ABSTRACT is no influenceof autofretage stages number on


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

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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







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

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

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

……………………. ( 1 )

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

2.2. Distribution of stress
of non – autofretage sylinder
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.

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

Fig. 2: Geometry of inspectedmodel.