Content uploaded by Kumar Ankit
Author content
All content in this area was uploaded by Kumar Ankit
Content may be subject to copyright.
Communication
Remaining Creep Life Assessment
Techniques Based on Creep Cavitation
Modeling
KUMAR ANKIT
The boiler and its components are built with assumed
nominal design and reasonable life of operation about
two to three decades (one or two hundred thousand
hours). These units are generally replaced or life is
extended at the end of this period. Under normal
operating conditions, after the initial period of teething
troubles, the reliability of these units remains fairly
constant up to about two decades of normal operation.
The failure rate then increases as a result of their time-
dependent material damage. Further running of these
units may become uneconomical and dangerous in some
cases. In the following article, step-by-step methodology
to quantify creep cavitation based on statistical proba-
bility analysis and continuum damage mechanics has
been described. The concepts of creep cavity nucleation
have also been discussed with a special emphasis on the
need for development of a model based on creep cavity
growth kinetics.
DOI: 10.1007/s11661-009-9781-9
ÓThe Minerals, Metals & Materials Society and ASM
International 2009
The importance of creep cavitation and its role in
failure of critical components has been studied in the
past. However, there has been the absence of a quan-
titative creep cavitation model that can effectively
correlate creep cavities with the remaining life of the
components. Efforts have been made in the past, but
until now, the methods already developed have been
able to provide only qualitative guidelines, for two
primary reasons: first, due to the lack of understanding,
especially about the creep cavity nucleation, which is the
least understood phenomenon to date; and second, due
to the lack of a justifiable model that can correlate the
surface cavities observed in the replica taken from
in-service components to the creep cavitation occurring
in the bulk, which, obviously, is more representative of
the creep life of the component. In the model that I
discuss here, the creep cavitation has been beautifully
correlated to the remaining life using mathematical
expression based on statistical probability distribution.
[1]
A remarkable achievement of the model is that it
correlates the Aparameter, i.e., number fraction of
cavitated grain boundaries observed on the replica, with
the continuum damage variable D, which is the area
fraction of cavities present on the grain boundary facets.
The model makes use of the Kachanov–Rabotnov creep
damage theory and involves minimum mathematical
calculations. The methodology of calculation is quite
economical, as the only experimental input required is
the value of A
cr
(which is the critical value of the A
parameter at failure that can be easily determined by
performing a hot tensile testing), as compared to creep
testing and strain rate monitoring, which require expen-
sive setup of a creep machine and diligent software to
incessantly monitor strain rate, a process that is pres-
ently very expensive.
Creep cavity nucleation has been one of the least
understood phenomena to date. The creep cavity nucle-
ation rate affects the remaining life of a component.
There are some rate laws that are specific to components
and the grades of steel such as the relationship given in
Eq. [1] for the type IV cracking in weldments:
tr¼Brnexp Q=RTðÞ3½ ½1
where Bis a constant depending on the grade of steel,
Qis the activation energy specific to the grade of steel,
R is the universal gas constant, and Tis the operation
temperature in Kelvin. The extensive research work
and literature survey have revealed the following facts.
(1) The presence of any non metallic inclusion; simply
put, any region that can act as a stress concentra-
tor acts as initiators of creep cavities (Figure 1).
(2) In the absence of inclusions, the creep cavities gen-
erally nucleate at grain boundary triple points
(Figure 2).
(3) The creep cavities generally grow and get linked to
each other in the direction perpendicular to the
stress axis (Figure 3).
(4) The number of cavities per unit grain boundary
area linearly increases with creep exposed time.
(5) As the amount of applied stress increases, the rate
of creep cavitation increases exponentially.
(6) High-purity cast materials have the lowest nucle-
ation rates and highest rupture life.
(7) Increase in austenizing temperature leads to an
increase in nucleation rate and decrease in rupture
life.
(8) Grain size and type of second-phase particles such
as carbides found on the prior austenitic bound-
aries increase the susceptibility to cavitations espe-
cially M
2
C carbides and SAEs, i.e., surface-active
elements such as P and Sn (Figure 4).
The following are the steps for quantifying creep
cavitation.
(1) Measurement of the A parameter
(a) Divide entire replica (standard preparation as per
ECCC recommendations
[2]
) into at least 400 parts
by drawing reference lines parallel to the stress axis,
as shown in Figure 5. The replica can be viewed at
KUMAR ANKIT, Student of Master of Technology, is with the
Department of Metallurgical Engineering, Institute of Technology,
Banaras Hindu University, Varanasi, India. Contact e-mail: kumar.
ankit.met05@itbhu.ac.in
Manuscript submitted October 18, 2008.
Article published online February 25, 2009
METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 40A, MAY 2009—1013
a comfortable magnification so that creep cavities
are clearly visible. Because the Aparameter is a
ratio, the methodology rules out any ambiguity due
to choice of magnification provided the number of
reference lines is statistically high. The value 400
stated previously is given to ensure a minimum
level of accuracy in calculation (Figure 5).
(b) Calculate N
C
, the number of grain boundary lines
that are cavitated intersecting the reference lines.
(c) Calculate N
T
, the number of grain boundary lines
that intersect the reference lines.
(d) Aparameter = N
C
/N
T
.
(2) Measurement of the cavity cut probability (P)
(a) Prepare the microstructure from a destructive sam-
ple to expose the grain boundary facet. Isolate the
grain boundary facet having maximum cavitations.
(b) Draw a circle of area approximately equal to that
of the facet. The circle is to be drawn around the
facet shown subsequently.
Fig. 2—Creep cavity nucleating at grain boundary triple point.
Fig. 3—Growth of creep cavities perpendicular to stress axis.
Fig. 4—Cavity nucleating at the interface of MnS.
Fig. 5—Calculation of Aparameter.
Fig. 1—SEM showing cavity nucleation at nonmetallic inclusions in
the HAZ.
1014—VOLUME 40A, MAY 2009 METALLURGICAL AND MATERIALS TRANSACTIONS A
(c) Draw lines through the cavities from all possible
directions cutting the facet circle and cavity in the
facet plane, as shown in Figure 6.
(d) Isolate a cavity on the facet (all cavities assumed
to be identical on a facet).
(e) Calculate S
C,
the event when lines cut the cavity.
(f) Calculate S
T,
the event when a line is drawn
through the facet circle.
(g) P=S
C
/S
T
.
(3) Measurement of the continuum damage variable D
(a) Measurement of f,i.e., average number of cavi-
tated facets:
f¼A=P½2
(b) Measurement of x,i.e., average local cavity area
fraction on the facets:
x¼mr=RðÞ
2½3
where m= number of cavities on the most cavi-
tated facet (Figure 7), r= average radius of the
cavities, and R= radius of the circle drawn
around the facet.
(c) Measurement of continuum damage variable D:
D¼fx½4
(4) Determination of L using the A-D relationship
(a) Measure the value of the Aparameter at creep fail-
ure by performing a hot tensile test and interrupt-
ing the test just before the failure of the sample.
(b) Calculate the value of D
cr
from A
cr
.
(c) Determine (D/D
cr
) and (A/A
cr
).
(d) Put the values in the A-Drelation:
D=Dcr
ðÞ11D=Dcr
ðÞ
L
hi
¼A=Acr
ðÞ
2½5
(e) Calculate the value of Lfrom the preceding equa-
tion.
(f) L=n/(k– 1), where n= creep exponent for engi-
neering alloy (3 <n<10) and k=e
f
/(de
min
/dtÆt
f
).
(g) Calculate kas the value of nis known for the
given alloy.
(5) Determination of remaining creep life
The remaining life of the components is given by
1D=Dcr
ðÞ¼1t=tf
1=Lk½6
The following is a case study for verifying the
quantitative creep cavitation model for remaining life
assessment.
The material used for microstructural examinations
was a heat ABE of 18Cr-8Ni steel tubes taken from a
heat exchanger for the purpose of remaining creep life
assessment. The heat ABE showed a medium level of
creep rupture strength and ductility for nine heats. The
material was randomly sampled from a commercial
stock of the heat ABE tube. From the center of the wall
thickness, creep and creep rupture specimens were
machined longitudinally with a diameter of 6 mm and
a gage length of 30 mm (Figures 8and 9).
For creep testing, the temperature was maintained to
within ±4°C. The creep strain data were tabulated
along with hardness at the temperature of 650 °C and
stress of 61 MPa. The mode of failure observed was
transgranular creep fracture with wedge-type cracking
at the rphase/austenite interface.
The data in Table Iwere obtained after analyzing the
creep voids that were clearly seen in the microstructure.
The parameters such as the Aparameter, area fraction,
Fig. 6—Experiment to cut an idealized GB facet by a line from all
possible directions and positions.
[4]
Fig. 7—Grain boundary facet with mcavities on it and a circle
drawn around it.
[4]
Fig. 8—Sampling location of longitudinal test specimens.
METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 40A, MAY 2009—1015
and number density of creep voids were calculated as
discussed earlier.
As can be clearly seen from the trend of the
calculated values (area fraction, Aparameter, and
number density), the real damage begins just before
the tertiary stage of creep sets in; therefore, it becomes
important to model the tertiary stage, and that is where
Kachanov–Rabotnov damage mechanics can play an
important part.
The values of the material specific parameters such as
kand Lcan be easily calculated by knowing the power-
law creep exponent nand the minimum creep rate e
min
for the secondary stage of creep. The corresponding
values of kand L18Cr-8Ni steels are 29.9 and 0.13,
respectively (e
min
= 6.01 910
6
and n= 4). The fol-
lowing plot can be used to compute the value of the
minimum creep rate (Figure 10).
Suppose we are interested in calculating the remaining
life of the heat exchanger tube that has been in operation
for 8.5 years. The component has been subjected to
repeated cycles of overloading (operated at a higher
temperature and pressure, as prescribed by the stan-
dards, frequently occurring phenomena in power plant
components especially during the start-up cycles of
boilers and turbines) also accompanied by frequent
startups and shutdowns of the component. Also, the
components are subjected to cyclic stresses, so failure is
bound to occur at a faster rate, as expected. The
corresponding Aparameter for the specified time is
0.007. For determining the A
cr
, a hot tensile test may be
performed instead of a creep test (A
cr
= 0.642 and
t
r
= 100491.4 hours) or parallel obtained from some
other reliable sources such as the materials database.
For a creep life prediction on a commercial scale, a
database for A
cr
may be generated for common power
plant steels operating at specified stress and temperature
so that life estimation can be done readily.
On applying Eq. [5], the value of D/D
cr
obtained is
0.33, and finally, on substituting the value in Eq. [6], the
value of tobtained is 81,498.1 hours, i.e., a remaining
life of 18,993.3 hours, which is quite close to the
experimental value obtained by creep test.
It is a known fact that cavity growth has a greater
role in creep failure than cavity nucleation. Most of the
cavity nucleation occurs in primary and secondary
stages, and cavity growth occurs only when true
tertiary creep has set in. Therefore, it is important to
know the kinetics of creep crack growth in the tertiary
Fig. 9—Specimen for creep test.
Table I. Calculation of Parameters Required for Quantitative Creep Life Assessment
Temperature
(ºC)
Stress
(MPa)
Time
(hours)
Area Fraction of
Creep Voids (pct) A-Parameter
Number Density
(mm
2
)
650 61 40,180.0 0.001 0.014 5
61,920.0 0.007 0.021 17
80,120.0 0.007 0.082 19
100,491.4 0.060 0.642 100
0
0
5
10
15
20
Time
Creep Strain (%)
Creep Strain (%) Vs Time (hrs)
100000
18
2
1.4
0.3
0
50000 150000
Fig. 10—Creep curve of 18Cr-8Ni steel tube for heat exchanger.
Fig. 11—Scanning electron micrographs of the ruptured specimen
(gage portion).
1016—VOLUME 40A, MAY 2009 METALLURGICAL AND MATERIALS TRANSACTIONS A
regime, and that is where the role of CDM sets in. The
time at which the tertiary strain sets in can be assessed
by knowing the time necessary to cause Monkman–
Grant ductility t
MGD
, which is the time at which total
secondary creep ductility is exhausted.
[7]
This is numeri-
cally expressed as
tMGD ¼1k1ðÞ=k½
k½7
The model described seems to work quite well with
most of the power plant steels in which grain bound-
ary sliding is the dominant mechanism of creep failure.
The morphology of the creep cracks in such situations
Fig. 12—Nucleation of wedge crevices on triple junctions depending on slip directions occurring in the materials after the long-term creep service
(arrows show the slip directions).
METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 40A, MAY 2009—1017
is wedge type (Figure 11), and nucleation takes place
at grain boundary triple points.
[5]
The mechanism of
grain boundary sliding and nucleation can be easily
understood from Figure 12.
There are a number of techniques that are available
at present to predict the remaining life of in-service
components, both destructively as well as nondestruc-
tively. Out of these, prediction of remaining creep life
has been an area of interest, as the phenomenon of
creep is responsible for a majority of failures in power
plants. The step- by-step methodology described pre-
viously seems to be quite flexible and can be easily
incorporated into computer software such as MAT-
LAB. To begin with, replicas can be taken from
inspection sites followed by image processing of these
replicas using fast fourier transformations (FFTs), i.e.,
filtering the image. In case the replica taken is not very
clear, the concept of fuzzy logic can be incorporated.
The output obtained from image processing, such as
the Aparameter, interparticle spacing, and dislocation
density, can be fed into Eq. [6] and the remaining creep
life can be calculated accordingly. The operating
parameters such as the skin temperature of the
component and stress are known, so life estimation
can be done effectively and that too, non-destructively
which in itself is an added advantage. It does not
involve any creep tests which are time consuming and
expensive processes. The life assessment can be done
on-site within a few minutes after the replica has been
taken. Efforts are still on, to incorporate this method-
ology into more sophisticated computer software for
more accurate life estimation.
REFERENCES
1. R. Viswanathan: Damage Mechanisms and Life Assessment of High
Temperature Components, ASM, Metals Park, OH, 1989.
2. ECCC Recommendations, Residual Life and Microstructure, Euro-
pean Creep Collaborative Committee, ECCC, 2005, vol. 6 (1).
3. C.W. Marschall, C.E. Jaske, and B.S. Majumdar: Final Report
EPRI TR-101835, Electric Power Research Institute, Palo Alto,
CA, 1992.
4. S. Murakami, Y. Liu, and Y. Sugita: Int. J. Damage Mech., 1992,
vol. 1, pp. 172–90.
5. H.-T. Yao, F.-Z. Xuan, Z. Wang, and S.-T. Tu: Nucl. Eng. Des.,
2007, vol. 237 (18), pp. 1969–86.
6. Y.N. Rabotnov: Creep Problems in Structural Members, North
Holland, Amsterdam, 1969.
7. C. Phaniraj, B.K. Choudhary, B. Raj, and K. Bhanu Sankara Rao:
J. Mater. Sci., 2005, vol. 40, pp. 2561–64.
1018—VOLUME 40A, MAY 2009 METALLURGICAL AND MATERIALS TRANSACTIONS A