GS-11-006
Fifth International Symposium on Cavitation (cav2003)
Osaka, Japan, November 1-4, 2003
CAVITATION EROSION IN MERCURY TARGET OF SPALLATION NEUTRON SOURCE
Masatoshi FUTAKAWA
JAERI/[email protected]
C. C. TSAI/ORNL
Yujiro IKEDA/JAERI
Takashi NAOE/Ibaraki Univ.
Hiroyuki KOGAWA/JAERI
Hitoshi SOYAMA/Tohoku Univ.
ABSTRUCT
A liquid-mercury target system for a MW-scale
spallation neutron source is being developed in the world.
Proton beam will be injected to the mercury target to induce
spallation reaction. The moment the proton beams bombard
the target, pressure waves will be generated in the mercury by
the thermally shocked heat deposition. Provided that the
negative pressure generates through its propagation in the
mercury target and causes cavitation in the mercury, there is
the possibility for the cavitation bubbles collapse to form
pitting damage on the interface between the mercury and the
target vessel wall. In order to estimate the pitting damage due
to high cycle impact up to 10 million, an off-line test was
performed by using Magnetic IMpact Testing Machine
(MIMTM). Additionally the obtained data were compared
with classical vibratory hone tests and the bubble dynamic
simulation was carried out to investigate the repeated
frequency effect. As a result, it is confirmed that the mean
depth erosion is predictable using a homologous line in the
steady state with mass loss independently of testing
machines and the incubation period is dependent on materials,
repeated frequency and imposed power or pressure.
INTRODUCTION
The Japan Atomic Energy Research Institute (JAERI) is
carrying out research and development on a Neutron Science
Project aiming at exploring basic researches such as materials
and life sciences and innovative nuclear technology such as
actinide transmutation with the Accelerator Driven System
(ADS) [1]. A MW-scale target can produce a high-intensity
neutron beam by the spallation reaction due to accelerated
protons impinging on the target material. A liquid-mercury
target system for the MW-scale target is being developed in
the world as taking into account the advantages of selfcirculating heat removal and neutron yield. Fig.1 shows a
schematic drawing of the liquid-mercury target structure
developed by JAERI. The proton beam with a 1 ms pulse
Shuichi ISHIKURA/JAERI
Hidefumi DATE/Tohoku-gakuin
duration is injected into the mercury through the beam
window at 25 Hz. The moment the proton beam hits the
target vessel, stress waves will be imposed on the beam
window and pressure waves will be generated in the mercury
by the thermally shocked heat deposition [2]. The pressure
waves travel from the mercury into the target vessel wall and
back again. Stress waves are excited by the pressure waves
propagating in the vessel wall. The resulting dynamic stress
distribution in the vessel becomes very complicated.
Provided that the negative pressure causes cavitation in the
mercury, the following collapse of the cavitation bubbles
generates microjets and/or shock waves forming pits on the
surface of the vessel wall. This cavitation erosion damage
accumulates on the surface of the vessel wall, compromising
the structural integrity and reducing the life of the vessel.
In JAERI, plane-strain-wave incident experiments have
been carried out using a modified SHPB, Split Hopkinson
Pressure Bar, in order to examine the impact response of the
liquid mercury and the impact damage at the interface
between the liquid mercury and the solid metal specimens[3].
Through a series of tests, the JAERI team found that the
solid surfaces in contact with the mercury were eroded by
pitting and suggested the possibility of pitting erosion in the
target vessel[4,5]. Following the SHPB off-line test, ORNL
team carried out the test at WNR facility in LANCE and
recognized the pitting damage in the cylindrical target vessel
[6]. From the above examinations, the pitting damage is
recognized as a new issue to decide the life of the target
vessel.
The SHPB test gives the quiet similar morphology of
the pitting to that observed in WNR on-beam test up to
hundred impact cycles[7]. However, the imposed number of
impacts is limited to ca 100 at maximum, because the SHPB
needs time to adjust for operation. The 100 cycles are not
enough to extrapolate the lifetime of candidate target structure
materials. The proton beams are injected into the target at 25
Hz for JSNS and at 60 Hz for SNS. The pitting damage at
1
high cycles over 10 millions should be evaluated to estimate
the lifetime of the target. The JAERI team, therefore, has
developed a novel device, MIMTM (Magnet IMpact Testing
Machine), to electromagnetically impose pulse pressure into
the mercury. The data on the pitting damage at the high cycle
impacts up to 10 million were given by the MIMTM. In this
paper, the pitting damage formation, repeated frequency
effect, power dependency and estimation of cavitation erosion
in the mercury target will be discussed.
surface hardening treatment: carburizing; Kolsterising [8], and
nitriding. The morphology and 3D-image of pits were
examined by a laser microscope ( Laser tech. LHD-15H) and
SEM. Mass change of button specimen was precisely
measured by a micro-balance (Chyo M1-20A). The eroded
area was evaluated digitally using an image analysis program.
15
Mercury
f100
Hg
Heavy water cooling
Vessel
Impact force
Plate specimen
Unit : mm
Beam window
Fig. 2 Mercury chamber in MIMTM
Blade distributor
100 mm
Proton beam
Fig.1 Schematic drawing of a MW-scale neutron
spallation target
EXPERIMENTAL
The MIMTM (Max. acc.: ca 300 G) was developed to
examine the pitting damage up to over 10 million cycles.
The MIMTM consists of the control unit, the amplifier of
magnet and the electrically driven pressure pulse actuator. A
short cylinder is filled with the mercury of ca 120cc. The
pressure pulse is repeatedly imposed at 1 Hz to 200 Hz to the
mercury through the circular plate contact with mercury,
which is driven by the actuator, as shown in Fig. 2. The
imposed pressure was precisely and quantitatively controlled
by changing the electric current for the magnet coils: i.e.
rising time, holding time, sine wave, rectangular wave,
repeated frequency, and amplitude of tensile or compressive
pressures. In particular, the tensile pressure; negative
pressure, is a key factor as the condition of the cavitation
formation. The imposed acceleration was measured by a
piezo-type accelerator and used as a controlled signal.
In the MIMTM, two types of specimens were used. One
is the plate specimen with a diameter of 100 mm and the
other is the button specimen with a diameter of 15 mm. The
surface of the specimens is in contact with mercury. In the
plate specimen, a sticky tape was used to mask and avoid
some areas from any pitting damage. The plate specimen was
divided into 6 regions and each region was exposed to
mercury separately for impact cycles variable up to 10
millions, in order to understand formation of the pitting
damage for each impact cycles. The button specimen is
screwed on the center of the strike plate, whose dimension is
the same as the plate specimen. The specimens are prepared
from 316SS materials (cold worked 20%) with and without
RESULTS
Pitting damage formation
(1) Mass loss
Mass loss was precisely measured from the button
specimens using a micro-balance. Figure 3 shows the
dependency of mass loss on the number of impact cycles. In
the case of 316SS, the mass loss increases slightly up to 106
impact cycles, and then jumps up at over 106 cycles. The
acceleration stage occurs between 106 and 107 cycles. That is,
a so-called incubation state is less than 106 cycles and a
steady state is more than 106 cycles. The mass loss of
Kolsterised one is much smaller than that of 316SS and does
not exhibit the acceleration stage even at more than 107
cycles.
In order to predict the pitting damage throughout the life
of target, it seems to be needed to evaluate the pitting
damage for the high cycle impact imposing up to 108 cycles
at least. In the case of the classical vibratory hone tests, the
repeated frequency is ca 20 kHz generally. The number of
cycles gets to be over 108 for 1.5 hours. Figure 4 shows the
relationship for mercury between MDE (Mean Depth of
Erosion) and the number of cycles, that is given from the
classical vibratory hone tests [9-12]. These data for each
material are replotted using the MDE normalized by that at
108 cycles, as shown in Fig.5. It is found out that the
normalized MDE is adequately plotted on the homologous
line given by the following equation:
LogMDE = ALogN + B ,
(1)
where, A=1.27 for mercury, B=f(materials, temperature,
pressure, etc.) and N is the number of cycles. The constant of
B, that is related with the incubation period, is strongly
dependent on the material surface and imposed pressure.
While, the A value is independent of materials and cavitation
intensity. This tendency has been confirmed in the case of
water cavitation erosion as well [13]. That is, the MDE in the
steady state is predictable by using Eq(1).
2
Mass loss ,g
10-2
316SS CW
Kolsterise
10-3
10-4
10-5
100 101 102 103 104 105 106 107 108
Number of cycles
Fig.3 Dependency of mass loss on number of cycles
Mean depth of erosion, mm
103
102
316SS ( 60W)
316SS (40W)
316SS (20W)
304SS RT
316SS RT
Mo-1/2Ti RT
T-111 RT
T-222 RT
CARBON STEEL RT
304SS 2600C
101
316SS 260oC
Mo-1/2Ti 260oC
T-111 260oC
T-222 260oC
CARBON STREEL 260oC
316SS CW
316SS Ann
100
107
108
109
1010
Number of cycles
Fig.4 MDE measured by vibratory hone
Normalized mean depth of erosion
MDE/MDE at 108
102
Log MDE = 1.27 Log N + B
316SS (60W)
316SS (40W)
316SS (20W)
304SS RT
316SS RT
Mo-1/2Ti RT
T-111 RT
T-222 RT
CARBON STEEL RT
101
304SS 260o C
100
316SS 260o C
Mo-1/2Ti 260o C
T-111 260o C
T-222 260o C
CARBON STEEL 260o C
316SS CW
316SS Ann
10-1 7
10
108
109
1010
Number of cycles
Fig.5 Normalized MDE
Mean depth of erosion, mm
The MDE in the MIMTM was evaluated from the data
of mass loss shown in Figure 3, and plotted together in the
log-log graph with the results obtained by the vertical SHPB
and the WNR with 0.4, 1.1 and 2.5 MW proton injection as
well as the data given by the vibratory hone [9-12], as shown
in Fig. 6. In Fig. 6, the lines given by Eq.(1) were drawn for
316SS and Kolsterised one in the MIMTM and 316SS in the
vertical SHPB. It is recognized in the case of 316SS for
MIMTM that the incubation period is present up to 106
cycles and after that the MDE increases with the number of
cycles as complying well with Eq. (1). The incubation period
is expanded up to 107 cycles by the surface hardening
treatment.
(2) Morphology
Figure 7 shows the pitting damage formation up to 107
cycles obtained from the disk specimens: the laser
microscope and 3-D images. The repeated frequency of
impact cycle is 20 Hz constant. The imposed acceleration
level is about 100 G (550W) that can reproduce the quite
similar morphology of pits observed in the WNR on-beam
tests [7]. The pitting damage is strongly dependent on the
number of cycles. It is found that the formation process of
the pitting damage is divided into 3 phases. Phase 1 (<104
cycles); the pitting damage up to 104 cycles looks to be
occupied by the individual isolated pits, the quite similar
morphology of pits was observed in the SHPB and WNR
tests. Phase 2 (105 to 106 cycles): as the number of cycles
increases to more than 105 cycles, the individual isolated pits
appear to be combined each other or overlapped and the
surface around pits is eroded by peeling out. Phase 3 (>106
cycles): the pitting damage spreads throughout the surface
and homogeneous erosion starts.
The trend of mass loss shown in Fig.3 is understandable
from the viewpoint of microstructure of damaged surfaces. In
the case of 316SS, original surface remains up to 105 cycles,
and over 106 impact cycles the original surface is hardly
observed and tiny holes with more than 10 mm in diameter
are present on the damaged surface after 107 cycles, as shown
in Fig.8. The formation of the tiny holes is associated with
the large mass.
Figure 9 shows the comparison of pitting damage
morphologies at 106 cycles between with surface hardening
treatment and without. It is unambiguously seen that the
damage is reduced dramatically by the Kolsterised surface
hardening treatment. In fact, the pitting damage of
Kolsterised ones was hardly observed up to 103 impact
cycles. The Kolsterised specimen exhibits little mass loss up
to 2x107 cycles. The individual isolated pits occupy damaged
surface in 106 impact cycles and overlapped and/or combined
pits are observed over 2x107 impact cycles, but no tiny holes
are recognized unlike 316SS.
In order to quantitatively understand the formation
behavior of the pitting damage, the image analysis was
carried out as illustrated in Fig. 10. The eroded area was
defined as the black parts distinguished from the black-white
image and the fraction of the eroded area to the observed area
103
102
316SS CW(MIMTM)
Kolsterise(MIMTM)
316SS(Kass. Amp.74mm)
316SS(Kass. Amp.47mm)
316SS(Kass. Amp.21mm)
Kolsterise(Pawel. Amp.25m)
316SS(V.SHPB 10in. Upper)
316SS(V.SHPB 10in. Lower)
Log MDE
= 1.27 Log N + B
Steady state
101
100
WNR
10-1
10-2
10-3
102
Incubation period
103
104
105
106
107
108
109 1010
Number of cycles
Fig.6 Relationship between MDE and number of cycles
3
Fraction of eroded area , Ae/A0
Pit formation
Micrograph
& 3D-image
E3
E4
102
100
101
100
10-1
Log MDE
= 1.27 Log N + B
10-1
10-2
10-2
316SS
MDE
Fraction
10-3
102
103
104
105
106
107
10-3
Mean depth of erosion, mm
was calculated. The fractions are plotted with the MDEs
in Fig. 11. Regardless of materials, the period in that the
fraction is less than 1 is equivalent to the incubation period
that is defined from the viewpoint of MDE, i.e. mass loss.
The locus of fraction appears to increase regularly with the
impact cycles.
10-4
109
108
Number of cycles , N
Fig.11 MDE & Fraction in 316SS
E5
E6
E7
Plate specimen
Fig.7 Pitting damage formation
107
Power and frequency effects
Figure 12 shows the power dependency of dynamic
responses measured by the accelerometer fixed at the actuator
of MIMTM. The power supplied to the MIMTM was varied
from 300W to 550W. At 560W, the high frequency
components are superimposed on the vibrational wave with
the period of some ms. On the other hand the high frequency
components are hardly observed at 300W. The high frequency
components seem to be related to the localized impacts due
to cavitation bubble collapse, that have high dense energy.
They were extracted through high pass filtering to estimate
the cavitation intensity. Fig. 13 shows the typical filtered
signal. The function of damage potential f was defined as the
following equation and calculated from the filtered signals:
10m
10mm
f=
Fig.8 Tiny hole
106
10mm
Fig.9 Comparison between 316ss and Kolsterised one
after one million shots
Before test
After test
Fig.10 Transformed to black & white image on pits
2
Úa
e
0
Ï
ae (t ) = Ì
a
(
t
)
- ath
Ó
†
(2)
(t)dt
a(t) £ ath
a(t) > ath
(3)
Here, the threshold ath for no damage was 59 m/s2. f in
Eq.(2) is associated with
† the accumulated energy for damage
due to localized impact. Fig.14 shows the relationship
between the fraction of eroded area at 105 cycles, the
normalized damage potential f/f 0 and the input power. Here,
f 0 is f at 550W and 25Hz. Since both the fraction and f/f 0
get to be nearly 0 at power lower than 300W, it is
understandable that the damage threshold appears to be
present at lower than 300W.
Fig. 15 shows the relationship between the fraction of
eroded area at 105 cycles and 550W, normalized damage
potential f/f 0 and the repeated frequency. The fraction
decreases with the increase of frequency in the experimental
frequency range. The fraction exhibits the similar trend on the
frequency with f/f 0. Fig.16 shows the relationship between
the fraction and f/f 0 . f/f 0 is correspondent to the trend of
the fraction; damage, for damage and frequency. Therefore, it
4
Fraction of eroded area , A e/A0
Response of acceleration , m/s 2
can be said that f/f 0.is a useful parameter to estimate the
damage.
3000
2000
1000
0
-1000
-2000
-3000
1
2
3
4
5
6
7
8
Time , mSec
Fig.12 Measured acc. signal at 25Hz and 550W
0.5
Liquid
2000
s : Surface tension
Pv:Vapor pressure
h :Viscosity
r: Density
g: Ratio of specific heat
1000
0
-1000
25 Hz
-2000
-3000
0
1
2
3
4
5
Time , mSec
6
7
1
8
0.8
0.6
0.2
0.4
0.2
Freq. 25Hz
400
500
Power , W
600
f/f0
0.4
300
0
700
P(t) = P0 + Pm sin(wt) .
0
1
1
0.8
0.8
0.6
f/f
0.6
0
0.4
0
0
20
40
60
0.4
550W
80
Frequency , Hz
Bubble
R
, (4)
(5)
†
†
Fraction of eroded area
f/f0
1
3g
ÈÊ
˘
˙
ˆ
˙˙ + 3 R˙ 2 = 1 ÍÁ P0 + 2s - PV ˜ÊÁ R0 ˆ˜ + PV - 2s - 4hR - P(t)˙
RR
2
r ÎË
R0
R
R
¯Ë R ¯
˚
Fig. 14 Relationship between fraction, f/f0 and power
0.2
0.9
DISCUSSION
In order to understand the frequency effect on pitting
damage formation, the bubble dynamic analysis was carried
out using the following equation derived by Plesset et
al.[14]:
1.6
1.4
1.2
1
200
0.8
Fig.17 Bubble dynamics simulation
0.6
0
100
0.7
f/f0
R0: Initial bubble radius
Fraction of eroded area
f/f0
0.8
0.6
P0: Hydrostatic pressure
Pm: Dynamic pressure
Fig.13 Filtered acc, signal
Fraction of eroded area , A e/A0
0.4
Fig.16 Relationship between fraction and f/f0.
3000
Fraction of eroded area , A /A
e
Frequency
Power
0.1
25 Hz
0
1
100
0.2
120
Fig.15 Relationship between fraction, f/f0 and frequency
Here, variables in Eqs. (4) and (5) are defined as shown in
Fig. 17. The properties of mercury at 300K were used for the
simulation using Eq.(4). Fig. 18 illustrates the time response
of bubble radius under the imposed impact with Pm=1MPa
and period T 0=w /2p=2ms.The bubble expands to ca 2x104
times and varnishes around 14 ms. Fig.19 shows the
relationship between the life time of bubble and the period of
imposed impact T 0. T 0 in the MIMTM is ca 2ms. The impact
pressure imposed to bubble is unknown and then Pm is varied
from 0.15MPa to 1.0 MPa. It is understandable from Fig.19
that the possibility that the bubbles remain between repeated
impacts is much higher in the cases of 100 Hz and 60Hz than
in 25 Hz. As a result, the residual bubbles might work as a
damper at 60 Hz or 100 Hz against the localized impact due
to cavity collapse and then the pitting damage is suppressed
by the damping effect of residual bubbles, as compared with
that at 25 Hz.
5
Bubble radius, R/R0
Input pressure , MPa
3 104
-1.5
2 104
-1
4
1 10
-0.5
Lifetime of residual bubble
0
0
2
4
6
8
10
12
Lifetime of residual bubble , mSec
Time , mSec
Fig.18 Dynamic response of bubble
0
14
50
1.0MPa
0.5MPa
0.15MPa
25Hz
40
30
20
60Hz
100Hz
10
0
0
2
4
6
T0 , mSec
8
10
number of cycles N. We carried out the numerical simulation
on the locus using random function[15] and derived the
following equation:
F=1-exp(C N) .
Here, C is dependent on material and power or pressure. This
equation is the similar to the empirical one to describe the
coverage of shot peening[16]. Fig.20 shows the fractions of
various materials and impact conditions. The loci of fractions
are adequately represented by using Eq.(5). Hereafter, the
incubation period is systematically defined as the period at
F=0.98. Fig.21 shows the relationship between the power
and the number of cycles in the incubation period estimated
using Eq.(5). It is clearly understandable that the number of
impact cycles is dependent on the power applied to the
mercury and the power threshold against the damage is
unambiguously present. The incubation period is prolonged
by the surface hardening treatment such as Kolsterising and
nitiriding.
Fig.22 shows the normalized power, the MDE and the
number of cycles, including data obtained by the WNR onbeam test. The power was normalized by 550 W in the
MIMTM and by 1.2 MW in the WNR, because the
morphology of the pitting damage at 550 W in the MIMTM
is equivalent to that at 1.2 MW in the WNR. It is found
from Fig. 21 that except for the 0.4 MW, the trend of the
acceptable number of pulses in the incubation periods Ni is
described by the following equation:
Fraction of eroded area ,A /Ao
e
Fig.19 Relationship between lifetime and
impact duration in bubble
1
0.1
316SS (MIMTM)
Calculated locus
Kol (MIMTM)
Calculated locus
316SS (VSHPB)
Calculated locus
Nitiriding (MIMTM)
Calculated locus
0.01
101 102 103 104 105 106 107 108 109
Number of cycles
Fig.20 Relationship between fraction of eroded area and
number of cycles in various materials and conditions
The incubation period is dependent on the power or
pressure of imposed impact. As shown in Fig.11, the
incubation period might be defined as the period in that the
fraction of eroded area is less than 1. In order to
systematically and quantitatively evaluate the incubation
period, we focused on the locus of fraction F against the
(5)
Log Ni = D – E Log Power
(6)
Here, D and E are constants in terms of materials and
environment. It was suggested from Fig.21 that E=3.8 in the
case of 316ss. If the acceptable number of pulses is known
from Eq.(6) with given power, the MDE at the certain
number of pulses might be estimated using Eq. (1). That is,
the formation of pitting damage is predictable by using
Eqs.(1) and (6), although it is still needed to explore in
detailed the relationship on the power between the off-line
and the on-beam tests. Postulated that the relationship
between the MDE and the residual strength of damaged
materials is given, the lifetime of the target associated with
the pitting damage might be predicted based on the diagram
illustrated in Fig.23.
CONCLUSION
In order to evaluate the cavitation erosion, that will be
caused by proton impinging against the mercury target, the
off-line test were performed by using the MIMTM, which
gives the quite similar morphology of the cavitation erosion
to that observed in the WNR on-beam test. The MDEs due to
cavitation erosion obtained in the MIMTM were compared
with classical vibratory hone tests and the lifetime of target
resulted from cavitation erosion was discussed. The results
are summarized as follows:
6
1. In the results of 3166SS by the MIMTM , the pitting
damage formation up to 10 million is divided into 3
phases: phase 1, isolate individual pits are formed up to
104 cycles; phase 2, pits are combined and overlapped and
the fraction of eroded area gets to be nearly 1 between 105
and 106 cycles, and; phase 3, homogeneous erosion with
mass loss starts between 106 and 107 cycles.
2. The pitting damage can be characterized in two steps, an
incubation period and a steady state erosion where mass
loss scales with the number of cycles to approximately the
1.27 power for mercury.
3. The length of the incubation period is primarily a function
of the material and the intensity of the power or pressure.
The threshold of power against the cavitation erosion is
present. The semi-empirical equation was derived as a
function of given power to estimate the incubation period.
4. The results of 2. and 3. provide a simple concept for
evaluating the cavitation erosion against different materials
and beam power.
5. The damage potential defined by high-frequency
acceleration signals related with localized impact by cavity
collapse is predictable for the cavitation erosion and might
be applicable for a diagnostic monitoring system in the
target.
Power , W
100
105
106
107
108
109
1010
Number of cycles (f=0.98)
Fig.21 Relationship between power and number of
pulse cycles in the incubation period.
Normalized power ,P/P ref
10
ACKNOWLEDGEMENTS
The authors would like to thank Emeritus Prof.
Watanabe of JAERI for his fruitful advices and
encouragement to this research work, Dr J.R. Haines and Mr
B. Riemer of ORNL for supplying specimens, Mr Suzuki of
JAERI for polishing specimens, Dr Kurata of JAERI for
SEM observation, and Messrs. T. Koyama and J. Yamamo
of students in Ibaraki Univ. for experiments.
REFERENCES
[1] Planning Division for Neutron Science (1999),
Proceeding of the 3rd workshop on neutron science project
–Science and technology in the 21st century opened by
intense spallation neutron source-, JAERI-Conf 99-003.
[2] Futakawa M., Kikuchi K., Conrad H., Stechemesser H.
(2000), Pressure and stress waves in a spallation neutron
source mercury target generated by high-power proton pulses,
Nucl. Inst. Meth. in Phys. Res. A, 439 pp.1-7.
[3] Futakawa M., Kogawa H. and Hino R. (2000),
Measurement of dynamic response of liquid metal subjected
to uniaxial strain wave, J. Phys. IV France 10 Pr9-237-242.
[4] Futakawa M., Kogawa H., Midorikawa R., Hino R., Date
H. Takeishi H. (2001), Impact erosion on interface between
solid and liquid metals, Proc. the 4th Int. Symp. Imp. Eng.,
339-344.
[5] Futakawa M., Kogawa H., Hino R., Date H. and Takeishi
H., (2003) Erosion damage on solid boundaries in contact
with liquid metals by impulsive pressure injection, Int. J.
Imp. Eng. 28-2, pp.123-135.
[6] Riemer B. et al, (2002), Int. Workshop, Spal. Mats.
Tech.-5, Charleston, South Carolina.
[7]Futakawa M., Kogawa H., Tsai C.C., Ishikura S. Ikeda Y.,
316SS (MIMTM)
N_Plasma (MIMTM)
Kol (MIMTM)
1000
316Ss (MIMTM)
N_Plasma (MIMTM)
Kol (MIMTM)
316SS (WNR)
2.5 MW
1
1.2MW
0.4 MW
0.1
3
10
4
10
5
10
10
6
7
10
10
8
9
10
10
10
Number of cycles
Fig.22 Relationship between normalized power
and number of pulse cycles in the incubation period
Pitting-damage evaluation diagram
Log MDE=1.3 Log N + B
Design
criteria
Power
P0
Log Nc=1 = A - 3.8Log P
MDE
or
RS
Lifetime
Number of pulses
Incubation period is dependent on the materials and imposed power.
Log Nc=1 = A - 3.8Log P
Nc=1:Number
Nc=1:Number of pulses to end of incubation period
A : Material constant, Repeated frequency, etc.
After the fraction becomes nearly 100%, mass loss may start.
Mass loss MDE will be able to describe as follow
Log MDE =1.3 Log N + B
N: Number of pulses, B: f(material, power, etc.)
What is relationship between MDE and RS ?
The residual strength with pitting damage has to be evaluated from the viewpoint of
the fatigue and environment effects (mercury and irradiation, etc.)
Fig.23 Concept of cavitation erosion evaluation
in the mercury target
7
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