Failure Assessment Diagram Analysis of Creep Crack Initiation in 316H Stainless Steel

Transcription

1 Failure Assessment Diagram Analysis of Creep Crak Initiation in 316H Stainless Steel C. M. Davies *, N. P. O Dowd, D. W. Dean, K. M. Nikbin, R. A. Ainsworth Department of Mehanial Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK British Energy pl, Barnett Way, Barnwood, Glouester GL4 3RS, UK. Abstrat In this work the time dependent failure assessment diagram (TDFAD) approah is applied to the study of rak initiation in Type 316H stainless steel, a material ommonly used in high temperature appliations. A TDFAD has been onstruted for the steel at a temperature of 550 o C, and was found to be relatively insensitive to time. The TDFAD proedure is then applied to predit initiation times, at inrements of reep rak growth Δa = mm and Δa = 0.5 mm, for tests on ompat tension speimens and the results ompared to experimentally determined values. It has been found that initiation time preditions are sensitive to the reep toughness values, and to the limit load (or referene stress) solution used. Conservative preditions of initiation times have been ahieved through the use of the lower bound reep toughness values in onjuntion with the plane strain limit load solution. The plane stress limit load solution has given onservative preditions for all bounds of reep toughness used. Keywords: Failure assessment diagram, reep rak initiation, stainless steel * Corresponding author. address: atrin.davies@imperial.a.uk

2 1 Introdution The failure assessment diagram (FAD) approah has been widely used to assess the safety of defets in engineering omponents, e.g. [1]. The time dependent failure assessment diagram (TDFAD), [2], an extended form of the FAD, has reently been developed in order to aommodate the high temperature reep regime within an FAD-based approah. The use of a TDFAD has many advantages detailed alulations of rak tip parameters suh as C* are not needed; it is not neessary to establish the frature regime in advane and the TDFAD an indiate whether failure is ontrolled by rak growth in the small-sale or widespread reep regime or by reep rupture. The TDFAD proedure is generally used to determine whether a speified rak extension will be ahieved within the assessment time. It may also be used to determine the time required for a limited rak extension to our. Hene approximate initiation times an be obtained, using an engineering definition of initiation, generally taken to be the time for a defined amount of rak extension (typially and 0.5 mm), [3]. The proedure is urrently limited to raks under Mode I loading and to the initiation of raking or rak extensions that are small ompared to the defet and omponent dimensions. In this work experimental reep rak growth (CCG) test data from [4] for an austeniti Type 316H stainless steel at 550 o C, have been analysed. The dependene of the reep toughness on time has been determined from these data. TDFADs have been onstruted for the material under study and alulations arried out on a seleted test to assess the onservatism of the TDFAD approah in the predition of reep rak initiation. The sensitivity of the reep initiation preditions to the satter in solution used is also examined. and to the limit load (referene stress) 2 Review of the Time Dependent Failure Assessment Diagram (TDFAD) Approah 2.1 TDFAD Parameters The proedures and parameters used in a TDFAD analysis are similar to that of the R6 Option 2 FAD [1] exept that frature toughness is replaed by reep toughness, to be defined later, and time dependent stress and strain parameters are required. In the TDFAD, for the ase of a single primary load, the parameters K r and are defined as follows: Page 2 of 26

3 K K r =, (1) K mat σ =, (2) ref σ In Eq. (1) K is the stress intensity fator and is the material reep toughness orresponding to a given rak extension at a given time. In Eq. (2) σ is the stress orresponding to % inelasti (reep and plasti) strain from an isohronous stress-strain urve at a partiular time and temperature. The definition of σ is illustrated in Figure 1 and it is seen that σ will derease as time inreases i.e. reep strain inreases. The referene P stress, σ ref in Eq. (2), may be related to the limit load via, σ ref = σ 0, where P and P L are P the applied load and the limit load orresponding to a yield stress σ 0, respetively. L max max A ut off point is also defined on the TDFAD. This is analogous to the parameter used in the R6 FAD [1] and is defined as follows: max σ = (3) σ r where σ r is the stress to ause reep rupture at the same time as σ is evaluated. If Lr exeeds max, failure is expeted to our by reep rupture rather than by frature. The reep rupture stress, σ r in Eq. (3), may be found from experimentally determined relationships between rupture time and stress, suh as r v r t r ( σ ) = Bσ, (4) where t r is the rupture time for a given rupture stress, and B and v are material onstants. Alternatively, values of σ r for a range of materials at different times may be obtained diretly from design odes [5, 6]. In order to be onsistent with the R6 proedure, max should not exeed σf /σ, where σ is the % proof stress and σ f is the flow stress whih may be taken as (σ + σ u )/2, where σ u is the ultimate tensile stress. Page 3 of 26

4 The evaluation of the material reep toughness parameter,, is fundamental to the TDFAD assessment method. Its value at a partiular time and rak extension, Δa, is determined from experimental load-displaement data from reep rak growth tests aording to the relationship shown below [7], K = E J, (5) mat T where E = E /(1-ν 2 ) and ν is the Poisson s ratio. The total J-integral value, J T, in Eq. (5) an be evaluated aording to the ESIS frature toughness testing proedure [8], from the total area under the load displaement urve, U, as shown in Eq. (6). T J T = ηut, (6) B ( W a) n where W is speimen width, a is the rak length, B is net speimen thikness (for a side grooved speimen, Bn = B s B, where Bs is the total sidegroove thikness; for a plane speimen, n B = B) and η is a geometry funtion, whih is equal to (1 a/w) for a ompat tension speimen. The ESIS proedure is slightly different from that reommended by ASTM E1820 [9]. However alulations have shown that for the ases examined here there is little differene between the results from both proedures. Typial load-displaement behaviour during a onstant load CCG test is shown shematially in Figure 2. The total axial displaement of the loading pins, Δ T, may be separated into elasti, plasti and reep omponents Δ e, Δ p, Δ, respetively. Similarly, the total area under the load displaement urve, U T, may be separated into elasti, plasti and reep omponents U e, U p, U, respetively. A single test may be used to generate values of n for a number of values of Δa at a single temperature. However these values will be for different assessment times. A number of different tests, at different load levels, are therefore required to generate the dependene of on time for a given Δa, or between and Δa for a given time. Creep toughness values,, are expeted to derease with time and at short times are expeted to approah the low temperature frature toughness of the material, [10]. K IC Page 4 of 26

5 2.2 Isohronous Stress-Strain Curves Isohronous stress-strain urves for the speified temperature are required for eah time of interest in order to determine the % inelasti strain, σ, and the overall TDFAD. The shemati diagram in Figure 1 shows how and are determined. If suffiient σ σ 0. 2 experimental data is not available, theoretial isohronous stress-strain urves an be onstruted from the summation of equations whih speify the dependene of elasti, plasti and reep strains on stress for the given material and temperature. Isohronous stress-strain urves an also be obtained from design odes [5, 6]. 2.3 Formation and Appliation of TDFAD A failure assessment diagram for a speifi time is defined by the equations: K r Eε = Lrσ L σ Eε 3 ref r + 2 ref 1 2 when max Lr L (7) r max K = 0 when L >. (8) r r In Eq. (7) E is Young s modulus andε ref is the total strain orresponding to the referene stress from the isohronous stress-strain urve at the partiular time and temperature (see Figure 1). An example of a TDFAD is shown in Figure 3, whih is based on isohronous data for an austeniti steel at 600 o C at times of 0, 3000 and 300,000 hours [2]. The TDFAD an be used to predit (i) if a rak will extend a distane Δa in a given time or (ii) the time required for a speified amount of rak extension. Sine the engineering definition of reep rak initiation is the period of time required for an inrement of rak growth Δa, the TDFAD may be used to predit initiation times. For many materials the urves do not vary greatly with time and urves for longer times an be used to provide a onservative TDFAD for an assessment at shorter times. The following steps desribe the TDFAD assessment proedure [2]: (i) (ii) Speify omponent and defet geometry, loading onditions, temperature, et. Define the maximum tolerable rak extension, or if prediting initiation times speify the initiation distane, Δa. Page 5 of 26

6 (iii) (iv) Obtain uniaxial reep data for speified times at the operating temperature (i.e. σ r, ). σ Construt the TDFAD for eah time of interest, using Eq. (7) and the isohronous stress-strain urves. (v) Determine values of material reep toughness,, for eah time of interest for the speified maximum tolerable rak extension / initiation distane, Δa. (vi) (vii) Calulate values of and K r at the urrent value of rak length, a. In initiation time assessments the initial rak length, a 0, is the appropriate value to use. (The rak extension at initiation Δa << a 0, so that hanges in rak size have a negligible effet on these alulations.) Plot the point (, K r ) on the TDFAD. If the point lies within the FAD then the rak extension is less than Δa and reep rupture is avoided in the assessment time. Alternatively, to determine an initiation time, t i, a time lous of points (, K r ) is onstruted, obtained for a single value of rak length, a 0, at various times. The time for a rak extension Δa is given by the intersetion of this lous with the failure assessment urve for the orresponding time. If the TDFAD is not signifiantly dependent on time, estimates of initiation times may be made from a urve evaluated at a single time or even from an R6 Option 1 urve. An iterative proess an then be implemented in order to refine the estimate, whih involves the onstrution of failure assessment urves for other times [2]. 3 Calulation Methodology for Stainless Steel Data Experimental reep rak growth (CCG) test data from for an austeniti Type 316H stainless steel at 550 o C have been analysed (see [4] for full details of the material speifiation). The material had been taken from an ex-servie superheater header removed from a power station that had previously been in servie for 76,000 hours at 520 C under a relatively low servie load. Data from a total of fourteen reep rak growth tests on ompat tension (CT) speimens of three different dimensions, large (L), standard (S) and half-size (HS), (see [4, 11]) have been analysed. Typial dimensions of these speimens are given in Table 1. The speimens were typially side-grooved by 20 or 40 % suh that BBn = 0.8B or B n = 0.6B respetively. Starter raks had been ut into the speimens using a wire noth eroder. Page 6 of 26

7 Constant load tests were arried out at a uniform temperature of 550 C and the applied loads were hosen to give test durations between 500 and 1,500 hours. The amount of rak growth was monitored using a diret urrent (DC) potential drop tehnique [3]. 3.1 Determination of Initiation Times The time for mm rak extension during the CCG tests of 316H at 550 o C has been determined by linearly interpolating between the test times of two onseutively reorded data points where Δa mm and Δa mm respetively. The time to ahieve 0.5 mm of rak growth has been determined similarly. The rak extension, Δa, vs. time data for one of these tests on a standard sized speimen is shown in Figure 4, indiating the method used to determine the initiation time for a rak extension of 0.5 mm. 3.2 Evaluating Creep Toughness Values, o As disussed in setion 2.1, the value of is obtained from the area under the load displaement urve up to rak initiation (see Eq. (6)). To determine this area a polynomial equation has been fitted to the load-displaement data during load up of the CCG test, and the integration of this equation gives the area under the loading part of the load displaement urve, (U L = U e + U p ). A typial polynomial fit is shown in Figure 5 using data from a test on a half size (HS) speimen, whih exhibits initial linear behaviour and, at the higher load levels, non-linear behaviour is seen due to plastiity effets. The total area under the load displaement urve at any time, U T, is then given by the summation of the area under the loading part of the urve (U L ) and the produt of the total applied load in the CCG test (whih is a onstant value) and the inrease in axial displaement of the loading pins, i.e. U T = U L + PΔ (9) Equations (5), (6) and (9) have been employed in order to determine the values of for eah set of data points measured at speifi times during a CCG test. Values of for a rak extension Δa, for example Δa = mm, have been determined by linearly interpolating between the values of at two onseutively reorded data points where Δa mm and Δa mm, respetively. Page 7 of 26

8 3.3 Referene Stress Solutions When alulating, a referene stress solution, representing either plane strain (PE) or plane stress (PS) onditions may be used. A general definition of the referene stress solution for a CT speimen may be desribed by: P σ ref = (10) mb W eff where P is the load applied to the speimen, W is the speimen width, m is a geometri funtion whih varies under onditions of plane stress and plane strain, and Beff is the effetive thikness of the speimen whih is determined from [12] B eff B = B n n 2 B (11) The value of m for the CT speimen using the von Mises solution is [13], a a m = λ 1+ γ + ( 1+ γ ) 1+ γ W W 2, (12) plane stress where, λ = { 2 3 ; γ = { 1 plane strain For a given a/w the value of m is lower under plane stress onditions than plane strain, resulting in higher values of in plane stress for the same applied load, (for a typial CT speimen examined here the plane stress referene stress is about 45% higher than the plane strain value). Assessments made using the plane stress solution will thus generally give a more onservative result than that obtained using the plane strain solution. 3.4 Time Dependent Stress-Strain Data Isohronous stress-strain data have been generated using the elasti, elasti-plasti and reep material response. The method used follows the proedure in the RCC-MR design ode [14] for primary-seondary reep of Type 316 stainless steel material. Thus, the primary and seondary reep strain inrements, Δ ε p and Δ ε s, are alulated aording to: Page 8 of 26

9 1/ p np/ p (1 1 / p) p pap Δ ε = σ ε Δ t, n Δ ε = σ Δ. s A t The reep strain inrement, Δε, is equal to the larger of the two inrements alulated from Eq. (13) i.e. (13) Δε = Δε p Δε p { for Δ ε s for Δε p < Δε s Δε s (14) The primary and seondary reep onstants in Eq. (13) are p = 0.746, A p = , n p = 7.45, A = and n = (for stress in MPa), whih were obtained by fitting to uniaxial reep data over a range of onditions [4]. For a partiular time, the total strain at any stress level is given by the sum of the elasti and plasti strain and the total reep strain aumulated in that time: (, t) = ( ) + ( ) + Δ (,Δt) ε total σ ε e σ ε pl σ ε σ. (15) t There were insuffiient tensile data in [4] whih ould be used to provide the elasti-plasti response of the material in Eq. (15). Therefore data were obtained from material of the same ast, whih had been exposed to similar, but not idential, servie onditions to that of the test speimens analysed here [4]. Isohronous stress strain urves based on Eqs. (13) to (15) have been produed for the times listed in Table 2, examples of whih are shown in Figure 6. It may be seen that the isohronous stress strain urves are relatively independent of time for times below 1000 hrs. Values of the % stress, are given in Table 2. σ, taken from these urves together with values of rupture stress Regression analysis of rupture time vs. stress, from the uniaxial reep data in [4], provided the values of the onstants in the reep rupture equation, Eq. (4), as B = and v = 1.41, with stress in MPa and time in hours. Thus Eq. (4) in onjuntion with Eq. (3) an be used to determine L max r at different times. Page 9 of 26

10 4 Results 4.1 Creep Toughness Variation of Creep Toughness with Time and Data Bounds of The reep toughness data from eah test have been ombined to determine the relationship between and time at temperature, T = 550 o C and rak extensions of Δa = mm and Δa = 0.5 mm as illustrated in Figure 7 and Figure 8, respetively. Different symbols have been used in the figures to illustrate the data for the different speimen size, although no obvious trend with speimen size is observed. A mean trend line was fitted to the as shown in Figure 7 and Figure 8. If the reep toughness is assumed to follow a normal distribution, then upper and lower bound K mat data values an be determined by offsetting the mean line in Figure 7 and Figure 8 to the data by ± 2 standard deviations (s.d.). These data bounds are shown in Figure 7 and Figure 8. By omparing Figure 7 and Figure 8 it may be seen that defining initiation at Δa = mm will lead to a lower value of, with a somewhat higher assoiated satter, ompared to that obtained using Δa = 0.5 mm. It is also apparent that the reep toughness is high, and not signifiantly redued by reep in the timesales of these tests Sensitivity of Creep Toughness to the Area under the Loading Curve Typial experimental load-displaement urves from the tests on CT speimens are illustrated in Figure 9 up to Δa = 0.5mm, where the load, P, has been normalised by the width, W, and thikness, B, of these (plane sided) speimens, and the Young s modulus of the material, E. The displaement here, whih has been normalised into non-dimensional form by the speimen width, W, is the total axial displaement that inludes the elasti, plasti and reep displaements. Note that the linear portion of the urve for the large and half size speimens (L and HS in Figure 9, respetively) should lie very lose to eah other when plotted in this normalised form, sine the speimens are geometrially similar (a/w = 0.45, B/W 0.5 in both ases). The measured stiffness during load-up of the large speimen is very lose to the theoretial value from [9], but the half size speimens exhibits a larger displaement. This is likely to be due to experimental error and suggests that the elasti area in Figure 2 would be better estimated from stress intensity fator solutions than from measured elasti displaement, as in some J-estimation methods [9]. However, the measured variability in the Page 10 of 26

11 loading urve for the HS speimen produes variability in reep toughness that is well within the upper and lower bound toughness lines for K in Figure 7. mat It is seen in Figure 9 that for all the speimens, partiularly the large CT speimen, a signifiant proportion of the area under the loading urve orresponds to the elasti and plasti area, i.e. reep initiation at these times is dominated by the elasti plasti response. The evaluation of the area under the load up part of the urve an therefore be of signifiane when alulating at short inubation times. This trend is illustrated more learly in Figure 10 where the ratio of the area under the loading part of the urve to the total area under the urve, U L /U T is shown for the three speimen sizes. In the ase of the large speimen, the area under the load up part of the urve is about 90% of the total area under the load displaement urve at the defined initiation inrements (Δa =, 0.5 mm). 4.2 TDFAD for 316 H at 550 o C Time dependent failure assessment diagrams, for the times listed in Table 2, have been produed for this material at 550 o C. The R6 Option 1 FAD [1], whih is appliable at low temperatures has also been determined. These diagrams are shown in Figure 11 and Figure 12, respetively. At times of 100 hrs and below, the value of L max given by Eq. (3), exeeds that obtained from an R6 analysis. max R6 proedure as disussed in Setion 2. r would therefore be set equal to the value given by the The TDFAD at time zero is ompared to the R6 Option 1 urve in Figure 11. Both urves lie lose to eah other espeially at lower values of. Figure 12 shows the evolution of the TDFAD up to a time of 100,000 hours. It is observed that the TDFAD is quite insensitive to time and the greatest notieable differene between the diagrams at eah time is the ut off value, max, whih dereases as time inreases, indiating the redution of time to failure by ontinuum damage, due to the redution in σr with inreasing time via Eq. (4). The insensitivity of the urves in Figure 12 to time is due to the high value of reep stress exponent, n, in the reep strain equation (see Eq. (13)) whih may not be valid at the longer times. 5 Appliation of TDFAD to Predit Initiation Times An example of the use of a TDFAD to predit initiation times is presented as an illustration of the appliation of the method. The initiation time of a test on a standard sized CT Page 11 of 26

12 speimen (P = 23.5 kn, a/w = 0.53, B/W = 0.5, Bn/W = 0.4), has been predited and ompared to the experimentally determined value. This test has not been used to produe a value of at initiation sine not all of the neessary data required were available for this test. The sensitivity of the initiation time predition to the variability in the reep toughness data and to the referene stress solution used have also been investigated. A lous of data points at times of 10, 100, 500, and 1000 hours has been onstruted on a TDFAD for this test. Figure 13 and Figure 14 fous on the parts of the TDFAD where the loi are lose to the urve when the plane strain and plane stress limit load solutions are used, respetively. The point on any single lous with the lowest or K r value orresponds to the lowest time of 10 hrs; subsequent points on the lous orrespond to the inreasing times 100, 500 and 1000 hrs. A TDFAD urve for a time of 100 hrs has been used in the analysis sine it is already known that the initiation times are in the range of 0 to 500 hrs for these tests, and little differene has been observed (Setion 4.2) between the TDFADs in this time range. Note that the small inrease in, in Figure 13 and Figure 14, is due to a redution in σ with time and the inrease in Kr is due to the derease in with time. Three loi are shown in Figure 13 and Figure 14, a lower bound (LB), mean and upper bound (UB) lous, for both initiation distanes Δa = and 0.5 mm, whih were produed using the lower bound, mean and upper bound values of K determined from Figure 7 and Figure 8. mat As explained in Setion 2.3, initiation is deemed to our at a time orresponding to the point where the lous intersets the TDFAD urve. It may be seen in Figure 13 that when the plane strain referene stress value is used, the predited initiation time orresponding to Δa = 0.5 mm is greater than 1000 hrs exept when the lower bound toughness value is used (labelled as LB Lous Δa = 0.5 mm in Figure 13) when the initiation time is approximately 100 hrs. (Values of (and hene predition loi) have not been extrapolated beyond 1000 hrs sine there may be a hange in the trend of the data for longer term tests [15]). The measured initiation time orresponding to Δa = 0.5 mm for this test was 275 hours thus a onservative predition is ahieved through the use of the lower bound data. For Δa = mm, the TDFAD analysis using the lower bound toughness predits that the initiation time is approximately 10 hrs, whih is onservative ompared to a measured time of 105 hrs (see Table 3). Page 12 of 26

13 If the plane stress referene stress definition is used, as illustrated in Figure 14, it may be seen that the initiation time for the speimen (for Δa = or 0.5 mm) is less than 100 hrs regardless of whether the lower, mean or upper bound value is used for the reep toughness,. This illustrates the strong dependene of the result on the hoie of referene stress solution. The initiation times predited by this method using the loi orresponding to mean, upper bound (UB) and lower bound (LB) values of and the plane stress and plane strain von Mises limit load solutions are ompared to the experimentally determined initiation times in Table 3. Although this side-grooved, standard-sized test speimen may be expeted to be represented more losely by the plane strain solution than plane stress, the initiation times predited by a plane strain analysis are not onservative, unless the lower bound reep toughness is used. A diret omparison is made in Figure 15 of the results obtained using the plane strain or the more onservative plane stress von Mises referene stress solution for Δa = 0.5 mm. On this sale the predition loi are lose to being vertial sine, as an be seen in Table 2, σ is approximately onstant over the timesale onsidered, and the only signifiant hange is in. The shift in the data due to the use of the different referene stress solutions is learly observed. For this speimen the plane stress solution gives an Lr value 1.44 times greater than that from the plane strain solution (see Eq. (11)) and the effets on the predited initiation times are signifiant. The sensitivity to the referene stress solution will depend on the region of the TDFAD in whih the predition loi are situated. For this material and temperature the failure assessment urve is approximately horizontal for values of greater than 1.7. Thus, a horizontal shift to the lous, due to the use of a different referene stress solution, will have very little effet on initiation time preditions in the region > 1.7. Similarly if the loi fall in the region, < 0.5, the results will not be very sensitive to the hoie of referene stress solution. However, as illustrated above, if the loi fall in the region, 0.5 < < 1.4 the predited initiation times an derease by up to two orders of magnitude when the referene stress inreases by less than 50 perent. Page 13 of 26

14 6 Conlusions Creep toughness values,, have been determined for austeniti Type 316H stainless steel at 550 o C from analysis of fourteen reep rak growth tests on CT speimens of different sizes and thikness. Values of were obtained for two initiation distanes, Δa = mm and Δa = 0.5 mm. It has been found that for the 316 steel at 550 o C the area under the loading part of the urve in a reep rak growth (CCG) test, whih is used to determine, annot be negleted. Aurate data from the load-up part of a CCG test are therefore essential in determining aurate values of. Time dependent failure assessment diagrams (TDFAD) have been produed at various assessment times and the shape of the urve is found to be insensitive to time. Initiation times have been predited using the TDFAD approah and the lower bound, mean and upper bound values, with both the plane stress and plane strain referene stress solution used in the alulation of Lr. When the plane strain referene stress solution is used onservative preditions have been obtained only through the use of the lower bound values. However, the plane stress solution has resulted in onservative preditions when used with all bounds of. Aknowledgements The assistane of Mr. Kilian Wasmer in the statistial analysis of the data is gratefully aknowledged. This paper is published with permission of British Energy Generation. Referenes 1. British Energy Generation Ltd., R6: Assessment of the Integrity of Strutures Containing Defets, Revision 4, British Energy Generation Ltd., Ainsworth R.A., Hooton, D. G. and Green, D., Failure Assessment Diagrams for High Temperature Defet Assessment, Engineering Frature Mehanis, 62, pp , Webster G.A., Ainsworth, R. A., High Temperature Component Life Assessment, 1 st ed., Chapman and Hall, London, Bettinson A.D., The Influene of Constraint on the Creep Crak Growth of 316H Stainless Steel, Ph.D. Thesis, Department of Mehanial Engineering, Imperial College London, ASME, Case of ASME Boiler and Pressure Vessel Code, Setion III-Class I Components in Elevated Temperature Servie. Code Case N47-29, New York, RCC-MR, Design and Constrution Rules for Mehanial Components of FBR Nulear Island, AFCEN, Page 14 of 26

15 7. Dean D.W., O Donnell, M. P. Alternative Approahes in the R5 Proedures for Prediting Initiation and the Early Stages of Creep Crak Growth, Creep and Fatigue at Elevated Temperatures, Tsukuba, Japan, 2001, pp ESIS, ESIS Proedure for Determining the Frature Behaviour of Materials, ESIS P2-92, European Strutural Integrity Soiety, ASTM, ASTM E : Standard Test Method for Measurement of Frature Toughness, Annual Book of ASTM Standards, Dean D.W., Ainsworth, R.A., Booth, S.E., Development and Use of the R5 Proedures for the Assessment of Defets in High Temperature Plant, International Journal of Pressure Vessels and Piping, 78, pp , Bettinson A.D., O Dowd, N.P., Nikbin K.M., Webster G.A., Experimental investigation of onstraint effets on reep rak growth, PVP, 434, Computational Weld Mehanis, Constraint and Weld Frature, ASME 2002, Ed. F.W. Brust, ASME New York, NY , pp Djavanroodi F., Webster G.A., Comparison Between Numerial and Experimental Estimates of the Creep Frature Parameter C*, Frature Mehanis, Philadelphia, 1992, pp Miller A.G., Review of Limit Loads of Strutures Containing Defets, International Journal of Pressure Vessel and Piping, 32, pp , RCC-MR, Design and Constrution Rules for Mehanial Components of FBR Nulear Islands, AFCEN, Dean D.W., Gladwin, D.N. Charaterisation of Creep Crak Growth Behaviour in Type 316H Steel Using Both C* and Creep Toughness Parameters, Pro 9 th Int. Conf. on Creep and Frature of Engineering Materials and Strutures, Swansea, 2001, pp Page 15 of 26

16 Speimen Size Width Thikness Net Thikness W (mm) B (mm) Bn (mm) Large (L) Standard (S) Half size (HS) Table 1: Typial dimensions of ompat tension speimens used in the analysis. Page 16 of 26

17 Time (hrs) σ (MPa) σ r (MPa) Table 2: Rupture stress and stress orresponding to % inelasti strain at speifi times. Page 17 of 26

18 Limit Load Solution t i (Δa = mm) (hrs) t i (Δa = 0.5 mm) (hrs) Exp UB Mean LB Exp UB Mean LB Plane Strain (PE) 105 > 1000 > > 1000 > Plane Stress (PS) 105 < 100 < 10 < < 10 < 10 < 10 Table 3: Comparison of experimentally determined initiation times (Exp) and TDFAD preditions using upper bound (UB), mean and lower bound (LB) data. Page 18 of 26

19 Stress σ σ ref Stress Strain Curve (t = 0) Isohronous Stress Strain Curve (t > 0) σ Total Strain Figure 1: Shemati isohronous stress strain urve, after [10] indiating the definition of σ and σ. ref ε ref Load U p U e U Δ p Δ e Δ Total Displaement Figure 2: Shemati load-displaement behaviour in a reep rak growth test, after [10]. Page 19 of 26

20 K r 1.0 R6 Option t = 0 t = 3000 h t = 300,000 h Figure 3: Shemati example of a time dependent failure assessment diagram (TDFAD) based on data from an austeniti steel [2]. 0.8 Crak Extension, Δa (mm) Time (hrs) t i Figure 4: Determination of initiation time, t i, for Δa = 0.5 mm from experimental data [4]. Page 20 of 26

21 P (kn) 10 9 P = 1367Δ Δ Δ 3-77Δ Δ Δ (mm) Figure 5: Load, P, vs. displaement, Δ, data during load up in a test on a HS speimen Stress (MPa) Total Strain (%) Tensile Data Isohronous Curve t = 100 hrs Isohronous Curve t = 1000 hrs Isohronous Curve t = hrs Isohronous Curve t = hrs Figure 6: Isohronous stress-strain urves generated for 316H stainless steel at 550 o C Page 21 of 26

22 1000 K mat (MPam 1/2 ) Large Standard Half Size Upper Bound (+ 2 s.d.) Mean Line Lower Bound (- 2 s.d.) Time (hours) Figure 7: Data bounds for the frature toughness,, for Type 316 Material at 550 (Δa = mm). o C 1000 K mat (MPam 1/2 ) Large Standard Half Size Upper Bound (+ 2 s.d.) Mean Line Lower Bound (-2 s.d.) Time (hours) Figure 8: Data bounds for the frature toughness,, for Type 316 Material at 550 (Δa = 0.5 mm). o C Page 22 of 26

23 2.5E E-04 P/(EBW) 1.5E E E E Δ T / W L S HS Figure 9: Typial normalised load-displaement urve for Large (L), Standard (S) and Half Size (HS) CT speimens in a CCG tests (up to Δa = 0.5 mm) UL / UT Crak Extension, Δ a (mm) Figure 10: Comparison of the ratio of the loading area, U L, to total area under, U T, the load displaement urve, as rak extension proeeds, for a Large (L), Standard (S) and Half Size (HS) CT speimen. L S HS Page 23 of 26

24 Kr R6 Option 1 FAD TDFAD t = 0 hrs Figure 11: TDFAD at time t = 0 hours and R6 Option 1 FAD TDFAD t = 0 hrs TDFAD t = 500 hrs TDFAD t = 1000 hrs TDFAD t = hrs TDFAD t = hrs Kr t = hrs t = 0 hrs Figure 12: TDFAD for austeniti Type 316H stainless steel over a range of times. Page 24 of 26

25 LB Lous Δa = mm LB Lous Δa = 0.5 mm Mean Lous Δa = mm Mean Lous Δa = 0.5 mm UB Lous Δa = mm UB Lous Δa = 0.5 mm Kr t = hrs TDFAD at t = 100 hrs Figure 13: Appliation of a TDFAD to predit initiation times of a test using the plane strain limit load solution. Kr t = hrs LB Lous Δa = mm LB Lous Δa = 0.5 mm Mean Lous Δa = mm Mean Lous Δa = 0.5 mm UB Lous Δa = mm UB Lous Δa = 0.5 mm TDFAD at t = 100 hrs Figure 14: Appliation of a TDFAD to predit initiation times of a test using the plane stress limit load solution. Page 25 of 26

26 TDFAD at t = 100 hrs Kr LB Lous Δa = 0.5 mm (PE) Mean Lous Δa = 0.5 mm (PE) UB Lous Δa = 0.5 mm (PE) LB Lous Δa = 0.5 mm (PS) Mean Lous Δa = 0.5 mm (PS) UB Lous Δa = 0.5 mm (PS) t = hrs Figure 15: Comparison of preditions at Δa = 0.5 mm, using plane stress (PS) and plane strain (PE) limit load solutions. (Points on predition loi are at times of 10, 100, 500 and 1000 hours). Page 26 of 26