Optimum Design of Pressure Vessel Subjected To Autofrettage

Process.Research is accomplished byResearch is accomplished byDr. Abu Rayhan Md. Ali.

Nidul Chandra Ghosh.(Now in Oklahoma state university)

Tanvir-E-Alam(Now in University of South Florida)

Dept. of Mechanical Engineering. BUET

Justification : Pressure vessels are widely used in the

nuclear, chemical , military industries and also for fluid transmission and storage applications.

Now a days we are facing world wide scarcity of materials and higher cost.

Which caused the researchers not to confine themselves to the customary elastic regime.

Justification :

And attracted their attention to the elastic plastic approach .

Which offers a more efficient use of materials.

In recent decades, various methods have been proposed for strengthening the pressure vessels.

There are two basic different elastic- plastic techniques to increase the pressure capacity of thick walled cylinders.

Autofrettage. Compound pressure cylinder.

Our main highlight is on autofrettage process.

Autofrettage

The idea of this method is to load a vessel by internal pressure Pa up to the appearance of plastic regime.

After releasing the pressure residual stresses developed.

Whose combined action with stresses caused by working pressure Pw decreases the total level of stresses.

Thus the pressure capacity of the cylinder increases.

Residual stress development

Key problem In autofrettage, the key problems are:

1. The optimum radius of

elasto-plastic junction opt r , &

2. The optimum autofrettage

pressure, opt p .

Where the equivalent von mises stress is minimum.

A simple case study:Here the mat. is aluminum

a = 0.01 m. b = 0.02m.

Now we see how the stress varies along the cylinder radius.

Stress distributionStress distribution

Mat. σy

(MPa)

E(GPa) Ep

(GPa)ν

Al 90 72 1.75 0.33

Design/methodology/approach:

1. Optimum radius opt r is determined by using Zhu Yang analytical approach.

2. ANSYS is used for numerical simulation to determine optimum autofrettage pressure opt p.

Residual stress pattern After applying autofrettage

pressure the wall goes plastic regime up to elastic plastic junction.

Residual compressive hoop stress at near-bore region

Residual tensile hoop stress occurs at outer portion.

Total stress pattern

Fig: comparison of stress with and without autofrettage

Because of Because of compressive compressive residual hoop stress residual hoop stress at inner bore, the at inner bore, the resultant hoop resultant hoop stress becomes stress becomes significantly lower.significantly lower.

Maximum stress Maximum stress occurs at elastic occurs at elastic plastic junction plastic junction rather than inside rather than inside radius.radius.

Evaluations of optimum elastic plastic radius

Ghomis equGhomis equn n s s are used to are used to deduce stresses deduce stresses at different radius at different radius of elastic plastic of elastic plastic junction by junction by the the help of C++.help of C++.

Here Here opt r opt r in in between 0.015 m between 0.015 m and 0.016 m.and 0.016 m. Fig: : Stress At Different Radius Of Elasto Plastic

Junction

Equations we used Zhu Yang has developed an equation to

determine opt r which we can calculate just using a pocket calculator.

ropt = a exp(√3pw/2σy)

In our case ropt is 0.0156 m

Ghomi also deduce ropt by using MATLAB.

Difference between two methods vary between 5-7%.

So we consider Zhu Yang model for calculating opt r.

Optimum autofrettage pressure

We have to generate such a pressure that the cylinder goes plastic regime up to Optimum elastic plastic radius.

Then we obtain the best possible autofrettage effect.

but how much pressure ??

Parameters

Two pressure that limits the autofrettage process.

Py1 = pressure at which yielding

commences at inner surface.

Py2 = pressure at which plasticity has

spread throughout the cylinder.

Significance

So if the pressure < Py1 then there will be no

autofrettage effect as any portion of the cylinder does not go to plastic regime.

Again if the pressure > Py2 then there will be

converse effect.

That means the pressure capacity of the cylinder will decrease, instead of increasing,

Numerical simulation using ANSYS 10.0

stress pattern

ForAutofrettage pressure 500 MPa Working pressure 200 MPa

Simple case studyHere the mat. is steel;

a=0.1 m ; b=0.2m ;

E= 207 Gpa;

Ep =4.5 Gpa ;

σy =800 Mpa ;

ν= 0.29;

Py1 = σy (1-1/k2 )/√3;

=347 MPa

Py2 = σy ln(k)

=555 MPa

Stress pattern

Fig: After applying Fig: After applying autofrettage pressureautofrettage pressure

Fig: Fig: After Unloading After Unloading Autofrettage PressureAutofrettage Pressure

Fig: After applying working Fig: After applying working pressurepressure

Variation of position of maximum stress (for constant working pressure 200MPa)

Fig : AP 450 MPaFig : AP 450 MPa Fig : AP 500 MPaFig : AP 500 MPa

Fig : AP 550 MPaFig : AP 550 MPa Fig : AP 600 MPaFig : AP 600 MPa

Evaluation of optimum autofrettage pressure

Autofrettage pressure < 347 (Py1) No effect

Pressure at which maximum von mises stress is minimum that’s the Opt. autofrettage pressure.

Autofrettage pressure > 555 (Py2) converse effect Fig: stress at different

autofrettage pressure

On our research work we will analyze the effect of

1. Working pressure

2. Value of k (b/a)

3. Material model ( elastic perfectly plastic and elastic plastic with different slope of strain hardening segment )

4. Autofrettage Stages

On optimum autofrettage On optimum autofrettage pressurepressure

Effect of working pressure on opt p

Fig: optimum autofrettage pressure for different working pressure

Optimum autofrettage

pressure is not a constant value

rather it depends on the working

pressure.

The optimum autofrettage

pressure increases along with the

increase of working pressure.

Effect of working pressure on Effect of working pressure on opt popt p

In case of 400 and 450 In case of 400 and 450 MPa the developed von MPa the developed von mises stress starts to mises stress starts to decrease only after decrease only after exceeding working exceeding working pressure.pressure.segment.segment. Auto pressure < Auto pressure < working pressure then working pressure then the flow stress remains the flow stress remains unchanged thus no unchanged thus no autofrettage effect.autofrettage effect.

% Reduction of von mises stress for different working pressure

Working pressure

von mises stress

Without autofrettage

von mises stress

After autofrettage

% Reduction

of von mises stress

100 225 193 14.22

200 450 348 22.67

300 676 496 26.62

400 840 615 26.78

( for same k)( for same k)% reduction % reduction of von mises of von mises

stress is stress is higher at higher at

higher higher working working pressurepressure

All the datas are on MPaAll the datas are on MPa

Effect of k (b/a) on opt p

Fig: optimum Fig: optimum autofrettage pressure for autofrettage pressure for

different K valuedifferent K value

For constant inner radius optimum autofrettage pressure obtain a higher value for thicker cylinder.

For constant outer radius the developed MVS and Optimum autofrettage pressure remains same.

Effect of material model on opt p

Optimum autofrettage pressure is higher at higher slope of strain hardening segment.

The resultant von mises stress is minimum for higher slope of strain hardening segment.

Fig: comparison of maximum Fig: comparison of maximum von mises stresses for von mises stresses for

different material modeldifferent material model

Working pressure of 300 Mpa, where autofrettage pressure is 500 Mpa

Stage 1

(Mpa)

Stage 2

(Mpa)

Stage 3

(Mpa)

Stage 4

(Mpa)

Stage 5

(Mpa)

Stage 6

(Mpa)

Stage 7

(Mpa)

Stage 8

(Mpa)

Stage 9

(Mpa)

350 0 400 0 450 0 500 0 300

Stage 1(Mpa)

Stage 2(Mpa)

Stage 3(Mpa)

500 Mpa 0 Mpa 300 Mpa

Effect of Effect of autofrettage stages

Fig: 3 stage autofrettage Fig: 9 stage AutofrettageFig: 9 stage Autofrettage

Conclusion

Opt p increases along with the working pressure.

For same working pressure , increasing the K value leads to an increase in the optimum Opt p.

If the slope of strain hardening segment increases, Opt p also increases.

% Reduction of von mises stresses are higher at higher value of K and higher slope of strain hardening segment.

Number of autofrettage stages has no effect.

Practical implications:

The results can be used for high pressure vessels such as

Artillery tubes & gun barrels Diesel engine components (such as fuel rails

and fuel lines) Hydraulic cylinders Oil filled components and so on.

Future development Autofrettage is a temperature

dependent technique. At low- temperature autofrettage is more

efficient than autofrettage at room temperature.

In this paper optimization is done by assuming bi-linear material model.

For further study temperature and non linear mat. model could be taken under concern.

Thanking you