioration.it is also
called as ability of the structure to sustain anticipated loads in the presence of fatigue,
corrosion or accidental damage until such damage is detected through inspections or
malfunctions and is repaired. This philosophy is based on repairs performed on defective
structures should restore its original strength. Although damage tolerance philosophy
increases the durability of the structure, it does not guarantee safety of airframe. This is
illustrated by the accident of aloha airlines, in which the Boeing 737 lost a significant
portion of upper fuselage structure and the cause of accident was due to multiple site
damage in riveted joints. These joints are insufficiently inspected which are susceptible
to corrosion. Figure 2 shows the lifecycle of damage tolerance, the graph shows that
once the damage is detected by NDI and visually, it partially repaired and its its initial
strength is achieved time to time period.
Figure 2: Lifecycle of Damage Tolerance
https://www.graspengineering.com/fatigue-analysis-concepts-and-definitions/
Fatigue Analysis Concepts and Definitions
Posted on October 19, 2021 by graspengineering
Fatigue is the Initiation, formation and propagation of cracks in a material due to cyclic
loads. These cyclic loads lead to repeated stresses and if material is subjected to such
repeated stresses, the components fail at stresses below the yield point stresses. Such
type of failure of material is Fatigue failure. The fatigue of material is affected by various
factors such as the number of load reversals, irregularities, size of the component,
relative magnitude of fluctuating loads, etc. There are few important concepts used in
fatigue analysis are discussed below:
Endurance Limit or Fatigue Limit
The Figure 1 shows the Stress Vs Number of cycle graphs. In this graph, if the stress is
kept below a certain value (dotted line) the material (component) will not fail. This stress
as represented by the dotted line is known as a fatigue limit (fe) or endurance limit. The
Fatigue limit or Endurance limit is the stress level below which an infinite number of
loading cycles can be applied to a material without causing fatigue failure. When a
material is subjected to a stress that is lower than its endurance limit, it should
theoretically be able to withstand an indefinite amount of load cycles.
Figure 1: Stress Strain Curve (Endurance Limit)
Fatigue Loading Types
The time based loading have mainly two types as discussed below:
1. Constant Amplitude loading:
Here, the maximum and minimum stress levels are constant. This is the simplest case
and has different loading type options; Such as Zero-based, Fully Reversed and Ratio (Rratio). Refer Figure 2 for constant loading type options.
Figure 2: Constant Amplitude Load Type
2. Variable Amplitude or Non-constant loading:
In this case, as name suggest the loads are not constant but varying drastically.
Figure 3: Non-constant Amplitude Loading
Furthermore, Loadings are classified as proportional and non-proportional loading;
Proportional loading: It means, the ratio of principal stresses is constant and principal
stress does not change over time.
Non-proportional loading: It means that there is no relationship between the stress
components. The typical examples are nonlinear boundary conditions, alternating
between two different load cases, alternating load superimposed on a static load, etc.
Important Definitions:
This paragraphs discussed various terminology used in fatigue analysis.
Figure 4: Constant Amplitude Load Ratio
Mean Stress Theories:
Fatigue failure happens when a component is subjected to repeated cyclic loads. These
cyclic loads forms stress cycle’s resulting alternating stresses which causes the fatigue
damage. Nevertheless, the amount of damage caused does not only depend on
alternating stress but also mean stress.
In real world, the loads coming on product used are not constant but varying as shown
in Figure 5. Some cycles have mean offset or some does not have; accordingly
alternating stress may also vary.
The SN curves are obtained by applying the cyclic loading to a laboratory specimen. The
typical loading is either pure axial or bending and reflects uniaxial state of stress. For
multiple cycle, multiple tests are required to get SN curves which are under different mean
stress conditions; which takes times and efforts. So, instead of shifting SN-Curve to
account for mean stresses, a more common procedure is to transform the rainflow matrix
of the load time history, which contains all the stress cycle information for a given load
time history.
Figure 5: Varying Alternating Stress and Mean Stress Cycles
Mean Stress Correction:
A mean stress correction is used to transform a stress cycle to an equivalent stress cycle
with zero mean stress as sown in Figure 6. The transformed stress cycle must still
contain the same fatigue damage potential.
Figure 6: Mean Stress Correction
Mean Stress Correction Methods:
Goodman, Soderberg, Ferber and ASME Elliptical are different mean stress correction
theories. Figure 7 shows all mean stress correction theories; in this graph, the right hand
side shows compressive mean stress while left hand are tensile mean stresses.
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Goodman Method: A straight line connecting the endurance limit and the ultimate
strength (on positive) follows the suggestion of Goodman. A Goodman line is used when
the design is based on ultimate strength and may be used for ductile or brittle materials.
Refer blue colour line for Goodman mean stress correction. In this, no correction is done
on compressive mean stresses.
Soderberg Method: Soderberg criteria is defined as the straight line joining on stress
amplitude axis and on mean stress axis. Refer red colour line from below graph, it is
more conservative than Goodman theory and sometime used for brittle materials.
Gerber Method: Gerber parabola refers to the parabolic line joining two points in x axis
(σut) and y axis (σw). According to the Gerber criteria, the region below this curve is
considered to be safe. It provides a good fit for ductile metals for tensile mean stresses
while incorrectly predicts the harmful effects for compressive mean stress.
ASME Elliptical Method: It is same as Soderberg line but it uses ellipse instead of
straight line while connecting yield stress as shown in below graph with yellow colour.
Figure 7: Mean Stress Correction Method
Mathematical Equation:
Figure 8 shows the different mean stress correction lines, here σa is the stress amplitude,
σw is the fatigue limit for completely reversed loading, σut ultimate tensile strength and n
is factor of safety.
The mathematical equations are represented as below:
Figure 8: Mean Stress Correction Method
Low cycle Fatigue Vs High Cycle Fatigue:
The fatigue has been segregated into two region such as High cycle fatigue and Low
cycle fatigue. The main difference between both is the number of cycles, elastic and
plastic deformation behavior.
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Low Cycle Fatigue: The low cycle fatigue is characterized by repeated plastic
deformations in each cycles. For example, if tensile load is applied to component until it
plastically deformed, that would considered as one half cycle of LCF and in order to
complete a full cycle part needs to deformed back to its original shape. Hence, the
number of cycle that part can withstand before failure is much lower than the regular
fatigue. In this, loading that typically causes failure in less than 104 cycles.
High Cycle Fatigue: The high cycle fatigue is characterized by elastic deformation & the
number of cycles to failure is high. HCF require more than 104 cycles to failure where
stress is low and primarily elastic.
The transition life between LCF and HCF is determined by stress level (transition between
plastic and elastic deformations). This transition life mainly depends on ductility of the
material. E.g. 104 as shown in Figure 9.
Figure 9: Low Cycle and High Cycle Fatigue
Rainflow Cycle Counting:
It is an algorithm that converts an irregular stress history or spectrum of varying stress
into blocks of simpler stress cycles (equivalent set of simple stress reversals) that can
be used for fatigue calculations. Real life loading is not necessarily cycle and often
appears to be varying (random or transient) in nature, for which the number of cycles
and their amplitudes does not easily determined. Rainflow counting is then used to
extract the number of cycles, and their respective range and mean. Tatsuo Endo
(Japan)and M. Matsuishi first introduce rainflow counting in 1967-68 and in 1986 the
first rainflow counting standard, E1049 was published. There are various method of
Rainflow counting; main four methods are mentioned below:
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Hysteresis Filtering
Peak-Valley Filtering
Discretization
Four Point Counting Method
Figure 10: Hysteresis Filtering Method
Fatigue Strength Reduction Factor (kf):
This factor is used to account the corrosion, surface finish, size factor, notch effect and
various other surface irregularities. This is also referred in few international codes to
calculate the fatigue life such as ASME; which states that, Fatigue strength Reduction
factor is a stress intensification factor which accounts for the effect of a local structural
discontinuity (stress concentration) on the fatigue strength. It is the ratio of the fatigue
strength of a component without a discontinuity to the fatigue strength of that same
component with a discontinuity.
Fatigue Analysis Outputs:
Fatigue Life:
Fatigue life is the available life for the given fatigue analysis. The analysis contour
results shows the number of cycles until failure due to fatigue. Fatigue Life can be over
the whole model or on parts, surfaces, edges, and vertices. If loading is of constant
amplitude, this represents the number of cycles until the part will fail due to fatigue. If
loading is non-constant, this represents the number of loading blocks until failure.
Figure 11 shows the fatigue life of bracket, in this the maximum life shown is 1e6 is
corresponds to maximum cycle to failure in SN curves and 7.27e4 corresponds to the
region (red colour) of minimum life cycles.
Figure 11: Fatigue Life
Fatigue Damage:
Fatigue damage is defined as the design life divided by the available life. For Fatigue
Damage, values greater than 1 indicate failure before the design life is reached.
Figure 12: Fatigue Damage
Damage Accumulation (Cumulative Damage):
In this Miner’s Rule is applicable; which assumes that the total damage is simply the
linear summation of the partial damages:
Safety Factor:
Fatigue Safety Factor is a contour plot of the factor of safety with respect to a fatigue
failure at a given design life. For Fatigue Safety Factor, values less than one indicate
failure before the design life is reached and the maximum factor of safety displayed is
15.
Figure 13: Fatigue Safety Factor
Biaxiality Indication:
Biaxiality indication gives the user some idea of the stress state over the model and
how to interpret the results. Real world stress states are usually multiaxial. Biaxiality
indication is defined as the principal stress smaller in magnitude divided by the larger
principal stress with the principal stress nearest zero ignored. A biaxiality of zero
corresponds to uniaxial stress a value of -1 corresponds to pure shear, and a value of 1
corresponds to a pure biaxial state.
Figure 14:
Biaxiality Indication
Fatigue Sensitivity:
It shows how the fatigue results such as life, damage, or safety factors varies as a
function of the loading at the critical location on the model. The user may set the
number of fill points as well as the load variation limits. For example, the user may wish
to see the sensitivity of the model’s life if the FE load was 50% of the current load up to
150% of the current load.
Figure 15:
Fatigue Sensitivity
References:
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https://en.wikipedia.org/wiki/Fatigue_(material)
https://community.sw.siemens.com/
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