FINITE ELEMENT ANALYSIS OF AUTOFRETTAGE

PROCESS OF THICK – WALLED CYLINDERS

Dr. Lattif Shekher Jabur

Dr. Dr. Hazim Ismael Radhi

Najah Rustum Mohsin

ABSTRACT

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.

The objective

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

pressure.

1.

INTRODUCTION

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

the

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.

2.

PRESSURE LIMITS AND STRESS

DISTRIBUTION IN NON – AUTOFRETTAGED CYLINDER

2.1.

Pressure Limits of Non – Autofretage

Cylinder

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

2.2.

Stress Distribution of Non

– Autofretage Cylinder

The

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.

3.

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-

nodes )

4.

VALIDATION OF NUMERICAL

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 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

operating pressure.

5.

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

stress for

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.

5.2.

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

A

C

D

B

5.3.

Effect of Autofretage

Stages on Maximum Von._misesStress

To

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.

6.

CONCLUSION

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 .

·

The

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.

REFERENCE

1

A. B. Ayob, M. N. Tamin and

Kabashi Elbasheer,” Pressure Limits of Thick – walled cylinders , Poceedings of

the international Multi Conference of Engineers and Computer scientist , IMECS

2009, Hong Kong, March 8 -20.

2

Wang Zhiqun,” Elastic –

plastic fracture analysis of a thick – walled cylinder “, International Journal

of pressure Vessels PiPing “, volume 63, 1995, pp. 165 – 168.

3

D. Dinesh Babu and T. Jega

Balaji,” Theoretical 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 Autofrettage Pressure in thick Cylinders “,

Jurnal Mekanikal, December 2007, N0. 24, pp. 1 – 24.

5

Noraziah Wahi, Amran Ayob

and M.Kabashi Elbasheer, ” Effect of Optimum Autofrettage on Pressure

Limits of thick walled Cylinders “, International Journal of Environmental

Science and Development, Vol. 2, No. 4, August 2011, pp. 329 – 333.

6

I.M.Jamadar, S.M.Patil,

S.S.Chavan, G.B.Pawar and G.N.Rakate, Thickness Optimization of Inclined

Pressure Vessel Using Non Linear Finite Element Analysis Using Design by Analysis

Approach. International Journal of Mechanical Engineering and

Technology (IJMET), 3(3), 2013, pp.682-689.

7

Noraziah Wahi, Amran Ayob

and Mohd Kabashi Elbasheer,” Effect of Autofrettage on Allowable Pressure

of thick – walled Cylinders “, International Conference on Environmental

and Agriculture Engineering “, 2011, Singapore, IPCBEE vol. 15, pp. 14 –

16, IACSIT Press.

8

Ruilin Zhu and Jinlai Yang,

” Autofrettage of thick cylinders “, International Journal of

Pressure Vessels and PiPing, Vol. 75, 1998, pp. 443 – 446..

9

Zhong Hu and Sudhir

Puttagunta, ” Computer modeling of Internal Pressure Autofrettage Process of a

Thick – Walled Cylinder with the Bauschinger Effect “, American Transactions on

Engineering and Applied Sciences, Volume 1, No.2, ISSN 2229-1652, eISSN

2229-1660.

10

Md. Tanjin Amin, Abu Rayhan

Md. Ali, Tousif Ahmed and Faisal Ahmed, ” Optimum Design of Autofrettaged

thicked – walled cylinders “, Global Journal of Researches in Engineering,

vol.13, Issue 8, Version 1, 2013, Online ISSN : 2249-4596, Print ISSN : 0975 –

5861

11

Prof. S. S. Deshpande, P.

N. Desai, K. P. Pandey and N. P. Pangarkar, Detailed Studies on Stress

Concentration by Classical and Finite Element Analysis. International Journal of Mechanical Engineering and

Technology (IJMET), 7(2), 2016, pp.148-167.

12

F. Tried, J. Schedelmaier

and M. Poelzl, ” Autofrettage – Basic Information and practical application on

components for waterjet cutting “, American Waterjet Conference, 2005

WJTA, 2005, August 21 – 23, Houston, Texas.

13

Abu Rayhan Md.Ali, Nidul

Ch. Ghosh and Tanvir-E-Alam, ” Optimum Design of Pressure Vessel Subjected to

Autofrettage Process “, International Journal of Mechanical, Aerospace,

Industrial, Mechatronic and manufacturing Engineering, vol.4, No. 10, 2011,

PP.1040 – 1045.

14

Dr. Lattif Shekher Jabur, “Effect of

Autofrettage Pressure on Stress Distribution and Operating Pressures of Thick

-Walled Cylinders” , International Journal of

Engineering Research & Technology (IJERT), Vol. 5, Issue 12, December-2016,

pp.79-87.

15

W. JR. Callister, ”

Material Science and engineering; An Introduction”, 7th

Edition, 2005, New delhi.

16

ABAQUS ver. 6.9, 2009,

Getting Started; standard User’s Manual.