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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