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A COMPARISON OF HIGH TEMPERATURE DEFECT ASSESSMENT METHODS

by

G.A. Webster, K.M. Nikbin, M.R. Chorlton, N.J.C. Celard & M. Ober Dept of Mechanical Engineering

Imperial College, London, SW7 2BX

ABSTRACT Cracked high temperature components which are subjected to creep or creep-fatigue loading may fail by crack growth, net section rupture or a combination of both processes. In this paper, models are presented for describing these modes of failure in terms of fracture mechanics concepts, limit analysis methods and cumulative damage laws. It is shown that these models form the basis of a number of high temperature defect assessment procedures that are available for plant. These procedures are then applied to a semi-elliptical defect in a plate which is subjected to creep-fatigue loading. It is found that the predictions are sensitive to the crack initiation criteria assumed and the limit analysis solutions adopted.

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INTRODUCTION Many high temperature plants have to undergo periodic mandatory inspection to determine their suitability for further use. Frequently non-destructive inspection methods are employed. The increasing sensitivity of this equipment is causing smaller and smaller defects to be found and there is a need for establishing reliable procedures for determining the significance of any defects identified. Failures in components which are subjected to creep-fatigue loading can occur by crack growth, net section rupture or a combination of both processes(1). Any assessment method therefore must be capable of allowing for all these modes of failure. The actual mechanism of failure to be anticipated in a particular circumstance will depend on the size of defect detected, the loading and temperature conditions imposed and the properties of the material used to manufacture the component. This study forms part of a European Commission BRITE project entitled ‘HIgh Temperature Defect Assessment’ (HIDA). Several methods are available for assessing defects in high temperature plant in Europe(2-7). They each make use of fracture mechanics concepts, cumulative damage mechanics, and limit analysis techniques. Here the basis of these procedures is presented using models for the development of damage ahead of a crack tip. The procedures are then applied to the case of an austenitic stainless steel plate, containing a part-through semi-elliptical crack subjected to combined creep-fatigue loading at a temperature of 650°C, and the results compared. MODELS OF CREEP CRACK GROWTH The creep crack growth characteristics of materials can be determined experimentally (using test procedures specified in ASTM E1457)(8) or they can be predicted from uni-axial creep data. In both instances fracture mechanics concepts are employed(9). Immediately after loading, in the absence of plastic deformation the stress distribution ahead of a crack tip is given by the elastic stress intensity factor K as illustrated in Fig 1. With time creep will cause stress redistribution until a steady state condition is reached which will be described by the creep fracture mechanics parameter C*. When the creep strain rate εD and rupture life tr properties of a material can be expressed in terms of stress σ as

n

=

oo σ

σεε �� (1)

and

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ν

σσ

εε

= o

o

for

�t (2)

where ε� , oσ , n and ν are material constants and foε represents the material uni-axial creep ductility at stress oσ , the time taken for this stress redistribution to be complete tT is given by(10)

*)1(T CnGt

+= (3)

where G is the elastic strain energy release rate. Usually, for most tests and components this time is a small fraction of life and it is found that creep crack growth rate a� can be correlated satisfactorily in terms of C* by the relation(9)

φ*oCDa =D (4)

where oD and φ are material constants which can be measured experimentally or determined from a model of the cracking mechanism. Steady state crack growth In order to model the cracking mechanism a process zone is postulated at a crack tip as shown in Fig 2. It is supposed that this zone of size cr encompasses the region over which creep damage accumulates locally at the crack tip and that a steady state distribution of damage has developed in this region. Also it is assumed that an element of material first experiences damage when it enters the process zone at crr = and that crack advance takes place when the creep ductility appropriate to the state of stress at the crack tip *

foε is exhausted there. With this approach(1,9), for a material with uni-axial creep properties given by eqns (1) and (2) the constants in eqn (4) become )1( += nνφ (5)

and

( )

( ) ( )1-1c

1

oo*fo

oo

11

1 +++

−++= nn

n

nr

InnD ν

ν

εσεε

ν >

> (6)

where nI is a normalizing factor which depends on n and the state of stress at the crack tip. For plane stress conditions *

foε is taken to be and foε for plane strain situations to be 50foε in the limiting case.

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For most materials 1>>n and ν≈n so that eqn (6) is relatively insensitive to the magnitude of cr . Furthermore, from examination of a wide range of experimental creep crack growth data(9), it has been found that Do is most sensitive to creep failure strain and that eqn (4) can be approximated reasonably for many materials by

*f

85.0*3ε

Ca =D (7)

where aD is in mm/h, C* is in MJ/m2h and *

fε is failure strain (as a fraction) which lies in he range εfo>εf

*>εfo* .

Influence of ligament deterioration So far no allowance has been made for progressive material deterioration in the ligament ahead of the process zone in Fig 2. This can be included(11) by applying the life fraction or strain faction rules to calculate the fraction of damage ω suffered in the ligament up to the present time from

⌡

⌠=⌡

⌠=ε

εεωω

0 f0 ror d

tdtt

(8)

(where fε is the creep failure strain appropriate to the ligament region) and replacing oD in the previous analysis by a variable D given by ( )ω-1oD so that eqn (4) becomes

( )ωφ

−=

1*oCD

a> (9)

Consequently, eqn (9) can be used to estimate creep crack growth into progressively deteriorating material. It can also be employed for making residual life assessments of plant provided the damage incurred to the present time in service exposed material can be established. It is appropriate(1) to use the reference stress refσ procedure when using eqn (8) to determine *C . The definition of reference stress in terms of load P is

YLC

ref σσPP= (10)

where PLC is the collapse load of the un-cracked ligament for a material of yield stress

Yσ .

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Transient crack growth So far it has been assumed that a steady state distribution of damage exists in the process zone at the crack tip. In this circumstance little extra strain is required to break an element dr ahead of the crack tip, as shown in Fig 3, since it will almost be broken before the crack reaches it. This situation will not exist on first loading as each element in the figure will not have suffered any creep strain at this stage. It can be shown(12) that when this build up of damage is taken into account, the initial crack growth rate oa� to break the first element is given by

)1/()1()1/(

oo*fo

oo )(* +−+

+

= nn

n

ndr

ICa ν

ν

εσεε

D

DD

(11)

In this expression dr is raised to a small fractional power so that

φν *1

1oo CD

nna

+−+≈� (12)

For typical values of n and ν therefore, the initial crack propagation rate is expected to be approximately an order of magnitude less than that predicted from the steady state analysis. This is consistent with most experimental observations. With each crack advance dr, each successive element in Fig 3 will progressively accumulate more damage prior to fracture. The damage accumulated in an element prior to the crack reaching it can be obtained from eqn (8) in the same way as for the ligament ahead of the process zone. Consequently, for the i th element when damage iω has been incurred in it, the crack growth rate iaD will be

)1/()1()1/(

oo*fo

)(*1

1 +−++

−= nn

n

nii dr

ICa ν

ν

εσεε

ω D

DD (13)

In evaluating this expression it is necessary to allow for a change in C* with crack advance. An illustration of the application of this equation and the steady state growth law eqn (4) to the prediction of crack propagation in a 1% CrMoV steel is presented in Fig 4(11). A transient 'tail' during which damage is building up at the crack tip prior to the onset of steady state growth is clearly apparent.

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Incubation Period The build up of damage at a crack tip prior to the onset of steady state behaviour can lead to an incubation period before measurable crack growth can be detected. If the minimum crack extension that can be resolved is a∆ then the incubation period ti is given by(13)

⌡

⌠=∆a

adrt

0 ii

D (14)

An upper bound ti can be obtained by replacing iaD in this equation by oaD and a lower bound by the steady state growth rate. The lower bound value tiL therefore becomes, φ*/ oiL CDat ∆= (15)

or when the approximate crack growth relation eqn (7) is used it becomes

85.0

*f

iL *3Cat ε∆

= (16)

CREEP-FATIGUE INTERACTION At room temperature under cyclic loading conditions, crack propagation usually occurs by a fatigue mechanism where crack growth/cycle ( )FdNda can be described in terms of stress intensity factor range K∆ by the Paris Law. ( ) mKCdNda ∆=F (17)

where C and m are material dependent parameters which may be sensitive to the minimum to maximum load ratio R of the cycle. At elevated temperatures combined creep and fatigue crack growth may take place. Previous studies(14) have shown that a simple cumulative damage law can be employed to describe this behaviour. The law states that the total crack growth/cycle ( )dNda can be obtained from

faKC

dNda m D

+∆=

(18)

where f is frequency and aD is the creep component of cracking which can be determined from any of the previous models of creep crack growth.

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PRACTICAL APPLICATION The models and analysis outlined form the basis of the several procedures used in Europe for making high temperature defect assessments. Each will now be used to examine cracking at 650°C in a 316 L(N) austenitic stainless steel plate containing a semi-elliptical surface defect(15). The geometry of the test-piece is shown in Fig 5a) and the types of loading imposed in Fig 5b). The principal dimensions of the plate were B = 175mm, W = 24.5mm, L = 350mm and the size of the defect at the onset of cracking was a = 7.9mm and c = 43.6mm. Creep-fatigue cycles with a 1 hour hold at a constant load of 14 kN were interspersed with high frequency fatigue cycles as indicated in Fig 5b). Each loading cycle was performed at R = -1.0. The fatigue cycles were included to provide beachmarks to identify the progression of cracking which was monitored by electrical potential methods. Load point displacement was also recorded to allow experimental estimates of C* to be obtained for further analysis. In addition to the tests on the plate, experiments were also performed on uni-axial tensile bars and compact tension specimens, taken from the same batch of material as the plate, to determine the creep deformation and crack growth properties of the material. It was found that the secondary creep strain rate and rupture behaviour can be represented by the parameters listed in Table 1 and the crack initiation and growth characteristics by the data shown in Figs 6 and 7. In Fig 6, the incubation periods were taken to correspond with the limit of resolution ( a∆ = 0.05mm) of the crack growth monitoring system employed. Predictions based on creep crack growth models The models of creep crack growth presented will now be used to interpret the compact tension and cracked plate data. Included in Figs 6b) and 7 are predictions of the incubation periods and crack propagation rates obtained for the compact tension specimens. From Fig 7, it is evident that the creep crack growth law derived from the uni-axial creep data (eqns 5 & 6) and the approximate expression (eqn 7) give satisfactory correlation with the experimental results. This agreement in terms of C* is to be expected as the redistribution time tT (eqn 3) to achieve a steady state creep stress field ahead of a crack tip was only a small fraction of the total duration of these experiments. Furthermore, the values of *

fε used in Fig 7 to fit the crack propagation results corresponds to the uni-axial creep ductility fε = 0.6 measured, implying that cracking occurred under plane stress conditions. Similarly, it is found in Fig 6b) that both eqns (15) and (16) provide realistic lower bounds to the incubation period data. These observations demonstrate for the stainless steel that when experimental data are not available, the creep crack initiation and growth properties of the material can be derived from its uni-axial creep properties or from the approximate relations.

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In making predictions for the cracked plate, formulae are needed for calculating K, K∆ , refσ and C*. Finite element analysis can be employed but the attraction of the different

assessment procedures is in enabling handbook(16-20) solutions to be adopted. All the procedures use the Newman and Raju(17) expression for determining K for a plate containing an elliptical surface defect and eqn (4) to calculate creep crack growth rate with C* estimated from

2

refrefref*

=

σεσ KC � (19)

where refε� is the creep strain rate at the reference stress. Each procedure, therefore, should predict the same steady state cracking rate if the same uni-axial creep properties and values of

oD and φ are employed in eqn (4). However, a different solution is used to calculate refσ in each procedure depending on the yield criterion adopted and whether plane stress or plane strain conditions are assumed. It is normally recommended that a lower bound estimate of the collapse load PLC in eqn (10) is produced to give an upper bound solution for refσ and conservative predictions. In order to determine the significance of the different methods(3,21,22) of calculating

refσ , incubation periods for the deepest point of the defect have been calculated based on eqns (15) and (16). The results are included in Table 2. It is apparent that refσ can vary from 93.2 to 153.4 MPa depending on how it is calculated. Also it is clear that the choice of method of determining refσ has a bigger influence on the lower bound estimates of incubation period than whether it is based on eqn (15) or eqn (16) or whether initiation is taken to occur after 0.050 or 0.2 mm of growth. The predictions of the transient analysis of the model (eqn 13) for creep crack growth at the deepest point of the defect in the plate using the creep data in Table 1 with 6.0*

fo =ε and dr = 0.050 mm, are compared in Fig 8 with the experimental results for the different reference stress definitions. It is evident that choice of refσ has a significant influence on the predictions. The effect of including the fatigue component of cracking into the transient analysis using the summation of eqn (18) is shown in Fig 9 for the case when the reference stress solution is taken from BSPD 6493. In making the estimate of the fatigue contribution, values of the coefficients C and m in eqn (18) were taken from A16 and K∆ was replaced by

effK∆ to account for crack closure effects where KqK ∆=∆ oeff (20)

and ( ) ( )RRq −−= 15.01o (21)

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which gives 75.0o =q for 0.1−=R . It is apparent from this figure that there is a significant contribution from the fatigue component of cracking when comparison is made with the relevant creep prediction of Fig 8. Predictions of BSPD 6539 BSPD 6539(5) makes no allowance for the transient period of cracking when making high temperature defect assessments. Instead it incorporates an incubation period, where appropriate, in conjunction with steady state growth to produce a conservative prediction. It recommends the use of actual creep crack growth data in the form of eqn (4) when this is available. When this information is not available, it allows the use of eqn (7) or a modified version of this equation

85.0

ref)(rref

25

=

tKa

σ� (22)

(which is obtained from eqn (19) with refε� replaced by r(ref)f tε where tr(ref) is the rupture life at the reference stress) for determining crack growth rates and

=

2ref)r(ref0025.0

Kt

tiσ

(23)

for estimating incubation periods. However, when a superimposed fatigue cycle is involved BSPD 6539 states that no allowance should be made for an incubation period and that the combined creep-fatigue crack growth should be obtained from the cumulative damage law eqn (18). A prediction of creep crack growth for the plate following the procedure of BSPD 6539 and using the experimental crack growth law (eqn 4) for the material, in conjunction with eqn (19) with the reference stress taken from BSPD 6493, is compared with the experimental data in Fig 10 for cracking at the deepest point. Comparison with Fig 8 shows that, as expected, more rapid growth is predicted than when the transient analysis (eqn 13) is used. The influence of including the fatigue component, using the same fatigue analysis as previously, is shown in Fig 9. The fatigue contribution is again significant. R5 procedure This procedure is similar to that presented in BSPD 6539 but it uses reference stresses taken from R6(22). It again combines an incubation period, where appropriate, with steady

S7-51 10

state crack growth to give conservative predictions. It recommends the use of actual incubation data and crack growth results as shown in Figs 6b) and 7, respectively, when available. An alternative expression for obtaining the incubation period when the crack opening displacement iδ at initiation has been reported is also supplied for use with a primary creep law of the form pntAσε = (24) where ε is creep strain and A, n and p are material constants. With this expression,

( ) p

n

nn

AERt

/1

ref

ref)1/(

ii

/'/

−=

+

σσδ

(25)

where ( )2

ref' σKR = .

Like BSPD 6539, R5 makes no allowance for an incubation period in the presence of fatigue loading. The predictions of applying the R5 procedure to the cracked plate are shown in Fig 10 for creep alone and in Fig 9 for creep-fatigue loading with the same fatigue analysis as previously. Comparison of the predictions indicate that, in this instance, the fatigue contribution is the largest. Predictions of A16 A16(3) follows the same philosophy as already outlined. It does however have a different procedure for estimating incubation periods. It states that initiation of cracking takes place when the sum of the creep ω and fatigue V components of damage at a distance d, which is taken as 0.05 mm in austenitic stainless steels, ahead of a crack tip add up to the fractions shown in Fig 11. Two options are available for estimating the stress dσ and strain range dε∆ at distance d from the crack tip. In one case these can be obtained from the elastic stress field ahead of a crack with a tip radius ρ

using the Neuber approximation for allowing for plasticity effects(23). In the other case, the stress field obtained from C* is used. This latter procedure is equivalent to that used in the transient crack growth analysis presented earlier which results in the incubation period given by eqn (14). Consequently only the Neuber route will be followed here. The definition of ω is given by eqn (8) and that of V by

⌡

⌠=N

NdNV

0 f (26)

where tr in eqn (8) is the rupture life at dσ and Nf in eqn (26) is the cycles to failure at dε∆ .

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The results of applying the A16 procedure to the cracked plate, assuming the secondary creep properties given in Table 1 and the crack growth characteristics shown in Fig 7 but with primary creep and fatigue data taken from A16, are presented in Table 3 and Figs 9 and 10. It can be seen that the fatigue contribution approximately halves the incubation period and doubles the extent of cracking. More detailed calculations applying the A16 procedure to the plate can be found in reference [24]. Two-criteria approach This procedure is only different to the others in its treatment of initiation. The basis of the method for determining crack initiation is shown in Fig 12. In this figure

irupref / and / KKRR K == σσσ

where rupσ is the stress to cause creep rupture in time ti and Ki is the stress intensity factor to cause crack initiation in time ti as shown in Fig 6a). No allowance is made for any fatigue contribution and the choice of refσ is left to the user. The predictions of this method, using the A16 reference stress, are shown in Table 3 and Fig 12. It is evident that the procedure gives the largest incubation period of any of the methods. No separate prediction of cracking is included since it will produce the same results as the other steady state methods depending on the reference stress chosen. DISCUSSION It has been shown that the procedures available for assessing defects in components which are subjected to creep and creep-fatigue loading are consistent with models for the build up of damage in a process zone at the crack tip. However, even when these procedures are employed with the same creep and fatigue data, it has been found that they produce different predictions when applied to the cracked plate. For estimating incubation periods, in some instances this is because different criteria are adopted for determining the onset of cracking. For determining cracking rates, the main cause is due to use of different definitions of reference stress. Nevertheless all the procedures gave conservative assessments as shown in Fig 9. However, in order to produce close agreement with the experimental data, it is clear that realistic estimates of reference stress are required. Even when these are available, it is also important that accurate materials data are used in the analysis.

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CONCLUSIONS Models for describing creep and creep-fatigue crack initiation and growth from defects in high temperature plant have been presented in terms of damage accumulation in a process zone at the crack tip using fracture mechanics, limit analysis and cumulative damage concepts. It has been established that these models form the basis of a number of procedures that are available for performing defect assessments. Despite this similarity, it has been found that different predictions are obtained when the procedures are applied to a semi-elliptical surface defect in a plate which is subjected to creep-fatigue loading, even when they are based on the same materials data. The main cause is attributed to the use of different reference stress solutions in the calculations. Nevertheless all the procedures produced conservative assessments. ACKNOWLEDGEMENTS The authors would like to thank CEA for the provision of the data on the cracked plate and the European Commision for financial support for Imperial College to participate in the HIDA project. REFERENCES (1) WEBSTER, G.A. & AINSWORTH, R.A., 'High temperature component life

assessment', Chapman and Hall, London, 1994. (2) EWALD, J. & KEIENBURG, K-H, 'A two criteria diagram for creep crack initiation',

Int. Conf. Creep, Tokyo, April 1986, 173-178. (3) AFCEN (1985) 'Design and construction rules for mechanical components of FBR

nuclear islands' RCC-MR, Appendix A16, AFCEN, Paris. (4) DRUBAY, B., CHAPULIOT, S., PAPIN, M.H., POETTE, C., DESCHANELS, H. &

MARTELET, B., (1997), ‘A French Guideline for Defect Assessment and Leak Before Break Analysis’, ASME, Proceedings of ACONE 5: 5th International Conference on Nuclear Engineering, 26-30/05, Nice, France.

(5) MOULIN, D., DRUBAY, B, ACKER, D & LAIARINANDRASANA, L., (1995), 'A practical method based on stress evaluation (σd criterion) to predict initiation of cracking under creep and creep-fatigue conditions', ASME, J. Press. Vessel Tech. 117, 335-340.

(6) Nuclear Electric (1990) 'R5 Assessment procedure for the high temperature response of structures, Report R5, Nuclear Electric Ltd, UK.

(7) British Standards Institution (1994) 'Guide to methods for the assessment of the influence of crack growth on the significance of defects in components operating at high temperatures', BSPD 6539; 1994.

S7-51 13

(8) ASTM (1992) 'Standard test method for measurement of creep crack growth rates in metals', ASTM E1457:1992, Vol 03.01, 1031-1043.

(9) NIKBIN, K.M., SMITH, D.J. and WEBSTER, G.A., 'An engineering approach to the prediction of creep crack growth', J. Eng. Mat. and Tech., ASME, 108, 1986, 186-191.

(10) RIEDEL, H., 'Fracture at high temperatures', Springer-Verlag, Berlin, 1986. (11) WEBSTER, G.A., 'Fracture Mechanics in the creep range'. J Strain Analysis, 29, No 3,

1994, 215-223. (12) WEBSTER, G.A., 'Lifetime estimates of cracked high temperature components'. Int. J.

Pressure Vessels & Piping, 50, 1992, 133-145. (13) AUSTIN, T.S.P. & WEBSTER, G.A., Prediction of creep crack growth incubation

periods, Fat. & Fract of Engng Mats and Struct, 15, No 11, 1992, 1081-1090. (14) WINSTONE, M.R., NIKBIN, K.M. and WEBSTER, G.A., 'Modes of failure under

creep/fatigue loading of a nickel-based superalloy', J. Mat. Sci., 20, 1985, 2471-2476. (15) POUSSARD, C. & MOULIN, D., (1998), ‘Creep-Fatigue Crack Growth in Austenitic

Stainless Steel Centre Cracked Plates at 650 °C - Part I: Experimental Study and Interpretation’, Proceedings of the 3rd Saclay International Seminar on Structural Integrity Conference oragnised in conjunction with the BRITE HIDA BE1702 Eurpean Project, SISSI 3 / HIDA, S3-22, Saclay, France.

(16) ROOKE, D.P. & CARTWRIGHT, D.J., (1976) 'Compendium of stress intensity factors, HMSO, London.

(17) NEWMAN, J.C. & RAJU, I.S., Stress Intensity Factor Equations for Cracks in Three-dimensional Bodies Subjected to Tension and Bendng Loads, NASA Technical Memorandum 85793, National Aeronautics and Space Administration, Langley, April 1984.

(18) TADA, H., PARIS, P.C. & IRWIN, G.R., The Stress Analysis of Cracks Handbook, 1985, Paris Productions Inc.

(19) MARAKAMI, Y, Stress Intensity Factor Handbook, Vols 1-2, 1987, Pergamon. (20) MILLER, A.G. (1988) 'Review of limit loads of structures containing defects", Int. J.

Pres. Vessels & Piping., 32, 197-327. (21) British Standards Institution, 'Guidance on methods for assessing the acceptability of

flaws in fusion welded structures', BSPD 6493; 1991. (22) Nuclear Electric, 'R6 Assessment of the integrity of structures containing defects '

Report R6, Nuclear Electric Ltd, UK, 1997. (23) EWALDS, H.L. & WANHILL, R.J.H., Fracture Mechanics, Edward Arnold, 1985. (24) POSSARD, C., CELARD, N., DRUBAY, B. & MOULIN, D., (1998), ‘Creep-Fatigue

Crack Growth in Austenitic Stainless Steel Centre Cracked Plates at 650 °C - Part II: Defect Assessment according to the A16 Document’, Proceedings of the 3rd Saclay International Seminar on Structural Integrity Conference organised in conjunction with the BRITE HIDA BE1702 European Project, SISSI 3 / HIDA, S7-48, Saclay, Fracnce.

S7-51 14

(25) LAIARINANDRASANA, L., PIQUES, R., DRUBAY, B. & FAIDY, C., ‘Crack Initiation under Creep and Creep-Fatigue on CT Specimens of an Austenitic Stainless Steel’, Nuclear Engineering and Design, 157, 1995, 1 - 13.

n υ oε� (h-1) oσ (MPa) foε 8.7 6.9 1 436 1.0

Table 1: Uni-axial creep properties for 316 L(N) stainless steel at 650°C based on minimum

creep rate.

Reference Stress (MPa) A16

R6

BSPD

A16

R6

BSPD

93.3 153.4 148.2 93.3 153.4 148.2

Incubation Periods (hours)

( )m µa∆ Experiment

Eqn (16) 75.0iL *27.2 C

at ∆= Eqn (15)

50 35 331 12.6 16 214 12.0 14.5 200 140 1325 50.5 64 857 48.0 58 Table 2: Prediction of incubation periods for onset of cracking in cracked plate based on

different definitions of reference stress.

Incubation Periods (hours) R5 (creep only) A16 BSPD 6539 2-criteria

( )m µa∆ Experiment

m500Ci µδ =

Expt data (Fig. 6b)

creep

creep-fatigue

Eqn (23)

Fig. 12

50 35 88.2 49.1 32 14 0.5 610 Table 3: Comparison of incubation periods for onset of cracking in cracked plate predicted by

different procedures assuming initiation occurs at 50 mµ .

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Fig. 1. Elastic and creep stress distributions at a crack tip

Fig. 2: Regions of local and ligament damage ahead of a crack tip

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Fig. 3 Damage development in creep process zone

Fig. 4 Prediction of transient crack growth for 1% CrMoV steel at 550°C

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Fig 5: a) Test-piece containing a semi-elliptical surface defect b) type of loading imposed

During hold time

l

2B

H

W

P

a

c

W

B

Fig 5.a

Creep-fatigue propagation

R=-1

Beachmarking

R=-1

Creep-fatigue propagtion

R=-1

Time

Load

R=-1

Fig 5.b

+14kN

-14kN

Beachmarking

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10-1

100

101

102

103

101 102

Ecole des Mines (Paris) - CT EDM notched (25)

Ecole des Mines (Paris) - CT fatigue pre-crack (25)

Imperial College - CT EDM notched

t i (hours)

Ki (MPa m1/2 )

Fig. 6a: Incubation periods determined on 316 L(N) stainless steel compact tension

specimens at 650°C as a function of initial stress intensity factor Ki.

10-3

10-2

10-1

100

101

102

103

104

10-5 10-4 10-3 10-2 10-1 100

CT expt 0.05 mm

Eqn (15) 0.05 mm

Eqn (16) 0.05 mm

t i (hrs)

C* (MJ/m2 h)

Fig. 6b: Incubation Periods determined on 316 L(N) stainless steel compact tension specimens at 650°C as a function of C*.

S7-51 19

10-4

10-3

10-2

10-1

100

10-6 10-5 10-4 10-3 10-2 10-1 100

CT exptCT exptCT exptCT exptEqn (6) Eqn (7)

da/dt (mm/h)

C* (MJ/m2 h)

ε f* = 0.6

ε f* = 0.6

Fig. 7: Correlation of creep crack growth rate with C* for 316 L(N) stainless steel compact

tension specimens at 650°C.

7

8

9

10

11

12

13

14

0 2000 4000 6000 8000 10000

experimentBS 6493 ref stressR6 ref stressA16 ref stress

Crack depth, a (m

m)

Time (hrs)

Fig. 8: Comparison of experimental crack growth at deepest point in plate with transient

creep crack growth analysis (eqn 13) with different definitions of reference stress.

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7

8

9

10

11

12

13

14

0 1000 2000 3000 4000 5000

experimentEqn (13)BSPD 6493R5A16

a (mm) exp

Time (hrs)

Fig. 9: Comparison of experimental crack growth at deepest point in plate with creep-fatigue

crack growth predictions made by the different assessment methods.

7

8

9

10

11

12

13

14

0 1000 2000 3000 4000 5000

experimentBSPD 6539R5A16

Crack depth, a (mm)

Time (hrs)

Fig. 10: Comparison of experimental crack growth at deepest point in plate with creep crack

growth predictions made by the different assessment methods.

S7-51 21

V

1

0 1

No initiation

Initiation

Damage after 1 cycle

Damage at initiation0.5

0.5

1

1

No initiation

Initiation

Variable boundary,set for thisassessment to 0.8

Rσ

RK

0.5

0.5

1h10h

100h

1000h

ω

0

Fig 11.Creep fatigue crack initiation interaction diagram for 316 L(N) austenitic stainless steel for use with A16

Fig 12. Two criteria method for estimating crack initiation