Prediction of creep crack initiation and growth for P91 at 600°C using MOD-NSW model

Abstract

In this paper, predictions of creep crack initiation times and growth rates using the NSW-MOD model are compared with experimental data for the parent and weld metals of P91 at 600°C. For the weld metal, creep crack growth rates are found to be bounded by upper and lower bounds of the predictions, but creep crack initiation times are close to the upper bound. For the parent material, creep crack growth rates are bounded by upper and lower bounds of the predictions using the minimum creep rates, but creep crack initiation times are bounded by those using the average creep rates.

Keywords

Creep crack growth rate creep crack initiation time analytical analysis modified NSW model P91 martensitic steel

Nomenclature

Δ a

crack length and its incremental value

ȧ

ȧ_{s}

creep crack growth rate and its steady state value

creep strain rate constant

creep stress exponent

C ^∗

$C^{*}$ -integral

D, m

plastic hardening constant and exponent

Young’s modulus

P _L

limit load

reduction of area

t_r, t_f

rupture time and failure time

t _i

creep crack initiation time

specimen width

stress

σ ₀

normalized stress, see Eq. (8)

σ_0.2, σ_y

0.2% offset yield stress

σ _u

tensile stress

ε _p

plastic strain

ε ₀

normalized strain, see Eq. (8)

ε_{f}^{*}

multiaxial creep ductility

ε_{f}^{EL}

creep ductility based on elongation

ε_{f}^{RA}

creep ductility based on reduction of area

{\dot{ε}}^{c}

power law creep strain rate

{\dot{ε}}_{min}^{c}

power law creep strain rate based on minimum creep

{\dot{ε}}_{ave}^{c}

power law creep strain rate based on average creep

{\tilde{\bar{ε}}}_{eq}

dimensionless equivalent strain, see Eq. (9)

r _c

creep process zone size at crack tip

crack tip angle

I _n

dimensionless integration constant, see Eqs (10a) and (10b)

1 Introduction

Creep crack growth properties are needed for assessing crack-like defects in high temperature components. Although such properties can be experimentally determined, testing often requires long time and thus predictive analytical/numerical tools would be quite useful. Nikbin et al. [1,2] proposed an analytical method to estimate upper and lower bounds of creep crack growth rates and creep crack initiation times, which is often referred to as the NSW model. The method is based on the ductility exhaustion concept incorporating the multi-axial stress effect on ductility. Using the NSW model, creep crack growth properties can be estimated solely from creep test data (idealised power-law creep properties and uni-axial ductility). Later the NSW model has been improved by considering angular variations of crack-tip stress and stress fields, which is often referred to as the modified NSW (NSW-MOD) model [3].

In literature, many researchers have applied the NSW and NSW-MOD models to predict creep crack growth rates and initiation times. For instance, Yatomi et al. [3] showed that the NSW model with average creep rates significantly overestimated the creep crack growth rates of a carbon–manganese steel at 360° but the NSW-MOD model gave more accurate upper bound prediction to the experimental data. Similar conclusions have been made for P92 welds at 650°C with minimum creep rates [4]. For Type 316H stainless steel at 525°C and 550°C, Dean and Gladwin [5] reported that experimental creep crack growth data was upper bounded by the NSW model using minimum creep rates. A more extensive test programme has been conducted on the same material at 550°C by Davies et al. [6,7], covering weld properties (parent material and heat-affected zone) and a range of specimen geometries at different temperatures. It was found that experimental creep crack growth rates overall lay between upper and lower bounds of the NSW-MOD prediction using minimum creep rates, and the initiation times were almost encompassed and close to the upper bound prediction. Above studies demonstrate that the NSW-MOD model gives better accuracy than the NSW model and application of appropriate creep properties (average or minimum) is important to the predictions of creep crack initiation times and growth rates.

The P91 martensitic steels have been used for high temperature components, for instance in ultra-supercritical fossil plants and more recently for structural components in Gen-IV reactors. As results, creep and creep-fatigue properties of P91 have been reported extensively in the literature (see for instance Refs [8–14]). Within research programs for developing Gen-IV reactors in Korea, short- and long-term creep crack growth tests of P91 were carried out for P91 parent and weld metals [15–17].

In this paper, the NSW-MOD model is applied to predict creep crack initiation times and growth rates of P91 at 600°C. A key issue to be resolved is “which power-law creep model (either minimum or average creep) gives better prediction for P91 parent and weld metals”. Section 2 presents tensile, creep and creep crack growth test results. Creep crack growth test results are compared with predictions using the NSW-MOD model in Section 3. Section 4 concludes the present work.

2 Tensile, creep and creep crack growth test data

In this section, test data of P91 parent and weld metals are summarized. Test data include tensile, creep and creep crack growth data. More detailed information on testing can be found in Refs [17,18].

Table 1
Chemical compositions of the P91 plate (weight %)

C	Si	Mn	P	S	Ni	Cr	Mo	Cu	V	Al	N	Nb
0.115	0.23	0.415	0.012	0.0014	0.22	8.9	0.869	0.038	0.194	0.02	0.0513	0.073

Fig. 1.

(a) Engineering stress–strain curve from smooth bar test and (b) true stress–strain curve.

2.1 Materials and tensile properties

A commercial grade hot-rolled P91 martensitic steel was considered in this work. The chemical composition is listed in Table 1. Engineering stress–strain curve of the parent material is shown in Fig. 1(a) with a solid line. Yield (0.2% proof) and tensile strengths at 600°C were about 247.5 MPa and 362.7 MPa, respectively. True stress–strain curve at 600°C is shown in Fig. 1(b) with a solid line. True fracture strain, measured from reduction of area, was about 1.5. Engineering stress–strain data of the weld metal at 600°C is shown in Fig. 1(a) with a dotted line. Yield (0.2% proof) and tensile strengths at 600°C were about 298.2 MPa and 330.4 MPa, respectively. True stress–strain curve at 600°C is shown in Fig. 1(b) with a dotted line. True fracture strain, measured from reduction of area, was about 1.13.

Figure 1(b) includes true stress-(plastic) strain curves given in RCC-MR [19]. Note that only parent tensile data are given in Ref. [19]. Material constants from present tests are compared with those given in Ref. [19] in Table 2. Average yield strength and hardening constant are similar but strain hardening capacity is quite different. This is probably due to different heat treatment.

Table 2
Tensile properties of parent and weld metals of P91 at 600°C. For comparison, tensile properties of P91 parent material, given in RCC-MR [19], are also given

		E (GPa)	Yield strength $σ_{0.2}$ (MPa)		Plastic constants

			Minimum	Average	$ε_{p} = D {(σ / σ_{y})}^{m}$

					D	m
RCC-MR [19] (parent material)		167	203	288	0.002	37.88
Present work	Parent material	164	247.5		0.0017	6.4
Present work	Weld metal	164	298.2		0.00191	12.99

Fig. 2.

(a) Comparison of experimental minimum creep rates with those in RCC-MR [19] and (b) experimental average creep rates.

2.2 Creep properties

Constant-load creep tests at 600°C were carried out with various stress levels ranging from 140 MPa to 180 MPa for the parent material and from 110 MPa to 160 MPa for the weld metal. From test data, constants for power-law creep can be fitted, as shown in Fig. 2. For the parent material, power-law creep properties based on minimum creep is given by ${\dot{ε}}_{min}^{c} = 1.28 \times 10^{- 27} σ^{9.98},$ (1) whereas based on average creep by ${\dot{ε}}_{ave}^{c} = 2.52 \times 10^{- 17} σ^{5.65},$ (2) where ${\dot{ε}}^{c}$ and σ denote creep rate in 1/h and stress for creep in MPa, respectively. The minimum creep rates from present tests are compared with those in Ref. [19] in Fig. 2(a). The minimum creep rate in Ref. [19] is much faster compared to that from the present test data for a given stress level.

For the weld metal, constants for power-law creep can be fitted as shown in Fig. 2. Power law creep properties based on minimum creep is given by

{\dot{ε}}_{min}^{c} = 2.28 \times 10^{- 29} σ^{11.37},

(3) whereas based on average creep by

{\dot{ε}}_{ave}^{c} = 1.82 \times 10^{- 23} σ^{8.92},

(4) where

{\dot{ε}}^{c}

and σ denote creep rate in 1/h and stress for creep in MPa, respectively. For the stress ranges tested, the weld metal creeps about ten times faster than the parent material.

Table 3

Summary of creep crack growth tests for the parent material and weld metal. Specimen dimensions: the width $W \approx 25.3 mm$ , initial crack length $a \approx 11.5 mm$ , thickness $B \approx 12.6 mm$ and net-thickness $B_{N} \approx 10.1 mm$

Material	Specimen ID	Load P (kN)	Rupture time $t_{f}$ (h)	Normalized load $P / P_{L}$	Initiation time $t_{i}$ (h)

					$Δ a = 0.2 mm$	$Δ a = 0.5 mm$
Parent material	G91-1	3.8	3148	0.421	2020	2487
	G91-3	4.5	2541	0.494	1380	2172
	G91-4	5.0	1249	0.564	1300	1972
	G91-7	4.0	3275	0.432	400	930
	G91-8	5.0	1078	0.536	430	743
	G91-9	5.0	1008	0.532	75	550
	G91-13	5.2	774	0.571	400	535
Weld metal	G91-W1	3.8	631	0.341	311	448
	G91-W2	4.0	652	0.369	198	436
	G91-W3	4.5	187	0.407	53	92
	G91-W5	3.6	449	0.323	174	266
	G91-W6	4.2	221	0.389	14	128
	G91-W7	3.5	680	0.333	320	495
	G91-W8	4.0	391	0.363	175	266

2.3 Creep crack growth properties

Creep crack growth tests at 600°C were performed using a compact tension (C(T)) specimen. Sustained loads were ranged from 3.8 kN to 5.2 kN for the parent material, and from 3.5 kN to 4.5 kN for the weld metal. Creep crack growth test results of the parent and weld metals are summarized in Table 3 where applied sustained load P is normalized by a limit load for the plane strain C(T) specimen, $P_{L}$ [20]: $P_{L} = 1.455 B_{N} (W - a) σ_{y} [\sqrt{{(\frac{2 a}{W - a})}^{2} + \frac{4 a}{(W - a)} + 2} - (\frac{2 a}{W - a} + 1)] .$ (5) Incubation times corresponding to 0.2 mm and 0.5 mm crack growth are also summarized in Table 3 and are shown in Fig. 3 in terms of $C^{*}$ . Results show that there is linear correlation between incubation times and $C^{*}$ , and the trend of incubation times versus $C^{*}$ of weld metal is quite similar with the parent material.

Fig. 3.

Experimental creep crack initiation times in terms of $C^{*}$ : (a) $Δ a = 0.2 mm$ and (b) $Δ a = 0.5 mm$ .

Fig. 4.

Experimental crack growth rate data: (a) parent material and (b) weld metal.

Experimental creep crack growth rates for the parent metal are shown in Fig. 4(a) in terms of $C^{*}$ . A regression fit for parent metal gives the following creep crack growth rate: $\frac{d a}{d t} = 1.89 \times 10^{- 2} {(C^{*})}^{0.77},$ (6) where a is in mm; t in hour; and $C^{*}$ in N/mm/h. Experimental creep crack growth rates for weld metal are shown in Fig. 4(b) in terms of $C^{*}$ and a regression fit gives $\frac{d a}{d t} = 3.62 \times 10^{- 2} {(C^{*})}^{0.85} .$ (7) When compared with creep crack growth rates for the parent material, those for the weld metal are slightly faster for a given $C^{*}$ . In RCC-MR [19], creep crack growth rates for parent metal are given, which are compared with present data in Fig. 4(a). Comparison shows that, for a given $C^{*}$ , the RCC-MR value gives slower creep crack growth rates than present data.

3 Comparison with NSW-MOD model predictions

When uni-axial creep properties are available, creep crack incubation times and growth rates can be predicted using the NSW-MOD model [3]. As the NSW-MOD model was developed for power law creep materials, a question arises on which power-law creep model (either minimum or average creep) gives better predictions for P91 parent and weld metals. This section investigates this issue.

3.1 NSW-MOD predictions for creep crack growth rates

Steady state creep crack growth rates in terms of $C^{*}$ can be predicted using the NSW-MOD model as follows. For a material characterized by the following power-law creep law ${\dot{ε}}^{c} = {\dot{ε}}_{0} {(\frac{σ}{σ_{0}})}^{n} = A σ^{n}$ (8) the steady-state crack growth rate, $ȧ_{s}^{NSW - MOD}$ , is given by $ȧ_{s}^{NSW - MOD} = (n + 1) {\dot{ε}}_{0} {[\frac{C^{*}}{{\dot{ε}}_{0} σ_{0} I_{n}}]}^{\frac{n}{n + 1}} r_{c}^{1 / n + 1} \frac{{\tilde{\bar{ε}}}_{eq} (θ, n)}{ε_{f}^{*} (θ, n)} |_{max} .$ (9) In Eq. (8), ${\dot{ε}}_{0}$ and $σ_{0}$ are the normalized strain rate and stress for creep, respectively; and n is the power-law creep exponent. Value of ${\dot{ε}}_{0}$ is taken in the present work to be 1 h⁻¹ [21]. A dimensionless integration constant, $I_{n}$ , in Eq. (9) can be calculated using the following equations [22], $\begin{array}{rclr} I_{n} = 10.3 \sqrt{0.13 + \frac{1}{n}} - \frac{4.6}{n} for plane strain, & (10a) \\ I_{n} = 7.2 \sqrt{0.12 + \frac{1}{n}} - \frac{2.9}{n} for plane stress . & (10b) \end{array}$ In Eq. (9), $r_{c}$ denotes the creep process zone size, which is usually taken to be the grain size of the material [23]. As many studies reported that measured values of the P91 grain size range from 20 µm to 30 µm [24–26], $r_{c} = 20 µm$ is taken in this study. For the weld metal, the value of $r_{c}$ was taken as $r_{c} = 10 µm$ [27]. It should be noted that the choice of $r_{c}$ is not so important, as predictions of the NSW-MOD model are almost insensitive to $r_{c}$ due to the ( $1 / n + 1$ ) power in Eq. (9).

In Eq. (9),

ε_{f}^{*}

denotes the multi-axial ductility which depends on the level of stress triaxiality. The multi-axial ductility

ε_{f}^{*}

can be found from uni-axial ductility,

ε_{f}

, using the expression by Cocks and Ashby [28,29]

\frac{ε_{f}^{*}}{ε_{f}} = \frac{sinh [\frac{2 (n - 1 / 2)}{3 (n + 1 / 2)}]}{sinh [\frac{2 (n - 1 / 2)}{(n + 1 / 2)} \frac{σ_{m}}{σ_{e}}]},

(11) where

σ_{m}

and

σ_{e}

denote the mean normal and equivalent stress, respectively. As crack-tip stresses and strains depend on the angle,

{\tilde{\bar{ε}}}_{eq} (θ, n) / ε_{f}^{*} (θ, n)

is taken as the maximum value from the Riedel–Rice crack tip fields [30]. Upper and lower bounds to creep crack growth rates can be estimated by assuming plane strain and plane stress condition, respectively. Values to estimate creep crack growth rates using the NSW-MOD model are summarized in Table 4.

Table 4

Summary of parameters in the NSW-MOD model

NSW-MOD values	Parent				Weld

	Minimum		Average		Minimum		Average

	Plane stress	Plane strain	Plane stress	Plane strain	Plane stress	Plane strain	Plane stress	Plane strain
n	9.98		5.65		11.37		8.92
A	1.28E−27		2.52E−17		2.28E−29		1.82E−23
$ε_{f}$	1.5				1.13
$ε_{f}^{*}$	0.741	0.049	0.729	0.005	0.56	0.039	0.557	0.034
${\dot{ε}}_{0}$	1				1
$σ_{0}$ (MPa)	495		867		330		354
$I_{n}$	3.09	4.48	3.41	4.89	3.03	4.4	3.14	4.55
$r_{c}$ (mm) [24–27]	0.02				0.01
θ for $ȧ_{max}$	0	58.3	0	23.7	0	60.4	0	55.7

Figure 5 compares predicted creep crack growth rates using the NSW-MOD model with experimental data. Two estimates are shown; one using the minimum creep data (indicated by $ȧ_{s}^{min}$ ) and the other using average creep data (indicated by $ȧ_{s}^{avg}$ ). For each case, two estimates are shown, upper (based on the plane strain assumption) and lower (based on the plane stress assumption) bounds. Results suggest that experimental creep crack growth rates for the parent material are bounded by upper and lower bound estimates using minimum creep data. For the weld metal, minimum and average creep rates are similar and experimental creep crack growth rates are bounded by upper and lower bound estimates.

Fig. 5.

Comparison of the experimental creep crack growth rates with NSW-MOD predictions: (a) parent and (b) weld metal.

3.2 NSW-MOD predictions for creep crack initiation times

Austin and Webster [21] have suggested that if the crack extension, $Δ a$ , can be measured reliably, creep crack initiation time, $t_{i}$ , can be predicted by substituting the NSW-MOD model into Eq. (12), $\frac{Δ a}{ȧ_{s}} < t_{i} .$ (12) Imposing plane stress and plane strain conditions, the upper and lower bounds for creep crack initiation times can be determined by $\frac{Δ a}{{(ȧ_{s})}_{plane stress}} < t_{i} < \frac{Δ a}{{(ȧ_{s})}_{plane stress}} .$ (13) Steady state creep crack growth rates for both plane strain and plane stress conditions were given in Section 3.1. Thus if the crack extension $Δ a$ is specified, creep crack initiation time, $t_{i}$ , can be estimated in terms of $C^{*}$ using Eq. (13).

Figure 6 compares predicted creep crack initiation times corresponding to $Δ a = 0.2 mm$ using the NSW-MOD model with experimental data. Corresponding results for $Δ a = 0.5 mm$ are shown in Fig. 7. Results suggest that experimental creep crack initiation times for the parent material are bounded by upper and lower bound estimates using average creep data, rather than minimum ones. Note that for creep crack growth rates, minimum creep rate data gave better predictions, see Fig. 5. For the weld metal, as minimum and average creep rates are similar, and experimental creep crack initiation times are close to the upper bound estimates.

Fig. 6.

Comparison of experimental creep crack initiation times with NSW-MOD predictions based on $Δ a = 0.2 mm$ : (a) parent and (b) weld metal.

Fig. 7.

Comparison of experimental creep crack initiation times with NSW-MOD predictions based on $Δ a = 0.5 mm$ : (a) parent and (b) weld metal.

4 Conclusions

This paper investigates applicability of the NSW-MOD model to predict creep crack initiation times and growth rates of P91 parent and weld metals at 600°C. From creep test data, power-law creep properties of P91 parent and weld metals are determined in two ways; based on minimum creep rates and average creep rates.

Experimental creep crack growth rates and initiation times are then compared with predictions using the modified NSW (NSW-MOD) model. The NSW-MOD predictions are made using either minimum or average creep rates, determined from creep tests. For the weld metal, predictions using the minimum creep rates are close to those using the average ones. Experimental creep crack growth rates are bounded by upper and lower bounds of the predictions, but experimental creep crack initiation times are close to the upper bound prediction. For the parent material, predictions using the minimum creep rates can be quite different from those using the average ones. Experimental creep crack growth rates are bounded by upper and lower bounds of the predictions using the minimum creep rates, but creep crack initiation times are bounded by those using the average ones.

Footnotes

Acknowledgements

This research was supported by National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2013M2B2B1075733, NRF-2007-0056094). The experimental data for the high-temperature tensile, creep, and creep crack growth tests used in this study were produced and supported by Korea Atomic Energy Research Institute (KAERI) and the authors would like to acknowledge with gratitude to KAERI.

References

[1] Nikbin

Smith

and Webster

, Influence of creep ductility and state of stress on creep crack growth, in: Advances in Life Prediction Methods at Elevated Temperatures, ASME, New York, 1983, pp. 249–258.

[2] Nikbin

K.M.

Smith

D.J.

and Webster

G.A.

, Prediction of creep crack growth from uniaxial creep data, Proc. Roy. Soc. Lond. A Mat.396 (1984), 183–197.

[3] Yatomi

O’Dowd

Nikbin

and Webster

, Theoretical and numerical modelling of creep crack growth in a carbon–manganese steel, Engng. Fract. Mech.73 (2006), 1158–1175.

[4] Yatomi

and Tabuchi

, Issues relating to numerical modelling of creep crack growth, Engng. Fract. Mech.77 (2010), 3043–3052.

[5] Dean

and Gladwin

, Creep crack growth behaviour of Type 316H steels and proposed modifications to standard testing and analysis methods, Int. J. Pres. Ves. Pip.84 (2007), 378–395.

[6] Davies

C.M.

Dean

Nikbin

and O’Dowd

, Interpretation of creep crack initiation and growth data for weldments, Engng. Fract. Mech.74 (2007), 882–897.

[7] Davies

C.M.

Dean

Yatomi

and Nikbin

, The influence of test duration and geometry on the creep crack initiation and growth behaviour of 316H steel, Mat. Sci. Eng. A510 (2009), 202–206.

[8] Panait

C.G.

Bendick

Fuchsmann

Gourgues-Lorenzon

A.F.

and Besson

, Study of the microstructure of the Grade 91 steel after more than 100,000 h of creep exposure at 600°C, Int. J. Pres. Ves. Pip.87 (2010), 326–335.

[9] Pétry

and Lindet

, Modelling creep behaviour and failure of 9Cr–0.5Mo–1.8W–VNb steel, Int. J. Pres. Ves. Pip.86 (2009), 486–494.

10.

[10] Massé

and Lejeail

, Creep mechanical behaviour of modified 9Cr1Mo steel weldments: Experimental analysis and modelling, Nucl. Eng. Des.254 (2013), 97–110.

11.

[11] Nonaka

Ito

Takemasa

Saitou

Miyachi

and Fujita

, Full size internal pressure creep test for welded P91 hot reheat elbow, Int. J. Pres. Ves. Pip.84 (2007), 97–103.

12.

[12] Li

Hongo

Tabuchi

Takahashi

and Monma

, Evaluation of creep damage in heat affected zone of thick welded joint for Mod. 9Cr–1Mo steel, Int. J. Pres. Ves. Pip.86 (2009), 585–592.

13.

[13] Ogata

Sakai

and Yaguchi

, Damage assessment method of P91 steel welded tube under internal pressure creep based on void growth simulation, Int. J. Pres. Ves. Pip.87 (2010), 611–616.

14.

[14] Yaguchi

Ogata

and Sakai

, Creep strength of high chromium steels welded parts under multiaxial stress conditions, Int. J. Pres. Ves. Pip.87 (2010), 357–364.

15.

[15] Kim

W.-G.

Park

J.-Y.

Hong

S.-D.

and Kim

S.-J.

, Probabilistic assessment of creep crack growth rate for Gr. 91 steel, Nucl. Eng. Des.241 (2011), 3580–3586.

16.

[16] Lee

H.-Y.

Lee

S.-H.

Kim

J.-B.

and Lee

J.-H.

, Creep–fatigue damage for a structure with dissimilar metal welds of modified 9Cr–1Mo steel and 316L stainless steel, Int. J. Fatigue29 (2007), 1868–1879.

17.

[17] Kim

W.-G.

Park

J.-Y.

Lee

H.-Y.

Kim

S.-J.

Hong

S.-D.

and Kim

Y.-W.

, A comparative assessment of creep and creep crack growth rates for Gr. 91 steel, Journal of Mechanical Science and Technology (2015), to appear.

18.

[18] Kim

W.-G.

Kim

S.-H.

and Lee

C.-B.

, Long-term creep characterization of Gr. 91 steel by modified creep constitutive equations, Met. Mater. Int.17 (2011), 497–504.

19.

[19]RCC-MR 2002-Annexe A16. Tome I, Vol. Z, AFCEN, Paris, 2002.

20.

[20] Kumar

and Shih

C.F.

, Fully plastic crack solutions, estimation scheme, and stability analyses for the compact specimen, in: Fracture Mechanics: Twelfth Conference, ASTM STP, Vol. 700, American Society for Testing and Materials, 1980, pp. 406–438.

21.

[21] Austin

T.S.P.

and Webster

G.A.

, Prediction of creep crack growth incubation periods, Fatigue Fract. Eng. Mater. Struct.15(11) (1992), 1081–1090.

22.

[22] Shih

C.F.

, Tables of Hutchinson–Rice–Rosengren singular field quantities, Report MRL E-147, Brown University, Providence, 1983.

23.

[23] Davies

C.M.

, Crack initiation and growth at elevated temperatures in engineering steels, PhD thesis, Department of Mechanical Engineering, Imperial College, London, 2006.

24.

[24] Ebi

and McEvily

A.J.

, Effect of processing on the high temperature low cycle fatigue properties of modified 9Cr–1Mo ferritic steel, Fatigue. Eng. Mater. Struct.7 (1984), 299–314.

25.

[25] Sawada

Takeda

Maruyama

Ishii

Yamada

Nagae

and Komine

, Effect of W on recovery of lath structure during creep of high chromium martensitic steels, Mat. Sci. Eng. A – Struct.267(1) (1999), 19–25.

26.

[26] Das

C.R.

Albert

S.K.

Bhaduri

A.K.

Srinivasan

and Murty

B.S.

, Effect of prior microstructure on microstructure and mechanical properties of modified 9Cr–1Mo steel weld joints, Mat. Sci. Eng. A – Struct.477 (2008), 185–192.

27.

[27] Thomas Paul

Saroja

Hariharan

Rajadurai

and Vijayalakshmi

, Identification of microstructural zones and thermal cycles in a weldment of modified 9Cr–1Mo steel, J. Mater. Sci.42 (2007), 5700–5713.

28.

[28] Cocks

A.C.F.

and Ashby

M.F.

, On creep fracture by void growth, Prog. Mater. Sci.27 (1982), 189–244.

29.

[29] Cocks

A.C.F.

and Ashby

M.F.

, Intergranular fracture during power-law creep under multi-axial stress, Met. Sci.14 (1980), 395–402.

30.

[30] Riedel

and Rice

J.R.

, Tensile cracks in creeping solids, in: Fracture Mechanics Twelfth Conference, ASTM International, 1980, pp. 112–130.

Prediction of creep crack initiation and growth for P91 at 600°C using MOD-NSW model

Abstract

Keywords

Nomenclature

1 Introduction

2 Tensile, creep and creep crack growth test data

Table 1 Chemical compositions of the P91 plate (weight %)

Table 2 Tensile properties of parent and weld metals of P91 at 600°C. For comparison, tensile properties of P91 parent material, given in RCC-MR [19], are also given

3.1 NSW-MOD predictions for creep crack growth rates

Footnotes

Acknowledgements

References

Table 1
Chemical compositions of the P91 plate (weight %)

Table 2
Tensile properties of parent and weld metals of P91 at 600°C. For comparison, tensile properties of P91 parent material, given in RCC-MR [19], are also given