Plastic Finite Element Analysis of Autofrettaged Ultrahigh Pressure Elbow

Physical and Numerical Simulation of Geotechnical Engineering
2nd ISSUE, March 2011
Plastic Finite Element Analysis of Autofrettaged Ultrahigh
Pressure Elbow
DENG Xisheng, DONG Shier
School of Civil Engineering and Architecture, Southwest Petroleum University, Chengdu, Sichuan 610500, P.R.China
ABSTACT: Finite element analysis software was used to conduct plastic element analysis on
ultrahigh pressure elbow of thick wall. Circumferential plastic stress on interior wall and outside wall
was compressive stress, the circumferential plastic stress on interior wall would decreases with the
pressure, and the circumferential plastic stress on outside wall would increase with the pressure, the
Von Mises stress on interior wall is greater than that of outside wall. The autofrettaged residual
stresses increase with the pressure, the autofrettaged circumferential residual stresses on interior wall
is tensile stress is tensile stress, but that of outside wall is compressive stress. The beneficial residual
stress distribution can be used to improve the strength capability of ultrahigh pressure elbow.
KEYWORDS: ultrahigh pressure elbow, stress distribution, residual stress, autofrettaged
1
INTRODUCTION
Ultrahigh pressure elbow is the important part of
ultrahigh equipment, such as polyethylene from high
pressure process chemical equipment. The reference [1]
consider the strain hardening and Bauschinger effect gain
the analytic solutions of autofrettaged thick walled
cylinder, but the author did not give the solution of elbow.
Ultrahigh pressure elbow undertake inner pressure in
work. The reference [2] gained the elastic stress
distribution rule of ultrahigh pressure elbow after elastic
analysis. In order to give full of play to the carrying
capacity of the pipes, Modern Design Theory on pipe
permit the pipe to take place partial plastic deformation,
therefore the plastic stress distribution research
calculation and the determination of the dangerous point
for the design of ultrahigh pressure elbow and safety
assessment has important reference value. In order to
improve the elastic bearing capacity of ultrahigh pressure
the most effective and most commonly used measure is
autofrettaged. The principle of autofrettaged is to load a
high inner pressure and the wall produces elastic-plastic
deformation, then unload, the favorable residual stress
distribution will be produced because the elastic
deformation recovery and the plastic deformation
irreparability after unload. The carrying capacity is
improved. So, the regularity of distribution of residual
Figure 1 The geometrical model of ultrahigh pressure elbow
© ST. PLUM-BLOSSOM PRESS PTY LTD
stress has important value on autofrettaged. Based on
plastic finite element analysis on ultrahigh pressure elbow
which was used in engineering, the author studied on the
regularity of plastic stress distribution and residual stress
distribution of ultrahigh pressure elbow.
2
THE FINITE ELEMENT MODEL OF
ULTRAHIGH ELBOW
With the ultrahigh pressure elbow whose dimensions is
D×t=78×22mm，R=3D (D is the external diameter) as
the research object, the geometric model of ultrahigh
pressure elbow shown in figure 1. Considering the
symmetrical, 3d finite element analysis on half of
ultrahigh pressure elbow, symmetry restriction was
imposed on the symmetry plane and normal restriction
was imposed on the transerse plane. The finite element
model and the gridding of ultrahigh pressure elbow is
shown in figure 2, 1-1 cross section diagram was shown
in figure3. Point A, B, C, D, E and F are in section 1-1.
The material of ultrahigh pressure elbow is 34CrNi3MoA,
whose mechanical properties are E=205GPa, σb=950MPa,
μ=0.28, Et=10.25GPa, σs=950MPa. Consider the material
to strengthen and Bauschinger effect, using bilinear
kinematic hardening model. The material constitutive
relation was shown in figure 4.
Figure 2 The gridding of ultrahigh pressure elbow
Physical and Numerical Simulation of Geotechnical Engineering
2nd ISSUE, March 2011
Figure 3
3
Cross section diagram
Figure 4
The material constitutive relation
circumferential stress on the interior wall surface and
outside wall surface were pressure stress based on the
figure 5 and figure 6. The circumferential pressure stress on
interior wall surface decreased gradually with increased the
internal pressure, which reached the minimum value when
the internal pressure reached the plastic ultimate load. But
the circumferential pressure stress on outside wall surface
increased gradually with increased the internal pressure.
PLASTIC FINITE ELEMENT SOLUTION
RESULTS
3.1 Plastic stress distribution of ultrahigh pressure
elbow
Under the action of internal pressure at all levels, the
circumferential stress on the cross section 1-1 was shown in
figure 5 and figure 6. We could gain that both the
Figure 5 Circumferential stress on interior wall
Figure 6 Circumferential stress on Outside wall
Under the action of internal pressure at all levels, Von
Mises equivalent stress of ultrahigh pressure elbow on
internal wall and outside wall shown in Table 1. The curve
of Von mises equivalent stress was shown Fig.7 and Fig.8.
Table 1 Von Mises equivalent stress of ultrahigh pressure elbow
point of action
Straight pipe
Outside wall
wall inside
straight
A
B
C
D
E
F
400
148.1
787.6
816.3
187.8
796.7
165.9
791.2
169.2
500
192.5
802.4
829.8
248.6
812.6
220.7
812.7
223.7
600
253
823
841.4
336.6
828.3
299.2
835.4
301.1
700
342.4
854.1
883.5
480.5
868.5
420.3
871.2
420.1
750
403.6
877.5
916
612.6
898
507.9
897.2
509.8
780
450.7
898.2
943.8
799.1
920
570.1
916.6
580.7
786
461.3
904.2
950
806.2
924
580.8
920.8
604.5
internal pressure
75
Plastic Finite Element Analysis of Autofrettaged Ultrahigh Pressure Elbow
DOI: 10. 5503/J. PNSGE. 2011. 02.015
790
468.3
908.5
954.6
809.6
928.3
585.4
923.5
608.6
800
485.4
920.9
968.2
818.3
941.2
601.4
930.3
642.6
820
521.9
945.4
1006
900.9
965.3
638.5
952.9
745.2
Figure 7 Equivalent stress on internal wall
Figure 8 Equivalent stress on outside wall
Data in the table 1 and the figure 7 and figure 8 show
that the Von Mises stress on point E is maximal, and the
Von Mises stress on point C is minimal, which shown that
the inboard Von Mises stress is greater than that of
outboard on internal wall and outside wall face.
Data in the table 1 also show that the Von Mises
equivalent stress on point C was 954.6MPa when the
internal pressure reached 790MPa, which has exceeded the
ultimate strength of materials, the Von Mises equivalent
stress on point D was 809.6MPa which has exceeded the
yield strength of materials. This shown that the inside
surface of the ultrahigh pressure elbow has completely
yield, and the point C would take the lead in destruction
under the action of internal pressure of 790MPa, and point
C was the danger point. The maximal Von Mises
equivalent stress on the point C would reach 949.8MPa
when the internal pressure was 786MPa, at the same time
all the equibalent stress on ultrahigh pressure elbow surface
didn’t reach the ultimate strength of materials, so the
ultimate internal pressure is 786MPa.
The most effective measures is autofrettaged in order to
in improve the ultimate load bearing capacity. The
principle of autofrettaged is to load a high internal pressure
and the wall produces elastic-plastic deformation, then
unload, the favorable residual stress distribution will be
produced because the elastic deformation recovery and the
plastic deformation irreparability after unload. The figure 8
and figure 9 give the curve of circumferential residual
stress and the equivalent residual stress on point A, point B,
point C, point D, point E, and point F of cross section 1-1
after autofrettaged.
Which shown that the residual stress of ultrahigh
pressure elbow surface was increased with the internal
pressure increases, and the residual stress on the internal
wall is greater than that of outside wall. The circumferential
residual stress was tensile stress on the internal surface wall,
but which is pressure stress on the outside wall surface.
Based on the ahead analysis we can understand that the
internal surface wall will produced biggish pressure, so the
autofrettaged ultrahigh pressure elbow will first cancel
residual tensile stress in normal work, which can obviously
improve the bearing capacity of ultrahigh pressure elbow.
3.2 Residual stress distribution of ultrahigh pressure
elbow after autofrettaged
76
Physical and Numerical Simulation of Geotechnical Engineering
2nd ISSUE, March 2011
Figure 9 Curve of circumferential residual stress
4
Figure 10 Curve of equivalent residual stress
tensile stress on the internal surface wall, but which is
pressure stress on the outside wall surface.
CONCLUSION
(1) The circumferential stress on the internal and outside
surface wall is pressure stress, the circumferential pressure
stress on the internal surface wall decrease with the internal
pressure increase, the circumferential pressure stress on the
outside surface wall increase with the the internal pressure
increase.
(2) The inboard Von Mises equivalent stress is greater
than that of outboard on internal wall and outside wall
surface. The danger poin is point C on cross section 1-1.
(3) The residual stress of ultrahigh pressure elbow
surface was increased with the internal pressure increases,
and the residual stress on the internal wall is greater than
that of outside wall. The circumferential residual stress was
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