Life estimation of pressurised pipe bends using steady-state creep

reference rupture stresses

T.H. Hydea, W. Suna,*, J.A. Williamsb

aSchool of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, Nottingham NG7 2RD, UKbIndependent Consultant, East Leake, Leicester LE12 6LJ, UK

Received 2 September 2002; revised 10 October 2002; accepted 10 October 2002

Abstract

Steady-state reference rupture stresses were obtained for a range of 908 pipe bends, subjected to internal pressure only, using simplified 2D

axisymmetric finite element (FE) models. The bends were considered to be circular in shape and not include any ovality. Creep damage FE

analyses were performed to obtain realistic failure lives and to determine the skeletal point rupture stresses, using the material properties,

obtained at 640 8C, for a service-exposed CrMoV pipe steel. The effects of the normalised pipe bend dimension on the reference rupture

stresses are presented. The results obtained confirm the validity of the use of the steady-state reference rupture stress in life estimation for a

wide range of pressurised pipe bend geometries. The life predictions were compared with those of the corresponding straight pipes and their

relevance considered.

q 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Steady-state creep; Damage; Reference rupture stress; Failure life; Pipe bend

1. Introduction

Plain pipe bends are commonly used in the piping

systems of power plants. At elevated temperatures, the bend

section may be a potential source of weakness during

service, due to long term creep, particularly in cases where

significant initial ovality and wall thickness variations exist,

which are introduced by the manufacturing process. There-

fore, the life assessment and failure prediction of pipe bends

is an important factor to be considered in the design and safe

operation of pipelines. An essential requirement in life

assessment is the choice of a suitable design stress for

comparison with material creep rupture data in order to

estimate the service life or the remaining life of the pipe

bend. Reference stress methods and continuum damage

modelling have been used to study the deformation

behaviour and to predict the failure life of pressurised

pipe bends [1,2].

For straight pipes, mean diameter formulae are used,

with published design stresses, to determine the design

minimum thickness, for both thick and thin walled

pressurised plain pipes [3]. Design stresses are used to

determine the creep rupture lives of pipes; the method is

applicable to the situations where significant system loads or

other external loads are not present. Very few parent pipe

failures have occurred in practice for the straight pipes,

clearly showing the conservatism of the design rule [4]. In

previous work [5,6], a simplified method, based on a steady-

state reference rupture stress, for estimating the creep failure

lives of pressurised straight pipes, is presented. The validity

of the steady-state approach was assessed and excellent

agreement between the life estimates using the simplified

steady-state approach and damage modelling, for a number

of CrMoV pipe steels, was obtained, for a wide range of

pipe geometry and loading cases. However, the case for pipe

bends is less clear and, over the years, there have been

failures at pipe bends during service operation, for example,

see Ref. [7]. Design of service-exposed bends generally

follows the basic design rules for defining a minimum wall

thickness for an equivalent straight pipe diameter and then

increasing the thickness by up to 12.5%, dependent on the

pipe diameter and bend radius. This ensures that no part of

the bend is thinner than the minimum radius for the straight

0308-0161/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved.

PII: S0 30 8 -0 16 1 (0 2) 00 1 34 -5

International Journal of Pressure Vessels and Piping 79 (2002) 799–805

www.elsevier.com/locate/ijpvp

* Corresponding author. Tel.: þ44-115-9513-809; fax: þ44-115-9513-

800.

E-mail address: w.sun@nottingham.ac.uk (W. Sun).

pipe. Codes such as BS 5500 also consider pipework design

in a similar manner but can consider combined loading.

The work presented in this paper is an extension of the

previous study on straight, plain pipes to pipe bends which

have a 908 bend angle and are subjected to internal pressure

only. This will allow direct comparison of the specific pipe

bends and straight pipes. Initial ovality and variable wall

thickness are not considered in the current work. Steady-

state reference rupture stresses were obtained using

simplified 2D axisymmetric finite element (FE) models.

Creep damage FE analyses were performed to obtain

realistic failure lives and to determine skeletal point rupture

stresses, using material properties at 640 8C for a typical

CrMoV pipe steel. The effects of the normalised pipe bend

dimensions on the reference rupture stresses were investi-

gated. The results obtained confirm the validity of the use of

the steady-state reference rupture stress in life estimation for

a wide range of pipe bend geometries. The life predictions

were compared with those for corresponding straight pipes

for completeness.

2. Pipe bend model and FE analyses

2.1. Pipe bend model

The 3D 908 pipe bend is shown in Fig. 1, where Rm is the

neutral axis radius and u is the angle of the bend. Previous

work on the creep of pipe bends [8] has shown that when

internal pressure, pi, is the predominant load, in a 908 pipe

bend, 2D axisymmetric models provide accurate stress

results, compared with those obtained from 3D models. In

3D 908 pipe bend modelling, only a symmetrical quarter was

modelled [8]. Deformations on the symmetrical plane of the

cross-section of the pipe (u ¼ 458, Fig. 1) were constrained

in the direction perpendicular to the cross-section. The free

end condition was applied to the end of the straight part of

the pipe, with a uniform tensile stress corresponding to that

of a closed-ended pipe. Comparison of stresses in the 2D

model with the corresponding 3D solutions have shown

good agreement. The values of the maximum principal

stress and equivalent stress, at the key locations on the

cross-section of the pipe, obtained from 2D analyses and 3D

analyses (on the symmetrical cross-section, u ¼ 458, for 3D

model), agreed to within 2.2% [8]. This obviously avoids

time consuming 3D FE calculations, particularly for damage

analyses. Therefore, in the work presented in this paper, 2D

axisymmetric models will be used for the FE analyses. The

corresponding 2D model (u ¼ 3608) is shown in Fig. 2, in

which the pipe bend dimensions are characterised by two

dimension ratios, Rm=2Ro and Ro=Ri; where Ri and Ro are the

inside and outside radii of the pipe. A typical 2D FE mesh is

shown in Fig. 3.

2.2. FE analyses and life estimation

Steady-state FE analyses were performed using a Norton

power law ð _1c ¼ AsnÞ to represent the material creep

behaviour. Creep damage FE calculations were performed

using constitutive equations of the form [9]

_1cij ¼

3

2Asn21

eq Sij

1

ð1 2 vÞntm ð1aÞ

and

_v ¼ Ms

xr

ð1 þ fÞð1 2 vÞftm ð1bÞ

Nomenclature

A, m, M, n, x, f material constants

pi internal pressure

r radial position

Ri, Ro inside and outside radii of pipe cross-

section

Rm neutral axis radius of pipe bend

Sij deviatoric stress

t, tf time and failure time

a tri-axial stress state parameter

(material constant)

_1c creep strain rate

seq, s1, sr equivalent, maximum principal and

rupture stresses, respectively

smdh mean diameter hoop stress

srref, sr

sp steady-state reference rupture stress

and skeletal point rupture stress

u pipe bend angle

w circumferential position on the cross-

section of pipe bend

v, _v damage and damage rate

Fig. 1. Three-dimensional 908 pipe bend.

T.H. Hyde et al. / International Journal of Pressure Vessels and Piping 79 (2002) 799–805800

where A, n, m, M, x and f are material constants and v is the

damage parameter ð0 , v , 1Þ: sr is a rupture stress, which

is assumed to be a linear combination of the maximum

principal stress, s1, and the equivalent stress, seq, as follows

sr ¼ as1 þ ð1 2 aÞseq ð2Þ

where a ð0 , a , 1Þ is the tri-axial stress state parameter

(material constant). Estimation of failure life, tf, using the

steady-state rupture stress was made by using the integrated

form of Eq. (1b), i.e.

tf ¼1 þ m

MðsrÞx

� �ð1=1þmÞ

ð3Þ

The material properties at 640 8C for a typical service-aged

CrMoV pipe steel, given in Table 1, were used in the

damage analyses as an example. Although the material data

used were obtained at 640 8C, which is above the normal

useable range of the material, the general creep character-

istics are similar to those expected at ,600 8C. Details of

the FE creep and damage analysis procedures are described

in Refs. [5,6]. Steady-state analyses were conducted using

the standard ABAQUS FE code [10], while damage

calculations were performed using the UMAT facility

within the ABAQUS code [11].

3. Reference rupture stresses

A set of practical geometry range in conventional power

plant was used in the FE analyses. The ratios of 1:1 #

Ro=Ri # 2:1 cover most practical pipe geometries and the

ratios of 4 # Rm=2Ro # 5 are the practical range for the pipe

bends used in the UK power plants. Hence, steady-state and

damage analyses were performed using the 2D model,

Figs. 2 and 3, for a range of practical pipe bend dimension

ratios of 4 # Rm=2Ro # 5 and 1:1 # Ro=Ri # 2:1: In all

cases, the values of the internal pressure, pi, were chosen to

be equivalent to a mean diameter hoop stress, smdh ½¼

piðRo=Ri þ 1Þ=2ðRo=Ri 2 1Þ�; of 38.065 MPa. Steady-state

and damage calculations were performed using the creep

properties at 640 8C for a 1/2Cr1/2Mo1/4V service-aged

pipe steel, which has an a value of 0.3. The effect of a value

on the rupture stresses has been investigated in previous

work on straight pipes [5,6].

3.1. Through wall rupture stress distribution

The through wall stress distributions within a pipe bend

vary with angular position, w, Fig. 3. These stress

distributions have been investigated at different angular

positions, characterised by w. Results obtained from both

the steady-state and damage analyses have shown that in the

full range of Rm=2Ro and Ro=Ri ratios considered, the peak

stress and damage area occurs at w ¼ 0: Therefore, in this

paper, the results of the steady-state reference rupture

stresses, srefr ; and the skeletal point rupture stresses, s

spr ;

obtained at w ¼ 0 only, are presented and used for life

estimations.

An example of the through thickness variations of the

steady-state rupture stress, with radial position, r, at w ¼ 0;

from the bore (A to B, Fig. 3), obtained with Rm=2Ro ¼ 4:5

and Ro=Ri ¼ 1:5; for different n-values, with a ¼ 0:3; is

shown in Fig. 4(a). The steady-state reference rupture stress,

srefr ; is defined from the intersection of the curves which

were obtained with different n-values [5,6]. It can be seen

that the reference rupture stress is practically independent of

n and can therefore be accurately determined. The

corresponding through thickness rupture stress distributions,

obtained from damage analyses, for different creep times

before failure, are shown in Fig. 4(b). The stress at the

intersection of the curves which were obtained from damage

analyses at different times is defined as the skeletal point

rupture stress, sspr : It can be seen that the skeletal point

rupture stress again can be accurately determined.

3.2. Reference rupture stresses and geometry effects

The steady-state reference rupture stresses, srefr ; and the

corresponding skeletal point rupture stresses, sspr ; obtained

from the through wall stress distributions, at w ¼ 0; Fig. 3,

for a range of Rm=2Ro and Ro=Ri ratios, are presented in

Table 2. It is interesting to see that, similar to the straight

Table 1

Material constants [5] used in the FE damage analyses (s in MPa and t in h)

A n m M f x a

6.599 £ 10216 6.108 0 5.998 £ 10214 4.5 5.767 0.3

Fig. 2. Axisymmetric pipe bend geometry (u ¼ 3608).

Fig. 3. A typical two-dimensional FE mesh ðRo=Ri ¼ 1:5Þ:

T.H. Hyde et al. / International Journal of Pressure Vessels and Piping 79 (2002) 799–805 801

pipes, the srefr and s

spr values for the full range of dimension

ratios of pipe bends, are very close to each other. The srefr

variations, normalised by the mean diameter hoop stress,

smdh, with Ro=Ri; for a range of Rm=2Ro; are shown in

Fig. 5(a), from which it can be seen that the srefr values

reduce slightly with increasing Rm=2Ro; but reduce signifi-

cantly with increasing Ro=Ri; this is consistent with

the corresponding results for straight pipes [6]. In the full

range of the dimension ratios considered, the srefr values are

much lower than the smdh value (38.065 MPa). Fig. 5(b)

shows an alternative presentation of the variations of srefr ;

with 1=½Rm=2Ro�; for a range of Ro=Ri; from which the

consistency of the results for the pipe bends with the

corresponding results of straight pipes, for which

1=½Rm=2Ro�! 0; can be seen more clearly. Approximately

linear relationships between srefr and 1=½Rm=2Ro� were

obtained for each Ro=Ri; allowing interpolation of srefr ; or

limited extrapolation of srefr outside the range of 4 #

Rm=2Ro # 5:

4. Life estimation using the reference rupture stresses

The failure life estimates obtained using srefr and s

spr in

Eq. (3) and the failure lives obtained directly from damage

analyses are given in Table 3, in which the corresponding

results for straight pipes, using srefr and smdh under

Table 2

srefr and s

spr (MPa) obtained from steady-state and damage analyses, for a

range of Rm=2Ro and Ro=Ri; with smdh ¼ 38.065 MPa and a ¼ 0.3

Ro/Ri Rm/2Ro ¼ 4 Rm/2Ro ¼ 4.5 Rm/2Ro ¼ 5 Straight

pipe [6]

srefr s

spr sref

r sspr sref

r sspr sref

r sspr

1.1 36.55 36.33 36.24 35.98 36.02 35.78 33.93 33.92

1.3 35.3 34.97 35.0 34.76 34.81 34.53 32.84 32.83

1.5 34.09 33.82 33.82 33.53 33.6 33.35 31.82 31.78

1.7 32.97 32.64 32.74 32.4 32.52 32.2 30.87 30.81

1.9 31.95 31.6 31.72 31.45 31.55 31.25 30 29.92

2.1 31.1 30.71 30.8 30.5 30.6 30.37 29.19 29.09

Fig. 5. (a) Variations of normalised steady-state reference rupture stresses

with Ro=Ri; for a range of Rm=2Ro; for a ¼ 0.3. (b) Variations of normalised

steady-state reference rupture stresses with 1=½Rm=2Ro�; for a range of Ro=Ri;

for a ¼ 0.3.

Fig. 4. (a) Variations of steady-state rupture stresses with radial position

(w ¼ 0, from Ri), for n ¼ 2, 4 and 6. Rm=2Ro ¼ 4:5; Ro=Ri ¼ 1:5 and a ¼

0:3 (smdh ¼ 38.065 MPa). (b) Variations of rupture stresses with radial

position (w ¼ 0, from Ri), at various times, obtained from damage analyses,

for a CrMoV steel ða ¼ 0:3Þ: Rm=2Ro ¼ 4:5 and Ro=Ri ¼ 1:5

(smdh ¼ 38.065 MPa).

T.H. Hyde et al. / International Journal of Pressure Vessels and Piping 79 (2002) 799–805802

closed-end conditions [6], are also shown for comparison. It

is clear that as with the cases of straight pipes, the failure

lives estimated using srefr are very close to those obtained

from damage modelling, and the failure lives estimated

from sspr are practically the same as those from damage

modelling, for the full range of dimension ratios investi-

gated. In general, the differences of the life predictions

between steady-state and damage analyses are ,4–5%,

clearly showing the validity of the use of the simplified

steady-state method. In addition, similar to the straight pipe

cases, the failure lives increase significantly with increasing

Ro=Ri: However, it has been found that there is no significant

benefit to the failure life when Rm=2Ro increases from 4 to 5.

It is clear from Table 3 that the predicted failure lives for

pipe bends are significantly lower than those of the

corresponding straight pipes. The life reductions, based on

steady-state results, presented as failure life ratios, are

shown in Fig. 6(a). It can be seen that in the range of 4 #

Rm=2Ro # 5 and 1:1 # Ro=Ri # 2:1; the life ratios are in a

range of 0.65–0.76, and the life ratios increase with

increasing Ro=Ri: The same life ratios, with 1=½Rm=2Ro�;

for different Ro=Ri; are shown in Fig. 6(b). It is interesting to

see that the life predicted by using the mean diameter hoop

stress in Eq. (3) is very conservative, even shorter than those

for pipe bends in all cases considered, particularly when

Ro=Ri is large.

5. Discussion

The results presented in this paper have shown the

validity of a simple life prediction method for 908 pipe

bends subjected to internal pressure only, using the steady-

state reference rupture stresses, obtained from FE analyses

of simplified 2D axisymmetric models. The fabrication

procedures for a bend will generate a degree of ovality and

wall thinning, dependent on the fabrication route. Such

variations are not considered in the current work and the

pipe bend is assumed to be of uniform thickness and round.

There is excellent agreement between the life estimates

using steady-state reference stress solutions and the

continuum damage solutions, for a wide range of pipe and

bend dimension ratios which cover the practical range in

conventional power plant. The ratios of 1:1 # Ro=Ri # 2:1

cover most practical pipe geometries and the ratios of 4 #

Rm=2Ro # 5 are the practical range for the pipe bends used

in the UK power plants. The differences between the steady-

state predictions and the damage solutions, over the full

range of dimension ratios considered, are generally ,5%.

Fig. 6. (a) Failure life ratios, of pipe bends relative to straight pipes,

estimated using srefr ; with Ro=Ri; for a range of Rm=2Ro; for a ¼ 0.3. (b)

Failure life ratios, of pipe bends relative to straight pipes, estimated using

srefr ; with 1=½Rm=2Ro�; for a range of Ro=Ri; for a ¼ 0.3.

Table 3

tf (h) estimated by srefr and s

spr and obtained from damage analyses, for a

range of Rm/2Ro and Ro/Ri, with smdh ¼ 38.065 MPa and a ¼ 0.3

Pipe bend: Rm/2Ro ¼ 4 Straight pipe [6] Design

Ro/Ri By srefr By s

spr Damage By sref

r Damage By smdh

1.1 16,174 16,747 16,931 24,842 24,860

1.3 19,768 20,869 20,966 29,979 30,042

1.5 24,173 25,307 25,711 35,955 36,120 12,797

1.7 29,309 31,059 31,004 42,846 43,123

1.9 35,132 37,436 37,166 50,516 51,096

2.1 41,043 44,141 44,099 59,154 60,083

Pipe bend: Rm/2Ro ¼ 4.5 Straight pipe Design

Ro/Ri By srefr By s

spr Damage By sref

r Damage By smdh

1.1 16,988 17,708 17,732 24,842 24,860

1.3 20,766 21,606 21,879 29,979 30,042

1.5 25,307 26,596 26,753 35,955 36,120 12,797

1.7 30,516 32,410 32,262 42,846 43,123

1.9 36,627 38,478 38,568 50,516 51,096

2.1 43,402 45,923 45,708 59,154 60,083

Pipe bend: Rm/2Ro ¼ 5 Straight pipe Design

Ro/Ri By srefr By s

spr Damage By sref

r Damage By smdh

1.1 17,595 18,287 18,385 24,842 24,860

1.3 21,428 22,449 22,627 29,979 30,042

1.5 26,278 27,434 27,622 35,955 36,120 12,797

1.7 31,726 33,588 33,254 42,846 43,123

1.9 37,780 39,920 39,719 50,516 51,096

2.1 45,064 47,068 47,039 59,154 60,083

T.H. Hyde et al. / International Journal of Pressure Vessels and Piping 79 (2002) 799–805 803

The required reference rupture stress for a given geometry

can be conveniently obtained with the knowledge of a

relatively small number of material constants, i.e. m, M, x

and a using steady-state analyses, thus avoiding the need for

detailed FE damage analyses.

It is useful to consider the interpretation of the current

data as follows. Firstly, from Table 3, the life of the pipe

bend is less than that of the straight pipe based on all of the

analyses reported here. This is not unreasonable but would

predict an earlier high failure rate in pipe bends at some

stage. However, it should be noted that the design lives of

the pipe bends are based on the simple mean diameter hoop

stress and the life corresponding to this stress is typically

around half of the calculated bend life from damage

analysis. Thus, the current mean diameter hoop stress rule

should still be conservative.

In addition, codes like BS 5500, for example, generally

require that following calculation of the straight pipe

thickness, this minimum thickness should be increased by

,10 to 12.5% to take account of any potential thickness

changes during fabrication. Table 4 considers this in a

simplistic manner for completeness. Here, a typical pipe of

Ro=Ri ¼ 1:5 is analysed in the bend and straight form using

both reference stress and damage analyses. The relevant

pressure and Rm=2Ro are 15.226 MPa and 4.5, respectively.

The table shows the calculated lives, using the reference

stress and damage analysis approaches as well as the more

normal mean diameter hoop stress for the straight pipe. Two

cases are considered, the basic model with Ro=Ri ¼ 1:5 and

a model where the thickness of the pipe and bend is

increased by 10% for the same internal diameter. Compari-

son of these data shows that, for both these cases, which are

practical options, the calculated life will be in excess of the

design life calculated using the mean diameter equation and

hence should be conservative. However, if components are

run in excess of their design life, or outside the design

envelop, then special consideration should be placed on

bends during any life assessment.

6. Conclusions

A number of conclusions can be drawn from the current

investigation which is concerned with the analysis of 908

pipe bends subjected to pressure loading only.

† srefr and s

spr values, for the full range of dimension ratios

considered, are similar. The srefr values reduce slightly

with increasing Rm=2Ro; but reduce significantly with

increasing Ro=Ri:

† An approximately linear relationship exists between srefr

and 1=½Rm=2Ro�; thus allowing easy interpolation or

limited extrapolation, outside the range of 4 #

Rm=2Ro # 5; of srefr :

† The failure lives, estimated from sspr ; are practically the

same as those obtained from damage modelling for the

full range of dimension ratios considered.

† In all cases, the life estimates obtained by using srefr are

lower than those obtained from damage modelling and

hence should be conservative.

† Compared with the corresponding straight pipes, the

existence of pipe bends may cause a 25–35% reduction

of calculated life, in the geometry range of 4 #

Rm=2Ro # 5 and 1:1 # Ro=Ri # 2:1: However, the

design life for a straight pipe, as calculated using the

mean diameter equation, is still around 0.5 of the bend

life, and thus would still be conservative.

The above results were obtained for the case of pressure

load alone. For the case of additional system loads, 3D

models would have to be used, and it is likely that these

conclusions could be influenced by the addition of bending

moment or additional axial loads. Extension of the steady-

state approach to realistic cases where pipe bends have

initial ovality or variable wall thickness and the study of

effects of geometric nonlinearity and system load, etc. will

be the subjects of future work.

Acknowledgements

The authors wish to acknowledge EPSRC, Innogy Plc,

British Energy Plc and PowerGen Plc for their support of the

work, through an EPSRC/ESR21 grant.

References

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method in estimating the life of pipe bends under creep conditions. Int

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Table 4

tf (h) estimated by srefr and obtained from damage analyses, for Rm=2Ro ¼

4:5 and Ro=Ri ¼ 1:5 and 1.55 with pi ¼ 15.226 MPa. Ro=Ri ¼ 1:55 gives an

increase of 10% wall thickness compared to Ro=Ri ¼ 1:5; with the same

inside radius Ri

Ro/Ri smdh (MPa) Pipe bend Straight pipe

By srefr Damage By sref

r Damage By smdh

1.5 38.065 25,307 26,753 35,955 36,120 12,797

1.55 35.297 40,439 42,936 58,075 58,342 19,779

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T.H. Hyde et al. / International Journal of Pressure Vessels and Piping 79 (2002) 799–805 805