FINITE ELEMENT ANALYSIS OF AUTOFRETTAGE
PROCESS OF THICK – WALLED CYLINDERS
Dr. Lattif Shekher Jabur
Dr. Dr. Hazim Ismael Radhi
Najah Rustum Mohsin
The process of producing residual
stresses in a thick-walled cylinder before it is put into usage is called
Autofrettage, which it means; a suitable large enough pressure to cause
yielding within the wall, is applied to the inner surface of the cylinder and
then removed. So that a compressive residual stresses are generated to a
certain radial depth at the cylinder wall.
of the present study, is to investigate the effect of Autofretage process on
radial, circumferential and total stresses by using von._misesyield criteria.
Numerical simulation carried out on ABAQUS software to investigate the stresses
distribution and calculate the Autofretage radius. The results reveal that, the
Autofretage process of thick-wall cylinder lead to decrease the hoob and
maximum von._misesstresses and relocate them from the inner surface of the
cylinder to somewhere along it’s thickness. The reduction in maximum stresses
is strongly depend on Autofretage pressure, it was varying from ( 3.6% at PAutofretage = 105 M.Pa.
to 19.2% at PAutofretage =
130 M.Pa. ) Also, it
has been found, there is no effect of number of Autofretage stages on both of
maximum von._mises stress and Autofretage radius.
Key words: autofrettage, radial, hoob
and axial stresses, von._mises yield criteria, autofrettage radius, optimum Autofretage
The wide applications of pressurized cylinder
in chemical, nuclear, armaments, fluid transmitting plants,
power plants and military equipment, in addition to the increasing scarcity and
high cost of materials lead
designers to concentrate their attentions to the elastic – plastic approach
which offers more efficient use of materials 1, 2.The process of producing
residual stresses in the wall of thick-walled cylinder before it is put into
usage is called Autofretage, which it means; a suitable large enough
pressure to cause yielding within the wall, is applied to the inner surface of
the cylinder and then removed. So that a compressive residual
stresses are generated to a certain radial depth at the cylinder wall. Then,
during the subsequent application of an operating pressure, the residual
stresses will reduce the tensile stresses generated as a result of applying
operating pressure 1,3.
The effect of residual stresses on load-carry capacity
of thick-walled sylinders have been investigate by Amran Ayob and Kabashi
Albasheer 4, using both analytical and numerical techniques. The results of
the study reveal three scenarios in the design of thick-walled sylinders. Amran
Ayob and M. Kabashi Elbasheer 5, used von._misesand Tresca yield criteria to
develop a procedure in which the Autofretage pressure determined analytically
resulting in a reduced stress concentration. Then they coM.Pa.red the
analytical results with FEM results. They concluded that, the Autofretage
process increase the maximum allowable internal pressure but it cannot increase
the maximum internal pressure to case whole thickness of the cylinder to yield.
Noraziah et al. 6 presented an analytical Autofretage procedure to predict
the required Autofretage pressure of different levels of allowable pressure and
they validate their results with FEM results. They found three cases of Autofretage
in design of pressurized THICK _WALLED sylinders.
Ruilin Zhu and
Jinlai Yang 7, by using both yield criteria von._misesand Tresca, presented
an analytical equation for optimum radius of elastic-plastic junction in Autofretage
cylinder, also they studied the influence of Autofretage on stress distribution
and load bearing capacity. They concluded, to achieve optimum radius of elastic
– plastic junction, an Autofretage pressure a bit larger than operating
pressure should be applied before a pressure vessel is put into use. Zhong Hu
and Sudhir Puttagunta 8 investigate the residual stresses in the thick-
walled cylinder induced by internal Autofretage pressure, also they found the
optimum Autofretage pressure and the maximum reduction percentage of the von._mises
stress under elastic-limit working pressure. Md. Tanjin Amin et al. 9
determined the optimum elasto – plastic radius and optimum Autofretage pressure
by using von._misesyield criterion , then they have been compared with Zhu and
Yang’s model 8. Also they observed that the percentage of maximum von._mises
stress reduction increases as value of radius ratio (K) and working pressure
increases. F. Trieb et al. 10 discussed practical application of Autofretage
on components for waterjet cutting. They reported that the life time of high
pressure components is improved by increasing Autofretage depth due to
reduction of tangential stress at inner diameter, on other hand too high
pressure on outside diameter should be avoided to prevent cracks generate. In
addition to determine the optimum Autofretage pressure and the optimum radius
of elastic-plastic junction , Abu Rayhan Md. et al.11 evaluated the effect of
Autofretage process in strain hardened THICK _WALLED pressure vessels by using
equivalent von._mises stress as yield criterion. They found, the number of Autofretage
stages has no effect on maximum von._mises stress and pressure capacity. Also,
they concluded that, optimum Autofretage pressure depends on the working
pressure and on the ratio of outer to inner radius.
PRESSURE LIMITS AND STRESS
DISTRIBUTION IN NON – AUTOFRETTAGED CYLINDER
Pressure Limits of Non – Autofretage
According to von._misesyield
criterion, Both of the internal pressure requires to yield the inner surface of
the cylinder ( i.e. partial Autofretage ), PYi , and that to yield the whole
wall of the cylinder ( i.e. completely Autofretage ), PYo , can be
calculated from equations ( 1and 2 )4, 7
Stress Distribution of Non
– Autofretage Cylinder
radial stress or, circumferential ( hoop ) stress o0 and axial stress oz,
distributions in non – Autofretage cylinder subjected to an operating pressure,
Pi, are given by Lame’s formulations which is available in 3, 4, 5, 6, 7 . As
shown in Fig. ( 1 ), it is clear that the tensile hoob, o0, compressive radial
, or, and maximum von._misesstresses have their maximum values at the inner
surface of the cylinder. The hoop stress has always positive value which
represents as tensile stress while the stress in the radial direction is always
compressive. Also the hoop tensile stress’s value is greater than radial
compressive stress’s value.
FINITE ELEMENT ANALYSIS AND
MATERIALS OF NUMERICAL SIMULATION MODELS
Fig. ( 2 ) illustrates the geometry
of investigated cylinder that is made up of carbon steel with young’s modulus
of ( 203 G.Pa. ), Poisson’s ratio of ( 0.33 ) and yield stress of ( 325 M.Pa. )
12 . It subjected to internal pressure ( Pi ). The material is
assumed homogeneous and isotroPic. To compute the required results, Numerical
simulation is carried out on ABAQUS ver.6.9 13. The investigated cases are
consider as 2D – planar problem and quadratic element have been used ( CPS8R-8-
VALIDATION OF NUMERICAL
In the present study, the
validation of software has been done by coM.Pa.ring the analytical calculation
results which obtained by solutions of equations are available in literatures
3, 4, 5, 6 7, with results of numerical solution using ABAQUS ver.6.9.
From Fig. ( 3 ) , it is clear that, the theoretical and numerical calculations
of circumferential, radial and maximum von._misesstresses for different
internal pressure are very closed and overlap each other. It means, a good
agreement is found between the results, and the static analysis shows that, the
percentage of errors between the result of analytical and numerical solution
are les than 0.5%. This low percentage of errors affirms, there are no
significsnt differences between the theoretical results and those obtained by
simulation. Consequently, FE modeling using ABAQUS software can be used to
study the effect of Autofretage process on the stress distribution and location
of Autofretage radius ( Ra ) of thick-walled cylinder subjected to
RESULTS AND DISCUSSIONS
5.1. Minimum Autofretage Pressure
By calaculating the minimum pressure
that needed to yield the inner surface of the tested cylinder ( PYi
) from equation (1) , it was found equal to ( 104.243 M.Pa. ). That is mean,
the effect of Autofretage pressure will start at (104.243 M.Pa.), then the
plastic deformation spreads through the cylinder thickness. Fig. (4) shows
that, the simulation solution of effect of Autofretage pressure on maximum von._mises
different operating pressure, it is clear that , there is no effect of Autofretage
pressure on maximum von._mises stress generating in the cylinder due to the
operating pressure as long as it is less than ( 104 M.Pa. ) for both value of
operating pressure. Then , when it is exceed ( PAutofretage > 104
M.Pa. ) the maximunm Von._mises stress decreases depending on the Autofretage
pressure, the bigger value of Autofretage pressure, the lower of maximum von._misesstress.
In addition to that , it has been observed from Table 1
that, the maximum von._mises stress decreases with increasing the Autofretage
pressure even PAutofretage reache value of about ( 130 M.Pa. ) then
starts increasing, which it means, this value of Autofretage pressure represents
the optimum Autofretage pressure 5,6. This results agree with result was
found by 1, 9, 11.
Effect of Autofretage
Process on Stress Distribution
Fig.s ( 5, 6 and 7 ) demonstrates the effect of Autofretage process on stress
distribution of thicked-walled cylinder subjected to operating pressure of (
100 M.Pa. ). It is obvious, the Autofretage process leads to decrease the value
of maximum von._mises stress and relocated the compressive circumferential and
maximum von._mises stresses from the inner surface of the sylinder to somewhere
through it’s thickness. This new location of maximum von._mises stress called Autofretage radius, Ra . It
does not depend on operating pressure while it is strongly affected by Autofretage
pressure as shown in Table 2, which shows the values of Autofretage radius, Ra
, with different values of Autofretage pressure. Also, it is found , the
reduction in maximum von._misesstresses varying from ( 3.6 % at PAutofretage
=105 M.Pa. ) to ( 19.2% at PAutofretage
=130 M.Pa. ). It is vital to see that , there is no significant effect of Autofretage
Effect of Autofretage
Stages on Maximum Von._misesStress
investigate the effect of Autofretage stages on maximum von._misesstress, the
investigated cylinder was subjected to ( 100 M.Pa. ) as operating pressure and Autofretage
pressures of ( 110, 120 and 130 M.Pa. ) are done by two steps, at first step,
the Autofretage pressure has been applied in one stage, while at second step it
was done by three loading stages ( see Table 3 ). As can be noticed clearly in
Table 3 and Fig. (7 ), the numerical results confirm there is no effect of Autofretage
stages on the maximum Von._mises stress generated in the cylinder due to
operating pressure. This results are very close to the with results have been
found by 3.
The results of
present investigation can be summarized as
The Autofretage process on
thick-walled cylinder leads to decrease the circumferential and maximum von._mises
stresses and relocate them from the inner surface of the cylinder to somewhere
along it’s thickness, which called as, Autofretage radius, Ra .
Autofretage , Ra , is strongly affected by Autofretage
pressure while it does not depend on the operating pressure.
There is no effect of
autoffrettage stages on maximum Von._mises stress developed in the cylinder
subjected to an operating pressure.
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