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FINITE-ELEMENT SIMULATION OF NON-LINEAR, TIME AND TEMPERATURE
DEPENDENT EFFECTS OF FLANGE GASKET MAT ERIALS
Dr.-Ing. Robert Kauer
TÜV Süddeutschland Bau und Betrieb GmbHGeschäftsbereich Energie und Technologie;
Risiko und Zuverlässigkeit80686 München, Germany
Robert.Kauer@tuevs.de
Prof. Dr.-Ing. K. Strohmeier
Technische Universität MünchenLehrstuhl für Apparate- und Anlagenbau,
Experimentelle Spannungsanalyse80748 München, Germany
ABSTRACTFinite-Element calculations more and more replace analytical
methods especially if problems have to be solved which are ad-justed to specific tasks.
In europe as well as in other countries a lot of efforts are car-ried out to get new code standards for the calculation of flangejoints under various loadings. All these calculation methods arebased on a linear description of the gasket material behaviour.Concerning the non-linear, time and temperature dependent charac-teristics of a lot of gasket materials (e.g. PTFE gaskets) standardlinear-elastic Finite-Element calculations in addition to code me-thods are often not suitable.
Therefore a new Finite-Element gasket model was developedto describe the real (visco-elastic-plastic) gasket behaviour withoutthe demand of transient calculations. The required input parame-ters can be obtained using standard compression tests.
The procedure is presented and results are compared with ex-perimental data.
INTRODUCTIONFlange connections as bolted joints have to be designed with
regard to meet strenght and tightness criterias. So, regulationsconcerning allowable leak rates of plants and components must besatisfied. Decisive for this effort is a sufficient knowledge of thedeformation behaviour of the entire system flange - gasket - bolts.
Beside an exact geometric modelling the description of the materialbehaviour of all components is very important for the quality ofperformed analyses. This applies to analytical as well as to nume-rical methods.
For components made of steel elastic or elastic-plastic materiallaws are able to simulate the real behaviour of those parts in suffi-cient accuracy by acceptable costs. The modelling of gasket materi-als is much more difficult, especially because the wide range ofcommon non-metal gasket materials and shapes. A good universaldescription for non metal gaskets is to simulate them as a visco-elastic-plastic element. The following figure 1 shows the associatedmechanical model. In 1996 Smith and Briggs show the results of arotational-symmetric Finite-Element calculation of a flange jointwith spiral-wound-gaskets using a non-linear-elastic-visco-plasticmaterial law.
As it is able to simulate the gasket behaviour using those timedependent material laws it is not very practicable because thedetermination of necessary material constants is difficult and ex-pensive. Additionally numerical calculations have to be performedas transient analyses, with the concerning increase of CPU-time. Soa common method is to neglect all these non-linear effects and tolinearize the behaviour of the gasket around the service point. Thisyields to an elastic description with all its unsatisfactory conse-quences. It should be noted that it is not possible to get the poissi-ons ratio which is also required for the input of numerical analyses.
Figure 1: Visco-elastic-plastic material
Soler developed in 1980 an analytical method to describe thenon-linear compression behaviour of flange joints with full facegaskets. Nagy presented in 1997 a rheological model for the analy-tical description of the time dependent effects.
Applying Finite-Element methods Bartonicek, Kockelmannand Schöckle (1996) and Kauer and Strohmeier (1996) emphasizethat there are differences concerning the calculated gasket pressureusing a more accurate elastic-plastic material description instead ofan elastic material formulation.
The following paper presents a gasket material model for theapplication within Finite-Element analyses. For this purpose aprocedure was developed which is able to describe the non-linear,time and temperature dependent behaviour without the necessityof transient calculations. Additionally the required material para-meters can be determined by accepted testing procedures.
GASKET MATERIAL BEHAVIOURFigure 2 shows a typical gasket compression curve. This parti-
cular curve was taken up using a fibre-sheet gasket and the bounda-ry conditions of DIN 28090.
As it can be seen in figure 2 there are non-linear elastic, plasticand time dependent components to be considered. Replacing thiscomplex, time dependent reality by a simple mechanical model it isnecessary to take the testing curves in a way that they representthe time-dependent effects.
For this purpose it is necessary to take note of the flange loa-ding conditions. Flange joints are mainly strengthed by the follo-wing conditions:
• Mounting• Loading and unloading at mounting temperature• Loading and unloading at service temperature.
The mounting condition is characterized by a certain time,which is necessary for a correct application of the requiredprestress. Creep and relaxation during this time can be neglected.To simulate the mounting procedure, the compression curve has to
be taken considering the mounting time. That means that the halt atthe several load levels have to be chosen concerning the mountingtime. The tests have to be carried out at mounting temperature.The end points after seating can be taken to build a stabilizedmounting curve (compare the dotted line in figure 2). This curve(stabilized mounting curve) can be simulated as a non-linear spring(c = c(ε)).
After mounting creep and relaxation start in dependence on theinvestigated gasket material and the stiffness of all concerned com-ponents. After a while (minutes to hours) this process is finished.To describe this effect a cuve has to be taken similar to those formounting. The difference is that the halt time has to be chosen in away that there is no more relevant change in stress and strain of thegasket. This curve is also simulated as a non-linear spring(stabilized service curve at mounting temperature)
After mounting the junction is loaded by pressure. For thosepoints of the gasket which are stressed the stress/strain relations-hip follows the stabilized service curve. Discrete points (nodes) onthe gasket, where unloading occurs, can be described by pressuredependent unloading curves. These unloading curves can be lineari-zed (see for example the procedure in DIN 28080), if hysteresiseffects can be neglected. The result is a relationship between gasketpressure and modulus of elasticity for unloading.
Figure 2: Typical gasket compression curve
damping element: η = η (dε/dt)
friction element: FR = const.
non-linear spring: c = c (ε)
Dichtung
Schrauben
Anschlußrohr
Flanschflange
pipe
bolts
gasket
0
10
20
30
40
50
60
70
80
1,50 1,45 1,251,30 1,20 1,15 1,10
Gasket thickness [mm]
loading history [s]
Gas
ket p
ress
ure
[M
Pa]
creep/relaxation after a certain time
non-linear elastic
remaining plasticdeformation
gask
et p
ress
ure
[MP
a]
pressure dependentunloading
end point
hysteresis
Next step in loading history of a typical flange connection is toput the junction to service temperature. Due to this effect gasketmaterials normally become smoother, that meens that a new creepand relaxation process starts. It ends when the stabilized pressurecurve at service temperature is reached. Loading and unloading ofthe gasket at service temperature, for example due to piping reacti-ons, can be simulated using the stabilized pressure curve at servicetemperature for loading and the concerning pressure dependentmodulus of elasticity for unloading effects.
THE FINITE-ELEMENT GASKET ELEMENTWithin the used Finite-Element programm system MARC it is
possible to introduce FORTRAN user subroutines. So a subrouti-ne GASKET for the simulation of the effects described in the lattersection was developed.
SubroutineGASKET
non-linear loading
pressure depending unloading
σ
ε
F
Figure 3: Calculated stress/strain behaviour due to alaoding history shown in figure 2
The necessary input data is reduced to the stabilized pressurecurves (mounting, service at mounting and at service temperature)and the concerning moduli of elasticity for unloading at mountingand service temperature. The subroutine GASKET controls theloading depending on the non-linear behaviour (progressive / de-gressive) of the gasket material. If unloading occurs the subroutineswitches to the pressure dependent linearized relationship.
Loading subsequent unloading follows the modulus of elastici-ty until the point of maximum prestress is reached. From here thesubroutine changes to the original non-linear loading curve. Figure 3shows the calculated stress/strain behaviour due to a laoding histo-ry as it can be depicted in figure 2.
The time dependent creep and relaxation effects are alsocontrolled by the subroutine GASKET. So if the end of mountingis reached, the subroutine starts the simulartion of gasket creep bydisplacing gasket nodes. This procedure is carried out indepen-dently for each discrete point of the gasket (node) until the concer-ning equilibrium is reached on the pressure service curve. Figure 4shows the entire procedure for two points (1 and 2) of the gasket,
where point 1 is stressed during the application of pressure, whilepoint 1 is unloaded.
Another important advantage of subroutine GASKET is that ifunloading occurs in a way that the gasket pressure is totally loosenthe contact condition is also considered.
Figure 4: Loading history for two discrete gasket points
0
10
20
30
40
50
60
70
80
90
0,00,10,20,30,40,50,60,70,80,91,0
Dehnverhältnis λ [-]
Dic
htu
ng
spre
ssu
ng
[M
Pa]
MontageT = 20° CT = 100° C
ExPTFE
FSD
GMEPTFE
0
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0 10 20 30 40 50 60 70 80 90 100Spannung [MPa]
Ela
stiz
itaet
smo
du
l [M
Pa]
PTFE 20°CPTFE 100°CExPTFE 20°CExPTFE 100°CGME 20°CGME 100°CFSD 20°CFSD 100°C
20°C
100°C
100°C
100°C
20°C
20°C
20°C
FSDGME
ExPTFE
PTFE
Gasket Pressure [MPa]
Gas
ket P
ress
ure
[MP
a]
Mounting
Un
load
ing
Mo
du
lus
of
Ela
stic
ity
[M
Pa]
Strain Rate λ = 1−ε [-]
Figure 5: Gasket compression curves for mounting, ser-vice at mounting temperature (20°C) and service at ser-vice temperature (100°C) and unloading moduli of elasti-
city for 20°C and 100°C
T = TM t : Time for mounting
σ
ε0
T = TM t :
T = TS t :
2
1
1 2
mounting
stiffness depending creep/relaxation
2’
A’
B
1’
B’
A
service
INVESTIGATED MATERIALSThe investigated materials were chosen in a way that they re-
flect a wide range of gasket materials. The following materials wereexamined.
• Fibre-sheet gasket (FSD)• Graphite gasket with metal inlay (GME)• PTFE gasket (pure PTFE and expanded PTFE ExPTFE).
Figure 5 shows the experimentally taken curves required forthe numerical input described in the latter section.
RESULTS OF FINITE ELEMENT SIMULATIONThe following section shows some numerical results and the
comparision with experimental data. For the shown calculation anaxisymmetric Finite Element model of a flange joint was chosen,the gasket material is simulated with subroutine GASKET.
So, in figure 6 the gasket pressure distribution is plotted overthe gasket width for the conditions mounting and creep/relaxationafter mounting. A calculation with an elastic gasket material modelis shown to compare the results. As it can be depicted especiallyfor lower gasket pressure (prestress 53 KN in figure 6) the simula-tion using subroutine GASKET yields to a nearly constant gasketpressure distribution, while an elastic formulation always shows alinear distribution. For higher gasket pressure (prestress 210 KN infigure 6) the distribution using subroutine GASKET results in aparabolic distribution (elastic material: linear). As it can be seen inthe lower part of figure 6 the experimental gasket pressure, recor-ded by sensor technics, also shows a nearly linear distribution.
-45,0
-40,0
-35,0
-30,0
-25,0
-20,0
-15,0
-10,0
-5,0
0,0
53 KN
105 KN
210 KN Elastisch
Montage
Nach dem Setzvorgang
Gas
ket P
ress
ure
[MP
a]
Gasket Width
Mounting
after creep/relaxation
pure elastic
Prestress
Experimental gasket pressure distribution:(Prestress 105 KN)
Figure 6: Gasket pressure distribution along gasket widthfor a flange DN 80 PN 40 for various prestress conditions
The good correlation of the time dependent characteristics ofthe gasket materials can be seen in figure 7. It should be noted, thatresults like this can be evaluated without a transient calculation.They can not be taken from an elastic analysis.
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0ExPTFE PTFE
Vo
rsp
ann
un
gsv
erlu
st [
%]
Tes
t
Tes
t
FE
M
FE
M
F: 1
,5 %
F: 1
,0 %
F: 0
,3 %
F: 0
,6 %
Failure (F)
70%40% 70%40%
Lo
ss o
f P
rest
ress
[%
]
Figure 7: Loss of prestress; comparison of Finite Ele-ment calculation and test results for a flange DN 80
PN 40 with gasket type ExPTFE for two differentprestresses (40% and 70% of bolt yielding strength)
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
040% 70%
Vor
span
nung
sver
lust
[%]
Normal bolt instead ofnecked-down bolt
Prestress
Lo
ss o
f P
rest
ress
[%
]
Gasket thickness3,0mm instead of 1,5mm
Figure 8: Loss of prestress; influence of bolt type andgasket thickness
So, in figure 7 gaskets made of PTFE and expanded PTFE(ExPTFE) are compared concerning the loss of prestress aftermounted in a flange joint. Two different prestress condition were
calculated (40% and 70% of the investigated bolt yield strength).The experimental data shows that the creep behaviour is totallydifferent due to the manufactoring process. The expanded ExPTFEgasket shows high creep rates if it is mounted at lower prestress(40% bar in figure 7) while at higher prestress the creep rate dec-reases and the loss of prestress can be depicted at about 5%. Thepure PTFE gasket shows a creep rate of about 10% at a prestressof 40% while it increases with higher prestress. So the loss ofprestress is at about 14% for a prestress of 70% bolt yieldstrength. As it is shown the calculated loss of prestress usingsubroutine GASKET shows a good agreement with experimentaldata.
In figure 8 the influence of the used bolt type and of gasketthickness on the loss of prestress after mounting can be detected.As it is shown the influence of the gasket thickness is much morehigher than those one of the used bolt type. Calculations like thiscan show the necissity of additional mounting procedures
CONCLUSIONThe presented procedure (subroutine GASKET) allows the
simulation of the mechanical bahaviour of gasket materials. Timeand temperature dependent effects are considered due to experi-mental data. The required experimental input data can be obtainedby standard compression tests.
Using subroutine GASKET, it is possible to calculate the realpressure distribution on the gasket under various loadings. Loss ofprestress due to effects like change in stiffness of the components,different gasket materials or tempearture loading can be determined.Comparision with experimental data shows satisfactory agreement.
The presented procedure is also applicable for gasket in metalto metal flange joints (for example O-Ring-connections). The ne-cessary gasket compression behaviour has to be obtained by cal-culation or by experiment concerning the geometric circumstances.
REFERENCESSmith, A.C., Briggs, G.: Finite Element Analysis of Bolted
Flange Assemblies. 4th International Symposium on Fluid Sealing,M andelieu-La Napoule, (1996), S. 181-192.
Soler, A.I.: Analysis of Bolted Joints with Nonlinear GasketBehaviour. Journal of Pressure Vessel Technology Vol. 102 (1980),S. 249-256.
Nagy, A.: Time Dependent Characteristics of gaskets at FlangeJoints. Int. J. Pres. Ves & Piping Vol 72 (1997), S. 219-229.
Bartonicek, J., Kockelmann, H., Schöckle, F.: Gewährleistungder Dichtheit von Flanschverbindungen und Stopfbuchspackungen.22. MPA-Seminar, (1996) S. 13.1-13.27.
Kauer, R., Strohmeier, K.: Determination of Leakage Gap andLeakage Mass Flow of Flange Joints Subjected to External BendingMoments. ASME PVP-Vol. 332 (1996), S. 115-120.
Kauer, R. Steil, U., Strohmeier, K.: Determination of LeakageGap of Flange Joints under non-axisymmetic loadings, using non-linear gasket material. 4th International Symposium on Fluid Sea-ling, Mandelieu-La Napoule, (1996), S. 259-269.
DIN 28090 September 1995: Statische Dichtungen fürFlanschverbindungen. Hrsg. Deutsches Institut für Normung.Berlin: Beuth-Verlag 1995.
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