Prognosis of the steel aging of the pipe elbow in the Lithuanian power station/ Vamzdzio alkunes darbo resurso prognozavimas Lietuvos elektrineje.
Daunys, M. ; Dundulis, R. ; Karpavicius, R. 等
1. Introduction
For transferring superheated steam from the turbine heat exchanger,
the pipes are used which are currently undergoing long-term working
temperature and mechanical stresses. Such pipeline performance depends
not only from the load and from the temperature but also from the
superheated water vapour content (aggressive hydrogen effect), diffusion
processes in metals. Transferring technological parameters of
superheated steam is very high: operating pressure in the pipe elbow
[empty set]219 then the wall thickness changes in tensile zone from 28
and compression zone to 42 mm is 13.2 MPa. These pipe elbow are also
affected by thermal stresses, by the weight of pipes elbow (including
insulation), by the vibrations caused by the steam pressure variation
and dynamic loads from the unbalanced pump rotor [1]. Working
environmental parameters along the pipe elbow is the same. Pipe elbow
during the manufacturing process is mechanically processed and at some
regions the wall become thicker and at some regions become thinner. We
modelled manufacturing process with spring back strains. Since this kind
of strains is always due to residual strains. In such a state where
residual stress-strain resides there is a big possibility to develop
crack, since in the pipe working pressure rises residual stress value.
In this work has been given a great attention to thick pipes elbow in
which during the manufacturing process emerged residual stresses [2-4].
To simulate the process of pre stress-strain conditions the finite
element method software LS-Dyna were employed. In this work the
attention was focused on the working pipe elbow which operated only half
of the potential work resource. There were determined all mechanical
properties along the pipe elbows and by given data there were designed
identical finite element model (FEM). The results obtained from finite
element analysis (FEM) compared with the results obtained from the
static tensile tests.
2. Methods of investigation of mechanical properties
In order to receive more precise mechanical properties from pipe
elbow we made specimens from normal and tangential direction [5-7].
During the investigation of pipe elbow, there were tested 9 small
specimens from the normal direction. Test was performed under the
working temperature of 550[degrees]C and at this temperature were tested
every 3 specimens. 16 small specimens taken from tangential direction
were tested, at working temperature of 550[degrees]C. Hereafter
specimens from tangential direction were divided into several zones:
zones where tension stress takes plane--9 peaces, neutral zone--3
peaces, compression zone--4 peaces. Main mechanical characteristics are
reliable, because the results of scatter correspond statistical
requirements. There were investigated the main mechanical properties:
[[sigma].sub.pl.]--limit of proportionality, [R.sub.p0,2]--yield
strength, [R.sub.m]--ultimate strength, [[sigma].sub.f]--stress at
fracture, Z--reduction of cross-section area. In the Fig. 1 can be seen
the scheme how the specimens were take from the pipe. In order to
minimize thermal influence to the mechanical properties of the tensile
test the specimens were cutted by high pressure water flow. Several
plates (45x55x3 mm) were cutted from which afterall were subtracted two
specimens with normal orientation and two specimens with tangential
orientation. The scheme of specimens which were cutted from the pipe
elbow and orientation of the small specimens in normal and tangential
direction can be seen in Fig. 1.
[FIGURE 1 OMITTED]
The main dimensions of specimens are showed in the Fig. 2. Given
small specimen were tested during static tensile test under the working
temperature of 550[degrees]C (Figs. 3 and 4) [8-9].
[FIGURE 2 OMITTED]
3. The results of the investigation of mechanical properties
In this work there were given the results from investigation of
pipe elbow mechanical properties after the studies were performed with
finite elements analysis. The investigation was performed under the
working temperature of 550[degrees]C [8, 9]. These mechanical
prosperities were compared depending on the zones and direction. The
tension strength curves are expressed taking into account real tension
stresses, when the force is divided from the momentary cross-section
area of the specimen (dotted lines), and taking into account so called
engineering tension stresses, when the force is divided from in the
initial cross-section area of the small specimen (continuous lines). One
of the most important mechanical characteristics is the ultimate
strength. In normal direction tensile zone ultimate strength is
[R.sub.m] = 230 MPa, it is the least value. This layer of pipe elbow is
the most vulnerable at work time. In tangential direction, tensile zone
[R.sub.m] = 238 MPa. Second of main mechanical characteristics is the
limit of proportionality. In normal direction, tensile zone,
[[sigma].sub.pl..] = 142 MPa it is less than in tangential direction
[[sigma].sub.pl..] = 197 MPa. Data of pipe elbow (operating time is
45000 h), under working temperature of 550[degrees]C of mechanical
characteristics from normal and tangential direction are given from the
tensile, neutral and the compression zones are shown in Table 1 and 2.
In Figs. 3 and 4 are tension curves from normal and tangential direction
specimens. The data are given from the normal, neutral and the
compression zones.
[FIGURE 3 OMITTED]
[FIGURE 4 OMITTED]
According to dependences [10] we can prognosticate the main
mechanical characteristics of pipe's elbow after 1 x [10.sup.4]-3 x
[10.sup.4] h of exploitation of T = 550[degrees]C. Mechanical
characteristics using ageing dependence are shown in Table 3. Obtained
application of the previously dependencies we can see aging of the
materials evaluate.
4. Investigation of the strength of pipe elbow by the methods of
finite element
In this work have been investigated stresses and strains of an
elbow which worked at 550[degrees]C and was loaded with 13.2MPa inner
pressure. An investigation has been conducted using two common methods:
static tensile loading and modeling with Ls-Dyna software. Data from
experiments was compared with results from finite element analysis. The
pipe elbow Fig. 5 was modeled with three different boundary conditions:
i.e. when the pipe is constructed from the separate tensile, compression
and the neutral zones. Analysis was performed with mechanical properties
from neutral and tangential zones. The second test has been investigated
under the dynamical load conditions using FEA [11-13].
[FIGURE 5 OMITTED]
Since the investigation concerns dynamic reaction in metal
forming--the FEA was conducted using program for nonlinear dynamic
analysis of structures in three dimensions ls971 single R4.2. To
simulate investigated model we used a fully integrated 8 nodes-cubic
element from LS-Dyna software elements range. This is three dimensional
solid element in which elastic strain before yielding is finite. The
type solid element and its formulation is specified though part ID
(*PART) and the section ID (*SECTION_SOLID_OPTION). Chosen material
model was *PIECEWISE_LiNEAR_PLASTICiTY. It is an isotropic
elasto-plastic no. 24 material with arbitrary stress versus strain curve
and arbitrary strain rate dependency can be defined. Failure based on a
plastic strain or a minimum time step can be defined. If considering
laminated or sandwich shells with non-uniform material prosperities, the
material model *MAT_MODIFIED_PIECEWISE_LINEAR_PLASTICIT Y is
recommended.
Also, a local coordinate system for orthotropic and anisotropic
materials can be defined by using the ORTHO option. If extra degrees of
freedom are needed, the DOF option should be used. The option
TET4TOTET10 should convert 4 nodded tetrahedrons to 10 nodded
tetrahedrons.
The INERTIA option allows the internal properties and initial
conditions to be defined rather than calculated from the finite element
mesh. This applies to rigid bodies, with keyword *MATRIGID only. The
REPOSITION option applies to deformable materials and is used to
reposition deformable materials attached to rigid dummy components whose
motion is controlled by either CAL3D or MADYMO. At the beginning of the
calculation each component controlled by CAL3D/MADTMO input. However,
deformable materials attached to these components will not be
repositioned unless this option is used.
5. Investigation results of FEA
LS-Dyna modelling software introduces mechanical characteristics of
each layer separately. There were also introduced data taken from normal
and the tangential direction of the pipe.
In order to evaluate overloaded pipe elbow during starting up and
ending up the steam dynamic loading case were evaluated. Pipe dynamic
loading in time moment is given in the Fig. 6. Modelled pipe working
pressure reaches 13.2 MPa.
After the initial analysis, results show that the weakest and the
most dangerous place in the pipe elbow is stretched area in oriented
normal direction. For more detailed assessment of the potential impact
of dynamic load in the pipe elbow we continued to study the particular
case.
After the examination of Lithuanian Power Company superheated steam
pipe elbows which worked 45000 hours the following conclusion can be
drawn. The pipe elbow was modelled with finite elements. The mechanical
properties of materials at 550[degrees]C were investigated.
Stress distribution the pipe elbow of normal direction D219x28.5
after 45000 h exploitations are shown in Table 4. Maximum compression of
radial stress was in compression zone inner layer stresses is
[[sigma].sub.R] = -12.525 MPa. In the neutral zone middle layer
[[sigma].sub.R] stress is 2.6 times less than in inner layer compression
zone. The maximum value of circumferential stress was in tensile zone
inner layer stresses is [[sigma].sub.H] = 31.793 MPa. In the neutral
zone middle layer stress is 1.3 times less than in tensile zone inner
layer. In tension zone outer layer the stresses is 1.2 times more than
in the neutral zone middle layer.
Stresses [[sigma].sub.R] in straight pipe [10] of normal direction
of outer layer is 1.35 times less than in pipe elbow in neutral zone
outer layer. Maximum stresses [[sigma].sub.H] is in straight pipe inner
layer, these stresses is 1.44 times more than in neutral zone inner
layer of pipe elbow.
Stress distribution the pipe elbow of tangential direction after
45000 h exploitations are shown in Table 5. Maximum compression of
radial stress was in compression zone inner layer stresses is
[[sigma].sub.R] = -12.076 MPa. In the neutral zone middle layer stress
is 2.85 times more than in compression zone inner layer. In tension zone
outer layer the stresses is 3.75 times more than in compression zone
inner layer. The maximum value of circumferential stress was in tensile
zone inner layer stresses is 1.29 times more than in neutral zone middle
layer, and in tension zone outer layer the stresses is 1.17 times less
than in neutral zone middle layer.
Stresses [[sigma].sub.R] in straight pipe [10] of tangential
direction of outer layer is 1.18 times less than in pipe elbow in
neutral zone outer layer. Maximum stresses [[sigma].sub.H] in straight
pipe is in inner layer , these stresses is 1.90 times more than in
neutral zone inner layer of pipe elbow. The results show that tension
layer is most dangerous layer of pipe elbow.
Different of value of stresses between normal and tangential
directions is about 8%.
Inflection in the normal direction in Table 6 of the tensile zone
inner layer stresses is [[sigma].sub.Misses] = 53.755 MPa. In the
neutral layer middle zone middle layer stress is [[sigma].sub.Misses] =
35.143 MPa and in tension zone outer layer the stresses is
[[sigma].sub.Misses] = 26.423 MPa.
Very similar results are obtained in the tangential direction in
Table 7 of the tensile zone inner layer stresses is [[sigma].sub.Misses]
= 53.994 MPa.
In order to investigate the influence of the human factor to the
possibility of the accident we loaded the pipe elbow with the dynamical
load. That's how it will be simulated quick opening of the
overheated steam pipe valve. Dynamic loading case revealed that more
than 95% of the work load pressure reaches its value in less than 1% of
over all loading time. Such a load in the pipe elbow is caused by
resonant simulation processes [14-16]. Tension drops across the layer to
normal direction to 64.696 MPa. That pipe bending admissible stress is
[[sigma].sub.adm.] = 66 MPa. We see that the dynamic loading of
saturated steam pipe elbow has almost reached this level. The results
stress distribution in time of tangential direction, tension zone
presented in Fig. 6, and the stress distribution in space of
presentation in Fig. 7.
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
We can see the influence of the human factor is very high. Because
the stress in the tensile zone of the pipe two times as higher as then
the stress at the normal working conditions.
6. Conclusions
One of the most important mechanical characteristics is the ultimat
limit--[R.sub.m]. Strength limit of normal direction small specimens
changes from 230 to 250 MPa. The ultimate limit of tangential direction
small specimens changes from 238 to 250 MPa.
Using FEA methods by Ls-Dyna was calculated stress strain von
Misses in 45000 h worked pipe. Minimum value of radial stress was of
normal direction in compression zone inner layer stresses is
[[sigma].sub.R] = -12.525 MPa, The maximum value of circumferential
stress was in tensile zone inner layer stresses is [[sigma].sub.H] =
31.793 MPa. In the normal direction of the tensile zone inner layer
stresses is [[sigma].sub.Misses] = = 53.755 MPa. In the neutral layer
middle zone middle layer stress is [[sigma].sub.Misses] = 35.143 MPa. In
middle of tension zone Von Misses maximal stresses was
[[sigma].sub.Misses] = = 67.967 MPa, then value of [[sigma].sub.adm.] =
66 MPa. The results show that tension layer is most dangerous layer of
pipe elbow.
Dynamic loading case revealed that more than 95% of the work load
pressure reaches its value in less than 1% of over all loading time.
Such a load in the pipe elbow is caused by resonant simulation
processes. Elbows are exposed to sudden impact loading. Tension drops
across the layer to normal direction to 64.696 MPa. That pipe bending
admissible stress is [[sigma].sub.adm.] = 66 MPa. We see that the
dynamic loading of saturated steam pipe elbow has almost reached this
level.
Received December 15, 2011
Accepted September 10, 2011
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M. Daunys, Kaunas University of Technology, Kestucio 27, 44312
Kaunas, Lithuania, E-mail:
[email protected]
R. Dundulis, Kaunas University of Technology, Kestucio 27, 44312
Kaunas, Lithuania, E-mail:
[email protected]
R. Karpavicius, Kaunas University of Technology, Kestucio 27, 44312
Kaunas, Lithuania, E-mail:
[email protected]
R. Bortkevicius, Kaunas University of Technology, Kestucio 27,
44312 Kaunas, Lithuania, E-mail:
[email protected]
Table 1
Mechanical characteristics of normal direction specimens
Zones Mechanical characteristics, MPa, %
[[sigma].sub.pl..] [R.sub.p0.2] [R.sub.m]
Tensile 142 175 230
Neutral 174 199 239
Compression 196 215 250
Zones Mechanical characteristics, MPa, %
[[sigma].sub.f] Z [A.sub.5]
304 97.59 18.12
Tensile 317 97.93 17.66
Neutral 292 95.22 17.03
Compression
Table 2
Mechanical characteristics of tangential direction specimens
Zones Mechanical characteristics, MPa, %
[[sigma] [R.sub.p0.2] [R.sub.m]
.sub.pl..]
Tensile 197 216 238
Neutral 182 202 240
Compression 189 225 250
Zones Mechanical characteristics, MPa, %
[[sigma].sub.f] Z [A.sub.5]
299 93.84 17.35
Tensile 317 96.89 17.69
Neutral 334 95.98 17.50
Compression
Table 3
Mechanical characteristics using ageing dependence of the
pipe elbow, operating time is 1 x [10.sup.4]-5 x [10.sup.4] h, under
working temperature of 55[degrees]C
Hours Mechanical characteristics, MPa
[[sigma].sub [R.sub.p0.2] [R.sub.m] [[sigma].sub.f]
.pl..]
100000 121.10 165.87 232.87 286.47
200000 117.33 162.74 230.29 271.17
300000 115.13 160.91 228.78 262.22
Table 4
Stress distribution in the pipe D219x28.5 elbow for
specimens orientated in normal direction
after 45000 h exploitations
Stresses, Mpa
Work Zone Stresses Outer Middle Inner
time, h
45000 Tension [[sigma].sub.R] -1.097 -4.752 -11.910
[[sigma].sub.H] 20.264 23.904 31.793
Neutral [[sigma].sub.R] -1.103 -4.737 -11.932
[[sigma].sub.H] 20.097 23.831 29.886
Compression [[sigma].sub.R] -1.031 -4.470 -12.525
[[sigma].sub.H] 17.313 22.306 30.093
Table 5
Stress distribution in the pipe D219x28.5 elbow for
specimens orientated in tangential direction
after 45000 h exploitations
Stresses, Mpa
Work Zone Stresses Outer Middle Inner
time, h
45000 Tension [[sigma].sub.R] -1.097 -4.752 -11.910
[[sigma].sub.H] 20.264 23.904 31.793
Neutral [[sigma].sub.R] -1.103 -4.737 -11.932
[[sigma].sub.H] 20.097 23.831 29.886
Compression [[sigma].sub.R] -1.031 -4.470 -12.525
[[sigma].sub.H] 17.313 22.306 30.093
Table 6
Von Misses stresses distribution in the pipe elbow for
specimens orientated in normal direction after 45000 h
exploitations
Zone Stresses, MPa
Outer Middle Inner
Tensile 26.423 35.258 53.755
Neutral 26.216 35.143 51.598
Compression 25.155 34.566 52.545
Table 7
Von Misses stresses distribution in the pipe elbow for
specimens orientated in tangential direction after 45000 h
exploitations
Stresses, MPa
Zone Outer Middle Inner
Tensile 26.683 35.882 53.994
Neutral 26.946 34.834 53.135
Compression 25.592 34.514 52.364
