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ABSTRACT

The process of producing residual
stresses in thick_walled cylinder  before
it is putin to usage is called Autofretage, which it means; a suitable large
enough pressureto cause yielding within the wall, is applied toinner surface of
a sylinder  and then removed. So that
acompressive residual stresses are generated to acertain radial depth at a sylinder
 wall.

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The objective
ofpresent study, is to investigate the influenceof autofretage treatment onthe
radial, circumferential andtotal stresses using von._mises yieldcriteria. Num.simulation
carried outon ABAQUS software to investigate thestresses distribution and
calculate the autofretage radius. The results revealthat, the autofretage treatmentof
thick_wall sylinder  lead to decrease the
hoob and max.von._mises stresses and relocate them from the inner surface of
the sylinder  to somewhere along it’s
thickness. The reduction in max.stresses is strongly depending on autofretage
pressure, it wasvarying from ( 3.6% at Pautofretage = 105 M.Pa.
to 19.2% at Pautofretage =

130 M.Pa. ) Also, it
has been found, there is no influenceof autofretage stages number on each of max.von._mises
stressand autofretage radius.

Key words: autofretage, radial, hoob and
axial stresses, von._mises yield criteria, autofretage radius, optimum autofretage
pressure.

 

 

 

 

 

1.    
INTRODUCTION

The wide applications of
pressurized sylinder  in chemical,
nuclear, armaments, fluid transmitting plants,
power plants and military equipment, in addition to the increasing scarcity and
high cost of materials lead

the designers to
concentrate their attentions to the elastic – plastic approach which offers
more efficient use of materials 1, 2.The treatment of producing residual
stresses in the wall of thick_walled sylinder  before it is put in to usage is called autofretage, which it means; asuitable large enough
pressure to cause yielding within thewall, is applied to the inner surface of
the sylinder  and then removed.
So that a compressive residual stresses are generated to a certain radial depth
at the sylinder  wall. Then, duringthe
subsequent application of an operating pressure, the residual stresses will
reduce the tensile stresses generated asa result of applying operating pressure
1,3.

The influenceof
residual stresses onload-carry capacity of thick_walled sylinders have been
investigate by Ayob and Albasheer 4, using each analytical andNum.techniques.
The results of the study reveal three scenarios in the design of thick_walled sylinders.
Ayob and Elbasheer 5, used von._mises and Tresca yieldcriteria to develop a
procedure in whichthe autofretage pressure determined analytically resulting in
a reduced stress concentration. Then they coM.Pa.red the analytical results
with F.E.A. results. They concluded that, the autofretage treatment increase
the max.allowable internal pressure but it cannot increase the max.internal
pressure to case whole thickness of the sylinder  to yield. Noraziah et al. 6 presented an
analytical autofretage procedure topredict the required autofretage pressure of
different levels of allowable pressure andthey validate their results with F.E.A.
results. They found three cases of autofretage in design of pressurized thick_
walled sylinders.

Zhu and Yang 7, using
each yield criteria von._mises and Tresca, presented an analytical equation for
optimum radius of elastic-plastic junction in autofretage sylinder , alsothey
studied the influence of autofretage on distribution of stress and load bearing
capacity. They concluded, to achieve optimum radius ofelastic – plastic
junction, an autofretage pressure a bit larger than operating pressure should
be applied before a pressure vessel is put in to use. Hu and Puttagunta 8
investigate the residual stresses in thick_ walled sylinder  induced by internal autofretage pressure, also
they found the optimum autofretage pressure andthe max.reduction percentage of
the von._mises stress under elastic-limit working pressure. Md. Amin et al. 9
determined the optimum elasto_plasticradius and optimum autofretage pressure using
von._mises yield criteria , then they have been coM.Pa.red with Zhu and Yang’s
model 8. Also they observed that the percentage of max.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 influenceof
autofretage treatment in strain hardened thick_ walled pressure vessels using
equivalent von._mises stress as yield criteria. They found, the number of autofretage
stages has no influenceon max.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.

II. Limits of pressureand Distribution
of stress in non – autofretaged sylinder

2.1. Limits of pressureof non – autofretage
sylinder

According to Von._Mises yield criteria,
Each of the internal pressure requires to yield the inner surface of the sylinder
 ( i.e. partial autofretage ), PYi
, and that to yield the whole wall of the sylinder  ( i.e. completely autofretage ), PYo
, can be calculated from equations ( 1& 2 )4, 7

PYi
=                                                                                    
……………………. ( 1 )

PYo
=                                                                                   
……………………. ( 2 )

 
2.2. Distribution of stress
of non – autofretage sylinder
The
radial stress ?r, circumferential stress ?? and axial stress ?z,
distributions in non _autofretage sylinder  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 obvious that the 
tensile hoob, ??,
compressive radial , ?r,
and max. Von._Mises stresses  have
their max. values at the inner surface of the sylinder . 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.

 

 

Fig.
1: Distribution of stress on non-autofretage thick-walled sylinder  subjected to operating pressure.

Fig. 2: Geometry of inspectedmodel.

 
 
III. Finite Element
Analysis and Materials of  Num.Simulation
Models

                                                                                                                                                                          

Fig. ( 2 )
explainthe geometry of  inspectedsylinder  that is made up of carbon steel with young’s
modulus of ( 203 GPa ), 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, Num.simulation is
carried out on ABAQUS ver.6.9 13. The inspected cases are consider as 2D –
planar problem with quadratic element have been used ( CPS8R–8– nodes )

 

IV.
Validation of Num.Simulation

 

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 Num.solution using
ABAQUS ver.6.9.

From Fig.
( 3 ) , it is obvious that, the theor. and Num.calculations  of circumferential, radial and max. Von._Mises
stresses 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 Num.solution are les than
0.5%. This low percentage of errors affirm, there are no significsnt
differences between the theor. results and those obtained by simulation.
Consequently, FE modeling using ABAQUS software can be used to study the influenceof
autofretage treatment on the distribution of stress and location of autofretage
radius ( Ra ) of thick_walled sylinder  subjected to operating  pressure.

 

a

 

b

 

Fig. 3 : Validation of Num.solution results with theor.
results at different operating pressure; a – operating pressure = 80 M.Pa., b
– operating pressure = 100 M.Pa..

 

V. Results and Discussions

5.1. Min.. Autofretage Pressure

 

By calaculating the min.. pressure
that needed to yield the inner surface of the tested sylinder  ( PYi ) from equation (1) , it was
found equal to ( 104.243 M.Pa. ). That is mean, the influenceof autofretage pressure
will start at (104.243 M.Pa.), then the plastic deformation spreads through the
sylinder  thickness. Fig. (4) shows that,
the simulation solution of influenceof autofretage pressure on max. Von._Mises stress
for different operating pressure, it is obvious that , there is no influenceof autofretage
pressure on max. Von._Mises stress generating in the sylinder  due to the operating pressure as long as it is
less than ( 104 M.Pa. ) for each 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 max. Von._Mises stress.

In addition to that , it has been
observed from Table 1 that, the max. 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.

 

Fig.
4 : Simulation solution results of autofretage pressures’ influenceon Max. von._mises
stress at different operating pressure.

 

Tab. 1 : F.E.A. results of influence of Autofretage Pressure
on Max. Von._Mises Stress

No.

Operating Pressure, M.Pa.

Autofretage Pressure, M.Pa.

Max. von._mises Stress, M.Pa.

1.

90

120

247.00

2.

90

125

241.40

3.

90

130

238.8

4.

90

131

240.20

5.

90

132

241.40

6.

100

120

273.10

7.

100

125

265.20

8.

100

130

260.00

9.

100

131

260.80

10.

100

132

261.00

 

5.2. Influenceof Autofretage treatment
on stress distribution

 

 Fig.s ( 5, 6 & 7 ) demonstrates the influenceof
autofretage treatment on distribution of stress of thicked–walled sylinder  subjected to operating pressure of ( 100 M.Pa.
). It is obvious, the autofretage treatment leads to decrease the value of max.
Von._Mises stress and relocated the compressive circumferential & max. Von._Mises
stresses from the inner surface of the sylinder  to somewhere through it’s thickness. This new
location of max. 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 max. Von._Mises stresses
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 influenceof
autofretage treatment on radial stress as that seen on the circumferential
stress.

 

 

 

Fig. 5 :Influenceof Autofretage Pr. on hoob & Radial stresses at
operating Pressure = 100 M.Pa..

Fig. 6 : Influenceof Autofretage Pr. on max. Von._Mises  stress at operating Pressure = 100 M.Pa..

 

Table 2 : F.E.A. results of influenceof Autofretage Pressure
on Max. Von._Mises Stress

 No.

Operating Pressure, M.Pa.

Autofretage Pressure, M.Pa.

Max. Von._Mises Stress, M.Pa.

Autofretage Radius, mm
 

Reduction in Max. Von._Mises stress %

1.

90

without

290.00

100

2.

90

105

278.975

101.99836

3.8 %

3.

90

110

264.108

103.99686

8.9 %

4.

90

120

246.88

111.9915

14.8 %

5.

90

130

238.792

125.9761

17.65 %

6.

100

without

321.836

100

7.

100

105

310.00

101.99836

3.6 %

8.

100

110

294.020

103.99686

8.6 %

9.

100

120

273.116

111.9915

15.2 %

10.

100

130

259.992

125.9761

19.2 %

 

a

 

b

 

c

 

d

 

Fig. 7 : F.E.A.of influenceof autofretage
Pressure on max. Von._Mises stress and location of autofretage radius at
operating Pressure = 100 M.Pa. ; a- without autofrettage,       b- Pautofretage = 110 M.Pa., c –
Pautofretage = 120 M.Pa., d –
Pautofretage = 130 M.Pa..

 

 

5.3. Influenceof Autofretage stages
on max. Von._Mises stress

 

To investigate the influenceof autofretage
stages on max.  Von._Mises stress,
the inspectedsylinder  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 Num.results confirm there is no influenceof autofretage
stages on the max. Von._Mises stress generated in the sylinder  due to operating pressure. This results are
very close to the  with results have been
found by 3.

Tabe 3 : F.E.A. results of influenceof Autofretage stages
on Max. Von._Mises Stress

No. of case

Autofretage pressure, M.Pa.
First
stage

Unloading
step
M.Pa.

Autofretage
pressure, M.Pa.
second stage

Unloading step
M.Pa.

Loading of Operating Pressure, M.Pa.

Max. Von._Mises Stress,
M.Pa.

Case I

110

0

100

294.020

Case II

120

0

100

273.116

Case III

130

0

100

259.992

Case IV

105

0

110

0

100

294.033

Case V

105

0

120

0

100

273.05

Case VI

105

0

130

0

100

260.254

 

 

 Fig. 7 : Num.solution results of influenceof autofretage
stagse  on Max. von_mises
stresses and autofretage radius  at operating Pressure = 100 M.Pa.

 

VI. Conclusion

 

The results of present
investigation can be summarized as :-

 

1. The autofretage treatment
on thick_walled sylinder  leads to
decrease the circumferential and max. Von._Mises stresses and  relocate them from the inner surface of the sylinder
 to somewhere along it’s thickness, which
called as, autofretage radius, Ra .

2. The autofretage radius, Ra ,
is strongly affected by  autofretage pressure
while it does not depend on the operating pressure..

3. There is no influenceof autoffrettage
stages on max. Von._Mises stress developed in the  sylinder  subjected to an operating pressure.

 

References

 

 

 1 A. B. Ayob, M. N. Tamin and Kabashi
Elbasheer,” Limits of pressureof Thick – walled sylinders , Poceedings of the
international MultiConference of Engineers and Computer scientist , IMECS 2009,
Hong Kong, March 8 -20. 

 

2 Wang
Zhiqun,” Elastic – plastic fracture analysis of a thick – walled sylinder  “, International Journal of pressure Vessels
Piping “, volume 63,  1995, pp. 165
– 168.

 

3 D.
Dinesh Babu and T. Jega  Balaji,” Theor.
and finite Element Analysis oof High Pressure Components “, IOSR Journal
of Engineering, Vol. 3, Issue 2, Feb 2013,              PP: 25 – 34.

 

4 Amran Ayob and M. Kabashi Elbasheer, ”
Optimum Autofretage Pressure in thick Sylinders “, Jurnal Mekanikal,
December 2007, N0. 24, pp. 1 – 24.

 

5 Noraziah Wahi, Amran Ayob and M.Kabashi
Elbasheer, ” Influenceof Optimum Autofretage on Limits of pressureof thick
walled Sylinders “, International Journal of Environmental Science and
Development, Vol. 2, No. 4, August 2011, pp. 329 – 333.

 

6 Noraziah Wahi, Amran Ayob and Mohd Kabashi
Elbasheer,” Influenceof Autofretage on Allowable Pressure of thick –
walled Sylinders “,InternationalConference on Environmental and
Agriculture Engineering “, 2011, Singapore, IPCBEE vol. 15, pp. 14 – 16,
IACSIT Press.

 

7  Ruilin
Zhu and Jinlai Yang, ” Autofretage of thick sylinders “,
International Journal of Pressure Vessels and Piping, Vol. 75, 1998, pp. 443 –
446..

 

8  Zhong Hu
and Sudhir Puttagunta, ” Computer modeling of Internal Pressure Autofretage Treatment
of a Thick – Walled Sylinder  with the
Bauschinger Influence”, American Transactions on Engineering and  Applied Sciences, Volume 1, No.2, ISSN
2229-1652, eISSN 2229-1660.

 

9 Md. Tanjin Amin, Abu Rayhan Md. Ali, Tousif
Ahmed and Faisal Ahmed, ” Optimum Design of Autofretaged thicked – walled sylinders
“, Global Journal of Researches in Engineering, vol.13, Issue 8, Version 1,
2013, Online ISSN : 2249-4596, Print ISSN : 0975 – 5861

 

10 F. Tried, J. Schedelmaier and M. Poelzl, ” Autofretage
– Basic Information and practical application on components for waterjet
cutting “, American Waterjet Conference, 2005 WJTA, 2005, August 21 – 23, Houston,
Texas.

 

11 Abu Rayhan Md.Ali, Nidul Ch. Ghosh and
Tanvir-E-Alam, ” Optimum Design of Pressure Vessel Subjected to Autofretage Treatment
“, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and
manufacturing Engineering, vol.4, No. 10, 2011, PP.1040 – 1045.

 

12 W. JR. Callister, ” Material Science and
engineering; An Introduction”, 7th Edition, 2005,  New delhi.

 

13 ABAQUS ver. 6.9, 2009, Getting Started;
standard User’s Manual.

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