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.

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.