Finite Element Creep Damage Analyses and Life Prediction of P91 Pipe Containing Local Wall Thinning Defect

Jilin Xue; Changyu Zhou

doi:10.1515/htmp-2014-0141

Article Open Access

Finite Element Creep Damage Analyses and Life Prediction of P91 Pipe Containing Local Wall Thinning Defect

Jilin Xue and Changyu Zhou

Published/Copyright: April 25, 2015

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From the journal High Temperature Materials and Processes Volume 35 Issue 3

Abstract

Creep continuum damage finite element (FE) analyses were performed for P91 steel pipe containing local wall thinning (LWT) defect subjected to monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment by orthogonal experimental design method. The creep damage lives of pipe containing LWT defect under different load conditions were obtained. Then, the creep damage life formulas were regressed based on the creep damage life results from FE method. At the same time a skeletal point rupture stress was found and used for life prediction which was compared with creep damage lives obtained by continuum damage analyses. From the results, the failure lives of pipe containing LWT defect can be obtained accurately by using skeletal point rupture stress method. Finally, the influence of LWT defect geometry was analysed, which indicated that relative defect depth was the most significant factor for creep damage lives of pipe containing LWT defect.

Keywords: creep damage; life prediction; local wall thinning; high temperature; skeletal point rupture stress

PACS® 2010: 62.20.Hg

Introduction

P91 steel was developed in the 1970s by Oak Ridge National Laboratory (ORNL) in the USA as a modified 9Cr1Mo steel. The modifications included additions of vanadium, niobium, nitrogen and a low carbon content to provide excellent long-term high-temperature strength. The chemical composition of P91 is listed in Table 1 [1]. The main application is tubing and piping for power plants and nuclear power plants.

Table 1:

Chemical composition of P91 (mass ％).

C	Mn	P	S	Si	Cr
0.08–0.12	0.30–0.60	0–0.02	0–0.01	0.20–0.50	8.00–9.50
Mo	V	Nb	N	Al	Ni
0.85–1.05	0.18–0.25	0.06–0.10	0.03–0.07	0–0.04	0–0.40

The service condition of P91 steel is at high temperature. One of the main concerns at high temperature is the service life prediction of pipe under creep condition.

At high temperature, continuum damage mechanics finite element (FE) analysis is useful in predicting creep failure lives of engineering components [2–5]. Skeletal point rupture stress was firstly proposed by Marriot [6] to estimate the creep life. Hyde [7] and Sun [8] verified that skeletal point rupture stress method was also useful to predict the failure lives of straight pipe and pipe bend. Zhang [9] conducted researches of life prediction for welded joint by using skeletal point rupture stress method, and the reasonable results were obtained.

Local wall thinning (LWT), as volumetric defect, is very common, which may be induced by high-temperature corrosion/erosion, mechanical damage (such as scratch and impact), crack ground and repaired process [10, 11]. The existence of LWT defect causes stress redistribution of the pipe, reduces the load carrying capability of the pipe. Finally, the service life will be shortened at high temperature in service.

In the past years, a lot of researches about pipe containing LWT defect have been conducted. Under room temperature the researches about pipe containing LWT defect focused on the stress analysis [12–16], limit load [17–23], fracture behaviour [24–29], safety assessment [30] and fatigue behaviour [31, 32]. Under high temperature the researches about pipe containing LWT defect were not enough, which only focused on the stress analysis [33–36], ultimate creep load [37] and plastic limit load [38]. At present, there is no literature related to life prediction for pipe containing LWT defect at high temperature. So, conducting the work of life prediction for pipe containing LWT defect accurately is very necessary.

In this paper, creep damage lives of pipe containing LWT defect subjected to monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment were researched by orthogonal experimental design method. And life prediction of pipe containing LWT defect was conducted using skeletal point rupture stress method. Finally, the influence of geometry of LWT defect for creep damage lives of pipe containing LWT defect was analysed.

Creep damage constitutive equation

Continuum damage mechanics approaches are commonly used by FE method to predict the failure lives of pipe under creep condition. These models generally attempt to characterize the full creep curve, including the tertiary creep, and are based on the concepts of Kachanov [39]. If the material constants in the constitutive equations are known, the creep failure life of a component can be assessed. Typical creep damage constitutive equations are of the form [40]:

(1)dεijcdt=32Bσen−1sij1−D−ntm

(2)dDdt=M1ϕ+1σrv1−Dϕtm

(3)Dcr=1−1−g1ϕ+1

where B, n, m, M, v, ϕ, g are material constants, D is damage parameter, Dcr is critical damage value, εijc is creep strain tensor, sij is stress tensor, σe is equivalent stress, σr is rupture stress and t is creep time.

In this paper, the FE creep damage analyses and life prediction of P91 pipe containing LWT defect are conducted at 625℃. The material constants are shown in Table 2 [41].

Table 2:

Constants in creep damage constitutive equation.

B	n	g	ϕ	M	υ	m	α
9.016×10⁻²⁷	10.286	0.92	9.5	1.321×10⁻²⁴	9.914	0	0.5

When material served under high temperature after a period of time of creep, damage occurs. It is commonly believed that if damage variable, D, reaches critical damage value, Dcr, the failure happens. So the creep damage equivalent Dˉ is defined as the ratio of damage variable and critical damage value:

(4)D¯=D/Dcr

The Dˉ value ranges from 0 to 1. When Dˉ=1, the life of pipe containing LWT defect is failure life.

Pipe model and FE analysis

Model of pipe containing LWT defect

FE analyses were performed using the standard ABAQUS code [42], while damage calculations were conducted using the UMAT facility within the ABAQUS code.

Three-dimensional FE model was established. The pipe containing LWT defect was modelled, as shown in Figure 1. The LWT defect is located at the inner surface. The outside radius of pipe is R_o, the inside radius of pipe is R_i, respectively. The thickness of the pipe is T, the half-length of the pipe is S. The dimensions of the pipe are that R_o = 161.95 mm, T = 28.6 mm. The pipe length was set to S = 1,000 mm, which is sufficient to ignore the boundary effect at the end of the pipe.

Figure 1:

FE model of pipe containing LWT defect.

The LWT defect geometry is characterized by three parameters, the depth of LWT defect is d, the half angle of LWT defect is θ and the half length of LWT defect is L. Three LWT defect parameters are transformed to the dimensionless form: relative defect depth c = d/T, relative defect angle b = θ/π and relative defect length a = L/(R_OT)^0.5.

The loads carried by pipe containing LWT defect are monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment. The thing to note here is that the bending moment is in-plane bending moment and the LWT defect is located at the side of tension.

Symmetry condition of pipe was considered to reduce the computing time. For the pipe under monotonic internal pressure, a quarter of full pipe was utilized, while for the pipe under monotonic bending moment and combined internal pressure and bending moment, a half of full pipe was utilized. On the symmetry surface, symmetry boundary is applied. For the pipe under monotonic internal pressure, internal pressure load is applied. In addition, an axial load, which is introduced by internal pressure, is applied to simulate a closed-end condition. In order to prevent the model moving, a fixed support is employed on the end of the model. For the pipe under monotonic bending moment, bending moment is applied by four-point bending load. On the both ends of pipe, the fixed supports are employed. On both sides of LWT defect, the forces are applied. For the pipe under combined internal pressure and bending moment, internal pressure load, axial load and four-point bending load are applied.

The meshing of model was shown in Figure 2. The element number was between 8,000 and 10,000, which was enough to ensure the accuracy of FE calculation. To avoid problems associated with incompressibility, the reduced integration element within ABAQUS (element type C3D20R) was used. And in order to simulate large inelastic deformation, the nonlinear geometry option (NLGEOM) with ABAQUS was used for the analysis procedure.

Figure 2:

FE mesh of pipe containing LWT defect.

Orthogonal experimental design

Orthogonal experimental design is an optimization method to discuss the problem of multi-factors and multi-levels. The main factors that could affect the creep damage lives of pipe containing LWT defect are defect parameters and load levels. The defect parameters include relative defect depth c, relative defect angle b and relative defect length a.

The loads include internal pressure P and bending moment M, which are usually applied on pipe. The design pressure of pipe referred above is 13.72 MPa. The total axial load introduced by P is applied by an equivalent axial stress σa, which corresponds to a closed-end condition, σa=P/[Ro/Ri2−1]. The bending moment M introduced by internal pressure P and axial stress σa is as follows [43]:

(5)M=π8kP[(RoRi+1)2−2]Ri3(Ro /RoRi−Ri)[(RoRi)2+1]

where k is an axial stress ratio, varies from 0 to 1. For the purpose of considering the maximum bending moment, k is taken as 1.

Four levels for each defect parameter and load are selected according to the possible region, as shown in Table 3.

Table 3:

LWT defect parameters and loads.

	Relative defect depth	Relative defect angle	Relative defect length	Internal pressure	Bending moment
Levels	c	b	a	P (MPa)	M (kN m)
1	0.1	1/6	1	10	55.1
2	0.3	1/3	1.5	12	66.1
3	0.5	1/2	2	13.72	75.6
4	0.7	2/3	2.5	15	82.6

Orthogonal tables L₁₆(4⁵) is the appropriate one for arranging the five factors above with four levels for each, as shown in Table 4. It is to investigate the effect of five factors on creep damage lives, and no interaction among these factors is assumed here.

Table 4:

Orthogonal experiment design.

	Factors
No.	1	2	3	4	5
1	1	1	1	1	1
2	1	2	2	2	2
3	1	3	3	3	3
4	1	4	4	4	4
5	2	1	2	3	4
6	2	2	1	4	3
7	2	3	4	1	2
8	2	4	3	2	1
9	3	1	3	4	2
10	3	2	4	3	1
11	3	3	1	2	4
12	3	4	2	1	3
13	4	1	4	2	3
14	4	2	3	1	4
15	4	3	2	4	1
16	4	4	1	3	2

FE analysis results

To obtain the failure lives of pipe containing LWT defect, the calculations were carried out until Dˉ = 1. At the same time, from the calculation results, the creep damage lives at different creep damage equivalent were also acquired. Here, Dˉ = 0.2, Dˉ = 0.4, Dˉ = 0.6 and Dˉ = 0.8, four creep damage equivalent values were selected. So, five groups of creep damage lives were obtained.

This paper discusses creep damage lives of pipe containing LWT defect subjected to three load types, monotonic internal pressure (P), monotonic bending moment (M) and combined internal pressure and bending moment (P + M).

Creep damage lives of pipe containing LWT defect under monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment were listed in Tables 5–7.

Table 5:

Creep damage lives of pipe containing LWT defect under internal pressure.

	LWT defect			Load	Creep damage life (h)
No.	c	b	a	P	Dˉ = 0.2	Dˉ = 0.4	Dˉ = 0.6	Dˉ = 0.8	Dˉ = 1.0
1	1	1	1	1	33,207	56,647	74,228	86,925	97,668
2	1	2	2	2	28,751	49,047	64,268	75,261	84,563
3	1	3	3	3	25,623	43,710	57,275	67,072	75,362
4	1	4	4	4	23,726	40,474	53,035	62,107	69,783
5	2	1	2	3	6,887	11,748	15,395	18,028	20,256
6	2	2	1	4	5,353	9,132	11,965	14,012	15,744
7	2	3	4	1	10,998	18,761	24,584	28,789	32,347
8	2	4	3	2	9,097	15,518	20,335	23,813	26,756
9	3	1	3	4	3,350	5,715	7,488	8,769	9,853
10	3	2	4	3	3,932	6,707	8,789	10,292	11,564
11	3	3	1	2	4,235	7,224	9,467	11,086	12,456
12	3	4	2	1	6,046	10,314	13,515	15,827	17,783
13	4	1	4	2	3,414	5,824	7,632	8,937	10,042
14	4	2	3	1	3,902	6,657	8,723	10,215	11,477
15	4	3	2	4	2,163	3,691	4,836	5,663	6,363
16	4	4	1	3	2,343	3,997	5,238	6,134	6,892

Table 6:

Creep damage lives of pipe containing LWT defect under bending moment.

	LWT defect			Load	Creep damage life (h)
No.	c	b	a	M	Dˉ = 0.2	Dˉ = 0.4	Dˉ = 0.6	Dˉ = 0.8	Dˉ = 1.0
1	1	1	1	1	71,884	123,550	163,984	190,941	224,636
2	1	2	2	2	62,238	106,972	141,981	165,320	194,494
3	1	3	3	3	55,466	95,333	126,532	147,332	173,332
4	1	4	4	4	51,360	88,275	117,165	136,425	160,500
5	2	1	2	3	27,708	47,623	63,209	73,600	86,588
6	2	2	1	4	24,388	41,916	55,634	64,779	76,211
7	2	3	4	1	36,607	62,919	83,511	97,238	114,398
8	2	4	3	2	32,492	55,846	74,123	86,307	101,538
9	3	1	3	4	16,116	27,699	36,764	42,807	50,361
10	3	2	4	3	17,791	30,578	40,586	47,257	55,597
11	3	3	1	2	18,767	32,256	42,813	49,851	58,648
12	3	4	2	1	22,688	38,995	51,757	60,265	70,900
13	4	1	4	2	13,791	23,703	31,460	36,632	43,096
14	4	2	3	1	16,447	28,268	37,520	43,687	51,397
15	4	3	2	4	12,462	21,419	28,429	33,102	38,944
16	4	4	1	3	13,392	23,018	30,551	35,573	41,851

Table 7:

Creep damage lives of pipe containing LWT defect under combined internal pressure and bending moment.

	LWT defect			Load		Creep damage life (h)
No.	c	b	a	P	M	Dˉ = 0.2	Dˉ = 0.4	Dˉ = 0.6	Dˉ = 0.8	Dˉ = 1.0
1	1	1	1	1	1	28,128	45,318	57,038	67,977	78,134
2	1	2	2	2	2	24,354	39,237	49,385	58,856	67,650
3	1	3	3	3	3	21,704	34,968	44,011	52,452	60,290
4	1	4	4	4	4	20,098	32,379	40,753	48,569	55,826
5	2	1	2	3	4	5,474	8,819	11,100	13,228	15,205
6	2	2	1	4	3	4,534	7,305	9,194	10,958	12,595
7	2	3	4	1	2	9,316	15,009	18,891	22,514	25,878
8	2	4	3	2	1	7,706	12,415	15,626	18,622	21,405
9	3	1	3	4	2	2,910	4,688	5,900	7,032	8,082
10	3	2	4	3	1	3,546	5,714	7,191	8,571	9,851
11	3	3	1	2	4	3,587	5,780	7,274	8,669	9,965
12	3	4	2	1	3	4,762	7,671	9,655	11,507	13,226
13	4	1	4	2	3	2,892	4,659	5,865	6,989	8,034
14	4	2	3	1	4	3,305	5,325	6,703	7,988	9,182
15	4	3	2	4	1	2,142	3,451	4,344	5,177	5,950
16	4	4	1	3	2	2,057	3,314	4,171	4,971	5,714

Creep damage contours of pipe containing LWT defect at Dˉ = 1 under different loads were shown in Figure 3. Under monotonic internal pressure, the maximum damage was located at interface edge of LWT on the inner surface of pipe along axial direction. Under monotonic bending moment, the maximum damage was located at interface edge of LWT on the inner surface of pipe along circular direction. Under combined internal pressure and bending moment, the maximum damage was located at the intersection of LWT axial direction and LWT circular direction on the inner surface of pipe.

Figure 3:

Creep damage contours of pipe containing LWT defect. (a) Under internal pressure; (b) under bending moment; (c) under combined internal pressure and bending moment.

Regression formula for creep damage life

Based on FE calculation results of creep damage lives of pipe containing LWT defect under monotonic internal pressure, the relation of creep damage life, creep damage equivalent, internal pressure and LWT defect geometry was established by regression method. The regression formula of creep damage life of pipe containing LWT defect under monotonic internal pressure was as follows:

(6)t= 4.38313⋅e10.52279⋅P−1.32926⋅D¯0.67323(dT)−1.15808(θπ)0.04995(LR0T)0.14832

Based on FE calculation results of creep damage lives of pipe containing LWT defect under monotonic bending moment, the regression formula of creep damage life, creep damage equivalent, bending moment and LWT defect geometry of pipe containing LWT defect under monotonic bending moment was obtained:

(7)t= 9.18969⋅e12.21409⋅M−0.92322⋅D¯0.69572(dT)−0.72444(θπ)0.03184(LR0T)0.01026

At the same time, based on FE calculation results of creep damage lives of pipe containing LWT defect under combined internal pressure and bending moment, the regression formula of creep damage life, creep damage equivalent, internal pressure, bending moment and LWT defect geometry of pipe containing LWT defect under combined internal pressure and bending moment was obtained:

(8)t= 6.38134⋅e11.04705P−1.08978⋅M−0.41343⋅D¯0.64301(dT)−1.15898(θπ)0.06757(LR0T)0.19088(PM≠0)

From the regression formulas of creep damage life of pipe containing LWT defect at high temperature, the index of every defect parameter can reflect the influence degree to creep damage life. For creep damage life under monotonic internal pressure and under combined internal pressure and bending moment, the influence factors of defect parameter from high to low are relative defect depth, relative defect length and relative defect angle. While for creep damage life under monotonic bending moment, relative defect length and relative defect angle change their order.

According to the regression formulas of creep damage life, creep damage lives of pipe containing LWT defect under different loads could be calculated. The creep damage lives of pipe containing LWT defect under monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment calculated by regression formulas were listed in Table 8.

Table 8:

Creep damage lives of pipe containing LWT defect calculated by regression formula.

	Under P		Under M		Under P + M
No.	Life (h)	Error (%)	Life (h)	Error (%)	Life (h)	Error (%)
1	100,398	2.80	229,000	1.94	79,482	1.73
2	86,622	2.43	198,719	2.17	68,431	1.15
3	77,202	2.44	178,353	2.90	60,742	0.75
4	71,903	3.04	166,243	3.58	56,535	1.27
5	19,621	–3.14	77,475	–10.52	14,391	–5.35
6	16,988	7.90	72,682	–4.63	13,137	4.30
7	34,044	5.24	108,010	–5.58	26,447	2.20
8	26,221	–2.00	91,931	–9.46	22,841	6.71
9	10,066	2.16	49,456	–1.80	8,364	3.49
10	12,127	4.87	54,993	–1.09	10,868	10.32
11	12,907	3.62	62,471	6.52	9,179	–7.89
12	17,720	–0.36	74,895	5.63	12,795	–3.26
13	9,480	–5.60	47,721	10.73	7,127	–11.28
14	12,098	5.41	57,582	5.86	8,417	–8.33
15	6,901	8.46	40,019	2.76	6,223	4.58
16	7,422	7.69	43,646	4.29	6,003	5.06

Compared with creep damage lives of pipe containing LWT defect obtained directly by FE method, creep damage lives calculated by regression formula was close. The maximum error of creep damage life of pipe containing LWT defect under monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment calculated by FE method and calculated by regression formula was up to 8.46%, 10.73% and –11.28%, respectively. And the mean error was 2.81%, 0.83% and 0.34%, respectively.

Life estimation of pipe containing LWT defect

Life estimation theory

σr is a rupture stress, which is assumed to be a linear combination of the maximum principal stress, σ1, and the equivalent stress, σe, as follows [5]:

(9)σr=ασ1+1−ασe

where α is material constant of the triaxial stress state parameter. The α value ranges from 1, where the maximum principal stress is dominant, to 0, where the equivalent stress is dominant. For P91 material at 625℃, α is 0.5 [41].

Estimation of failure life, tf, using the rupture stress, can be made by using the integrated form of eq. (2):

(10)tf=[1M(σr)v](1/(1+m))

Skeletal point rupture stress

From creep damage FE calculations, stress distributions have shown that there is a position, at which the rupture stress is practically independent of creep time. Marriot [6] defined this stress as a skeletal point rupture stress in previously work. In this paper the skeletal point rupture stress denoted as σsp. The path m–n is chosen to as stress distribution path, as is shown in Figure 1. Figure 4 shows the stresses of pipe containing LWT defect along the path m–n at different creep times from damage analysis from FE results under different loads. It could be seen that the intersection of the curves could be accurately determined. Here, skeletal point rupture stress was used to replace the rupture stress in eq. (10) for life prediction of pipe containing LWT defect at high temperature.

Figure 4:

Skeletal point rupture stress of pipe containing LWT defect. (a) Under internal pressure; (b) under bending moment; (c) under combined internal pressure and bending moment.

The skeletal point rupture stresses of pipe containing LWT defect under monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment obtained from FE results were listed in Table 9.

Table 9:

Skeletal point rupture stresses.

	Under P			Under M			Under P + M
No.	By FE (MPa)	By eq. (11) (MPa)	Error (%)	By FE (MPa)	By eq. (12) (MPa)	Error (%)	By FE (MPa)	By eq. (13) (MPa)	Error (%)
1	80.3	78.2	–2.62	73.7	73.1	–0.81	82.0	80.3	–2.07
2	81.2	81.0	–0.25	74.7	74.4	–0.50	83.3	83.0	–0.39
3	82.4	83.1	0.83	75.4	75.3	–0.14	84.3	85.0	0.85
4	82.9	84.6	1.97	75.9	75.9	0.06	84.9	86.4	1.81
5	94.5	93.6	–0.88	80.8	81.6	1.02	96.2	95.7	–0.45
6	96.0	94.2	–1.92	82.3	82.3	0.04	97.9	96.2	–1.71
7	89.4	90.5	1.20	78.6	79.6	1.34	91.6	93.1	1.67
8	91.6	92.5	1.03	80.3	80.9	0.72	94.1	94.6	0.57
9	100.2	101.2	0.95	85.7	85.5	–0.30	102.9	102.8	–0.15
10	99.1	100.4	1.34	85.3	85.0	–0.34	101.4	102.1	0.61
11	98.4	96.8	–1.68	84.3	84.0	–0.34	101.0	99.7	–1.29
12	95.1	95.1	–0.06	82.7	82.8	0.03	99.0	98.2	–0.76
13	100.3	102.3	1.94	86.8	86.0	–0.87	102.5	104.6	2.13
14	99.1	99.3	0.23	85.0	84.8	–0.22	102.3	102.4	0.11
15	105.3	104.7	–0.57	87.7	87.8	0.11	106.2	106.5	0.26
16	104.4	102.6	–1.70	87.0	87.2	0.18	106.3	105.1	–1.21

Based on the skeletal point rupture stresses of pipe containing LWT defect under monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment, the relations of skeletal point rupture stress, internal pressure, bending moment and LWT defect geometry were established by regression method. The regression formulas of skeletal point rupture stress of pipe containing LWT defect under monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment were shown in eqs (11)–(13), respectively:

(11)σsp= 73.48602⋅P0.14324⋅(dT)0.11501(θπ)0.00123(LR0T)0.01970

(12)σsp= 61.94311⋅M0.08543⋅(dT)0.07536(θπ)0.00203(LR0T)0.00103

(13)σsp= 76.03629⋅P0.11738M0.01393⋅(dT)0.11510(θπ)0.00363(LR0T)0.01620 (PM≠0)

According to the regression formulas of skeletal point rupture stress of pipe containing LWT defect under different loads, skeletal point rupture stress could be calculated. The skeletal point rupture stresses of pipe containing LWT defect under monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment calculated by regression formulas were listed in Table 9.

Compared with skeletal point rupture stresses of pipe containing LWT defect calculated by FE method, skeletal point rupture stress calculated by regression formula was close. The maximum error of skeletal point rupture stress of pipe containing LWT defect under monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment calculated by FE method and calculated by regression formula was up to –2.62%, 1.34% and 2.13%, respectively. And the mean error was –0.01%, 0.00% and 0.00%, respectively.

Life estimation of pipe containing LWT defect

By the substitution of skeletal point rupture stress for rupture stress in eq. (10) under different loads, the creep damage lives of pipe containing LWT defect could be calculated. The creep damage lives of pipe containing LWT defect under monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment calculated by skeletal point rupture stress obtained from FE results and regression formulas were listed in Table 10.

Table 10:

Creep damage lives calculated by skeletal point rupture stress.

No.	Under P				Under M				Under P + M
	Life (h)		Error (%)		Life (h)		Error (%)		Life (h)		Error (%)
	By FE	By eq. (11)	By FE	By eq. (11)	By FE	By eq. (12)	By FE	By eq. (12)	By FE	By eq. (13)	By FE	By eq. (13)
1	98,453	128,079	0.80	31.14	232,450	251,991	3.48	12.18	80,452	98,992	2.97	26.69
2	88,343	90,567	4.47	7.10	201,783	212,118	3.75	9.06	68,677	71,355	1.52	5.48
3	76,466	70,439	1.46	–6.53	184,677	187,224	6.55	8.01	61,329	56,399	1.72	–6.45
4	71,804	59,204	2.90	–15.16	173,248	172,300	7.94	7.35	57,288	47,953	2.62	–14.10
5	19,771	21,578	–2.39	6.53	93,456	84,484	7.93	–2.43	16,573	17,328	9.00	13.96
6	16,835	20,404	6.93	29.60	77,897	77,614	2.21	1.84	13,876	16,460	10.17	30.69
7	33,977	30,194	5.04	–6.66	122,660	107,461	7.22	–6.06	26,951	22,864	4.15	–11.64
8	26,862	24,259	0.40	–9.33	98,542	91,786	–2.95	–9.60	20,574	19,453	–3.88	–9.12
9	11,029	10,038	11.94	1.88	51,788	53,355	2.83	5.95	8460	8587	4.67	6.24
10	12,347	10,816	6.77	–6.47	54,719	56,585	–1.58	1.78	9763	9192	–0.90	–6.69
11	13,156	15,568	5.62	24.99	61,357	63,477	4.62	8.23	10,195	11,599	2.31	16.40
12	18,460	18,568	3.81	4.42	73,554	73,326	3.74	3.42	12,482	13,461	–5.63	1.78
13	10,878	8989	8.33	–10.48	45,871	50,001	6.44	16.02	8848	7182	10.14	–10.60
14	12,339	12,062	7.51	5.10	56,439	57,659	3.75	6.00	8966	8867	–2.35	–3.42
15	6742	7139	5.96	12.19	41,147	40,708	5.66	4.53	6198	6038	4.16	1.47
16	7373	8740	6.98	26.81	44,616	43,806	6.61	4.67	6114	6900	7.01	20.76

Compared with creep damage lives of pipe containing LWT defect obtained directly by FE method, the creep damage lives calculated by skeletal point rupture stress obtained from FE results was also close. But the bigger error existed between creep damage lives of pipe containing LWT defect obtained directly by FE method and calculated by skeletal point rupture stress obtained from regression formulas.

The maximum error of creep damage life of pipe containing LWT defect under monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment calculated by FE method and calculated by skeletal point rupture stress obtained from FE results was up to 11.94%, 7.94% and 10.17%, respectively. And the mean error was 4.78%, 4.26% and 2.98%, respectively.

The maximum error of creep damage life calculated by FE method and calculated by skeletal point rupture stress obtained from regression formulas was up to 31.14%, 16.02% and 30.69%, respectively. And the mean error is 5.94%, 4.43% and 3.84%, respectively. This is because the creep damage life was very sensitive with skeletal point rupture stress. A smaller error in skeletal point rupture stress may lead to a larger error in creep damage life.

Effect of defect geometry for creep damage life of pipe containing LWT defect

Creep damage life of pipe containing LWT defect affected by defect geometry under different loads were discussed in this part. In order to research the effect of defect geometry for creep damage life of pipe containing LWT defect, in the three defect geometry parameters, two of which were kept constants and the other was changed only.

Effect of defect geometry under monotonic internal pressure

The creep damage lives of pipe containing LWT defect at different relative defect depth, different relative defect angle and different relative defect length under monotonic internal pressure were listed in Table 11.

Table 11:

Creep damage lives at different defect geometries under internal pressure.

No.	Load	LWT defect			Creep damage life (h)
	P (MPa)	c	b	a	Dˉ = 0.2	Dˉ = 0.4	Dˉ = 0.6	Dˉ = 0.8	Dˉ = 1.0
1	13.72	0.1	1/6	1	22,314	35,583	46,751	56,742	65,940
2		0.3			6,252	9,970	13,099	15,899	18,476
3		0.5			3,460	5,518	7,250	8,799	10,225
4		0.7			2,344	3,737	4,910	5,960	6,926
5	13.72	0.3	1/6	1	6,700	10,685	14,038	17,039	19,800
6			1/3		6,605	10,532	13,838	16,795	19,518
7			1/2		6,472	10,321	13,561	16,459	19,127
8			2/3		6,252	9,970	13,099	15,899	18,476
9	13.72	0.3	1/6	1	7,162	11,421	15,006	18,213	21,165
10				1.5	6,929	11,050	14,518	17,620	20,476
11				2	6,640	10,588	13,911	16,884	19,621
12				2.5	6,252	9,970	13,099	15,899	18,476

Based on the calculation results of creep damage lives under monotonic internal pressure in Table 11, the effect curves of defect geometry for creep damage life were plotted, as shown in Figure 5.

Figure 5:

Effect of defect geometries for creep damage life under monotonic internal pressure. (a) Relative defect depth; (b) relative defect angle; (c) relative defect length.

From Figure 5, creep damage life increased with creep damage equivalent increasing. At the same creep damage equivalent, creep damage life decreased with defect geometry increasing. The creep damage life decreased sharply with relative defect depth increasing, decreased slightly with relative defect angle increasing and decreased slowly with relative defect length increasing. The relation of creep damage life and relative defect depth was approximate parabola, the relation of creep damage life and relative defect angle was approximate straight line and the relation of creep damage life and relative defect length was also approximate straight line. From the rate of decrease of creep damage life, the influence factors of defect parameter from high to low were relative defect depth, relative defect length and relative defect angle.

Figure 6 gave the relation curves of creep damage equivalent and creep damage life under monotonic internal pressure. From the compact degree of different curves, the same conclusion was obtained.

Figure 6:

Relation of creep damage equivalent and creep damage life under monotonic internal pressure. (a) Relative defect depth; (b) relative defect angle; (c) relative defect length.

Effect of defect geometry under monotonic bending moment

The creep damage lives of pipe containing LWT defect at different relative defect depth, different relative defect angle and different relative defect length under monotonic bending moment were listed in Table 12.

Table 12:

Creep damage lives at different defect geometries under bending moment.

No.	Load	LWT defect			Creep damage life (h)
	M (kN m)	c	b	a	Dˉ = 0.2	Dˉ = 0.4	Dˉ = 0.6	Dˉ = 0.8	Dˉ = 1.0
1	75.6	0.1	1/6	1	55,810	90,395	119,855	146,412	171,001
2		0.3			25,181	40,785	54,077	66,059	77,153
3		0.5			17,392	28,170	37,350	45,626	53,289
4		0.7			13,630	22,076	29,271	35,756	41,762
5	75.6	0.3	1/6	1	26,317	42,625	56,517	69,040	80,635
6			1/3		26,077	42,237	56,002	68,411	79,900
7			1/2		25,743	41,695	55,283	67,533	78,875
8			2/3		25,181	40,785	54,077	66,059	77,153
9	75.6	0.3	1/6	1	25,418	41,170	54,587	66,683	77,882
10				1.5	25,360	41,076	54,463	66,530	77,704
11				2	25,286	40,955	54,302	66,334	77,475
12				2.5	25,181	40,785	54,077	66,059	77,153

Based on the calculation results of creep damage lives under monotonic bending moment in Table 12, the effect curves of defect geometry for creep damage life were plotted, as shown in Figure 7. Figure 8 gave the relation curves of creep damage equivalent and creep damage life under monotonic bending moment.

Figure 7:

Effect of defect geometries for creep damage life under monotonic bending moment. (a) Relative defect depth; (b) relative defect angle; (c) relative defect length.

Figure 8:

Relation of creep damage equivalent and creep damage life under monotonic bending moment. (a) Relative defect depth; (b) relative defect angle; (c) relative defect length.

From Figures 7 and 8, some similar regulars were shown with creep damage lives under monotonic internal pressure. But the most difference was that the rate of decrease of creep damage life with relative defect length was less than the rate of decrease of creep damage life with relative defect angle. So, the influence factors of defect parameter from high to low were relative defect depth, relative defect angle and relative defect length.

Effect of defect geometry under combined internal pressure and bending moment

The creep damage lives of pipe containing LWT defect at different relative defect depth, different relative defect angle and different relative defect length under combined internal pressure and bending moment were listed in Table 13.

Table 13:

Creep damage lives at different defect geometries under combined internal pressure and bending moment.

No.	Load		LWT defect			Creep damage life (h)
	P (MPa)	M (kN m)	c	b	a	Dˉ = 0.2	Dˉ = 0.4	Dˉ = 0.6	Dˉ = 0.8	Dˉ = 1.0
1	13.72	75.6	0.1	1/6	1	17,553	27,410	35,575	42,803	49,407
2			0.3			4,908	7,665	9,948	11,969	13,816
3			0.5			2,714	4,238	5,501	6,618	7,639
4			0.7			1,837	2,869	3,723	4,480	5,171
5	13.72	75.6	0.3	1/6	1	5,390	8,418	10,925	13,145	15,173
6				1/3		5,287	8,256	10,715	12,892	14,881
7				1/2		5,144	8,032	10,425	12,543	14,479
8				2/3		4,908	7,665	9,948	11,969	13,816
9	13.72	75.6	0.3	1/6	1	5,847	9,130	11,849	14,257	16,457
10					1.5	5,603	8,749	11,355	13,663	15,770
11					2	5,303	8,282	10,748	12,932	14,928
12					2.5	4,908	7,665	9,948	11,969	13,816

Based on the calculation results of creep damage lives under combined internal pressure and bending moment in Table 13, the effect curves of defect geometry for creep damage life were plotted, as shown in Figure 9. Figure 10 gave the relation curves of creep damage equivalent and creep damage life. The same regular existed with creep damage lives of pipe containing LWT defect under monotonic internal pressure. The influence factors of defect parameter from high to low were relative defect depth, relative defect length and relative defect angle.

Figure 9:

Effect of defect geometries for creep damage life under combined internal pressure and bending moment. (a) Relative defect depth; (b) relative defect angle; (c) relative defect length.

Figure 10:

Relation of creep damage equivalent and creep damage life under combined internal pressure and bending moment. (a) Relative defect depth; (b) relative defect angle; (c) relative defect length.

Above all, relative defect depth was the most significant effect factor for creep damage life of pipe containing LWT defect under monotonic internal pressure and combined internal pressure and bending moment. The second significant effect factor was relative defect length. The effect of relative defect angle was slight. Relative defect length and relative defect angle changed their order when pipe containing LWT defect under monotonic bending moment. This showed a good agreement with the results of regression formula of pipe containing LWT defect under different loads.

Conclusions

In this paper, creep damage lives of pipe containing LWT defect under different loads were calculated and life prediction of pipe containing LWT defect by skeletal point rupture stress was conducted. Some conclusions can be acquired as follows:

Creep damage life regression formulas of pipe containing LWT defect subjected to monotonic internal pressure, monotonic bending moment and combined internal pressure and bending moment were obtained.
Failure lives of pipe containing LWT defect under different loads can be predicted using the skeletal point rupture stress.
Relative defect depth was the most significant factor to creep damage lives of pipe containing LWT defect.

Funding statement: Funding: The authors gratefully acknowledge the financial support by Jiangsu Natural Science Funds (BK2008373) and Graduate Student Scientific Innovation Project of Jiangsu Province (CX10B_164Z), China.

References

[1] W.Bendick, L.Cipolla, J.Gabrel and J.Hald, Int. J. Press. Ves. Pip., 87(6) (2010) 304–309.10.1016/j.ijpvp.2010.03.010Search in Google Scholar

[2] D.Q.Shi, X.A.Hu and X.G.Yang, Mater. High Temp., 30(4) (2013) 287–294.10.3184/096034013X13764057121845Search in Google Scholar

[3] F.R.Hall and D.R.Hayhurst, Proc. R. Soc., London, A443 (1991) 383–403.Search in Google Scholar

[4] T.H.Hyde, W.Sun and J.A.Williams, Int. J. Press. Ves. Pip., 76 (2000) 925–33.Search in Google Scholar

[5] T.H.Hyde, W.Sun and J.A.Williams, Int. J. Press. Ves. Pip., 79 (2002) 799–805.Search in Google Scholar

[6] D.L.Marriott, Proc. IUTAM Symp. Cre. Strut., Berlin (1970), pp. 137–152.Search in Google Scholar

[7] T.H.Hyde, W.Sun and J.A.Williams, Int. J. Press. Ves. Pip., 79(12) (2002) 799–805.10.1016/S0308-0161(02)00134-5Search in Google Scholar

[8] W.Sun, T.H.Hyde, A.A.Becker and J.A.Williams, Int. J. Press. Ves. Pip., 79(2) (2002) 135–143.10.1016/S0308-0161(01)00133-8Search in Google Scholar

[9] G.D.Zhang and C.Y.Zhou, 12th Int. Conf. on Press. Ves. Tech., Jeju Island, 9 (2009), pp. 672–678.Search in Google Scholar

[10] Y.Lu, S.D.Jing, L.H.Han and C.D.Liu, Chem. Mach., 25(2) (1998) 112–115.Search in Google Scholar

[11] L.H.Han, C.D.Liu, Y.P.Wang and J.Chen, Petro. Chem. Equip., 27(4) (1998) 38–42.Search in Google Scholar

[12] Y.J.Kim and B.G.Son, Int. J. Press. Ves. Pip., 81(12) (2004) 897–906.10.1016/j.ijpvp.2004.06.002Search in Google Scholar

[13] Y.J.Kim, D.J.Shim, H.Lim and Y.J.Kim, J. Press. Vess. T. ASME, 126 (2004) 194–201.Search in Google Scholar

[14] Y.J.Kim, C.K.Oh, C.Y.Park and K.Hasegawa, Int. J. Press. Ves. Pip., 83(7) (2006) 546–555.10.1016/j.ijpvp.2006.03.001Search in Google Scholar

[15] S.H.Ahn, K.W.Nam, K.Takahashi and K.Ando, Nucl. Eng. Des., 236(2) (2006) 140–155.10.1016/j.nucengdes.2005.07.010Search in Google Scholar

[16] D.J.Shim, Y.J.Kim and Y.J.Kim, J. Press. Vess.-T. ASME, 127 (2005) 76–83.Search in Google Scholar

[17] J.W.Kim, S.H.Lee and C.Y.Park, Nucl. Eng. Des., 239(12) (2009) 2737–2746.10.1016/j.nucengdes.2009.10.003Search in Google Scholar

[18] H.Hui and P.N.Li, Nucl. Eng. Des., 240(10) (2010) 2512–2520.10.1016/j.nucengdes.2010.05.009Search in Google Scholar

[19] L.H.Han, S.Y.He, Y.P.Wang and C.D.Liu, Int. J. Press. Ves. Pip., 76(8) (1999) 539–542.10.1016/S0308-0161(99)00031-9Search in Google Scholar

[20] J.W.Kim, M.G.Na and C.Y.Park, Nucl. Eng. Des., 238(6) (2008) 1275–1285.10.1016/j.nucengdes.2007.10.017Search in Google Scholar

[21] Y.J.Kim, J.Kim, J.Ahn, S.P.Hong and C.Y.Park, Eng. Fract. Mech., 75(8) (2008) 2225–2245.10.1016/j.engfracmech.2007.10.007Search in Google Scholar

[22] Y.J.Kim, K.H.Lee, C.S.Oh, B.Yoo and C.Y.Park, Int. J. Mech. Sci., 49 (2007) 1413–1424.Search in Google Scholar

[23] C.K.Oh, Y.J.Kim and C.Y.Park, Nucl. Eng. Des., 239(2) (2009) 261–273.10.1016/j.nucengdes.2008.10.019Search in Google Scholar

[24] S.H.Ahn, K.W.Nam, Y.S.Yoo, K.Ando, S.H.Ji, M.Ishiwata and K.Hasegawa, Nucl. Eng. Des., 211(2–3) (2002) 91–103.10.1016/S0029-5493(01)00447-2Search in Google Scholar

[25] K.Miyazaki, S.Kanno, M.Ishiwata, K.Hasegawa, S.H.Ahn and K.Ando, Nucl. Eng. Des., 211(1) (2002) 61–68.10.1016/S0029-5493(01)00438-1Search in Google Scholar

[26] K.Miyazaki, S.Kanno, M.Ishiwata, K.Hasegawa, S.H.Ahn and K.Ando, Nucl. Eng. Des., 191(2) (1999) 195–204.10.1016/S0029-5493(99)00141-7Search in Google Scholar

[27] K.Miyazaki, A.Nebu, M.Ishiwata and K.Hasegawa, Nucl. Eng. Des., 214(1–2) (2002) 127–136.10.1016/S0029-5493(02)00021-3Search in Google Scholar

[28] K.Takahashi, K.Ando, M.Hisatsune and K.Hasegawa, Nucl. Eng. Des., 237(4) (2007) 335–341.10.1016/j.nucengdes.2006.04.033Search in Google Scholar

[29] K.Takahashi, A.Kato, K.Ando, M.Hisatsune and K.Hasegawa, Nucl. Eng. Des., 237(2) (2007) 137–142.10.1016/j.nucengdes.2006.03.016Search in Google Scholar

[30] J.Peng, C.Y.Zhou, J.L.Xue, Q.Dai and X.H.He, Nucl. Eng. Des., 241(8) (2011) 2758–2765.10.1016/j.nucengdes.2011.06.030Search in Google Scholar

[31] K.Takahashi, S.Tsunoi, T.Hara, T.Ueno, A.Mikami, H.Takada, K.Ando and M.Shiratori, Int. J. Press. Ves. Pip., 87(5) (2010) 211–219.10.1016/j.ijpvp.2010.03.022Search in Google Scholar

[32] K.Takahashi, S.Watanabe, K.Ando, Y.Urabe, A.Hidaka, M.Hisatsune and K.Miyazaki, Nucl. Eng. Des., 239(12) (2009) 2719–2727.10.1016/j.nucengdes.2009.09.011Search in Google Scholar

[33] J.L.Xue, C.Y.Zhou, X.H.He and J.W.Sheng, 12^th Int. Conf. on Press. Ves. and Tech., Jeju Island, 9 (2009), pp. 529–537.Search in Google Scholar

[34] J.L.Xue, C.Y.Zhou and J.Peng, Mater. Sci. Forum., 704–705 (2012) 1304–1309.Search in Google Scholar

[35] J.L.Xue, C.Y.Zhou and J.Peng, 18th Int. Conf. on Nucl. Eng., 5 (2010), pp. 523–528.Search in Google Scholar

[36] C.Y.Zhou, J.L.Xue and G.D.Zhang, J. Press. Equip. Syst., 6(1) (2008) 41–44.Search in Google Scholar

[37] J.L.Xue, C.Y.Zhou and J.Peng, Int. J. Mech. Sci., 93 (2015) 136–153Search in Google Scholar

[38] J.L.Xue, C.Y.Zhou, X.F.Lu and X.C.Yu, Eng. Fail. Anal. (2015) (under review).Search in Google Scholar

[39] L.M.Kachanov, Izv. Akad. Nauk. 8 (1958) 26–31.Search in Google Scholar

[40] D.R.Hayhurst, Eng. App. High Temp. 1 (1983) 85–176.Search in Google Scholar

[41] T.H.Hyde, A.A.Becker, W.Sun, A.Yaghi, J.A.Williams and S.Concari, 5th Int. Conf. on Mech. and Mater. in Des., Porto-Portugal (2006), pp. 1–13.Search in Google Scholar

[42] ABAQUS, ABAQUS User’s Manual, Pawtucket, USA, (2001).Search in Google Scholar

[43] T.H.Hyde and W.Sun, Int. J. Press. Ves. Pip., 79(5) (2002) 331–339.10.1016/S0308-0161(02)00027-3Search in Google Scholar

Received: 2014-8-15

Accepted: 2015-3-10

Published Online: 2015-4-25

Published in Print: 2016-3-1

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Articles in the same Issue

https://doi.org/10.1515/htmp-2014-0141

Keywords for this article

creep damage; life prediction; local wall thinning; high temperature; skeletal point rupture stress

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