ARTICLE IN PRESS
International Journal of Pressure Vessels and Piping 84 (2007) 185–194
www.elsevier.com/locate/ijpvp
Creep analysis of bolted flange joints
Akli Nechache, Abdel-Hakim Bouzid
Ecole de Technologie Superieure, 1100 Notre-Dame Ouest, Montreal (Quebec), Canada H3C 1K3
Received 22 January 2006; received in revised form 24 May 2006; accepted 24 June 2006
Abstract
In the petrochemical and nuclear industries, the difficulty in assessing the effect of creep on the tightening load of bolted flanged
connections is recognized. Under high temperatures, the leak tightness of bolted joints is compromised due to the loss of the bolt load as
a result of creep of not only the gasket and bolt materials but also the flange material. Apart from acknowledgment of this effect, there
exists no established design calculation procedure that accounts for creep. This is because the relaxation of the bolt load and the
corresponding loss of the gasket contact stress are not easy to assess analytically. The main objective of the work is the development of a
simple analytical solution to the creep-relaxation problem encountered in bolted flange connections of the float type. Particular emphasis
is put towards relaxation caused by the flange and bolt material creep.
The validation of the methodology is carefully checked against the more complex 3D numerical FE method using different size flanges.
Based on the creep constants of the different joint elements (bolt, flange and gasket), the implemented analytical method is shown to
predict the bolt and gasket load relaxation with reasonable accuracy. In some flange cases, up to 70% of bolt load relaxation is found
with both methods depending on the flange creep material and size.
r 2006 Elsevier Ltd. All rights reserved.
Keywords: Bolted flanged joints; Analytical modelling; Bolt load relaxation; Flange creep; Finite element analysis
1. Introduction
Bolted flanged joints are the most popular means of
connecting piping systems and pressure vessels containing
fluid or gas under pressure. Although this type of
connection is practical in terms of disassembly, it is a
source of potential leakage failure especially when operating under high pressures and temperatures. Some flanged
joint assemblies may begin to leak at some time following a
successful hydrostatic test. One reason for this is that the
gasket experiences a drop in its initial compressive stress
due to gasket creep. Furthermore, above a temperature of
650 1F, flange and bolt creep become important contributing factors to the relaxation of the joint. Although it is
widely acknowledged that creep relaxation of bolted joints
increases with elevated temperature, [1,2] show that even at
room temperature relaxation can also be significant with
certain types of gaskets such as PTFE-based gaskets.
Corresponding author.
E-mail addresses: anechache@mec.etsmtl.ca (A. Nechache),
hakim.bouzid@etsmtl.ca (A.-H. Bouzid).
0308-0161/$ - see front matter r 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijpvp.2006.06.004
The ability of a joint to remain tight over a long period
of time is jeopardized due to the creep phenomenon that
takes place not only within the softer gasket material but
also the flange and bolt materials. Over the past 20 yr, with
strict emission laws and environmental protection consciousness, the technology of bolted flanged joints has
fostered considerable research and development worldwide. The research has evolved to the point where several
countries have already adopted new flange design procedures [3,4] and others are in the process of implementing
new design rules [5]. Nevertheless, apart from acknowledging the effect of creep-relaxation, these flange design
procedures do not give specific guidelines to help the design
engineer make a quantitative assessment [4–6]. Research
into the effect of creep on load relaxation in bolted joints
has recently re-emerged with the implementation of the
strict environmental laws and the recent development of
the two new gasket materials PTFE and flexible graphite.
In the absence of a specific method to evaluate the load
change due to creep, the experienced engineer has no choice
but to make an ‘‘educated guess’’. However, from a
practical standpoint it would be safer to provide the
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186
Nomenclature
KfP
Dn
n
e
y
yfM
yfP
sy
as
at
A
Ag
Ab
Ap
bs
bt
C
d
Ef
Eg
Eb
Fb
Fg
G
hG
lb
m
M
Mf
n
N
P
Q
r
ri
ro
tf
tg
u
y
w
hP
Kb
Kg
KfM
nut displacement (mm)
Poisson’s ratio of joint element
strain deformation
flange rotation (rad)
flange rotation due to bending moment (rad)
flange rotation due to pressure (rad)
tangential stress (MPa)
gasket stress creep constant
gasket time creep constant
creep constant for steel
full gasket contact area (mm2)
bolt area (mm2)
pressurized area encircled by G (mm2)
gasket stress creep constant
gasket time creep constant
bolt circle diameter (mm)
bolt nominal diameter (mm)
Young’s modulus of flange material (MPa)
gasket compression modulus (MPa)
Young’s modulus of bolt material (MPa)
bolt force (N)
gasket force (N)
gasket reaction force diameter (mm)
radial distance from bolt circle to gasket force
(mm)
radial distance from bolt circle to flange inner
diameter (mm)
bolt uniaxial stiffness (N/mm)
gasket uniaxial stiffness (N/mm)
flange uniaxial stiffness due to moment
(mm N/mm)
designer with a method that predicts the loss of load
accurately in order to guarantee a leak-tight joint over a
specified period of time. In critical applications, because of
the lack of creep data and the unavailability of a design
procedure, common practice is to apply hot torquing to
recover the load loss due to gasket creep.
Although recognized, long-term creep-relaxation in
bolted gasketed joints remains a subject that has received
little research attention. In the literature, very few papers
address analytically the effect of creep to help engineers
estimate accurately the load relaxation in bolted joints.
Creep analyses of bolted flange connections are presented
in [7–9]. A constant creep rate known as steady creep was
assumed to take place in the flange and bolts. The radial
growth of the hub and shell due to creep that alters the
stiffness of the flange as well as the gasket creep were not
considered. The paper presented in [10] extends the
analytical approach of [9] by using a strain-hardening rule
to estimates the bolt load loss due to flange creep.
However, the flexibility of the gasket and attached
structural components of the joint assembly were not
flange uniaxial stiffness due to pressure
(N/mm2)
initial bolt length (mm)
creep constant for steel
Discontinuity edge moment (mm N/mm)
flange moment (mm N/mm)
creep constant for steel
gasket contact width (mm)
internal pressure (N/mm2)
Discontinuity edge load (N/mm)
radial distance (mm)
flange inner radius (mm)
flange outer radius (mm)
thickness of the flange (mm)
thickness of the gasket (mm)
radial displacement (mm)
axial distance from flange centroid (mm)
axial displacement of joint element (mm)
Superscript
c
f
i
T
refers
refers
refers
refers
to
to
to
to
creep
final state
initial state
steady state temperature
to
to
to
to
bolt
an element of the joint
flange
gasket
Subscript
b
e
f
g
refers
refers
refers
refers
taken into account. Finally, a model based on the flexibility
and interaction of all joint elements presented in [11,12]
accurately predicts load relaxation due to gasket creep
only. This paper extends that work to include the creep
effect of the flange and bolts used in high temperature
applications.
2. Analytical flexibility model
The determination of the bolt load relaxation requires a
flexibility analysis to be conducted on the bolted joint
assembly. Fig. 1 shows the flexibility interaction model
used in this study that is limited to the raised face flange
type only. Due to the flexibility of the flange, the gasket
and the bolts, the deflections and rotations due to the
different loads and creep together with the interaction
between them is considered. Based on the work presented
in [13], this model can accommodate the creep-relaxation
behaviour of the flange, the gasket and the bolts
concurrently.
ARTICLE IN PRESS
A. Nechache, A.-H. Bouzid / International Journal of Pressure Vessels and Piping 84 (2007) 185–194
187
relationship exists between the final relaxed force and the
initial bolt-up force. This is established by considering the
axial displacement compatibility, which involves all individual joint element axial displacements caused by forces,
moments, pressure, thermal expansion and creep. A
compatibility equation is obtained based on the axial
distance travelled by the nut Dn during the tightening
process as shown in Fig. 2. In the absence of bolt selfloosening, this must remain the same during the operating
stages of pressurization and relaxation when creep takes
place. The elongation of the bolts, the compression of the
gasket and the displacement of the flange due to rotation
and their associated thermal expansion and creep components represent this amount of fixed absolute displacement.
The sum of the axial displacement of all joint elements in a
flange pair is
Either a time or strain hardening creep law of the bolts,
the flange ring and the gasket could be introduced in this
model to evaluate the load relaxation as function of time.
The theoretical calculation procedure that considers this
effect is presented in detail hereafter.
2.1. Axial displacement compatibility
A bolted flanged joint is a statically indeterminate
structure. The flexibility interaction analysis in the axial
direction is the key solution in determining the final
remaining load in terms of the initial one. Therefore a
PAp
Dn ¼
3
X
wie ¼
e¼1
3
X
wfe ,
(1)
e¼1
wib þ wig þ 2wif ¼ wfb þ wfg þ 2wff þ wT þ wc
(2)
where the axial displacements in terms of stiffness for the
individual joint elements, are given by
P
Fg
,
Kg
Mf
P
þ 2hG
.
wf ¼ 2hG
K fP
K fM
wb ¼
KfM ,KfP
Mf
θf
wb
wg
Fg
Fb
Fig. 1. Bolted flange model.
Initial Free
state
Initial pretightening
with rigid flange
and end closure
( virtual)
ð3Þ
Initial pretightening
with all elements
flexible
Operating state
with all elements
flexible
i
θc
CYLINDER
f
θc
i
FLANGE
θf
b
Hi
H
θf
wfi
wi
e
BOLT
wi2
f
tf
GASKET
wg ¼
While the bending of the bolts is not accounted for, the
gasket reaction location shift due to flange bending causing
the lever arm hG to change as detailed in [14] is considered.
wf is the flange axial displacement induced by flange
rotation caused by the bolt and pressure loads. wT is the
equivalent axial displacement due to the thermal expansion
difference of the individual elements. Although its effect
might be important as detailed in our previous papers
[15,16], it is not considered here for dissociation purposes
and ease of comprehension. wc is the total axial creep
Kb
Kg
Fb
;
Kb
lo
b
lo
whi
wi
lo
Hf
whf
w1f
1
REFERENCE EDGE
END CLOSURE
Fig. 2. Axial compatibility.
w2f
wff
wf
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188
displacement of the gasket, the bolts and the flange
c
w ¼
wcg
þ
wcb
þ
to a moment are detailed in [13]:
wcf .
(4)
It is to be noted that the axial displacement corresponding to the gasket is obtained at the gasket load
reaction location and that of the bolt and flange is
considered at the bolt circle. Substituting Eqs. (3) and (4)
into Eq. (2) gives
f
F fb F g
Mf
P
þ
þ 2hG f þ 2hG
þ wc
K fP
Kb Kg
K fM
ð5Þ
with axial equilibrium requiring that for initial bolt-up
F ib
¼
F ig
(6)
F fb ¼ F fg þ PAp .
(7)
The moment Mf acting on the flange about the bolt circle
is given by considering the discontinuity edge loads in
addition to the gasket force and hydrostatic end force. For
the initial bolt-up:
¼
F ig hG
i
þ 12Q tf þ M
i
(8)
and for pressurization
M ff
¼
hG F fg
þ PAp hP þ
2.3. Axial displacements
wg ¼
Fg
þ wcg .
Kg
(13)
wb ¼
Fb
þ wcb .
Kb
(14)
The resulting axial displacement of the flange as a result
of rotation at the bolt circle relative to the gasket reaction
location is given by
wf ¼ 2hG
Mf
P
þ 2hG
þ wcf ,
K fP
K fM
(15)
where, wcb , wcg and wcf are, respectively, the axial displacement of the bolt, gasket and flange ring due to creep.
3. Creep models and analysis
1 f
2Q tf
f
þM .
(9)
The rigidities of the individual elements of the bolted
flanged joint are then calculated. The gasket stiffness Kg
depends on the level of stress achieved during bolt-up and
is considered to vary across the gasket width. An average
value is obtained as follows:
Z
DSg
K g ¼ 2p
r dr,
(10)
DDg
where DSg over DDg is the slope
curves obtained at different stress
gasket width using an interpolation
gives the detailed analysis of Eq. (10).
given by
3.1. Creep model of flange and bolts
The power creep law used to model the flange and bolt
steel material is given by the following equation:
2.2. Rigidity calculations
Ab E b
Kb ¼
,
lb
(12)
The axial displacement of the bolt is given by
and for pressurization
M if
P
Mf
and K fM ¼
.
yfp
yfM
The axial displacements of the different elements of the
joint including creep are given as follows:
The axial displacement of the gasket is given by
i
F ib F g
Mi
þ
þ 2hG f
Kb Kg
K fM
¼
K fP ¼
of the unloading
levels across the
method. Ref. [17]
The bolt rigidity is
c ¼ Asm tn .
(16)
Differentiation with respect to time gives the time
hardening solution of the creep strain rate:
_c ¼ nAsm tn1 .
(17)
The strain hardening solution used in this paper is
obtained by isolating the time t from Eq. (16) and
substituting it into Eq. (17) such that the creep rate is
expressed as follows:
_c ¼ nA1=n sm=n ðn1Þ=n
.
c
(18)
3.2. Creep model of gasket
(11)
where l b ¼ 2tf þ tg þ 0:5d.
The rigidity of the flange with or without a hub when
subjected to a bending moment or a radial pressure may be
determined by a study of the compatibility of radial
displacement and rotation required at the junction between
the flange and the shell. The expressions of the flange
rotational stiffness KfP due to radial pressure and KfM due
For the gasket, although other forms of creep law could
be used, based on experimental data conducted in [2], the
gasket creep displacement law considered here has a
logarithmic trend of both stress and time and is detailed
as follows:
wcg ¼ f ðsÞ gðtÞ
¼ ðas lnðsÞ þ bs Þ ðat lnðtÞ þ bt Þ.
ð19Þ
ARTICLE IN PRESS
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For the time hardening model, this equation is represented by the displacement creep rate as follows:
w_ cg ¼ at ðas ln s þ bs Þt1 .
(20)
For the case of strain hardening, the time t, is isolated
form Eq. (19) and is substituted into Eq. (20) to give the
creep displacement rate as
c
w_ cg ¼ at ðas ln s þ bs Þeððbt =at Þðwg =ðat ðas
ln sþbs ÞÞÞÞ
.
(21)
The moment acting on the flange ring is given by
Z ro Z tf =2
sy y dy dr.
M¼
ri
189
(27)
tf =2
Substituting for sy and integrating gives
Z ro Z tf =2
E f t3f y
ro
ln
E f c y dy dr
M¼
12
ri
tf =2
ri
(28)
Differentiating M with respect to time t gives
3.3. Creep displacements
Using Eq. (18) for the bolt and substituting the stress s
by the force over the area, the increment of creep axial
displacement of the bolt considered as a single axial
member is given for an interval of time Dt as follows:
m=n
1=n F b
c
Dwb ¼ l b Dc ¼ l b Dt_c ¼ l b Dt nA
cðn1Þ=n . (22)
Ab
The increment of creep axial displacement of the gasket
considered as a single axial member is obtained by
substituting the stress s by the gasket force over the area
in Eq. (21) and multiplying by the time increment Dt:
Fg
Dwcg ¼ Dt w_ cg ¼ Dt at as ln
þ bs
Ag
c
e ðbt =at Þðwg =at ½as lnðF g =Ag Þþbs Þ .
ð23Þ
Although the attached hub and shell are considered in
the interaction analysis, their radial growth due to creep is
not considered. Therefore, only creep of the flange ring is
assumed to take place. In addition, the flange ring portion
is considered to act as a ring taking stress in the
circumferential direction only. This stress is caused by
radial pressure and bending due to rotation or twist. The
radial stress due to pressure is generally small compared to
the hoop stress because the flange ring is thick and
therefore is neglected. The total hoop strain is given by
the elastic and creep components:
sy
y ¼ e þ c ¼
þ c .
(24)
Ef
Neglecting shear and assuming that the flange ring cross
sections remain plane after bending, the total strain is given
by
y ¼
yy u sy
þ ¼
þ c .
r
r Ef
ð29Þ
From a numerical stand point it can be assumed that the
moment remains constant during only a small time interval
Dt, in order to evaluate the increment of the flange rotation
Dy due to creep. Obviously, this increment of rotation is
used to re-evaluate the new moment. Eq. (2) becomes
Z ro Z tf =2
12Dt
Dy ¼ 3
(30)
_c y dy dr.
tf lnðro =ri Þ ri tf =2
Using the strain hardening law of Eq. (16), the increment
of flange rotation during a time increment Dt is therefore
Dy ¼
12Dt nA1=n
t3f lnðro =ri Þ
Z ro Z tf =2
m=n
sy ððn1Þ=nÞ
y dy dr.
c
ri
ð31Þ
tf =2
The creep axial displacement of the flange ring at the
bolt circle relative to the gasket reaction location is given as
follows:
Dwcf ¼ hG Dy.
(32)
Finally, knowing the creep axial displacement of the bolt
the gasket and the flange; Eqs. (21), (22) and (31), the final
bolt operating force is therefore obtained by substitution of
Eqs. (6), (7), (12), (13) and (14) into Eq. (5):
F fb ¼ F ib K e
Ap p 2hG hp Ap p 2hG p
c
c
þ
þ
þ Dwb þ Dwg þ hG Dy ,
Kb
K fM
K fP
ð33Þ
(25)
y is the flange rotation and u is the radial displacement of
the flange due to pressure obtained by considering the ring
to act as a thick cylinder. Finally, the flange hoop stress is
given by
sy ¼ E f e
E f yy
r2i P
r2o
þ 2
¼
1 þ 2 E f c .
r
r
ro r2i
E f t3f lnðro =ri Þ dy
dM
¼
dt
dt
12
Z ro Z tf =2
dc
y dy dr.
Ef
dt
ri
tf =2
ð26Þ
where Ke is the joint equivalent rigidity and is given by
1
1
1
2h2
¼
þ
þ G.
K e K b K g K fM
(34)
These creep models have been incorporated into the
SuperFlange program [18] that can evaluate not only
the bolt load relaxation but also the resulting change in the
gasket contact stress and its distribution in the radial
direction [14].
ARTICLE IN PRESS
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A. Nechache, A.-H. Bouzid / International Journal of Pressure Vessels and Piping 84 (2007) 185–194
4. Finite element model
To validate the analytical model that estimates the
relaxation of the bolt and the gasket, three-dimensional
numerical FE models were constructed. Because of
symmetry with respect to the plane that passes through
the gasket mid-thickness and the evenly repeated loading in
the angular direction, it is possible to model only an
angular portion (Fig. 3) that includes half of the bolt and
half of the gasket thickness.
The program developed using ANSYS 7.1 [19] was used
to treat four different size bolted joints namely a NPS 3cl.
150 slip-on, a NPS 4cl. 600 welding-neck and 24 in.
(610 mm) and 52 in. (1320 mm) heat exchanger flanges.
The loading is applied in three steps. The first step consists
of applying an initial bolt-up. This is achieved by imposing
to the bolt mid-plane nodes, an equivalent axial displacement to produce the target initial bolt-up stress of
275 MPa. An internal pressure that depends on the case
studied is applied in the second step. For the FE model,
this consists of applying a radial pressure load to the shell
and flange and an equivalent longitudinal stress to the shell
to simulate the hydrostatic end thrust. The third step,
which is of most interest in our study, is the application of
creep while the relaxations of the bolt and gasket loads
over time are evaluated. In the second and third steps, the
loading is applied while all the nodes of the bolt mid-plane
are constrained in the axial direction.
In practice, creep of all joint components takes place at
the same time. Nonetheless, for the purpose of the
validation of the model and to illustrate the creep effect
of each component on the load relaxation, creep is applied
to the bolt and the flange separately and together and to
the gasket using their corresponding material creep
constants. At 400 1C, the creep constants taken from
[10,20,21] are A ¼ 1:64 1023 , m ¼ 6:9 and n ¼ 1 for the
bolt material and A ¼ 3:8 1015 , m ¼ 5:35 and n ¼ 0:22
or A ¼ 7:22 1017 , m ¼ 5:5 and n ¼ 1 for the flange
materials. The first set of flange creep constants was
applied to the NPS 4cl. 600 and the 52 in. HE flanges while
the second set of constants was applied to the NPS 3cl. 150
and the 24 in. HE flanges. However, the gasket creep
constants in Eq. (19) are as ¼ 0:01427, at ¼ 1, bs ¼
0:003764 and bt ¼ 0 [11,12]. These were obtained
experimentally on a PTFE gasket style. However, they
have been modified to fit a power function for the ANSYS
software as it does not allow a logarithm form of creep. In
addition since the gasket contact element of ANSYS 7.1
does not have the creep option, a dummy rigid plate of half
the size of a compressed gasket and modelled with a
volume element was placed beneath the gasket to handle
the creep effect. The presence of this thin rigid plate has no
significant effect on the bolt stiffness or the overall joint
stiffness. The materials selected to run the analysis of these
bolted joints are:
ASTM A-105 or equivalent for the flange for which
E ¼ 210 210 Gpa, n ¼ 0:3
ASTM A-193 B7 for the bolt for which
E ¼ 210 210 GPa, n ¼ 0:3.
Two types of gaskets were used: CMS (corrugated metal
sheet) for the NPS 3 class 150, 24 and 52 in. flanges and
CAF (Compressed Asbestos Sheet) for the NPS4 Class 600
flange. The mechanical behaviours of these gaskets are
represented by non-linear curves of gasket contact stress
300
250
CMS gasket
Gasket stress, MPa
CAF gasket
200
150
100
50
0
0
Fig. 3. 3D FE Model.
0.1
0.3
0.2
0.4
Gasket displacement, mm
0.5
Fig. 4. Mechanical behaviour of gasket materials.
0.6
ARTICLE IN PRESS
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40
Bolt-up: 172 MPa
Pressure: 5.5 MPa
Tangential stress, MPa
versus axial displacement as shown in Fig. 4. These curves
are obtained from load-compression tests conducted on
rigid platens. Due to the limited gasket creep data and its
availability for short term only and for a better assessment
of the method, PTFE sheet was used to illustrate the
relaxation of the NPS4 Class 600 and 24 in. flanges.
Therefore, the gasket creep model was verified for up to
10,000 s while the flange and bolt creep models were
verified for a much longer time of 10,000 h. It is worth
noting that, in general, bolted joints relax extensively
during the first few hours of service due to the excessive
short term creep of the gasket. However, in the long term,
the contributions of the flange and bolt creep become
significant especially at high temperature, in addition to the
gasket degradation and weight loss resulting from thermal
exposure [22].
191
20
Neutral axis
0
Total creep time
0 hr
500 hr
-20
5000 hr
10000 hr
Dotted lines: FE model (Ansys)
Solid lines: Analytical model
-40
-0.5 -0.4 -0.3 -0.2 -0.1
5. Discussion of the results
0
0.1
0.2
0.3
0.4
0.5
Flange thickness ratio
Fig. 6. Stress relaxation in NPS 4cl. 600 WN flange.
80
Bolt-up: 214 MPa
No pressure
40
Tangential stress, MPa
The results of flange creep after 10,000 h obtained from
the proposed analytical approach are compared to those of
FE model for the three different sizes of flanges. Figs. 5–8
show the distribution of the tangential stress across the
flange thickness at the flange OD and its variation with
time. At t ¼ 0, the distribution is linear with maximum
stress values located at the flange upper and lower surfaces.
As creep takes place, at these locations, the stress
relaxation is therefore more important than at the vicinity
of the flange mid-thickness where the stress is very small.
While the analytical and FEA stresses for the NPS 4cl. 600
flange and the 24 and the 52 in. HE flanges are in a fairly
good agreement; the NPS 3cl. 150 flange show a significant
difference especially after 5000 h. This is attributed to the
fact that the flange circular portion is assumed to behave as
a ring instead of a plate. It is also to be noted that the effect
Neutral axis
0
Total creep time
-40
0 hr
500 hr
5000 hr
-80
10000 hr
Dotted lines: FE model (Ansys)
Solid lines: Analytical model
60
-120
-0.5 -0.4 -0.3 -0.2 -0.1 0
0.1 0.2
Flange thickness ratio
Bolt-up: 276 MPa
Pressure: 0.76 MPa
40
0.3
0.4
0.5
Tangential stress, MPa
Fig. 7. Stress relaxation in 24 in. HE flange.
20
Neutral axis
0
Total creep time
0 hr
-20
500 hr
5000 hr
10000 hr
-40
Dotted lines: FE model (Ansys)
Solid lines: Analytical model
-60
-0.5 -0.4 -0.3 -0.2 -0.1
0.0
0.1
0.2
0.3
Flange thickness ratio
Fig. 5. Stress relaxation in NPS 3cl. 150 SO flange.
0.4
0.5
of creep over time on the distribution of the tangential
stress with time depends on the creep constants used. The
first set of creep constants corresponds to a much higher
creep resistant material. This explains why the stress
distribution variations over time are less significant in the
case of NPS 4cl. 600 and 52 in. HE flanges as compared to
the case of NPS 3cl. 300 and 24 in. HE flanges.
Nonetheless, the bolt load relaxation which is a more
important parameter in terms of leakage control is worth
investigating. The results of the bolt stress relaxation
caused by creep at 400 1C of the bolt and the flange
considered to take place separately as well as simultaneously for all cases studied seem to have a better
agreement. Figs. 9–12 show that the bolt relaxations due
ARTICLE IN PRESS
A. Nechache, A.-H. Bouzid / International Journal of Pressure Vessels and Piping 84 (2007) 185–194
192
120
200
Bolt stress relaxation, MPa
80
Tangential stress, MPa
Bolt-up: 172 MPa
Pressure: 5.5 MPa
Bolt-up: 276 MPa
Pressure: 0.69 MPa
Neutral axis
40
0
Total creep time
0 hr
-40
500 hr
5000 hr
180
160
Bolt creep
Flange creep
140
Flane & bolt creep
10000 hr
-80
Dotted lines: FE model (Ansys)
Solid lines : Analytical model
Dotted lines: FE model (Ansys)
Solid lines: Analytical model
-120
-0.5 -0.4 -0.3 -0.2 -0.1
0.0
0.1
0.2
0.3
0.4
120
0
0.5
2000
Flange thickness ratio
4000
6000
Time, hours
8000
10000
Fig. 10. Bolt stress relaxation in NPS 4cl. 600 WN flange.
Fig. 8. Stress relaxation in 52 in. HE flange.
240
Bolt-up: 214 MPa
Pressure: 0 MPa
Bolt-up: 276 MPa
Pressure: 0.76 MPa
250
Bolt stress relaxation, MPa
Bolt stress relaxation, MPa
300
200
150
Bolt creep
Flange creep
Flange & creep
100
50
200
160
Bolt creep
Flange creep
Flange & bolt creep
120
Dotted lines: FE model (Ansys)
Solid lines: Analytical model
80
Dotted lines: FE model (Ansys)
40
Solid lines: Analytical model
0
0
0
2000
4000
6000
Time, Hours
8000
10000
Fig. 9. Bolt stress relaxation in NPS 3cl. 150 SO flange.
to creep of these two bolted joint elements are significant.
In some cases, more than 50% relaxation is obtained after
10,000 h. The resulting bolt stress relaxation has a direct
impact on the loss of joint tightness. These figures show
that, when bolt creep is considered alone, the load
relaxation results are in better agreement indicating that
the one-dimensional bolt creep model is representative of
the real behaviour. However, when only flange creep is
considered, the FEM results show greater relaxation as
compared to the analytical model. This is attributed mainly
to two factors. Firstly, the developed analytical model is
based on ring theory and therefore neglects the radial and
shear stresses. Depending on the ratio of the flange outside
2000
6000
4000
Time, hours
8000
10000
Fig. 11. Bolt stress relaxation in 24 in. HE flange.
to inside diameters, the flange annular portion behaves as a
ring, a thick or a thin plate with a central hole. Secondly,
the creep of the flange attached structures namely the hub
and the cylinder have not been considered in the analytical
model.
Table 1 gives the differences in the load relaxation after
10,000 h between the FEM and the proposed analytical
model for the three different creep cases. In general, the
effect of creep is higher with FEM, and in particular when
flange creep alone is considered. This is more pronounced
in the case of the NPS 4cl. 600 and 52 in. HE flanges and is
due to the creep of the attached structures that contribute
to unload the gasket. The relaxation produced by only
flange creep in these two flanges is 8% and 31% with FEM
and 2% and 18.5%, respectively. Nevertheless, Table 1
ARTICLE IN PRESS
A. Nechache, A.-H. Bouzid / International Journal of Pressure Vessels and Piping 84 (2007) 185–194
140
300
Bolt-up: 276 MPa
Pressure: 0.69 MPa
120
Bolt-up to 214 MPa
Bolt creep after 10000 h
250
100
Gasket stress, MPa
Bolt stress relaxation, MPa
193
200
150
Solid lines: Analytical model
80
60
40
Bolt creep
Flange creep
Flange & bolt creep
Dotted lines : FE model (Ansys)
Solid lines : Analytical model
20
100
0
Dotted lines : FE model (Ansys)
2000
4000
6000
Time, hours
8000
0
10000
0
Fig. 12. Bolt load relaxation in 52 in. HE flange.
0.2
0.4
0.6
Gasket width ratio
0.8
1
Fig. 13. Gasket stress relaxation in 24 in. HE flange.
250
Table 1
Percentage of bolt relaxation due to creep
Bolt-up to 276 MPa
Flange
Bolt creep
Flange creep
Total creep
Anal.
FEA
Anal.
FEA
Anal.
FEA
42.5
10
19.3
44.2
38
13.2
19.2
42
50
2
64.5
18.5
51.7
8.8
70.2
31
55.2
14.4
66
43.2
56.5
15.2
73
44.5
Pressurization to 0.69 MPa
200
shows that the relaxation values compare well when bolt
creep is also included with a maximum difference of 9.6%
between the two methods. It is to be noted that the effect of
both the bolt and the flange creep cannot be obtained from
the superposition of the individual effects but is deduced
from a combination of the two effects considered
simultaneously in the calculation because the effect is
nonlinear. The gasket contact stress distributions shown in
Figs. 13 and 14 for the three loading conditions are
obtained from the estimated gasket load, flange rotation
and the load deflection curves. Interpolation was used for
points lying between the curves as detailed in [14]. The
contact stresses are relatively higher at the outside diameter
due to flange rotation and can be beneficial for some gasket
types provided the crush limit is not reached. However,
these contact stresses decrease with the application of
pressure and time. The reduction of the contact stress with
time can sometimes result in a leak and therefore needs to
be evaluated with reasonable accuracy.
Fig. 15 shows the relaxation of the bolt stress of NPS 4cl.
600 and 24 in. HE flanges over a period of 2.8 h or 10,000 s
when only gasket creep takes place. Even though, the
available PTFE creep data used are for a short period of
time, the analytical model capability is acknowledged. A
Bolt creep after 10000 h
Gasket stress, MPa
NPS 3cl. 150
NPS 4cl. 600
24 HE flange
52 HE flange
150
100
50
Dotted lines : FE model (Ansys)
Solid lines : Analytical model
0
0
0.2
0.4
0.6
0.8
1
Gasket width ratio
Fig. 14. Gasket stress relaxation in 52 in. HE flange.
loss of more than 30% and 60% of load is observed for
these two flanges, respectively. In general, the results of the
short-term creep relaxation of the gasket obtained with the
analytical model are in good agreement with those
obtained by with FEM. The difference between the two
methods is less than 5%.
6. Conclusion
An analytical model has been developed to account for
the creep effect of the bolt, flange ring and gasket
separately or simultaneously in the design of bolted joints.
The proposed analytical approach considers the flexibility
ARTICLE IN PRESS
A. Nechache, A.-H. Bouzid / International Journal of Pressure Vessels and Piping 84 (2007) 185–194
194
240
PTFE gasket
Bolt stress relaxation, psi
200
24 HE flange
Bolt-up: 206 MPa
No pressure
160
120
4 cl. 600 WN flange
Bolt-up: 172 MPa
Pressure: 5.5 MPa
80
Analytical model
40
FE model(Ansys)
0
0
2000
4000
6000
Time, second
8000
10000
Fig. 15. Bolt load relaxation due to gasket creep.
of the bolts and the gasket in addition to the flange. Creep
of these elements has been coupled to the axial deflection
compatibility equations to determine the resulting gasket
and bolt load relaxations. The model could be used to
verify the suitability of the initial bolt-up load in high
temperature applications where creep can have a major
effect on bolt relaxation. The analysis was verified against
the more accurate 3-D FEM on four different size flanges.
The analytical results of the bolt stress relaxation and the
change of gasket contact stress compare quite well with
those of FEM.
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