Fatigue & Fracture of Engineering Materials & Structures

Predicting creep crack initiation in austenitic and ferritic steels using the creep toughness parameter and time-dependent failure assessment diagram

C. M. DAVIES

Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK Received in final form 11 August 2009

ABSTRACT Methods for evaluating the creep toughness parameter, Kcmat, are reviewed and Kcmat data are determined for a ferritic P22 steel from creep crack growth tests on compact tension, C(T), specimens of homogenous parent material (PM) and heterogeneous specimen weldments at 565 °C and compared to similar tests on austenitic type 316H stainless steel at 550 °C. Appropriate relations describing the time dependency of Kcmat are determined accounting for data scatter. Considerable differences are observed in the form of the Kcmat data and the time-dependent failure assessment diagrams (TDFADs) for both the 316H and P22 steel. The TDFAD for P22 shows a strong time dependency, but is insensitive to time for 316H. Creep crack initiation (CCI) time predictions are obtained using the TDFAD approach and compared to experimental results from C(T) specimens and feature components. The TDFAD based on parent material properties can be used to obtain conservative predictions of CCI on weldments. Conservative predictions are almost always obtained when lower bound Kcmat values are employed. Long-term test are generally more relevant to industrial component lifetimes. The different trends between long- and short-term CCI time and growth data indicate that additional long-term test are required to further validate the procedure to predict the lifetimes of high temperature components.

Keywords creep crack initiation (CCI); creep toughness; P22 steel; TDFAD; weldments; 316H steel.

NOMENCLATURE a, Aa = crack length, crack extension a = crack growth rate A = creep strain rate coefficient Ap = primary creep strain coefficient Bn = specimen net section thickness between side-grooves Br = coefficient in the stress rupture time law C* = steady state creep characterising fracture mechanics parameter CCG = creep crack growth CCI = creep crack initiation

D = constant coefficient in creep crack growth rate correlation with C* Di = constant coefficient in creep crack initiation time correlation with C* E = elastic (Young's) modulus E = effective elastic modulus

H = correlating coefficient in the K^at versus time relation HAZ = heat affected zone

Correspondence: Catrin M. Davies. E-mail: catrin.davies@imperial.ac.uk

J = elastic-plastic fracture mechanics parameter j = the power-law exponent in the Kmat versus time relation Jic = material mode I plane strain elastic-plastic fracture toughness K = linear-elastic stress intensity factor Kic = material mode I plane strain fracture toughness Kr = TDFAD parameter measuring proximity to fracture Kmat = creep toughness parameter LB = lower bound

Lr = TDFAD parameter measuring proximity to plastic collapse or creep rupture LJnax = maximum value of Lr at the cut-off point in TDFAD n = creep stress exponent np = primary creep stress exponent P = load

p = primary creep parameter Plc = plastic collapse load of cracked body PM = parent material ROA = reduction of area t, At = time, time increment

tj = creep crack initiation time t^Exp = experimentally measured creep crack initiation time tjPredicted = predicted value of the creep crack initiation time UB = upper bound

Up = area under the load displacement curve associated with plasticity v = Poisson ratio vr = rupture stress exponent W = specimen width WM = weldment

Ac = load line displacement associated with creep ec = strain component associated with creep deformation Ee = strain component associated with elastic deformation epl = strain component associated with plastic deformation Etotal = total strain Ef = plastic ductility Ef = creep failure strain (creep ductility) Eref = total strain at reference stress

E^ef = strain at reference stress associated with elastic deformation Erpef = strain at reference stress associated with plastic deformation Ercef = strain at reference stress associated with creep deformation AECp, AeC = primary and secondary creep strain increments

fa = exponent in correlation of initiation time with C* 0 = exponent in correlation of creep crack growth rate with C* n = factor relating J/C* to the plastic/creep area under a load displacement curve a0.2 = 0.2% proof strength a uts = ultimate tensile stress a0.2 = 0.2% proof stress of the material a02 = 0.2% creep strength (stress at 0.2% inelastic strain) a flow = flow stress (aOTs + a0j)/2

INTRODUCTION > j r , r ,

the period of time prior to the onset of crack extension

The lifetime of components operating in high temper- from an existing defect due to CCG and can occupy a large ature plant is limited by the mechanisms of creep crack fraction (>80%) of a components service lifetime.1 The initiation (CCI) and growth (CCG). The CCI time is CCI time is generally defined as the time for a defined

small measureable crack extension, typically 0.2 mm for laboratory specimens or 0.5 mm.2 Reliable predictions of CCI time are fundamental in high temperature component lifetime assessments due to the duration of the CCI period.

The time dependent failure assessment diagram (TD-FAD) approach has become increasingly recognised for the prediction of CCI times.3 The development of the TDFAD has mainly been based on austenitic type 316H stainless steel which differs from ferritic steels in their tensile and creep material behaviour and further verification is required before the procedure may be recommended for ferritic steels.4'5 Two widely used alloys for high-temperature plant components with contrasting properties are ferritic P22 (2 1/4 Cr1Mo) steel and austenitic type 316H stainless steel. The favourable qualities of these steels include high creep ductility and relatively high weldability.6'7 These two steels are considered here in the evaluation of the TDFAD method.

The TDFAD approach for CCI time predictions relies on the availability of reliable creep toughness (Kmat) data. The main advantage of the TDFAD approach is that detailed calculations of crack tip parameters such as C* are not required and that the TDFAD can indicate whether failure is controlled by crack growth, creep rupture or plastic collapse, i.e. the fracture regime need not be specified in advance. Methods for evaluation or estimating the Kmc at parameter have been developed and modified over recent years.

A considerable amount of creep toughness data have been determined for austenitic type 316H stainless steel in the region of 500-700 °C, though mainly at 550 °C.8'9 Limited Kmat data have also been determined for a range of ferritic steels,4'5'8'10-12, and in some cases TDFADs have also been produced. Creep toughness data often show appreciable scatter8'9 which must be considered when obtaining CCI time predictions. In the majority of cases, where TDFADs have been determined together with creep toughness data, explicit CCI times have not been obtained. Generally, the CCI data for a given crack extension have been plotted on a TDFAD for a range of times and an assessment made to determine if the TDFAD approach leads to conservative predictions, or sometimes the limits between which the CCI times' prediction lie are indicated. The degree of conservatism/non-conservatism however, is not indicated.

Considerably high loads are often applied to specimens in CCG tests, leading to relatively short test durations compared to the lifetimes of high temperature components operating in plants. Therefore, the application of methods based on CCG test data to predict real component lifetimes require validation.4 Components are often welded and the application of the TDFAD approach for weldments has been considered.12-16 However, a

number of complications arise when considering weld-ments such as material mismatch effects that may require consideration.

In previous work,9 the TDFAD approach has been applied to predict CCI times in austenitic type 316H stainless steel at 550 °C, and the sensitivity of predictions to creep toughness data bounds and reference stress solutions have been examined. In this work methods for Kmc at evaluation and estimation are reviewed and K mc at data are determined for a ferritic P22 steel from CCG tests on compact tension, C(T), specimens of homogenous parent material (PM) and heterogeneous specimen weldments at 565 °C. The weldments consist of PM, weld metal and a heat affected zone (HAZ). The crack tip is located on the HAZ/PM boundary where cracking is often observed in practice. Appropriate relations describing the time dependency of Kmc at are determined accounting for data scatter. The TDFAD diagram and its associated parameters are then compared for the austenitic type 316H and ferritic P22 steel. The influence of test duration, and material condition are also considered and CCI time predictions obtained and compared to experimental results from short and long-term laboratory tests specimens and feature components.

THE FAILURE ASSESSMENT DIAGRAM (FAD) APPROACH

The FAD procedure considers that failure will occur by plastic collapse or brittle/ductile fracture. The proximity to failure by fracture and plastic collapse are measured by the parameters Kr and Lr' respectively, defined by

aref ^0.2

where Kic and Jic are fracture toughness values (critical values of K and J for fracture under mode I, tensile loading), E the effective elastic modulus (equal to E for plane stress or E/(1 - v2) for plane strain conditions where v is the Poisson ratio). In Eq. (2) aref is the reference stress1 of a geometry, a 0.2 is the 0.2% proof stress (measure of the materials yield stress), P the applied load and PLC the collapse load of the cracked geometry.1 The R6 Option 1 curve17'18 is material independent and defined by

Kr = (1 - 0.14Lr2) [0.3 + 0.7 exp (-0.65L«)]

for Lr < Lmx'

Kr = 0 for Lr > Lm

The cut-off, Lrmax, which indicates failure by plastic collapse is defined by the ratio

L^ax _

gflow ^0.2 '

where a gow is the mean of the ultimate tensile stress, a uts , obtained from the engineering stress-strain curve and the 0.2% proof stress, i.e. aflow = (auTS + a0.2)/2.

The R6 Option 2 FAD has a material specific failure assessment curve which has been derived based on the assumption that crack growth occurs when the J-integral attains a critical value.

The time-dependent failure assessment diagram (TDFAD)

The R6 Option 2 FAD has been extended to a TDFAD which addresses limited high temperature crack growth.3 This is done by replacing Kjc, in Eq. (1) by a creep toughness corresponding to a given crack extension at a given time, denoted Kmat( Aa, t), and a0 2 in Eq. (2) by the 0.2% inelastic (creep and plastic) strain from an isochronous stress-strain curve at a particular time and temperature, a02, also called the 0.2% creep strength. The value of a02 will decrease as time increases, i.e. creep strain increases. In the TDFAD, for the case of a single primary load, the parameters Kr and Lr are therefore defined

failure assessment diagram for a specific time is defined by the equations

r a0. 2

Kr= 0 for Lr > Lm

In Eq. (10) £ref is the total strain at reference stress at a given time, given by the sum of the elastic and plastic strain and the total creep strain accumulated in that time, i.e.

eref(t) = <f + eref + <ef (t) •

Note that eref is the true strain at true stress aref ( = Lra0.2) (and not the engineering strain). Note also that at short times eref(t) ~ e^f + epef and ac0 2 ~ a0.2, and Eq. (10) reduces to the R6 Option 2 curve. At long times eref(t) ~ eref and Eq. (10) tends to

Equation (13) can be derived for steady state creep conditions, where the creep strain rate is a constant, based on the assumption that at long times J(t), evaluated, can be approximated by the product of C* and time (i.e. J(t) ~ C*t19) and C* is given by the reference stress estimate.1 The TDFAD can therefore measure the proximity to failure by fast fracture, CCG, plastic collapse and creep rupture. Therefore, in the TDFAD approach, a failure mode does not have to be pre-defined.

(7) Application of TDFAD to predict CCI

The cut off point L^3" is defined on the TDFAD as

Lmax _

where ar is the stress to cause creep rupture at the same time as a0.2 is evaluated. If Lr exceeds Lrmax, failure is expected to occur by creep rupture rather than by fracture. In order to be consistent with the R6 procedure, Lrmax in the TDFAD should not exceed the value of LJnax defined in Eq. (5). The time to rupture in a uniaxial creep test over a range of stresses can often be approximated by the power-law relation,

tr = Br a-Vr, (9)

where Br and vr are the rupture coefficient and exponent, respectively.

The time-dependent failure assessment curve is based on the assumption that crack growth occurs when the dependent time parameter, J(t), attains a critical value. A

The TDFAD can be used to predict if a crack will extend a distance Aa in a given time or the time required for a specified amount of crack extension. Because CCI can be defined as the period of time required for a small increment of crack growth, Aa, the TDFAD may be used to predict CCI times. For some materials the curves may not vary greatly with time and curves for longer times can be used to provide a conservative TDFAD for an assessment at shorter times.8

To predict CCI an initial time estimate is made and the values of Lr and Kr, and their associated parameters, are determined for the specified initiation distance, Aa, at that time. The point (Lr, Kr) is then plotted on the TDFAD. If the point lies within the TDFAD then the crack extension is less than Aa and creep rupture is avoided in the assessment time. To determine an initiation time, tj, a time locus of points (Lr, Kr) is constructed at various times. The time for a crack extension Aa is given by the intersection of a point on this locus (for a given time) with the failure assessment curve for the corresponding time.

Lr< Lm3*

Table 1 Material properties for homogeneous PM 316H stainless steel at 550 °C and P22 steel at 565 °C

316H P22 (PM)

A (MPa1/n h-1) 1.47 x 10-34 3.21 x 10

n 11.58 10.68

np 7.45 2.47

Ap (MPa-np t-p ) 2.60 x 10-23 1.0 x 10-i

p 0.746 0.3

E (MPa) 140 000 140 135

a 0.2 (MPa) 170 284

a UTS (MPa) 442 365

Br (MPavr h) 5.27 x 1031 1.43 x 10

vr 11.3 9.11

a flow (MPa) 306 327

ef (%) (Eng) 37 27

ef (%) (Axial) 8 31

ecf (%) (ROA) 21 65

An iterative process is required to match the times associated with the point of intersection of the locus and the TDFAD constructed. The procedure is further detailed in Refs [8,9].

Isochronous stress-strain data

Isochronous stress-strain curves for the specified temperature are required in order to determine oc0 2 and the overall TDFAD. Isochronous stress-strain data are generated here using the elastic-plastic and creep material response. The method used follows the procedure in the RCC-MR design code20 for primary-secondary creep of type 316 stainless steel material. Thus, the primary and secondary creep strain increments, Aep and Ae^, are calculated according to

Aep = pAlJf a np/p e(1-

AeC = Aan At.

1/ P)At,

The creep strain increment, Aec , is equal to the larger of the two increments calculated from Eqs (14) and (15),

AeP for Asp > AeS

for Aecp < Aecs

The primary and secondary creep constants in Eqs. (14) and (15) are given in Table 1 for 316H stainless steel at 550 °C and P22 steel at 565 °C. For a particular time, the total strain at any stress level is given by the sum of the elastic and plastic strain and the total creep strain accumulated in that time, i.e.

„total

(a, t) = ee (a) + epl (a) + ^ Aec (a, A t). (17)

EVALUATION OF THE CREEP TOUGHNESS PARAMETER, K^

The £mat parameter is evaluated from the load displacement curve generated during a CCG test using the relation.3'8

-"-mat

E ' P Ac

Bn (W- a) ' n + 1 Bn (W- a)

where Up is the area under the load displacement curve associated with plasticity, W is the specimen width, Bn is the net specimen thickness between any side-grooves, a is the crack length and n the secondary creep power-law stress exponent (see Eq. 15) and n a geometry function (n = 2.2 for C(T) specimens21). Note that the Kcmai relation has been modified since the work in Ref. [9].

In the absence of specimen load-displacement data a method has been proposed to estimate Kmat from CCI and CCG data. Under steady state conditions the CCG rate, a, may be described by the expression2

= DC «

where D and 0 are temperature-dependent crack growth constants. The CCI time may also be described by the C* parameter according to the power-law relationship

ti = DiC

where Dj and fy are temperature-dependent CCI constants. Assuming widespread creep conditions, a constant secondary creep strain rate and using the reference stress estimate of C*,1 it can be shown that Kmat may be estimated from CCI data according to the relation22

[ED)/^i t(1—1/^i)

Alternatively, if crack growth is assumed a continuous process commencing at zero time, then Kmat may be estimated from CCG data22 using

E, i№ ,1-1/«

It can therefore be seen from Eq. (22) that Kmat is expected to decrease with time according to

mat„ (t1 —1/« )1/2

CCI and growth models23-25 predict that = 0 = n/(n + 1) thus, substituting for 0 in Eq. (23) it may be written

Kmata t—1/2n

500.0 1 P22 565 °C \

| 300.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 True Strain

Fig. 1 Comparison of the high temperature tensile behaviour of 316H stainless steel at 550 °C and ferritic P22 steel at 565 °C.

It is therefore expected that Kcmat follows the power-law relationship

Kcmat(A«, t) = Hti

where H is the correlating coefficient and, j is the power-law exponent.

CREEP DEFORMATION AND CCG BEHAVIOUR OF P2 2 AND 316H STEEL

Firstly, the high temperature tensile and creep deformation and rupture behaviour of the two materials are compared to reveal their differences, which will be reflected in the form of their TDFADs. The true-stress versus true-strain curves of both materials are shown in Fig. 1 up to the point in the tests where a failure mechanism intervened. The tensile properties are given in Table 1. The shape of the tensile behaviour of P22 and 316H are clearly different. The 0.2% proof stress of P22 is almost 70% higher than that of 316H and exhibits relatively little hardening. On the contrary, 316H has a high degree of work hardening and has a 10% higher plastic ductility, Sf, than P22 steel, based on engineering strain (Eng) values.

The secondary creep strain rate and rupture-time versus stress relations for the two steels are compared in Fig. 2a and b, respectively. Note that the stress values for 316H are true-stress values accounting for plastic strain on loading. However, in the absence of loading data, and because the applied stresses are significantly less than the a 0 . 2 of the steel (thus little plastic strain is expected on specimen loading), the engineering stress has been used for the P22 tests. In Fig. 2 a the stress to cause a given strain rate or rupture time is around a factor of three higher for 316H than P22. The creep strain rates for a given stress are therefore significantly higher, and rupture times lower, for P22 steel in comparison to 316H at these tempera-

(a) 1.E-02

1.E-03

1.E-04

1.E-05

1.E-06

: o P22 Data

□ 316H Data P

-316H Trendline

- P22 Trendline i

0 6 □

_ c P = / I 0

(b)100000

100 a (MPa)

O P22 Data b □ 316H Data Q

.......316H Trendline

----P22 Trendline

100 a (MPa)

Fig. 2 Comparison of (a) secondary creep strain rates and (b) creep rupture time with stress for 316H at 550 °C and P22 at 565 °C.

tures. The uniaxial creep failure strain (creep ductility), sf, of P22 is over twice that of 316H based on both axial and reduction of area (ROA) measurements (see Table 1).

Isochronous stress-strain curves

The materials tensile data and creep laws have been combined to generate isochronous stress-strain curves as specified in Section 2.3 using the material properties given in Table 1. The resultant curves are very different for the 316H and P22 steel as shown in Fig. 3a and b, respectively, for times up to 100 000 h. The P22 steel's curves are strongly time dependent even at short times. In fact the P22 curve for a time of 1 h almost overlays the 316H curve at 100 000 h. The corresponding 0.2% inelastic (creep and plastic) strain, a^ 2, are illustrated and compared in Fig. 4. Little change in a^ 2 for 316H steel is observed for the first 1000 h whilst creep strains dominate in the P22 steel. Even at very short times it can be seen that for P22 ac0 2 reduces by 50% due to creep strain accumulation in the first hour alone.

0.00 0.05 0.10 0.15 0.20 0.25 0.30 Total Strain

Total Strain

CREEP FRACTURE BEHAVIOUR

CCG behaviour

CCG test data on the compact tension specimen, C(T), from Ref. [28] for P22 and Refs [26,27] for 316H steel have been re-analysed in accord with recent changes in data analysis procedures.2'3 A sizable data set is available

Fig. 3 The isochronous stress-strain curves at a range of times for (a) 316H stainless steel at 550 °C and (b) ferritic P22 steel at 565 °C.

for 316H with test durations ranging between 100 and 18 000 h. The CCG tests on P22 steel were relatively short, ranging between 300 and 4,400 hrs. The significance of plasticity on loading of the 316H steel specimens and its influence on CCG behaviour has been described in Refs [9,29,30] The P22 test load-up data were not available for analysis. However, it is expected that there is little

300.0 -

250.0X316H

_ 200.0

si 150.0

G 100.0 50.0 0.0

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 Time (h)

Fig. 4 Evolution of the 0.2% creep strength, o^ 2, with time for the 316H stainless steel at 550 °C and P22 steel at 565 °C.

plasticity on loading of P22 specimens because the ratio ff ref lo0 . 2 on load up is less than 0.5 for all specimens and is on average 0.31 and 0.45, assuming plane strain and plane stress conditions, respectively. For the 316H specimens this ratio was close to or exceeded unity assuming plane strain conditions, except for the long-term tests where the ratio was approximately 0.78.

Mean line power-law regression fits have been made to the CCG data as shown in Fig. 5. Upper bound (UB) and lower bound (LB) fits are obtained by offsetting the mean line by ±2 standard deviations of the regression fit, assuming a constant slope. Separate fits have been made to the long- and short-term tests of 316H in Fig. 5 a due to the distinct CCG behaviour observed in the long-term tests, where plasticity is limited and thus high specimen constraint effects maintained.30 The CCG rate constants for these fits (see Eq. 5) are given in Table 2. Similar CCG behaviour is exhibited by both steels for C* > 1 x 10-5 MPamh-1; however, significant tails are observed for P22 though the validity criterion2 are met.

CCI behaviour

The CCI times for 0.2 mm and 0.5 mm of crack extension are plotted against the experimentally determined C* parameter at the corresponding time in Figs 6 and 7 for 316H and P22 steel, respectively. Regression fits have been made to the data and the constants in Eq. (20) determined, accounting for the degree of data scatter (see Table 3). The CCI time data for 316H (Fig. 6) appear to form reasonable correlations with the C* parameter, though the power-law correlation exponent, &, is significantly less than n/(n + 1) as predicted from CCI models.25'29 The value of & obtained from the regression fit for P22 data for Aa = 0.2 mm is greater than unity indicating that the experimentally determined C* parameter

is not an appropriate correlating parameter in this case because, as indicated by the tails shown in Fig. 5, steady state CCG conditions have not been achieved.2 Also, because the data set for P22 is relatively small it can be difficult to establish the data trend. More reasonable correlations are obtained for the P22 data at Aa = 0.5 mm, though again & is significantly less than n/(n + 1). A significant degree of data scatter is observed for both materials, quantified by the UBILB values of Dj, which are generally a factor of 5 greater or less than the mean value, respectively.

Creep toughness data, Km"

The Kcmat values at Aa = 0.2 and 0.5 mm of crack extension have been calculated using Eq. (18) for both materials in homogenous PM and weldment (WM) conditions. A regression fit has been made to the data to obtain the values of H and j in Eq. (25) and again UBILB fits made by offsetting the mean by ± 2 standard deviations of the data set (see Tables 4 and 5). In addition, the best line fit has been made to the data assuming a slope of 1/(2 n) as predicted in Eq. (24). Note that sensible trendlines have not been obtained using Eqs (21) and (22) in conjunction with the CCG and CCI regression data detailed in Tables 2 and 3, respectively, and thus are not shown in the following figures.

Homogenous PM Kcmat data

The creep toughness data of 316H PM at 565 °C have previously been presented in Refs [9,31-33]. However, this data have been re-analysed here for consistency, and to be in accord with recent modifications in the Kcmat evaluation procedure. The slope j of the regression fits to the 316H data in Fig. 8, is a factor of 5 steeper than predicted using Eq. (24). The best fit line to the data using Eq. (24) provides a reasonable fit to the data for less than 500 h and 800 h for Aa = 0.2 and 0.5 mm, respectively. For times greater than these, a change in the data trend can be observed.

The corresponding Kcmat data for PM P22 steel are presented in Fig. 9. Creep toughness data for P22 steel at 550 °C has been presented in Ref. [12]. Kcmat is expected to be insensitive to such small variations in temperature,8 thus the data in12 at 550 °C have been combined with the data analysed here at 565 °C. The influence of temperature on Kcmat is further discussed for materials of similar compositions to those analysed here in Ref. [10].

The regression fit values for Aa = 0.2 mm were not sensible as the negative j value in Table 4 indicates an increase in Kcmat with time. For Aa = 0.5 mm, however, j ~ 1/(2n) as predicted in Eq. (24). For the P22 data therefore the mean lines shown in Fig. 9 are the best fits of Eq. (24) to the data set, and the UBILB factors are

P22 316H

(a) 1.0E+01

1.0E+00

1.0E-01

1.0E-02

□ Long Term Test Data o Short Term Test Data

.......UB

----LB

1.0E-03

1.0E-04

316H 550 °C

1.0E-05

1.0E-07 1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01

C* (MPam/h)

(b) 1.0E+01

1.0E+00

1.0E-01

Test Data ■UB - Mean -LB

1.0E-02

1.0E-03

1.0E-04

P22 565°C

1.0E-05 -I.....................1—..........1—.........1—.........1—..............Fig. 5 CCG rate correlations with the C*

1.0E-07 1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 parameter for (a) 316H stainless steel at

550 °C and (b) P22 steel at 565 °C including data bounds.

C* (MPam/h)

assumed to be equal to that obtained from a regression fit to PM data in16 where full details of the weldment geom-

to the data. etry can be found. This weldment data are compared to

additional and re-analysed PM data in Fig. 10. Due to

the limited amount of weldment data available the slope Comparison of parent and weldment data ,, ji-tj ijil

of the weldment trend line fitted to the data has been

The creep toughness data of 316 steel compact tension assumed to be equal to that of the regression fit to the

specimen weldments have been determined and compared PM. A relatively good fit is observed, the coefficients for

Table 2 Regression fit constants to CCG rate versus C* data (Eq. 19) from long-term (LT) and short-term (ST) tests on 316H and tests on P22 steel

316H (LT) 316H (ST) P22

D Mean 9.25 3.45 4.52

D UB 16.91 8.26 16.87

D LB 5.06 1.44 1.21

0 0.73 0.75 0.75

(a) 1.E+05 =

1.E+04 =

1.E+03 ;

^ 1.E+02 ; 1.E+01 i 1.E+00 -

1.0E-07 1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 C* (MPam/h)

(b) 1.E+05 =

1.E+04 =

1.E+03 = ^ 1.E+02 i 1.E+01 = 1.E+00 -

1.0E-07 1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 C* (MPam/h)

Fig. 6 CCI time correlations with the C* parameter at (a) Aa = 0.2 mm and (b) Aa = 0.5 mm for 316H stainless steel at 550 °C, including data bounds.

which are given in Table 4. For a given time, the mean Kcmat value of the 316 weldment specimens is a factor of approximately 2 less than that for PM.

Creep toughness data from C(T) weldment specimens of P22 steel are compared to PM specimens at 565 °C and 550 °C for both Aa = 0.2 and 0.5 mm in Fig. 11a and b, respectively. The PM and weldment data at both temperatures fall within the same scatter bands. A best fit

(a) 1.E+05 1

1.E+04 =

1.E+03 1 ^ 1.E+02 1 1.E+01 1 1.E+00 -

1.0E-07 1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 C* (MPam/h)

(b) 1.E+05 1 1.E+04 = 1.E+03 =

^ 1.E+02 ! 1.E+01 =

1.E+00

1.0E-07 1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 C* (MPam/h)

Fig. 7 CCI time correlation with the C* parameter at (a) Aa = 0.2 mm and (b) Aa = 0.5 mm for P22 steel at 565 °C, including data bounds.

Table 3 Regression fit constants to CCI time versus C* data (Eq. 20) from tests on homogenous PM 316H and P22 steel for crack extensions, Aa, of 0.2 and 0.5 mm

316H P22

Aa (mm) 0.2 0.5 0.2 0.5

Dj Mean 0.7 3.9 9.3 x : 10-4 22.1

Dj UB 5.0 17.9 4.0 x : 10-3 4.5

D, LB 0.1 0.8 2.2 x : 10-4 0.93

0j 0.55 0.47 1.1 0.44

line assuming a slope j = 1 /(2n), as in Eq. (24), has been made to the PM and weldment data sets, where n has been taken to be equal to the PM value. This assumption is justified by the fact that the value of n determined from tests performed on cross-weld uniaxial specimens of P22 at 550 °C, which are considered to most represent the behaviour of C(T) weldments, were found equal to the

o Test Data

Aa = 0.5 mm

o Test Data

.......UB

xo -----LB

\o o \

Aa = 0.5 mm

Mean LB

Table 4 Mean, UB and LB regression fit constants to K^31 versus time data (Eq. 25) of homogeneous PM and weldment 316H and P22 PM specimens

316H 316H P22

PM Weldment PM

Aa (mm) 0.2 0.5 0.2 0.5 0.2 0.5

H Mean 242.4 224.5 117.8 173.0 29.8 73.3

H UB 449.7 611.5 211.8 289.0 51.5 136.8

H LB 130.6 224.5 65.5 103.5 17.3 39.3

j 0.20 0.23 0.20 0.23 -0.06 0.04

Table 5 Mean, UB and LB constants for the Kcmat versus time

relationship of Eq. (25) for homogenous PM specimens of 316H

and of P22 steel, and weldment specimens of P22 steel assuming

j = 1/(2n)

316H P22

PM PM Weldment

Aa (mm) 0.2 0.5 0.2 0.5 0.2 0.5

H Mean 119.8 135.1 51.35 71.96 47.2 62.1

H UB 222.2 223.0 88.68 134.3 69.5 88.3

H LB 64.5 81.9 29.73 38.56 32.0 43.7

j = 1/(2n) 0.043 0.047 0.047

PM test values.28 Note that sensible regression fits were not obtained for this data set. On average there is a 10% difference between the PM and weldment value of Kcmat for a given time and bound, whereas there is around a 40% and 80% difference between the UB or LB and mean value of Kcmat for a given time, for the PM and weldment data, respectively, as can be deduced from Table 5. Therefore, within the extent of data scatter, little difference in creep toughness behaviour is observed between the two material conditions for the P22 steel.

TDFAD FORMATION

The TDFADs for a range of times (t = 0, 1, 10, 100, 1000, 10 000 and 100 000 h) have been determined from Eqs (10), (11), (14)-(17), using the PM data given in Table 1, and are shown in Fig. 12. Also shown in Fig. 12 for comparison purposes is the R6 Option 1 curve (see Eq. (3)). Note that the R6 cut off point, LJnax (see Eq. (5)) is the appropriate value to use (see Section 2.1) for times less than 10 000 h for the 316H material and for all times in the case of P22.

As can be seen in Fig. 12a and described in9 the 316H TDFAD is insensitive to time and deviates little from the R6 option 1 curve. The P22 TDFAD however, is in relatively good agreement with the R6 Option 1 curve at

(a) 1000

fM ioo

1 10 100 1000 10000 t (h)

(b) 1000 T-

CL ^ 100

1 10 100 1000 10000 t (h)

Fig. 8 Creep toughness versus time data for 316H stainless steel at 550 °C at (a) Aa = 0.2 mm and (b) Aa = 0.5 mm, including mean and UB/LB regression fits and the best fit using Eq. (24).

time 0 h, but almost instantly deviates significantly from it. These trends are due to the relatively low and high creep strain rates experienced in 316H and P22, respectively, (see Figs 2a & 3) at these temperatures.

CCI TIME PREDICTIONS

The TDFAD procedure for predicting CCI times is evaluated for both steels. A program has been developed that determines the intersection of a point (Kr , Lr) for a given time and crack extension with the TDFAD of corresponding time. Predictions for both PM and weldment data have been determined, though note the TDFADs have strictly been derived from PM data. The CCI times have been predicted for the tests on homogenous PM and weld-ment C(T) specimens.16'21'26 These tests have been used to derive the relationship of creep toughness on time, thus appropriate predictions are expected. In addition, CCI data are available for feature tests on P22 PM and

Aa = 0.2 mm

-Meanf Regression Fit

------lb j

-------Best Fit using Eqn (24)

316H 550 °C

Aa = 0.5 mm

□ -----

□ Data □

.......UB ,

-Meant Regression Fit -

- — LB J

-----Best Fit using Eqn (24)

(a) 1000

P22 ■ 565 °C

□ 550 °C

.........UB

-----LB

. » -

■ a-

■— —-------

Aa = 0.2 mm

(a) 1000

ti (h)

(b)1000

- P22 ■ 565 °C

I □ 550 °C

.........UB

-----LB

100 I .......................................

Aa = 0.5 mm

100 ti (h)

Fig. 9 Creep toughness versus time data for ferritic P22 steel PM at (a) 0.2 mm (b) 0.5 mm, including mean, UB/LB fitted lines.

weldmentpipe components, as detailed in Ref. [34]. These results are also predicted here using the TDFAD procedure. Predictions on C(T) specimens have been based on the plane strain reference stress solution. Details of the stress intensity factor and reference stress solution for the pipe component are given in Ref. [34].

TheTDFADs predicted CCI time, ijPredicted, is compared to the experimentally determined value, i,Exp, in Figs 13 and 15. Included in these figures is the line for tjPredicted = t,Exp. Points situated below this line indicate a conservative prediction, and vice-versa. Predictions have been obtained using the mean and LB values of K mat calculated using Eq. (25) with the regression fit values shown in Table 4 for 316H and the best fit values with an assumed slope of j = 1/(2n) (see Eq. 24) as shown in Table 5 for the P22 material. The predictions based on mean or LB K mat values are shown as open and grey symbols, respectively.

The weldment and PM specimen predictions are shown together in Fig. 13 for the 316 steel. Similar trends are

□ PM Data ■ WM Data

----Mean PM

-Mean WM

316 550 °C

Aa = 0.2 mm

(b) 1000

100 1000 10000 t (h)

316 550 °C □ PM Data

■ WM Data

- Mean PM

■ Mean WM

□□ 3

□ ST,

-■..p

■ □ ^^

■ Y-

Aa = 0.5 mm

100 t (h)

Fig. 10 Comparison of the creep toughness versus time data for 316H stainless steel at (a) 0.2 mm (b) 0.5 mm, for homogenous PM and weldment C(T) specimens.

observed for the two material conditions at both Aa = 0.2 and 0.5 mm. Predictions based on mean Kcmat values are often, but not always, conservative whereas the use of LB Kcmat values consistently gives conservative predictions. The same is true for C(T) specimen PM and weldment data for P22 material shown in Figs 14 and 15, respectively, except for one point in Figs 14b and 15a which is just above the line using a LB Kcmat value. However, because the data set available for P22 is limited, less confidence can be assigned to the appropriateness of the TDFAD for predicting CCI for P22, especially for long-term conditions because long-term data are unavailable for this material.

An initiation distance Aa = 0.5 mm has been deemed suitable for the feature components,34 thus pipe data are not included in Figs 14a and 15 a. Predictions for the pipe

(a) 1000 z

2 100 :

1 10 100 1000 10000 ti (h)

(b)1000 z

2 100 :

1 10 100 1000 10000 ti (h)

Fig. 11 Comparison of the creep toughness versus time data for P22 steel at 565 °C at (a) 0.2 mm (b) 0.5 mm, for homogenous PM and weldment C(T) specimens.

components are found to be very conservative in all cases with £Predlcted being less than 5% of tExp. The degree of uncertainty associated with iExp measurements, and the approximations made in evaluating the parameters K and aref for these components, leads to higher uncertainties in their CCI time predictions compared to that for laboratory test specimens. These additional uncertainties may contribute to the excessive conservatism in the CCI times predicted for these components. This uncertainty is however not easily quantified. The influence of the reference stress solution on the CCI predictions has previously been examined and discussed in Ref. [9].

DISCUSSION

The appropriate isochronous stress-strain response of a location being either within the parent, weld or HAZ of a weldment will be affected by the isochronous stress-strain

response of the surrounding material region. An equivalent isochronous stress-strain response may be defined, with intermediate isochronous properties, which will be a function of weldment geometry, loading, crack geometry, size and location. Note that for the weldment tests considered in this work the crack was located in the HAZ adjacent to the HAZ/PM interface. The equivalent isochronous stress-strain curve is based on the mismatch limit load and equivalent material stress-strain curve described in R6.17 A conservative assessment is however obtained using the tensile properties of the weaker material, which would be the 316H PM in the case of the 316 specimen weldments which consist of 316H PM and 316L weld metal.16 The mismatch reference stress for an overmatched weld is expected to be greater than that for a homogeneous specimen (see e.g. Ref. [35]). Thus, should a conservative prediction be obtained for an overmatched weldment using the materials PM properties and a homogeneous reference stress solution then the use of the mismatch reference stress would further increase the degree of conservatism. Tensile test data are not available for the P22 weld material at 565 °C; however, results in36 from a similar weld tested at 550 °C indicates that the welds yield strength is slightly (7%) less than the PM, however their general stress-strain behaviour of the weld is very similar to that of the PM. Therefore, it is considered that mismatch effects may not be significant for the P22 weldments analysis. The influence of mismatch on the isochronous stress-strain curves of Cr-Mo steel, following the R6 approach, have been examined in15 where the influence of geometry, crack size and time on the TDFAD was found negligible. A simplified procedure for evaluating isochronous stress-strain curves has been proposed in13 (neglecting plasticity and assuming the elastic response of the entire weldment is equal to the PM's response) and applied to a 1Cr0.5Mo steel weldment. The dependency of the TDFAD on time was shown in13, however, the deviation of the weldments TDFAC from the PM is curve was not demonstrated.

Because the TDFAD is being used to predict CCI it is expected that creep fracture would be the failure mode predicted. This is true for all cases examined for the 316H PM and weldments and the majority of cases for the P22 PM and weldment analyses using the LB Kcmat, which leads to higher Kr values. However, for the vast majority of cases failure by plastic collapse is predicted for the P22 PM and weldment analyses when the mean Kcmat values are employed, which is considered unrealistic. This is due to the strong time dependence of a0 2 causing a rapid increase of Lr to values greater than LJnax. The time dependency of the rupture stress ar is small in relation to a^ 2, thus Ljnaxcalculated from Eq. (8) which indicates creep rupture, does not fall below that of Eq. (5) which indicates plastic collapse.

P22 ■ PM 565 °C

□ PM 550 °C ♦ WM 565 °C o WM 550 °C

.........Mean PM

-----Mean WM

D" 1 »

Aa = 0.2 mm

P22 ■ PM 550 °C

□ PM 550 °C

♦ WM 565 °C

o WM 550 °C Mean PM Mean WM

......... □

Aa = 0.5 mm

Fig. 12 Comparison of the TDFADs at various times with the R6 Option1 curve for homogenous PM (a) 316H stainless steel at 550 °C and (b) P22 steel at 565 °C.

316H 550°C

-R6 Option 1

-TDFAD t = 0 hrs

-----Cutoff R6

------Cutoff t = 10000 hrs

-------Cutoff t = 100000 hrs

-TDFAD t = 1

100,000 h/

■i-L " II---»'

(a) 1.00

0.90 0.80 0.70 0.60 ^ 0.50 0.40 0.30 0.20 0.10

0.00 1................................^ I'M i ii

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

(b) 1.00 t^t 0.90 ;

0.80- -

0.70 ; \\

: '"v. '■■•■

0.60 ; ^ 0.50 ; 0.40 ;

: ------TDFAD t = 1 ^ 100,000 h ,

0.30 ;

0.20 ] -R6 Option 1

There are considerable differences between the TD-FADs for both steels. It has been demonstrated here and previously elsewhere (see e.g.8), that due to the insensi-tivity of the 316H steels TDFAC to time a single curve for a given time or even the R6 Option 1 curve may suffice. However, the significant time dependency of the P22 steel shown here demonstrates that this is not the case for this ferritic steel. This was also noted for the similar steel examined in Ref. [37]. An influence of tensile curve fitting on the accuracy of the results was noted in Ref. [7]. The Ramberg-Osgood material model which is widely employed to describe a materials tensile response is known

to cause inaccuracies especially for high strain hardening austenitic steels.38 In this work however such issues are negated by employing the materials experimentally measured tensile test data.

The Kcmat estimates obtained from using CCI and CCG data (see Eq. (21) and (22)) have been unsuccessful for the cases examined here, though they have provided satisfactory results elsewhere.8'10 The best fit line from Eq. (24) has provided a reasonable fit to all the P22 Kcmat versus time data and to the short-term 316H data, but cannot describe the longer term 316H steel data. The apparent change in slope between the long- and short-term Kcmat

(a) 1.E+04 i 1.E+03 i 1.E+02 i

1 1.E+01 -

i _ ; ~ 1.E+00 =

1.E-01 =

1.E-02 -

1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

tExp (h)

(b) 1.E+04 i

1.E+03 =

1.E+02 = jz :

1 1.E+01 -1.E+00 5 1.E-01 i 1.E-02 -

1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

tExp (h)

Fig. 13 Comparison of the predicted and experimentally determined CCI times from tests on homogenous PM and weldment C(T) specimens of316 steel at 550 °C for (a) 0.2 mm and (b) 0.5 mm, using mean and LB Kcmat values.

versus time data may indicate a change in material fracture behaviour, as suggested in Ref. [31]. However, within the extent of data scatter no firm conclusions can be made. The influence of using the LB bound or mean Kcmat value has been examined here, and significant differences are obtained in both cases, including a change of predicted failure mode for the P22 steel. The influence of the reference stress solution on the CCI predictions has previously been examined in Ref. [9]. The plane stress reference stress is greater than the plane strain reference stress and therefore leads to higher degrees of conservatism. Using the plane stress reference stress solution with a LB Kcmat value will therefore lead to conservative predictions for all cases considered here.

Long-term CCI and CCG tests are more representative of component operating conditions. The difference

(a)1.E+04 1.E+03 1.E+02

1 1.E+01 ~ 1.E+00 1.E-01 1.E-02

1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

tEP (h)

(b) 1.E+04 = 1.E+03 ; 1.E+02 |

1 1.E+01 i " 1.E+00 = 1.E-01 ! 1.E-02 -

1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

tExp (h)

Fig. 14 Comparison of the predicted and experimentally determined CCI times from tests on homogenous PM C(T) specimens and pipe components of P22 steel at 565 ° C for (a) 0.2 mm and (b) 0.5 mm, using mean and LB Kcmat values.

between the CCG rate and Kcmat trends for long- and short-term data signify that more long-term tests are required to verify the TDFAD prediction method for use in high temperature components.

CONCLUSIONS

The creep toughness parameter, Kcmat, for a crack extension of 0.2 mm and 0.5 mm has been determined for an austenitic 316H steel at 550 °C and ferritic P22 steel at 565 °C from CCG tests on the compact tension, C(T), specimen geometry. Both homogenous PM and weldment specimen tests have been considered. Kcmat shows a relatively weak dependency on time for the P22 steel, however a clear decrease in Kcmat with time is observed for the 316H material, especially at long times. Significant data scatter

(a) 1.E+04 1.E+03 1.E+02

1 1.E+01 ~ 1.E+00 1.E-01 1.E-02

1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

t*xp (h)

(b) 1.E+04 i 1.E+03 i 1.E+02 =

1 1.E+01 I

£ ; ~ 1.E+00 i

1.E-01

1.E-02

1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04

tiExp (h)

Fig. 15 Comparison of the predicted and experimentally determined CCI times from tests on C(T) weldment specimens and welded pipe components of P22 steel at 565 °C for (a) 0.2 mm and

(b) 0.5 mm, using mean and LB Kcmat values.

has been observed in the Kcmat data for both materials, which has been quantified. For the P22 steel the influence of Kcmat on time had to be predicted using models because, due to the extent of data scatter within the relatively small data set, a sensible regression line fit could not be achieved. For a given time, the mean Kcmat values of the 316 weldment specimens are found to be a factor of 2 less than that of the PM specimens. Within the extent of data scatter, little difference in creep toughness behaviour is observed between the two material conditions for the P22 steel. Isochronous stress-strain curves and TDFAD have been shown for a range of times for both the 316H and P22 PM steels. Due to the relatively low creep strain rates in the 316H steel at 550 °C, these curves are relatively insensitive to time and little change is observed in the 316H

materials' 0.2% creep strength, a^ 2, for times less than 10 000 h. On the contrary the P22 curves rapidly deviate from their tensile curves (at t = 0 h) and a^ 2 halves within the first hour of creep. A program has been developed to obtain explicit CCI time predictions using the TD-FAD method. CCI time predictions have been obtained for the CGG tests on the PM and weldment C(T) specimens and in addition for CCG data on PM and welded P22 pipe feature tests using the TDFAD derived from PM data. Reasonable predictions are generally obtained using the mean bound value of Kcmat, though not always conservative assuming plane strain conditions. Conservative predictions are almost always obtained when LB Kcmat values are employed and may be ascertained by assuming plane stress conditions. Although considerable differences are observed in the form of the Kcmat data and TDFADs of both austenitic 316H steel at 550 °C and ferritic P22 steel at 565 °C reasonable and conservative CCI time predictions can be achieved for both materials following the TDFAD approach. It is however essential that the influence of time on the TDFAD is considered for the P22 steel.

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