Science__Life Estimation of Pressurised Pipe Bends Using St
Transcript of Science__Life Estimation of Pressurised Pipe Bends Using St
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: [email protected] (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
[1] Hyde TH, Yaghi A, Becker AA, Proctor M. Use of the reference stress
method in estimating the life of pipe bends under creep conditions. Int
J Pressure Vessel Piping 1998;75:161–9.
[2] Hyde TH, Yaghi A, Becker AA, Earl PG. Finite element creep
continuum damage analysis of pressurised pipe bends with ovality.
Proceedings of the Seventh International Conference on Creep and
Fatigue at Elevated Temperature, Tsukuba, Japan; June 2001.
[3] Specification for unfired fusion welded pressure vessels, BS 5500,
BSI, London; 1997.
[4] Aburrow AF, Cane BJ, Carmichael GDT, Dewar A, Hart RV, Heather
CW, Plastow B, Williams JA, Womersley S. Creep of CrMoV piping
systems. Conference on pipework design and operation. London:
I. Mech. E; 1985.
[5] Hyde TH, Sun W, Williams JA. Prediction of creep failure life of
internally pressurised thick walled CrMoV pipes. Int J Pressure Vessel
Piping 2000;76:925–33.
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
T.H. Hyde et al. / International Journal of Pressure Vessels and Piping 79 (2002) 799–805804
[6] Sun W, Hyde TH. A simplified method for predicting creep failure life
of internally pressurised pipes. Proceedings of the Fourth Japan-Sino
Bilateral Symposium on High Temperature Strength of Materials,
Tsukuba, Japan; June 2001.
[7] Bendick W, Weber H. Utersuchung von Zeitstandschadigung und
Erschopfung an einem Rohrbogen aus 14MoV 6 3 VGB Kraftswerk-
stechnik, vol. 69, 9; 1989. p. 936–44.
[8] Hyde TH, Yaghi A, Becker AA, Earl PG. Comparison of toroidal
pipes and 908 pipe bends during steady-state creep. Proceedings of the
Fifth International Colloquium on Ageing of Materials and Methods
for the Assessment of Lifetimes of Engineering Plant, Cape Town;
April 1999. p. 305–17.
[9] Hayhurst DR. The role of creep damage in structural mechanics. In:
Wilshire B, Owen DR, editors. Engineering approach to high
temperature. Swansea: Pineridge Press; 1983. p. 85–176.
[10] ABAQUS Version 5.8, Hibbitt, Karlsson and Sorenson Inc; 1998.
[11] Becker AA, Hyde TH, Sun W, Andersson P. Benchmarks for finite
element analysis of creep continuum damage mechanics. 10th
International Workshop on Computational Mechanics of Materials,
Galway, Ireland; August 2000.
T.H. Hyde et al. / International Journal of Pressure Vessels and Piping 79 (2002) 799–805 805