a finite element program for on-line life assessment

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Engineering Failure Analysis 16 (2009) 85–111

www.elsevier.com/locate/engfailanal

A finite element program for on-line life assessmentof critical plant components

M.K. Samal *, B.K. Dutta, S. Guin, H.S. Kushwaha

Reactor Safety Division, Bhabha Atomic Research Centre, Mumbai 400085, India

Received 21 May 2007; accepted 26 January 2008Available online 8 February 2008

Abstract

An on-line structural safety evaluation system (BOSSES) has been developed over the years at Bhabha AtomicResearch Centre (BARC), India, which is capable of assessing the damage due to creep and fatigue in critical plant com-ponents. The system acquires plant transients in real time and processes them to evaluate the stress, temperature and dam-age distribution in the components and provides information through a visual module. The aim of the paper is to brieflydescribe the details of the damage assessment methodology adopted by BOSSES with some case studies of real life plantcomponents.� 2008 Elsevier Ltd. All rights reserved.

Keywords: On-line monitoring; Creep and fatigue; Erosion–corrosion; Critical plant components

1. Introduction

The issue of remaining life prediction has attracted considerable attention in the power generation industry[1–11]. Integrity of important components is essential for operational safety, reliability and economic plantoperation. In the design, the life of a plant is estimated based on assumed process transients. However, becauseof conservatism in the design the actual lives of these plants are expected to be much more than the estimatedvalue. The sustained interest in the area of remaining life prediction arises from the need to avoid costly out-ages, safety considerations and the necessity to extend the component operation life beyond the original designlife [2]. Many of the structural components used in fossil power plant, nuclear industry and chemical processplants, are subjected to cyclic stresses due to the fluctuation of process transients. On the other hand compo-nents like steam pipes, superheater headers, turbine rotors, casings, etc., operate at elevated temperatures[1,2,6,7]. Cyclic stresses with a high mean stress at an elevated temperature lead to a damage mechanismdue to combined creep and fatigue. It is worth to note that among the various aging effects, fatigue, creep,

1350-6307/$ - see front matter � 2008 Elsevier Ltd. All rights reserved.

doi:10.1016/j.engfailanal.2008.01.007

* Corresponding author. Tel.: +91 22 25591523; fax: +91 22 25505151.E-mail addresses: [email protected], [email protected] (M.K. Samal).

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86 M.K. Samal et al. / Engineering Failure Analysis 16 (2009) 85–111

creep–fatigue interaction and creep–fatigue crack growth are commonly responsible for most of the failures invarious industrial components.

Several researchers have stressed the need to develop a life prediction methodology to address the variousaspects of failure mechanisms. Sakurai et al. [6] have presented the life assessment procedure of high temper-ature components of thermal power plants in Japan. Maekawa et al. [9] and Sakai et al. [12] have discussed theoperating data monitoring and fatigue evaluation system for Japanese Nuclear Power Plants (NPPs). Thedevelopment and implementation details of the French transient monitoring Fatiguemeter SYSFAC has beendescribed by Aufort et al. [5], Morilhat et al. [10] and Balley et al. [13]. FatiguePro, a fatigue monitoring systemdeveloped by EPRI, USA [14], has the additional features of on-line fatigue crack growth monitoring. Barto-nicek et al. [15] and Jovanovic and Verelst [16] have also discussed various issues related to fatigue and creepmonitoring of power plant components. An on-line creep–fatigue monitoring system (BOSSES) has beendeveloped over the years in Bhabha Atomic Research Centre, Mumbai, India. The system has many advan-tages over similar existing systems. The system is being currently used to monitor many critical nozzles andcomponents of heavy water plants and thermal power plants in India. A brief description of the theoreticalbackground of damage assessment methodology used in BOSSES is provided in Section 2. Section 3 describessome typical features of the program. Some case studies of components from heavy water plants and thermalpower plants are provided in Sections 4 and 5, respectively. In addition to the on-line deterministic damageassessment module, BOSSES also has a probabilistic module for calculating the on-line probability of failureof components due to various mechanisms such as creep, fatigue and erosion–corrosion, etc., and it isdescribed in Section 6.

2. Theoretical background

In recent years considerable progress has been made in research on the behaviour of defect-free structuresand structures containing defects at elevated temperature. Developments have been made both in structuralanalysis techniques and in methods for collecting relevant material data. For the assessment of defects in plantthat operates in the creep range under cyclic loadings, creep–fatigue interaction is the failure mechanism.Hence a prediction method for the accumulation of damage due to creep and fatigue throughout their lifetimeis important for remaining life assessment of components. The early approaches to high temperature lifeassessment describe methodologies that were based on defect-free assessment codes, i.e., ASME code caseN-47 (Now, it is known as Section-III, Subsection-NH) [17] and French RCC-MR [18], which have many sim-ilarities and are based on life time assessment of an un-cracked structures. The fracture mechanics based pro-cedures basically followed the low temperature assessment procedures such as R6 [19].

ASME code case N-47 was the first design code to formally embrace the concept of linear damage summa-tion as a method of predicting material failure at high temperature, consisting of a fatigue (Miner’s cycle sum-mation) component and a creep (Robinson’s creep time summation) component. The French code RCC-MRincorporates many of the concepts of ASME N-47, but with modified stress analysis procedures. The BritishR5 procedure [20] augments and replaces certain sections of RCC-MR and ASME N-47. But, it providesdesign and construction rules for mechanical components operating at high temperature. One advantage ofR5 approach is that a notional defect may be postulated and subsequent behaviour predicted for likely servicecycles. Together with the low temperature defect assessment procedure R6, it may be used in any of the threeways, i.e., safe life (no degradation of property), damage tolerant (life extension) and fail safe (leak beforebreak) of design. Recently API-579 code [21–24] has provided a detailed methodology for predicting damagedue to creep–fatigue interaction in components. The different techniques for evaluation of creep and fatiguedamage in components with and without defects are described in the following sections.

2.1. Evaluation of damage in defect-free components

According to the conventional method, when any component is subjected to cyclic loading under high tem-perature and pressure environment, failure is assumed to occur when the summation of damage fractions dueto fatigue and creep becomes unity. In this method, one calculates separately the damage due to the fatigueand creep and linear damage summation rule is used. Miner’s cycle summation is used to calculate fatigue

M.K. Samal et al. / Engineering Failure Analysis 16 (2009) 85–111 87

damage and Robinson time summation is used for creep [25]. The method is outlined in Fig. 1. Letr1,r2, . . . ,rn, are the maximum applied stress intensities for n1,n2, . . . ,nn number of cycles. S1,S2, . . . ,Sn arethe corresponding stress amplitudes. Corresponding to these stress amplitudes, N1,N2, . . . ,Nn are the allow-able cycles calculated from the S–N diagram (Fig. 2). The fractional damage due to fatigue is calculated as

Df ¼Xn

i¼1

ni

N i: ð1Þ

Similarly, rm1,rm2, . . . ,rmn are average values of equivalent stresses applied for hold times t1, t2, . . . , tn, respec-tively. Corresponding to these stresses, T1,T2, . . . ,Tn are the creep rupture lives calculated from the creep rup-ture time curve of the material for the given operating temperature (Fig. 3). The fractional damage due tocreep is calculated as

Dc ¼Xn

i¼1

ti

T i: ð2Þ

The creep rupture life of the material is expressed by the equation: T = Ar�v, where A and v are materialconstants.

2.1.1. R5 method

Here, linear damage summation rule is used. The component will fail if

Dtotal ¼Xn

k¼1

½ðDfÞ þ ðDcÞ� 6 Dallowable: ð3Þ

Assessment of damage due to creep and fatigue interaction (for defect free components)

Assessment of damage due to fatigue Assessment of damage due to creep

For defect free structures, evaluate fatiguedamage (S-N curve)

(ASME III-NH/ RCC-MR/ R5/ API-579)

For defect free structures, evaluate creep damage (creep-rupture curve)

(ASME III-NH/ RCC-MR/ R5/ API-579)

Combine damage due to creep and fatigue(ASME III-NH/ RCC-MR/ R5/ API-579)

Fig. 1. Flowchart for assessment of damage due to creep–fatigue interaction in defect-free components.

S

N

(Si, Ni)

Fig. 2. Schematic S–N curve of a material.

mσ

σ

T

( )mi i,T

temperature = constant

Fig. 3. Schematic stress rupture curve (due to creep) of a material.


2.1.2. API method

Here, the following rule is used:

Dtotal ¼Xn

k¼1

ðDfÞf þ ðDcÞfh i

6 Dallowable; ð4Þ

where f = 0.3 for carbon and low alloy steels and f = 0.5 for austenitic and high alloy steels.

2.2. Evaluation of damage in components with defect (fracture mechanics based methods)

Creep–fatigue interaction tends to be a low cycle phenomenon. Once a significant dwell time is included, ittakes a long tome to accomplish the 105 plus cycles needed to get into the high cycle regime. Consequently, lowcycle fatigue is commonly dominated by crack propagation, with crack initiation taking place early in the life.The flowchart for the assessment of damage by fracture mechanics based method for components with defectsis shown in Fig. 4. From the assumption that crack growth governs creep/fatigue damage accumulation, sev-eral research workers have developed theories based on tracing the process of a crack, growing by the twinmechanics of creep during dwell periods and by a Paris type law based on fracture mechanics during rapidcycling. This approach assumes that damage is represented by the crack depth a. The cyclic crack growthis then added to the creep crack growth during the dwell period (thold) to calculate the total growth per tran-sient as [26,27]:

dadN

��cycle

¼ dadN

��fatigue

þ dadN

��creep

� thold: ð5Þ

2.2.1. Crack growth rate due to fatigue

(a) R5 method: If conditions during the transient are in the linear static range, cyclic crack growth would becalculated using Paris’s law:

dadN

��fatigue

¼ CðDKeffÞf ; ð6Þ

where DKeff is an effective stress intensity range adjusted for crack closure

DKeff ¼ qDK: ð7Þ
R5 gives the following empirical expressions for q:
q ¼0:5 for R < �2:5;

1þ R=5 �2:5 6 R < 0;

1 R P 0;

8><>: ð8Þ

Assessment of damage due to creep and fatigue interaction (Fracture mechanics based method for components with defect)

Assessment of damage due to fatiguecrack growth

Assessment of damage due to creep crack growth

Evaluate stress intensity factor range(RCC-MR A16/ API-579)

Evaluate reference stress and stress intensity factor

(RCC-MR A16/ API-579)

Combine crack growth due to creep and fatigue in each cycle

(RCC-MR A16/ R5/ API-579)

Use modified Paris’ law to evaluate crackgrowth per cycle

(RCC-MR A16/ R5/ API-579)

Evaluate C* or C(t) integral (RCC-MR A16/ R5/ API-579)

Use proper creep crack growth law toevaluate crack growth for given holding

periods in a cycle (RCC-MR A16/ R5/ API-579)

Fig. 4. Flowchart for assessment of damage due to creep–fatigue interaction in components with defect.


where R is the ratio of minimum and maximum values of stress intensity factors, i.e., Kmin/Kmax. If the strainranges falls in elasto-plastic range, DKeff then is replaced by DJeff (J being Rice’s path independent integralused as a loading parameter in elastic–plastic fracture mechanics).

(b) API-579 method:

dadN

��fatigue

¼ C DKEamb

ET

� �n

; ð9Þ

where Eamb and ET are Young’s moduli at ambient temperature and working temperatures, respectively.

2.2.2. Crack growth rate due to creep

(a) Use of C* integral for steady state condition: It is based on the assumption that a cracked body is sub-jected to a steady loading at elevated temperature and the load has been applied for sufficiently long time forsteady state creep to engulf the remaining ligament. The stress and strain rates of the component are related bycreep constitutive equation, which is analogous to the relationship between plastic stain and stress in the sub-creep temperature regime. In the analogy, strain is replaced by strain rate and the stress coefficient is replacedby the creep stress coefficient and the plastic strain hardening constant is replaced by creep strain rate hard-ening constant. The integral C* is defined analogous to Rice’s J-integral as

C� ¼Z

CW � dy � T i

o _ui

ox

� �ds where W � ¼

Z _eij

0

rij deij; ð10Þ

where C is the line contour, W* is the strain energy density associated with the point stress and the strain rate_eij. Ti is the traction in i-direction, oui

ox is the gradient of velocity components in x-direction, ds is the incrementallength of contour. The C* integral can be also explained in terms of energy release rate (per unit time).

(b) Use of C(t) integral for transient condition: The crack tip stress fields under small scale creep can becharacterized by a time dependant C(t) integral, whose value is determined along a contour taken very closeto the crack tip, i.e.,


CðtÞ ¼Z

C!0

W � dy � T io _ui

ox

� �ds: ð11Þ

It may be noted that C(t) is the same as C*, but its value is determined close to crack tip within a region wherethe creep strain dominates over the elastic strains. C* is only valid as a measure of creep crack load once astationary state has been reached. In the transient phase of stress redistribution leading to the steady state,C(t) is more appropriate criterion. Since C(t) is generally larger than C*, ignoring the transient phase canunderestimate the severity of creep induced crack growth. Transient conditions are usually important underrepeated loading conditions, where new high stresses are reestablished at the beginning of each cycle. A cri-terion to know whether transient conditions need to be considered is to compare the cycle period, tcyc, withthe Reidel transition time [28], ttr. If tcyc > ttr, steady state dominates and C* is acceptable and if tcyc < ttr,the transient state dominates and C(t) is the preferred measure.

(c) R5 method: In this method, the reference stress is calculated as, rref = ryP/PL where is the yield stress ofthe material, P is the applied load and PL is the limit load at which stress in the net section at the crackedlocation reaches yield stress. Under different combination of loads and moments, the reference stress canbe calculated by finite element modeling of the component or using Handbook solutions [29]. The referencestrain rate can be evaluated using the creep constitutive equation:

_ec ¼ C1rn1 ;

where C1 and n1 are the creep strain rate coefficient and hardening exponents, respectively. The C* integral canbe represented as

C� ¼ rref _erefR0; ð12Þ
where R0 ¼ DKeff
rref

� �2

and _eref is the reference strain rate evaluated using. The crack growth rate due to creep canbe expressed in terms of C* integral as

dadt¼ D � C�/; ð13Þ

where D and / are material constants. To know that steady sate creep condition has been achieved, the stressredistribution time tred is evaluated using the equation, tred ¼ K2

EC�, where K is the stress intensity factor and E isYoung’s modulus. In case of transient creep condition, the C(t) integral is evaluated using Reidel’s approxi-mation, i.e., and C(t) integral is used in the creep crack growth equation instead of C*.

(d) API-579 method: This method is also based on calculation of reference stress and use of C* and C(t)integral. The only difference is that these are to be evaluated using the specified expressions given in the doc-ument and the stress intensity factor and reference stresses for different geometries have to be calculated usingthe appendices of API-579 (e.g. Appendix C for stress intensity factor K, Appendix D for reference stressesand Appendix F for creep and fatigue material properties). The time tred is calculated as

tredðai; ciÞ ¼0:91½Kðai; ciÞ�2

ðnBN þ 1Þ � EY � C�ðai; ciÞ; ð14Þ

where ai and ci correspond to crack depth and crack width for a semi-elliptical surface crack, EY is Young’smodulus at mean temperature of the cycle, K is the stress intensity factor and nBN is the Bailey–Norton coef-ficient evaluated at the reference stress in the current load increment. C* and C(t) are evaluated as

C�ðai; ciÞ ¼_eref

1� Dbc � Diac

� �½Kðai; ciÞ�2

rref

and CðtÞðai; ciÞ ¼ C�ðai; ciÞtredðai; ciÞ

ti

� � nBN�3

nBN�1

� �þ 1

264

375; ð15Þ

where ti is the cycle time, Dbc is the local creep damage before initiation of crack and this is computed using thenet section stress considering the pre-crack loading history. Dac is the local creep damage after initiation ofcrack and this is computed using the reference stress (Appendix D of API-579) considering the post-crackloading history. The creep crack growth rate is computed using the equation da

dt ¼ D � ½CðtÞ�l where D and lare creep crack growth rate constants for the material.


3. BARC on-line structural safety evaluation system (BOSSES)

The various modules of the BARC on-line structural safety evaluation system (BOSSES) are explainedthrough a flowchart in Fig. 5. The transient acquisition module collects the plant transients, e.g. pressure, tem-perature and flow rate, at certain time intervals through a data acquisition system interfaced to a PC. In on-line fatigue–creep monitoring, the conversion of plant transients to the temperature/stress responses in thestructure is one of the most important tasks. The technique generally used is Green’s function technique(GFT). This is a method, which transforms the plant transients to temperature/stress responses using a pre-determined transfer function. The primary advantage of this method is the less computation time. However,the GFT has a number of limitations. Strictly the GFT cannot be applied to the nonlinear analysis because ofthe inherent assumptions of linear superposition. The GFT provides information on some predeterminedpoints of the structure. If the number of points is increased, the computation time also increases. Variousinvestigators, e.g. Chen and Kuo [30], Mukhopadhyay et al. [8,11,31] and Maekawa et al. [9], have discussedthese aspects in detail. Sakai et al. [12] have outlined an approximate strategy to account for the effect ofchange of convective heat transfer coefficient using GFT.

To overcome the limitations of GFT and also to utilize the computing power of modern computers, thepresent system BOSSES employs on-line finite element technique to compute temperature transients and thethermal stresses in the structure due to fluctuation of the process transients. The system can take care ofthe variations of heat transfer coefficient and can provide whole-field information. The damage evaluationmodule finds out the fatigue usage factor, creep damage and fatigue–creep interaction effect. Various algo-rithms are available for cycle counting in an irregular stress history. The most widely used is the rain-flow cyclecounting technique. The stress time history is converted to stress frequency spectrum using the rain-flow cyclealgorithm as introduced by Socie [32]. Later various investigators, e.g. Downing and Socie [33], Rychlik [34]and Glinka and Kam [35], have presented various algorithms of rain-flow cycle counting technique. In this

Fig. 5. Flowchart of various modules of BOSSES.


method the effect of small stress excursions are separated and the relevant dominant cycles capable of produc-ing damage are computed. The cycle counting algorithm of the present system is based on this method. Thefatigue usage factor is evaluated from the computed cycles using material fatigue data. The creep damageindex is evaluated from the computed temperature and stress histories and the material creep curve, usingthe procedure shown in API reports [21–24]. To account for the combined damage mechanism, the damageaccumulation approach is adapted [26,27]. Availability of an user’s friendly menu driven graphical displaymodule for plant transients, computed temperature/stress responses, damage related information and remain-ing life assessment are another features of the present system. There is a provision for efficient data storage,data backup and data restoration. The system has been integrated to a data acquisition system and hence thefatigue–creep degradation of several components of a plant can be monitored using a single PC.

4. Monitoring of critical nozzles of heavy water plants

There are different types of heavy water plants in India depending upon the type of process used. The heavywater plant Tuticorin is based on a mono-thermal process whereas the heavy water plant Kota is based on abi-thermal process of heavy water production. In the mono-thermal process, the feed gas is taken usually froma fertilizer plant in the form of synthesis gas mixture (73% H2 and 24.4% N2, rest other gases). The gas ispassed through a drier and purification column to remove impurities. The cooled gas is then introduced intothe exchange column. Subsequently further processing produces heavy water. In this type of plant, the drierunit is subjected to regular thermal cycling.

There are usually two drier vessels, which operate in tandem. The flow diagram of gases from and to thetwo drier vessels along with the sensor signals for BOSSES is shown in Fig. 6a. The drier vessel performs fourdifferent functions, i.e., service, regeneration, cooling and standby. The operation stage is typically 8 h of dura-tion. The total time for regeneration, cooling and standby is also 8 h. During operation, the temperature of theprocess gas entering into the vessel is around 0 �C. In the regeneration, it is heated to around 185 �C and it iscooled down again to around �2 �C during cooling operation. The drier is exposed to fatigue damage due tothis thermal cycling. As the maximum temperature (i.e., 185 �C) is low, creep effect is not significant. The

Fig. 6a. Line diagram of flow of process gas and associated instrumentation for the drier unit of a heavy water plant.


objective of the on-line monitoring system is to calculate the stress and thermal transients seen by the driernozzle and then to calculate the fatigue damage over the period of monitoring. This value of fatigue damagecan be extrapolated to know the life to which the component can be operated safely. The finite element (FE)models of the top and bottom end of the drier vessel (with nozzles) used for computation of material temper-ature; stress and damage in BOSSES are shown in Figs. 6b and 6c. The typical plant transients of variousparameters as acquired by the data acquisition system are plotted in Fig. 7.

BOSSES computes the material temperature, stress and damage due to fatigue at all the Gauss points of theFE models and stores the information for further use by the plant operator. A typical computed informationhistory for a shell-nozzle junction of the bottom end of drier vessel is shown in Fig. 8. Similarly, FE model ofsome of the components of a bi-thermal process heavy water plant (i.e., heavy water plant Kota) are shown inFigs. 9a and 9b. The computed stress (von Mises equivalent stress in MPa) and damage (i.e., usage factor dueto fatigue) contour at any instant of time (e.g., after 16 h of online data processing) is shown in Figs. 10 and11, respectively. From the damage information, one can easily estimate the remaining life of a componentassuming that the design life of the component is over when the total damage fraction becomes unity. Inthe following section, various information regarding stress and damage state of some components of a thermalpower plant as computed by BOSSES are provided.

5. Monitoring of critical components of thermal power plants

In a thermal power plant, high energy piping, boiler headers, turbine rotors, casings, steam chests, valves, etc.,are the most critical components subjected to creep and fatigue damage under service conditions. To prevent anyunforeseen outages of the plant due to steam leakage preceded by crack formation leading to plant unavailabilityand down-time cost, it is necessary to generate some information on localized degradation due to various damagemechanisms in real-time basis. For this purpose, BOSSES has been implemented in two units of a coal-firedpower plant (each unit generates 210 MW). The units are in service for approximately 10 years. The main steampressure and temperatures are approximately 140 kg/cm2 and 535 �C, respectively. The corresponding pressureand temperature in the hot reheat lines are 34 kg/cm2 and 535 �C, respectively. Some of the components undermonitoring are superheater outlet header, reheater inlet and outlet header and the hot reheat pipe bends, etc. Thematerial of these headers and pipe bends is ASME SA 335 P22 (a low alloy ferritic steel).

5.1. Monitoring of creep and fatigue damage

The finite element models of some of the components monitored by BOSSES are shown in Figs. 12a–12c.The actual plant transients used by BOSSES are main steam pressure, temperature and flow and similarparameter in other circuits such as hot and cold reheat lines. Some of the plant transients of the thermal powerplant (e.g. main steam pressure, temperature and flow) are shown in Figs. 13–15, respectively. It may be notedthat the piping load is an important loading on a component apart from internal pressure and thermal stresses.

The piping loads on a component are evaluated by carrying out stress analysis of the whole piping loop(with associated supports and restraints) using various types of straight and bend pipe finite elements due

Fig. 6b. FE model of shell-nozzle junction of the top end of a drier column.

Fig. 6c. FE model of shell-nozzle junction of the bottom end of a drier column.

Fig. 7. Actual service data recorded for the drier unit of a heavy water plant.


to various load such as dead weight, pressure and thermal loads. The layout of such a piping loop (where thehot reheat piping bend is a part) is shown in Fig. 16a and the associated piping loads computed on both endsof the pipe bend are shown in Fig. 16b.

With all the loads known, BOSSES evaluates the material temperature, stress and damage (due to creep andfatigue) in all the components. The computed values of material temperature, maximum stress intensity anddamage history at a shell-nozzle junction of a superheater outlet header of the thermal power plant are shownin Fig. 17. Similarly, one can obtain the whole-field information on stress and damage in a component at anyinstant of time and as an example, the stress and damage contours of the hot reheat pipe bend after 24,000 h ofon-line computation are shown in Figs. 18a and 18b, respectively. Calculation procedure of crack growth due

Fig. 8. Computed material temperature, stress intensity and accumulated damage for the shell-nozzle junction.

Fig. 9a. FE model of shell-nozzle junction of a waster stripper column of a heavy water plant.


to creep and fatigue are described in Section 2.2. In the following section, some details of creep and fatiguecrack growth for a hot reheat pipe bend is described.

5.2. On-line computation of crack growth for assessing fitness for purpose of service of components

The geometrical details of the pipe bend are given as: internal radius = rj = 224 mm; external radiusre = 254 mm; average radius = rm = 239 mm; bend radius = Rc = 1500 mm; thickness = h = 30 mm; initialcrack size a0 = 0.5, 0.1 and 1.5 mm; c0/a0 = 3

X ¼ Rm

h; k ¼ hRc

r2m

; z ¼ pr2mh:

Nomenclature for loading: pressure = P; bending moment = M2 = M (in-plane). The nomenclature for variousgeometrical parameters of the pipe bend is provided in Fig. 19. The different postulated crack configurations

Fig. 9b. FE model of shell-nozzle junction of a hot tower column of a heavy water plant.

Fig. 10. Computed von Mises equivalent stress (in MPa) contour of a cylindrical shell-nozzle junction due to different loading conditions.

Fig. 11. Computed damage contour of a cylindrical shell-nozzle junction due to different loading conditions.


used in the analysis are shown in Fig. 20. The details of stress intensity factor and limit load calculation used byBOSSES for the pipe bend are described in the following section. The variation of stress intensity factors (atbottom and side end of the semi-elliptical crack) and limit load ratios (i.e., ratio of reference stress to the materialyield stress) for four cases (Cases 1–4 as shown in Figs. 20a–20d) with initial crack size to thickness ration areplotted in Figs. 21–23, respectively. The stress intensity factors for different crack configurations were calculated

Fig. 12a. FE model of a superheater outlet header.

Fig. 12b. FE model of a reheater outlet header.

Fig. 12c. FE model of a hot reheat pipe bend.


using RCC-MR A16 procedure. The nominal stresses were evaluated using on-line FE analysis for the combinedinternal pressure and in-plane bending moment acting on the elbow. The stress intensity factor is expressed as

K ¼ r0i0 þ r1i1

ah

� �þ r2i2

ah

� �2

þ r3i3

ah

� �3

þ r4i4

ah

� �4� � ffiffiffiffiffiffi

pap

; ð16Þ

where a is crack depth and r0 and r1 are the derived stresses and calculated in the following way for differentcrack configurations with nominal longitudinal membrane stress (r1m), nominal circumferential stress (r2m),nominal longitudinal bending stress (r1b), nominal circumferential bending stress (r2b) and internal pressureP. The stresses for various crack configurations of the pipe bend are given as:

For circumferential crack (internal): r0 = r1m � r1b + P and r1 = 2r1b.For circumferential crack (external): r0 = r1m + r1b and r1 = �2r1b.For longitudinal crack (internal), r0 = r2m � r2b + P and r1 = 2r2b.For longitudinal crack (external), r0 = r2m + r2b and r1 = �2r1b.

The coefficients i0 and i1 in Eq. (16) are obtained from the tables provided for straight pipes with corre-sponding crack configurations in A16. r2, r3 and r4 are the stresses corresponding to second- to fourth-order

Fig. 13. Recorded history of main steam pressure of a thermal power plant.

Fig. 14. Recorded history of main steam temperature of a thermal power plant.


nonlinear stress distributions across the thickness and are neglected in this analysis. The reference stress can beevaluated using modified limit load option or elasto-plastic stress option of A16. Both the options are usedhere and the maximum among the two limit loads is selected for further calculation. The crack growth com-puted by BOSSES for various crack configurations with initial crack size of 1.5 mm are shown in Fig. 24 whereon-line computation has been carried out for a period of 24,000 h of plant operation. The maximum crackgrowth is for the longitudinal semi-elliptical crack at external surface of the intrados of the pipe bend. Once,

Fig. 15. Recorded history of main steam flow of a thermal power plant.

Fig. 16a. Piping layout of the reheat line.


the damage fraction and crack growth are known, BOSSES can estimate the life consumed for the componentfor the entire service life using suitable extrapolation techniques. As an example, the life for the hot reheat pipebend under consideration has been extrapolated for a service life of around 12 years and is plotted in the form

Fig. 16b. Computed piping loads on a reheat pipe bend.

Fig. 17. Computed material stress intensity, temperature and damage history at a shell-nozzle junction of the superheater outlet header.


of a bar chart in Fig. 25. Life consumed by the pipe bend for both conventional and fracture mechanics basedmethods are shown in the above figure. This information is available for all the critical components of a ther-mal power plant and serves as an important information base for scheduling and prioritizing maintenance ofvarious components.

Fig. 18a. Snapshot of contour of maximum stress intensity (MPa) in a hot reheat pipe bend at any time instant (e.g. after 24,000 h ofprocessing of online data).

Fig. 18b. Current damage contour in a hot reheat pipe bend at any time instant (e.g., after 24,000 h of processing of online data).

Fig. 19. Geometric and loading details of the a typical pipe bend.


6. On-line evaluation of failure probabilities due to creep, fatigue and erosion–corrosion

The crack growth due to creep and fatigue depends upon the stress intensity factor, C* integral, etc., of theassumed cracked configurations and the methods to evaluate them are already described in Section 2.2. Themethod to incorporate them in the calculation of various state probabilities of pipe bend will be described here.On the other hand, the erosion–corrosion rate depends upon the process parameters such as fluid velocity, pH,temperature and oxygen content [36,37]. When water reacts with steel, an oxide film is formed on the metal sur-face. When water is deoxygenated, this layer consists of magnetite (Fe3O4). According to experiments, four dif-ferent ferrous ion complexes are formed upon dissolution of this magnetite, as written below [38]:

Fig. 20a. Pipe bend with circumferential part-through external crack at the intrados.

Fig. 20b. Pipe bend with circumferential part-through internal crack at the intrados.

Fig. 20c. Pipe bend with longitudinal part-through external crack at the intrados.


Fe3O4 þ 3ð2� bÞHþ ¼ 3FeðOHÞð2�bÞþb þ ð4� 3bÞH2O; where b ¼ 0; 1; 2; 3:

The equilibrium constants Kb are calculated as Kb ¼ ½FeðOHÞð2�bÞþb �=½Hþ�ðP H2

Þ1=3, where ½FeðOHÞð2�bÞþb ] is the

concentration of bth ferrous ion, [H+] is that of hydrogen ion and P H2is the partial pressure of molecular

hydrogen gas. The corrosion rate depends upon two factors, i.e.,

(a) Oxide dissolution: This rate is governed by the Arrhenius relationship: Rk = R0 exp(�Ek/RT), whereEk = activation energy = 31,580 cal/mol, R0 = 9.55 � 1032 atoms/cm2 S, T = fluid temp in K, R = universalgas constant = 2 cal/mol/K.

(b) Mass transfer based on oxide dissolution: This transfer rate is given by: RMT = K(CS � CB), whereK mass transfer coefficient ¼ 0:0791ðDO2

=dÞðUd=nÞxðn=DO2Þ0:335, (d = inner diameter of pipe, U = flow

velocity, n = kinematic viscosity, x = 0.54 for fully turbulent flow)

Fig. 20d. Pipe bend with longitudinal part-through internal crack at the crown.

Fig. 21. Variation of stress intensity factor at bottom of the semi-elliptical crack with various a/h ratio.

Fig. 22. Variation of stress intensity factor at side tip of the semi-elliptical crack with a/h ratio.


DO2oxygen diffusivity = 7.4 � 10�8T (2.6 � 18)0.5/(290)0.6

CS surface concentration of ferrous ions ¼P½FeðOHÞð2�bÞþ

b � ¼P

Kb½Hþ�ðP H2Þ1=3

CB a given bulk concentration

Fig. 23. Variation of limit load ratio of the pipe bend (for different crack configurations) with a/h ratio.

Fig. 24. Computed crack growth (in mm) due to creep–fatigue due to various crack configurations for the hot reheat pipe bend.


Equivalent erosion–corrosion rate can be defined as: Rate = [(Rk)�1 + (RMT)�1]�1. It may be noted that Kb

and P H2are functions of temperature. To calculate the occurrence rates of flaw, leak and rupture in a com-

ponent, Markov model [39] is used (Fig. 26). To find out the erosion–corrosion rate, various process param-eters (such as flow velocity, pH, temperature, etc.) are used. Figs. 27a–27d show the variation of corrosion ratewith flow velocity; pipe inner diameter; fluid pH and temperature, etc., for a typical feed water pipe. The fourstates of the Markov model for stable (flaw and leak) and unstable (rupture) crack propagation mechanisms asshown in Fig. 26 are:

Fig. 25. Predicted life consumed (in %) by a typical hot reheat pipe bend using various methods.

S

F

R

μ φ ω

λ

ρ ρL F

L

Fig. 26. Flowchart of the Markov model.


(a) S = success (depth of corrosion less than 0.125t),(b) F = flaw (depth of corrosion 0.125–0.45t),(c) L = leak (depth of corrosion 0.45–0.8t),(d) R = rupture (depth of corrosion beyond 0.8t),

where t is thickness of the component (e.g. a pipe). The various state transition rates used in the Markovmodel (Fig. 26) are:

(i) / = flaw occurrence rate;(ii) k = leak failure rate;

(iii) qF = rupture failure rate given flaw;(iv) qL = rupture failure rate given leak;(v) x = flaw repair rate;

(vi) l = leak repair rate.

500 750 1000 1250 1500 1750 2000 2250 2500 2750 30000.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

OTHER PARAMETERS:PIPE INNER DIAMETER = 7 cmTEMPERATURE = 553 KFLUID pH = 10.2C

orro

sion

Rat

e (m

m/y

ear)

Flow Velocity (cm/s)

Fig. 27a. Variation of corrosion rate with velocity of fluid flow.

5 10 15 20 25 30 35 40 45 500.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

OTHER PARAMETERS:FLOW VELOCITY = 1500 cm/sTEMPERATURE = 553 KFLUID pH = 10.2

Cor

rosi

on R

ate

(mm

/yea

r)

Diameter (cm)

Fig. 27b. Variation of corrosion rate with diameter of pipe.


Different limit state functions to calculate the state transition rates for a pipe are shown in Table 1.Notations: rate = erosion–corrosion rate in mm/year; T = time of inspection (usually 10 years);

Pop = operating pressure; Pf = failure pressure (defined as in Shell-92 model [38]) which is given as

P f ¼1:8UTSt

D

1� dðT Þt

1� dðT ÞMt

!; ð17Þ

where M ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 0:805 L2

Dt

qand

dðT Þ ¼ 0:45t þ rate� tðLSF 3ÞdðT Þ ¼ 0:8t þ rate� tðLSF 4Þ

�, D = pipe outer diameter; L = axial length

of corrosion defect; t = pipe thickness; UTS = ultimate tensile strength of the piping material; YS = yield

340 360 380 400 420 440 460 480 500 520 540 560 580 6001E-4

1E-3

0.01

0.1

1

10

OTHER PARAMETERS:FLOW VELOCITY = 1500 cm/sPIPE INNER DIAMETER = 7 cmFLUID pH = 10.2

Cor

rosi

on R

ate

(mm

/yea

r)

Temperature (K)

Fig. 27c. Variation of corrosion rate with fluid temperature.

9.5 9.6 9.7 9.8 9.9 10.0 10.1 10.2 10.3 10.4 10.50.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

OTHER PARAMETERS:FLOW VELOCITY = 1500 cm/sTEMPERATURE = 553 KPIPE INNER DIAMETER = 7 cm

Cor

rosi

on R

ate

(mm

/yea

r)

pH

Fig. 27d. Variation of corrosion rate with pH of fluid.

Table 1Limit state function used by BOSSES for various date transition rates of a pipe

State transition rate Limit state function

Flaw occurrence rate (/) LSF1 (d,T) = 0.45t � (0.125t + rate� t)Leak failure rate (k) LSF2 (d,T) = 0.8t � (0.45t + rate � t)Rupture failure rate given flaw (qF) LSF3 (Pf) = Pf � Pop

Rupture failure rate given leak (qL) LSF4 (Pf) = Pf � Pop (with a different Pf)



strength of the piping material; d(T) = depth of corrosion, x = PflPFD/(TFI + TR); Pfl = probability that thepiping element with flaw will be inspected per inspection interval, PFD = probability that a flaw will be de-tected, TFI = mean time between inspection of flaw, TR = mean time to repair a flaw or a leak,l = PlkPLD/(TLI + TR); Plk = probability that the piping element with leak will be inspected per inspectioninterval, PLD = probability that a leak will be detected, TLI = mean time between inspection of leak.

The state transition probabilities are calculated using first-order reliability methods (FORM). The calcula-tion procedure followed in Markov model is briefly described here. Once the state transition rates are known,one can set four differential equations, one for each state, as follows:

dSdt¼ �/S þ xF þ lL;

dFdt¼ /S � ðkF þ qF þ xÞF ;

dLdt¼ kFF � ðqL þ lÞL;

dRdt

¼ qFF þ qLL: ð18Þ

In vector form these equations can be rewritten as

dX

dt¼ AX; ð19Þ

where XðtÞ ¼

SðtÞF ðtÞLðtÞRðtÞ

2664

3775; A ¼

�/ x l 0/ �ðkF þ qF þ xÞ 0 00 kF �ðqL þ lÞ 00 qF qL 0

2664

3775. The solution of this linear matrix differ-

ential equation is given by: Xftg ¼ C0E0ez0t þ C1E1ez1t þ C2E2ez2t þ C3E3ez3t where the eigen-values are givenby: z = {z0,z1,z2,z3}, and the eigenvectors are given by: {E0,E1,E2,E3}. The constants Cj, j = 0,1,2,3 are con-stants of integration and can be determined by the following boundary conditions (assuming that at t = 0 thepipe segment is free of detectable flaws):

Xðt!1Þ ¼

0

0

0

1

2666437775 ð20Þ

and

Xðt ¼ 0Þ ¼

1

0

0

0

2666437775: ð21Þ

The eigen-values are determined by solving the fourth-order polynomial equation given by

det½A� zI � ¼ 0; ð22Þ
where I is the identity matrix. All the expressions of the corresponding eigen-values, eigenvectors and the inte-gration constants are calculated. Fig. 28a shows the variation of different state probabilities due to erosion–cor-rosion damage in the feed water pipe with increasing plant operational time (using an offline calculation), usingthe parameter values given in Tables 2 and 3, respectively. Fig. 28b shows the on-line calculation of variousstate probabilities over time of 2 years due to creep and fatigue crack growths in the reheat pipe bend (Fig. 12c).
7. Discussion

The prevailing approach of the plant operator to estimate the need for inspection (i.e., inspection schedule)is often on the basis of offline inspection and past operation and maintenance (O&M) experience. Such anapproach results in frequent inspection of problem-free equipments and many times critical shell-nozzle junc-tion are overlooked due to lack of detailed information. The application of the present system helps in makingrealistic decisions to schedule maintenance intervals on certain selected components and hence it can be used

10 20 30 40 50 60 70 80 90 100

1E-3

0.01

0.1

1

Sta

te p

roba

bilit

ies

Plant operational time (years)

SUCCESS FLAW LEAK RUPTURE

Fig. 28a. Offline calculation of various state probabilities for the erosion–corrosion model.

Table 2Process parameters of the flow through a feed water pipe

Process parameter Mean value Standard deviation

Fluid flow velocity (cm/s) 1500 50Pipe inner diameter (cm) 7 0.14Pipe thickness (mm) 7 0.14Fluid temperature (K) 553 25Fluid pH 10.2 0.51Pipe outer diameter (cm) 8.4 0.168Material ultimate strength (MPa) 455 32Operating fluid pressure (MPa) 8.7 0.87

Table 3Other plant operational parameter used in the Markov model

Other plant operational parameters Value

Mean time between inspection of flaws (year) 10Mean time between inspection of leaks (year) 1Mean time to repair flaw or leak (h) 200Pipe element flaw inspection probability per inspection 0.25Flaw detection probability 0.9Leak detection probability 0.9Pipe element leak inspection probability per inspection 0.9


to save lot of resources. The system can be merged with existing O&M planning and scheduling activities forefficient plant management and thus provide a cost effective solution. The system can also be used to rankvarious components of the plant based on the ‘Risk’ associated with their failure (Risk is defined as the prod-uct of probability of failure and consequences of that failure mechanism). Such a risk-based monitoringshould be a part of the overall concept of risk-based life management of different plant components.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.01E-20

1E-16

1E-12

1E-8

1E-4

1

Sta

te p

roba

bilit

ies

Time (year)

successflaw leak rupture

Fig. 28b. On-line calculation of various state probabilities for the creep–fatigue crack growth model.


Acknowledgement

The authors acknowledge the cooperation extended by operation and maintenance personnel of variousheavy water and thermal power plants for successful implementation and operation of the above on-line struc-tural safety evaluation system.

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a finite element program for on-line life assessment

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