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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
2 Hitachi-GE Nuclear Energy, Ltd.
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
3 Hitachi-GE Nuclear Energy, Ltd.
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
4 Hitachi-GE Nuclear Energy, Ltd.
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
5 Hitachi-GE Nuclear Energy, Ltd.
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
6 Hitachi-GE Nuclear Energy, Ltd.
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
7 Hitachi-GE Nuclear Energy, Ltd.
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
8 Hitachi-GE Nuclear Energy, Ltd.
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
9 Hitachi-GE Nuclear Energy, Ltd.
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
10 Hitachi-GE Nuclear Energy, Ltd.
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)
11 Hitachi-GE Nuclear Energy, Ltd.
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.
12 Hitachi-GE Nuclear Energy, Ltd.
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).
13 Hitachi-GE Nuclear Energy, Ltd.
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
14 Hitachi-GE Nuclear Energy, Ltd.
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.
15 Hitachi-GE Nuclear Energy, Ltd.
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
16 Hitachi-GE Nuclear Energy, Ltd.
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.
17 Hitachi-GE Nuclear Energy, Ltd.
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.
18 Hitachi-GE Nuclear Energy, Ltd.
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
19 Hitachi-GE Nuclear Energy, Ltd.
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