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Fatigue & Fracture

mechanics


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Purely static loading is rarely observed in modern engineering components.

The majority of structures involve parts subjected to fluctuating or cyclic loads, often resulting

in fatigue-caused structural failure.

In fact, 80% to 95% of all structural failures occur through a fatigue mechanism.

For this reason, design analysts must address the implications of repeated loads, fluctuating

loads, and rapidly applied loads.

As a result, fatigue analysis has become an early driver in the product development processes of

a growing number of companies.

Introduction


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What is fatigue? Fatigue is the progressive and localized structural damage that occurs when a material is

subjected to cyclic loading.

The nominal maximum stress values are less than the ultimate tensile stress limit, and may

be below the yield stress limit of the material.

What causes fatigue failures? Fatigue failures always begin with a crack

Cracks and other imperfections are typically present in most materials (manufacturing, etc.)

and can propagate under cyclic loading.

New cracks can also be generated as a result of the fatigue process and typically initiate at

sites of stress concentrations (notches, etc.)

Eventually a crack will reach a critical size, and the structure will suddenly fracture


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Characteristics of fatigue

Fatigue life is influenced by a variety of factors, such as temperature, surface finish,

microstructure, presence of oxidizing or inert chemicals, residual stresses, contact (fretting), etc.

Fatigue is a stochastic process, often showing considerable scatter even in controlled

environments. The greater the applied stress range, the shorter the life.

Fatigue life scatter tends to increase for longer fatigue lives.

Damage is cumulative. Materials do not recover when rested.

Some materials exhibit a theoretical fatigue limit below which continued loading does not leadto structural failure.

The primary factors that contribute to fatigue failures include:

Number of load cycles experienced

Range of stress experienced in each load cycle

Mean stress experienced in each load cycle

Presence of local stress concentrations


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Factors that affect fatigue-life :

Cyclic stress state: Depending on the complexity of the geometry and the loading, stress

amplitude, mean stress, biaxiality, in-phase or out-of-phase shear stress, and load sequence,

Geometry: Notches and variation in cross section where fatigue cracks initiate.

Surface quality. Surface roughness cause microscopic stress concentrations that lower the fatigue

strength.

Material Type: Fatigue life, behaviour during cyclic loading, varies widely for different materials

Residual stresses: Decreases the fatigue strength.

Size and distribution of internal defects: Casting defects such as gas porosity,non-metallic

inclusions and shrinkage voids can significantly reduce fatigue strength

Direction of loading: For non-isotropic materials, fatigue strength depends on the direction of the

principal stress.

Grain size: For most metals, smaller grains yield longer fatigue lives,

Environment: Erosion, corrosion affect fatigue life. Corrosion fatigue is a problem encountered in

many aggressive environments.

Temperature: Extreme high or low temperatures can decrease fatigue strength.


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Terminology :

Mean Stress (Sm)

Alternating stress (Sa)

Stress Range (S)

Stress Amplitude (Sa)

Strain Range ()

Strain Amplitude

Endurance Limit (SFL) / Fatigue Limit (SFL) / Fatigue Strength (SFL)

Ultimate Strength (Su)

Stress Concentration Factor (Kt)

Fatigue Notch Factor (Kf)

Loading Factor (kL) Size Factor (ksize)

Surface Finish Factor (KSF)

Hysteresis Loop

Strain Life Curve

Cyclic Stress-Strain Curve Neuber's Rule


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Fatigue technologies :

Constant Amplitude

Variable Amplitude

Multi-axial

Probabilistic

Temperature

Welded Structures


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Fatigue technologies Contd..

Constant Amplitude: Used to make a simple and quick estimate of the likely fatigueperformance or durability. It is typically found in power transmission applications such as shafts,

gears etc. It is frequently used in the early stages of design to set the overall stress levels and to

select appropriate materials. Many design and testing specifications are written in terms of

constant amplitude loading.

Variable Amplitude: Based on the same concepts as constant amplitude fatigue analysis withthe addition of cycle counting and damage summation. In a variable amplitude loading history,

equivalent constant amplitude cycles must be identified. This is accomplished with a process called

rainflow counting. Once cycles have been identified, the fatigue damage for all of the cycles in the

loading history are summed with Miners linear damage rule to obtain the damage for the entire

loading history.

Multi-Axial: Multiaxial states of stress are very common in structures and components. Fatigue is

usually a surface phenomena so that the state of stress is biaxial because the stress normal to a

free surface is zero.


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Probabilistic approach: A much better tool to obtain estimates of the failure probability and toquantify the relative influence of variability and uncertainty in all of the input parameters so that

the life drivers can be identified. Simply use lower bound material properties to account for

variability. This simple minded approach ignores variability and uncertainties associated with

loading, analysis and geometric variables.

Temperature: Thermal mechanical fatigue (TMF) is caused by combined thermal and mechanicalloading where both the stresses and temperatures vary with time. This type of loading can be

more damaging by more than an order of magnitude compared with isothermal fatigue at the

maximum operating temperature. Material properties, mechanical strain range, strain rate,

temperature, and the phasing between temperature and mechanical strain all play a role in the

type of damage formed in the material. These types of loadings are most frequently found in start-up and shut-down cycles of high temperature components and equipment. Typically, design lives

are a few thousand cycles and involve significant plastic strains.

Welded Sturctures : Complex weld shapes and residual stresses require special fatigueconsiderations for welded structures. The heat from the welding process causes local tensile

residual stresses at the weld toe, geometric distortions which lead to additional bending stress and

changes in material properties near the weld. In addition the local geometry along the weld toe

varies along its length. Several approaches have been developed to analyze welded structures.


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There are three major fatigue life methods used in design and analysis:

1- Stress-Life Method / HCF

Often called the SN approach and is appropriate for long life situations. Stress based

Stresses always remain elastic even around stress concentrations.

The fatigue resistance is controlled by nominal stresses and material strength . Most of the live is consumed nucleating small microcracks

2- Strain-Life Method / LCF

Used for situations where plastic deformation occurs around the stress concentrations

Involves more detailed analysis of the plastic deformation at localized regions

where the stresses and strains are considered for life estimates.

3- Linear-Elastic Fracture Mechanics Method / FM

It assumes a crack is already present and detected. It is then employed to predict crack growth with respect to stress intensity.

Fracture mechanics, LEFM, is used to determine how long it will take a crack to grow to a critical

size.


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Stress Life Analysis


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Stress Life analysis :

The basis of the method is the materials S-N curve. Historically, these tests have been conductedin rotating bending. Today, it is often common to find test data for axial loading as well.

Used for long life situations (millions of cycles) where the stresses are elastic.

It is based on the fatigue limit or endurance limit of the material.

Material properties from polished specimens are modified for surface conditions and loadingconditions being analyzed.

Stress concentration factors are used to account for locally high stresses. An effective stress

concentration in fatigue loading is computed.

An estimate of the fatigue life is determined from the Goodman diagram. Fatigue lives are

assumed to be infinite in the safe region and a factor of safety is computed.

Stresses in the component are compared to

the fatigue limit of the material.


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What you need for Stress Life analysis

1. LoadingLoads can be entered as either the maximum and minimum values or as the alternating stress

and mean stress.

2. MaterialThe endurance limit/fatigue limit is determined from polished laboratory specimens. In the

absence of test data, it can be estimated from the ultimate strength of the material

The fatigue limit is approximated as one half of the tensile strength.

The fatigue strength at 1000 cycles is approximately 0.9 Su.

Stress life curves are characterized by a slope and an intercept.

Four material parameters are used to describe the materials stress life curve, Sf

', b, SFL

and NFL.


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3. Modifying Factors

Many factors effect the endurance limit of a mechanical part or structure. Modifications are made

to the endurance limit found in laboratory specimens. Some of the more important ones are

listed here; the surface finish factor, kSF, the loading factor, kL, and the size factor, ksize

Surface finish factor KSF

Fatigue limits are determined from small polished laboratory specimens. A surface finish

correction is made to the fatigue limit of the material to obtain an estimate of the fatigue limit of

the part in the condition it is actually being used.

Loading Factor KL

Historically, fatigue limits have been determined from simple bending tests where there is a stressgradient in the test specimen. A specimen loaded in tension will have a lower fatigue limit than one

loaded in bending. An empirical correction factor, called the loading factor, is used to make an

allowance for this effect.


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Size Factor KSIZE

Experimentally, larger parts have lower fatigue limits than smaller parts. Since the materials data isobtained from small specimens, a correction factor, called the size factor, is used for larger

diameters. For non-circular sections an effective diameter is computed. The effective diameter is

obtained by equating the volume of material subjected to 95% of the maximum stress to a round

bar in bending with the same highly stressed volume.

Once these correction factors are determined, the fatigue limit of the machine component in thecondition that it is being used in can be evaluated from the standard test specimen.

Effective diameter


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4. Stress Concentrations

All mechanical components are structures contain some form of stress concentrators which can

cause cracks to form.

The effective stress concentration/ the fatigue notch factor, Kf in fatigue is less than that

predicted by the stress concentration factor, Kt.

The variation between Kf and Kt is dependant on the size of the notch and strength of thematerial.

A material that is very sensitive to notches will have Kf equal to Kt. If the material is very

insensitive to notches, Kf will be close to 1. A notch sensitivity factor, q, is introduced to quantify

this sensitivity .


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5. Mean Stress Correction (Stress Life)

Tensile mean stresses are known to reduce the fatigue strength of a component. Compressive

mean stresses increase the performance and are frequently used to increase the fatiguestrength of a manufactured part. The most common method for accounting for mean stresses

is the Goodman Diagram.

Safety Factor

The safety factor represents how much you have underestimated the strength of the

material in order to ensure a safe design with a life equal to the fatigue limit.

Two stresses, alternating and mean are needed to calculate fatigue lives.


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Strain Life method/LCF


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Although most engineering structures and components are designed such that the nominal

stresses remain elastic, local stress concentrations often cause plastic strains to develop in

regions around them.

Fatigue damage is dependant on the local plastic strains around stress concentrators.

The strain resistance of the material is a better measure of the fatigue performance than the

stress resistance.

The strain-life method assumes that the smooth specimens tested in strain control simulate

fatigue damage in local region around the stress concentration.

Use of the strain-life analysis method is limited to situations where crack nucleation and thegrowth of small microcracks consumes the majority of the service life.

Strain Life analysis :


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What you need for Strain Life analysis

1. LoadingLoads can be entered as either the maximum and minimum values or as the stress range and

mean stress

2. MaterialStrain controlled tests are always conducted in axial loading. Deflections are controlled and

converted into strain. The resulting forces are measured to compute the applied stress

The total strain that was controlled during the test is divided

into the elastic and plastic part. The elastic strain is

computed as the stress range divided by the elastic

modulus. Plastic strain is obtained by subtracting the elastic

strain from the total strain.


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Strain-life curves and cyclic stress-strain curves are needed for this analysis.

During the fatigue test the strain range,

, is controlled and the resulting

stabilized stress range, , is recorded

along with the cycles to failure

Each strain range tested will have a

corresponding stress range that is

measured. The cyclic stress strain

curve is a plot of all of this data.

Test data is then fit to a simple power function

to obtain the material constants; fatigue

ductility coefficient, 'f, fatigue ductility

exponent, c, fatigue strength coefficient, 'f,

and fatigue strength exponent, b.

Plastic strainElastic strain

Total strain

It characterizes the fatigue

behaviour of the material

Fatigue strength exponentFatigue strength

coefficient


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3. Surface Finish Effects

Fatigue cracks usually nucleate on the surface so that the condition of the surface plays a majorrole in the fatigue resistance of a component, but only at long lives. At short lives cyclic

plasticity dominates the behaviour of the material and surface finish is less important.

Surface finish effects are included in the analysis by

altering the slope of the elastic portion of the strain-life curve. The surface finish corrected slope is given by


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4. Stress Concentrations

The stress concentration, Kt or Kf, describes the elastic deformation around a notch. But in the

strain approach, the plastic strains must be determined. Neuber's rule is used to convert an

elastically computed stress or stain into the real stress or strain when plastic deformation occurs

Neubers rule state that

Replacing with amplitudes


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5. Mean Stress Correction (Strain Life)

Tensile mean stresses are known to reduce the fatigue strength of a component. Compressive

mean stresses increase the performance and are frequently used to increase the fatigue

strength of a manufactured part.

The Strain-life equation has been modified to account for mean stress effects. Morrow

suggested that the mean stress effect could be taken into considered by modifying the elastic

term in the strain-life equation by mean stress, m .

where

The Smith-Watson-Topper (SWT) parameter is used to account for the effect of mean

stresses in the strain approach. The major variables are the maximum stress, max, and

strain range, , of the stable hysteresis loop.


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Methodology for

LCF life analysis


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Most existing methods for fatigue assessment are based on elastic finite element analysis.

Repetitive plastic deformation is the main cause of low cycle fatigue failure. Therefore,Local Plastic Stress and Strain Analysis (LPSA) approach was selected for fatigue assessment.

This method takes into account only the local volume of material around the criticallocation that goes plastic.

The real state of stress and strain at this critical volume is a fundamental input into LPSAmethod.

These values can be obtained either from elastic-plastic FE analysis or from simple elasticFE analysis.

However, in the case of elastic FE analysis the elastic results must be recalculated andadapted to the real plastic (and therefore nonlinear) material behaviour.

The second essential input into LPSA method are coefficients defining fatigue behavior ofthe material. The values of these coefficients must be determined experimentally or taken

from the database.

Theoretical Background


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FEA Technique to assess LCF life

Two approaches were employed

1. First approach is based on the elastic finite element analysis. Fictive elastic results are

recalculated using Neubers rule and the equivalent energy method. Triaxial state of stress is

reduced using von Mises theory. Strain amplitude is calculated employing the cyclicdeformation curve.

2. Second approach is based on elastic-plastic FE analysis. Strain amplitude is determined

directly from the FE analysis by reducing the triaxial state of strain. Fatigue life was assessedusing uniaxial damage parameters.

Both approaches are compared and their applicability is discussed.


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Steps in FEA technique

Step1 : First, material testing have to be carried out in order to identify the cyclic and fatigue

properties of the material The values of these coefficients must be determined experimentally or

taken from the database.

Step2 : Then, FE analysis is performed. The results of the FE analysis are stress and strain components

ij and ij at the critical location. The real state of stress and strain can be obtained either fromelastic-plastic FE analysis or from simple elastic FE analysis.

Step3 : Results of the elastic FE analysis are just fictive (on account of the simplifying assumption of

linear material behaviour). The elastic results must be recalculated and adapted to the real plastic

(and therefore nonlinear) material behaviour.

Step4 : Strain amplitude is then calculated using cyclic deformation curve. By contrast, true strain

amplitude is the direct output of the elastic-plastic FE analysis.

Step5 : Using uniaxial damage parameters.

Step6: Cycle counting( Rain Flow Counting) and Mean stress correction.

Step7: linear Palmgren-Miner approach of damage cumulation.


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Step1

It characterizes the fatigue


E Youngs modulus of elasticity,K cyclic stress hardening coefficient,

n cyclic stress hardening exponent.

The values of these coefficients must be determined experimentally or taken from the database

it characterizes the cyclic


'f -- fatigue ductility coefficient,c -- fatigue ductility exponent,

'f --fatigue strength coefficient,

b -- fatigue strength exponent


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Step2

FE analysis is performed.

The results of the FE analysis are stress and strain components ij and ij at the critical

location.

In the case of elastic-plastic FE analysis, resulting values of stresses and strains are real.

Results of the elastic FE analysis are just fictive (on account of the simplifying assumption of

linear material behavior).

Reduction of the triaxial state of stress and strain

Uniaxial damage parameters were used to assess fatigue life. The fictive uniaxial equivalent

stress and strain was then used as an input to the uniaxial damage parameters


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Step3

Recalculation of the fictive elastic stresses (elastic FE analysis)

The elastic results must be recalculated and adapted to the real plastic (and therefore

nonlinear) material behaviour. Afterwards, equivalent stress and strain is calculated.

Only simple linear FE analysis can be performed and fictive elastic results can be recalculated

with respect to the nonlinear behavior behind the yield strength of the material.

Two techniques how to recalculate fictive elastic stresses are introduced.

The simplest and most commonly used is the Neubers rule.

Second technique that can be used is the equivalent energy method (Glinkas rule).


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Strain life Neubers Rule (Notch

fatigue)

=>

Nominal stress/strain, simply put, is stress/strain in an un-

notched component (or remote from the notch)

=> KT2 Se = KT2 E = eq-1

Also, and are related as per the plastic curve, as:

K' = cyclic strength coefficient,n = cyclic strain hardening exponent,

Equation 1 and 2 are solved iteratively for and . These values are

subsequently used for fatigue life calculations at the notch root.

eq-2

Step3


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Step4

Strain amplitude calculation

In the case of elastic FE analysis true stress amplitude has to be calculated first.

Fictive elastic equivalent upper stress h,fic and mean stress m,fic have to be recalculated.

Then the true stress amplitude can be calculated as the difference between true upper stress

and true mean stress.

The strain amplitude can be calculated using the cyclic deformation curve which defines the

relationship between stress and strain during cyclic loading.

In the case of elastic-plastic analysis, the stress amplitude calculation is slightly more

complicated. A method how to determine the equivalent uniaxial strain amplitude had to be

developed.


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Step5

Damage parameters

Uniaxial damage parameters are used to evaluate the cycles to failure. Three damage

parameters were used

It can be observed that the fatigue life prediction based on linear elastic FE analysis is significantly

more conservative in comparison with the prediction based on elastic-plastic FE analysis.

elastic-plastic FE analysis true strain amplitude is the direct output of the FEA. For this reason, thefatigue assessment based on the elastic-plastic FE analysis is considered to correspond better

with reality.

Morrows Hypothesis

SWT Hypothesis

S 6


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Cycle counting & Mean stress correction

Each flight cycle contains many sub cycles, which means that the stress changes direction. Every

cycle causes damage on the structure and cycle counting is done by using the Rain-Flow-Counting

(RFC) principle.

The principles of RFC are based on the facts that the largest stress range causes most damage.

Results from the prior Maximum principal strain method are used as data in these calculations.

The first step in the RFC is to rearrange the stresses in order to set the largest stress as initialstress.

The largest stress is also put in the end of the sequence which result in maximum stress in the

start and the end of the plot. The measured points that are not turning points are removed since

they do not affect the number of cycles. The remaining stresses are now arranged as in Figure 11

and adapted for RFC to be counted. All cycles are set up in order with the smallest cycle first andthe largest in the end. Every cycle has a value of its maximum and minimum stress which results in

a mean stress

Initial stress plot Simplified curve Final RFC curve with remaining sub cycles

Step6


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When a material is exposed to stresses, not only the range of these affect the LCF life, but also

the mean value of them. The remaining stresses from RFC have been transformed to a uniaxialstress state, and when performing LCF calculations from these, the mean stress influence must

be considered. Mean stress is characterised by its R-value according to the following equation

The Walker hypothesis transforms material parameters from a certain R-value to an

arbitrary level. The correction on life from the Walker hypothesis is calculated from

Where R=0 is the strain range from material testing and R0 is the strain range of the

analysis with a certain R value. The walker exponent, m, is a material constant, usually

with a value between 0.2 and 0.7


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Step7Cumulative damage

Life calculations are carried out using a strain-life method assuming that the response from

loading is strain dependent.

This method do not take into consideration that the temperature of the material is not constant.

Hence, material data from different temperatures is therefore used to correct this during the

calculations.

For every node in the FE model, the life will be computed for three temperatures: the highest, the

lowest and the average temperature.

The case giving the lowest life value for an extracted cycle will be used and set as hypothetical

life. Each cycle in a loading sequence gives more or less damage.

The total sum of the damage values gives the total damage, called the cumulative fatigue

damage, according to the Palmgren-Miner rule


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Cumulative

Fatigue Damage


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Damage tolerance

Variable amplitude fatigue analysis is based on the same concepts as constant amplitude

fatigue analysis with the addition of cycle counting and damage summation. In a variable

amplitude loading history, equivalent constant amplitude cycles must be identified. This is

accomplished with a process called rainflow counting. Once cycles have been identified, the

fatigue damage for all of the cycles in the loading history are summed with Miners linear

damage rule to obtain the damage for the entire loading history

Rain flow counting


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Once individual cycles have been identified by rainflow counting the fatigue damage for each cycle mustbe summed. Consider a simple loading sequence consisting of nH high amplitude cycles of SH and nL low

amplitude cycles of SL. The corresponding fatigue lives for these two stress levels are denoted Nf H and

Nf L.

A linear damage accumulation rule such as Miner's Rule simply states that if you use up half of the fatiguelife at the one stress level you have half of the life remaining at any other stress level. This may be

mathematically stated as

Fatigue damage for an individual cycle is the recriprical of the fatigue life, Nf.

Fatigue lives for a cycle are computed using constant amplitude methods with theappropriate stress or strain ranges, mean stresses and material properties. Damage

is then summed for all cycles in the loading history.


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Thermo Mechanical Fatigue


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Thermo Mechanical Fatigue (TMF) is a variation of mechanical fatigue of materials where heating and coolingcycles are applied to a test material additional to a mechanical cyclic loading. The temperature cycles have -

in most cases - the same frequency as the loading cycles, but have different phase shifts.

If the phase shift is =0 the TMF tests are called in-phase tests, i. e. a tensile force is applied to the specimen

while heating is done. If the phase shift is =180 the TMF test are called out-of-phase tests, i. e. the sample is

cooled while in tension. For special testing parameters the phase shift can be applied between 360 > > 0,

to fit the real requirements for the tested material in later application fields

Inroduction

TMF testing is mainly done, to determine the total lifetime of technical components (e. g. turbine blades of

aeroplane engines (jet engines) and gas turbines) previous to the technical implementation of that part. The

material is tested with parameters (i. e. given temperature range, given maximum forces or stresses, coolingrates, phase shifts, etc.) that resemble the later usage profile of that material. So it is made sure, that the

material can withstand the later technical requirements. The TMF test results are used (among other test

results) to determine the total lifetime of a part as well as maintenance intervals for aeroplanes.

Comparison of TMF Tests

TMF tests need to be done, because the results cannot be predicted from isothermal mechanical fatigue tests.

Many materials undergo a recovery process at high temperatures, and some material coatings have a ductile

to brittle transition in the temperature range, that affect the total lifetime of a sample a lot. TMF test results

cannot be compared with other TMF results either, if one of the testing parameter differs, like e. g.

temperature range, cooling rate, applied forces or stresses, phase shift.

Application


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Thermo-mechanical fatigue (short TMF) is the overlay of a cyclical mechanical loading, that leads to fatigue of a

material, with a cyclical thermal loading. Thermo-mechanical fatigue is an important point that needs to be

considered, when constructing turbine engines or gas turbines

Failure Mechanisms

There are three mechanisms acting in thermo-mechanical fatigue

Each factor has more or less of an effect depending on the parameters of loading. In phase (IP) thermo-mechanicalloading (when the temperature and load increase at the same time) is dominated by creep. The combination of

high temperature and high stress is the ideal condition for creep. The heated material flows more easily in tension,

but cools and stiffens under compression. Out of phase (OP) thermo-mechanical loading is dominated by the

effects of oxidation and fatigue. Oxidation weakens the surface of the material, creating flaws and seeds for crack

propagation. As the crack propagates, the newly exposed crack surface then oxidizes, weakening the material

further and enabling the crack to extend. A third case occurs in OP TMF loading when the stress difference is muchgreater than the temperature difference. Fatigue alone is the driving cause of failure in this case, causing the

material to fail before oxidation can have much of an effect.

TMF still is not fully understood. There are many different models to attempt to predict the behavior and life of

materials undergoing TMF loading. The two models presented below take different approaches.


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Models of Thermo-Mechanical Fatigue

There are many different models that have been developed in an attempt to understand and explain TMF. This

page will address the two broadest approaches, constitutive and phenomenological models. Constitutive modelsutilize the current understanding of the microstructure of materials and failure mechanisms. These models tend to

be more complex, as they try to incorporate everything we know about how the materials fail. These types of

models are becoming more popular recently as improved imaging technology has allowed for a better

understanding of failure mechanisms. Phenomenological models are based purely on the observed behavior of

materials. They treat the exact mechanism of failure as a sort of "black box". Temperature and loading conditions

are input, and the result is the fatigue life. These models try to fit some equation to match the trends foundbetween different inputs and outputs.

Damage Accumulation Model

The damage accumulation model is a constitutive model of TMF. It adds together the damage from the three

failure mechanisms of fatigue, creep, and oxidation.

where Nfis the fatigue life of the material, that is, the number of loading cycles until failure. The fatigue life foreach failure mechanism is calculated individually and combined to find the total fatigue life of the specimen.

The damage accumulation model is one of the most in-depth and accurate models for TMF. It accounts for the

effects of each failure mechanism.

The damage accumulation model is also one of the most complex models for TMF. There are several material

parameters that must be found through extensive testing

F ti


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FatigueThe life from fatigue is calculated for isothermal loading conditions. It is dominated by the strain

applied to the specimen

where Cand dare material constants found through isothermal testing. Note that this term does not account

for temperature effects. The effects of temperature are treated in the oxidation and creep terms.

Oxidation

The life from oxidation is affected by temperature and cycle time.

where

and

Parameters are found by comparing fatigue tests done in air and in an environment with no oxygen (vacuum or

argon). Under these testing conditions, it has been found that the effects of oxidation can reduce the fatigue life of a

specimen by a whole order of magnitude. Higher temperatures greatly increase the amount of damage from

environmental factors


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Creep

where

Strain-Rate Partitioning

Strain-rate partitioning is a phenomenological model of thermo-mechanical fatigue. It is based on

observed phenomenon instead of the failure mechanisms. This model deals only with inelastic strain and

ignores plastic strain completely. It accounts for different types of deformation and breaks strain into four

possible scenarios:

PP plastic in tension and compression

CP creep in tension and plastic in compression

PC plastic in tension and creep in compression

CC creep in tension and compression

The damage and life for each partition is calculated and combined in the model


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where

and N'pp etc, are found from variations of the equation

where A and C are material constants for individual loading.

Strain-Rate Partitioning is a much simpler model than the damage accumulation model. Because it breaks down

the loading into specific scenarios, it can account for different phases in loading.

The model is based on inelastic strain. This means that it does not work well with scenarios of low inelasticstrain, such as brittle materials or loading with very low strain. This model can be an oversimplification. Because

it fails to account for oxidation damage, it may overpredict specimen life in certain loading conditions.

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