chapter 2: mechanisms and major contributions to fatigue · chapter 2: mechanisms and major...

1 Hitachi-GE Nuclear Energy, Ltd.

Technical meeting on ‘Fatigue Assessment in Light Water Reactors for Long Term Operation : Good Practice and Lessons Learned’, 6th -8th July, 2016, Erlangen, Germany

Chapter 2: Mechanisms and major contributions to fatigue

Hitachi-GE Nuclear Energy, Ltd.

8th July, 2016

Presentation of draft document & discussion

Motoki Nakane

Japan


Contents

1. Purpose of Chapter 2 2. Table of contents of Chapter 2 3. Basic mechanism of fatigue 4. Categories of fatigue 5. Influence factor 6. Fatigue loading 7. Fracture mechanics approach to fatigue 8. Conclusions


Fatigue is one of major elements for time limited ageing analysis.

Fatigue is the structural deterioration that can occur as the result of repeated stress/strain cycles caused by fluctuating loads or temperatures.

The fatigue lives are influenced by a number of factors so that their effects need to be taken into account properly for evaluating structural integrity of the susceptible components

Purpose of Chapter 2 is to provide the importance basic mechanism and influence factors on the complex fatigue phenomenon in a way that laymen can clearly and easily understand

Purpose of Chapter 2


Table of contents of Chapter 2

2. Mechanisms and Major Contributions to Fatigue 2.1. Basic mechanism of fatigue 2.1.1. Stress/Strain versus Life Diagram 2.1.2. Initiation of fatigue crack and crack propagation

2.2. Categories of fatigue 2.2.1. High cycle fatigue 2.2.2. Lower cycle fatigue

2.3. Influence factor 2.3.1. Mean stress effects 2.3.2. Stress concentration effects 2.3.3. Size effects 2.3.4. Surface condition 2.3.5. Environmental effects/corrosion fatigue

2.4. Fatigue loading 2.4.1. Vibration fatigue 2.4.2. Thermal fatigue 2.4.3. Environmental fatigue (in LWR)

2.5. The fracture mechanics approach to fatigue


2.1 Basic mechanism of fatigue

Very fundamental characteristic and mechanism of fatigue are explained, such as S-N curve, classification by fatigue crack initiation and propagation

100

150

200

250

300

350

400

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09

Stre

ss a

mp

litu

de

(MP

a)

200

300

100

400

104 105 106 108107 109103

Number of cycles to failure (cycle)

Fatigue strength

Fatigue life

S-N curve

Crack propagate

direction

Stage

Ⅰ StageⅡ

Final fractureⅡa Ⅱb Ⅱc

Cyclic max. principle stress direction

Striation

Surf

ace

Surf

ace

Ext

rusi

on

Slip

ba

nd

‥

Extrusion

IntrusionInitiation of fatigue crack

Ma

in s

lip s

urf

ace

Pe

rsis

ten

t sl

ipb

an

d

Fatigue Crack

Followings are mainly presented in Sec. 2.1 - Fatigue can be occurred even if elastic stress region - Maintaining the stress of the component much lower than

fatigue limit or target stress amplitude in the fatigue design

Time

Stress (or strain)

0

Stress amplitude:

σa

Mic

ros

co

pic

c

on

ve

xo-

co

nca

ve


2.2.1 Categories of Fatigue(HCF)

This section describes two categories of fatigue, high cycle fatigue(HCF) and low cycle fatigue(LCF)

HCF is; - a cause of a large number of the fatigue failures in the NPPs - associated with high speed rotating or reciprocating components,

vibrations, local thermal cycling due to hot and cold fluid mixing - concerned with low amplitude, elastic stress, and numbers of

cycles in over the millions

Important design concept of high cycle fatigue is fatigue limit

HCF failures generally occur rapidly and without warning since cracks can only be seen almost the end of fatigue life


2.2.3 Categories of Fatigue(LCF)

LCF is; - occurred stress concentration part such as notch, fillet, etc. - taken into account in the reactor coolant system component

design of the cumulative combined effects of reactor coolant system pressure and temperature design analysis

- characterized in terms of cyclic local strain range rather than stress, and the number of cycles is less than about 104 to 105.

LCF design also commonly uses the concept of linear cumulative damage, "Miner's Law," to estimate fatigue damage associated with cycling at different amplitudes

The total strain range Δεt can be described as sum of the Baskin’s law and Coffin’s law as Δεt = Ce Nf

-a ＋ Cp Nf –b

Coffin’s law : Δεp = Cp Nf –b Baskin’s law : Δεe = Ce Nf

–a

Δεp : plastic strain range Ce , Cp : coefficient

Δεt= Δεe＋Δεp


2.2.2 Fatigue penalty factor, Ke

Sa = Ke . Se , e

ep

eε

εK 　

εep : strain derived from e-p analysis, εe : strain derived from elastic analysis

Basically, the designer doesn't perform e-p analysis to determine the local strain, and the stress obtained from elastic analysis is compared to S-N curve expressed by factitious stress

International codes and standard prescribe simplified e-p analysis method that evaluates alternating e-p stress Sa by increasing stress amplitude Se calculated by elastic analysis by multiplying fatigue penalty factor Ke


2.3.1 Influence factor (Mean stress)

Time

Str

ess

(Str

ain

)

σmin

σm

σmax

σa

σm：Mean stress

0

σy

A

σw0

Mean stress

σyB

C

DE

F

G

σy：Yield stress

σB：Tensile stress

σwa

σm：Mean stress

σw0：Fatigue limit ofsmooth specimen

σwa：Fatigue limit under mean stress σm

①

②Str

ess

am

plit

ude

σBσm0

σwa =σw0(1-σm/σB)

：Modified Goodman diagram

(Note: Area of ADFC is design range)

：Max. or min. stress which does not exceed yield stress

Illustration of mean stress Fatigue limit diagram

The mean stress is covered as one of the most important influence factor to reduce fatigue strength of the materials

For example, in the piping system, internal pressure with pulsation is regarded as combination of stresses of constant internal pressure (mean stress) and its fluctuations.

Though several prediction equations to estimate the relationship between the mean stress and the fatigue limit are proposed, Modified Goodman diagram is introduced


2.3.2 Influence factor (Stress concentration factor: SCF)

P P

σmax

a

2b

σ0

0

max

σ

σα

wn

w0

σ

σβ

stress concentration factor α

Many components has discontinuity portion, e.g., key groove, fillet, notch, etc., and nuclear power plant history shows that a lot of fatigue failures initiate at such a notched part of component.

σw0 is the fatigue limit for smooth specimen

Fatigue strength reduction factor vs. stress concentration factor※

In terms of stress concentration, welds regions are also object of concern in pressure vessels and piping.

This subsection provides basic concept of SCF α and difference between SCF α and fatigue strength reduction factor β.

Fatigue strength reduction factor β σwn is the fatigue limit for notched specimen

※Ishibashi, T., Prevention of metallic fatigue failure and fracture, Yokendo, p.53 (1969）


σmax

MM

: stress gradient

Stress gradient of large and small smooth specimen Diameter (mm)

En26 steel

En36 steel

0.37% C steel

0.07% C steel

10 20 30 400100

200

300

400

500

600

700

Fat

igue

lim

it (

MPa)

Compared with small specimen, stress gradient of large specimen is small and this leads to the fact that the fatigue strength of larger specimen is much lower than that of smaller specimen

2.3.3 Influence factor (Size effect)

For statistical reason, when the size of component becomes larger, the risk volume is also getting bigger, and these risk volume expansion brings reduction of fatigue strength

Fatigue limit derived from tension/compression test does not depend on the size of the specimen, so that in practically, these fatigue data can be used for fatigue evaluation

Fatigue limit vs. diameter of specimen※

※Heywood, R.B., Design against Fatigue, (1962), Chapman and Hall, London.


2.3.4 Influence factor (Surface condition)

Fatigue strength vs. Vickers hardness※

Surface condition is one of the significant factors to the fatigue strength of component since most of the fatigue crack initiated from the surface of the materials

The fatigue limit correlated with the hardness of the material so that the fatigue strength can be improved by enhancing the hardness of component surface

Asperity of surface plays a same role of notch effect on fatigue strength so that surface smoothing is effective method to prevent fatigue failure

※Nishijima, S., Statistical Analysis of Fatigue Test Data, Materials, The Society of Materials Science, Japan, Vol.29, No.316, pp.24-29(1980).


2.3 5 Influence factor (Environmental effects/corrosion fatigue)

It is well known that the fatigue strength in air is reduced by high temperature

- Fatigue limit of some materials disappear in the high temperature region

- The difference between fatigue characteristic of RT and high temperature is that the former depends only on the number of cycles, but the later also depends on the time

The reduction of fatigue strength by temperature is practically not serious problems because temperature effect on fatigue is already enough considered in the design stage

In many international codes and standards, fatigue strength in the high temperature is calculated by multiplying the ratio of Young’s modulus of high temperature to RT to fatigue strength of RT


2.3.5 Influence factor (Environmental effects/corrosion fatigue)

The surface of component is roughened by corrosion and induced stress concentration. As a result, the surface deterioration reduces the fatigue strength

- The corrosion fatigue failure can not generally be assessed by only superimposing the influence of cyclic loading and corrosion

- Predicted fatigue lives for corrosive materials are much lower than the estimated lives by considering only the effect of SCF.

Prevention or mitigation of corrosion is very significant to maintain the fatigue life of the component by following point

- In a certain material, corrosion fatigue may not have fatigue limit even if the material has the fatigue limit in air.


2.4.1 Fatigue loading(Vibration fatigue)

Vibratory fatigue is one of the main mechanical fatigue elements in NPPs in all ages

For example, the failures would occurs in small-diameter piping system mainly at weldolets and socket by the high-cycle mechanical fatigue

Following main contributing factors for mechanical vibration fatigue are introduced for attention

- Pump-induced pressure pulsations occurring at frequencies, multiple of the pump speed.

- Cavitation which occurs when the fluid pressure approaches its vapour pressure. The collapse of the cavities on a solid surface removes material by mechanical erosion, damaging piping and other components.

- Flashing that occurs when the temperature of water is higher than its saturation temperature at a given pressure and the water flashes into steam


2.4.2 Fatigue loading(Thermal fatigue)

When the thermal cycle is introduced in the components, thermal stresses occur by constraining the component’s expansion or contraction resulting from temperature changes.

The fatigue analysis of these components used to considered only the design basis transients but not phenomena such as thermal stratification present in the surge and spray lines, and thermal cycling present in the branch lines; these phenomena were discovered after the plants were placed in operation

Thermal fatigue is the major ageing mechanism for surge, spray and branch lines and their nozzles that are subject to thermal stratification, thermal shock, turbulent penetration, and thermal cycling including during power manoeuvring, plant start-up/shutdown.


2.4.3 Fatigue loading(Environmental fatigue:EF)

In the last two decades, EF in LWR has been actively studied because it was found that a LWR environment significantly accelerates the fatigue life of the materials

- Fen is defined by Fen = Nair/ Nwater, where Nair is number of cycles in air,

at R.T, Nwater is fatigue life number of cycles in LWR, at temperature.

According to experimental data, the fatigue life in a LWR environment is affected by not only strain amplitude but also strain rate, DO content, temperature and material sulphur content and so on.

Some codes and standards or guideline adopt to environmental fatigue multiplier ‘Fen’ to obtain the fatigue usage in the associated environment with design fatigue curve in air

Detail of environmentally assisted fatigue is discussed in Chap. 5.


2.5 Fracture mechanics approach to fatigue

mΚ)( Cda/dn

Fatigue life can be classified in two phases: fatigue crack initiation and fatigue crack propagation. Once a fatigue crack is initiated, it is important to evaluate fatigue strength of the material with a crack appropriately to manage the safety or residual life of the component

K : SIF range

At very low ΔK level, the material shows almost no crack growth. This level of ΔK indicates that the fatigue crack growth threshold is similar to the fatigue limit at the high cycle of the S-N curve.

The basis of the fracture mechanics is introduced in this section with explanation of stress intensity factor(SIF) and Paris Law

2a : crack length

C, m : material constant

aπσK SIF :

Paris Law :

s : nominal stress

σ

σ

aa

Crack

Crack tip

Stress intensity factor log (ΔK)

Cra

ck g

roth

rate

log(

da/

dN

)

1

m

ΔKth

When crack length can be detected or estimated in the actual component, it is possible to predict the residual fatigue life

Kth SIF log(K)

Cra

ck g

row

th r

ate

log(

da

/dn

)

s

s


Conclusions

Chapter 2 provides the importance basic mechanism on the complex fatigue phenomenon

The category of fatigue (HCF, LCF) and fatigue loading are also mentioned

The well-known influence factors on the fatigue strength such as mean stress, SCF, surface conditions, size effect, environmental/corrosion are presented

The crucial fatigue loadings based on lessons learned of NPPs history are described with some example of actual operation condition

The concept of the fracture mechanics is introduced to estimate fatigue strength of the materials with flaw


Thank you for your attention

chapter 2: mechanisms and major contributions to fatigue · chapter 2: mechanisms and major...

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