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Autofrettage in pressure
vessels
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Residual stress analysis of Autofrettaged thick-walledspherical
pressure vessel
•
Results are obtained by developing an extension of variable
materialproperties (VMP) method ( Find out the Autofrettaged stress
and strains byusing the formula).
• By performing a parametri study! the optimum autofrettage
pressure andorresponding autofrettage per ent for reating desirable
residual stress
state are introdu ed and determined.•
"he modi# ation ma$es VMP method appli able for analyses of
spheri alvessels based on a tual material behavior both in loading
and unloadingand onsidering variable Baus hinger e%e t.
• &n addition! the optimum pressure for autofrettage of the
spheri al pressurevessels made of A' and *B' steels is dis ussed
here.
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Residual stress analysis of Autofrettaged thick-walledspherical
pressure vessel
Boundary conditions:
The maximum applied working pressure for A723 steel. the maximum
internal pressure without causingyielding! is
The yield strength of A723 steels are considered ""3#$%a.
+,- MPa
outer radius/inner radius+
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Residual stress analysis of Autofrettaged thick-walledspherical
pressure vessel
• &y using the 'ame(s e)uations for calculating the hoop
stress* radial stress* along thethickness of the cylinder* when the
ends of the cylinder are open and unconstrained so that thecylinder
is in a condition of plane stress.
• "he radial displa ement is
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Residual stress analysis of Autofrettaged thick-walledspherical
pressure vessel
Calculation of autofrettage pressure (Pa):0et 1n2 be denoted as
the ratio of operating pressure to yield stress.
0et 1m2 be the ratio of Autofrettaged radius to inner radius
3in e! the value of autofrettaged radius 4as not found! an
e5uation
4hi h gives a relation bet4een 1n2 and 1m2 4as used to found
thevalue of 1m2 based on von Misses riterion.
+ .,-
-.,-
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Residual stress analysis of Autofrettaged thick-walledspherical
pressure vessel
+67 MPa
Determination of autofrettaged radius (ρ)
Calculation of maximum von-Mises stress (σvon-max)
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F8M A9A0:3&3
;A< Model and F8 model=
Slno
Speci cations value
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Bi and Multi linear stress strainurve=
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Boundary ondition
Pressure is applied ,- MPaA : axis free! Both !C axis #xedB axis
free! Both :!C axis #xed
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linear isotropi Results=•
Pressure is applied for - y le.
• 85uivalent stress=
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axial stress*oop stress
Radial stress
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Bilinear isotropi Results=•
Pressure is applied for - y le.
• 85uivalent stress=
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*oop stressAxial stress
Radial stress
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Bilinear isotropi Results=•
Pressure is applied for ' y le.
• 85uivalent stress=
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*oop stressAxial stress
Radial stress
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Bilinear isotropi Results=•
Pressure is applied for ' y le 4ithD extra.
• 85uivalent stress=
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*oop stressAxial stress
Radial stress
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Bilinear isotropi Results=•
Pressure is applied for ' y le 4ith?D extra.
• 85uivalent stress=
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*oop stressAxial stress
Radial stress
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Multi linear isotropiResults=
•
Pressure is applied for - y le.
• 85uivalent stress=
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Axial stress*oop stress
Radial stress
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Multi linear isotropiResults=
• Pressure is applied for ' y le 4ithautofrettage .
• 85uivalent stress=
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Axial stress*oop stress
Radial stress
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Multi linear isotropiResults=
• Pressure is applied for ' y le 4ith Dautofrettage .
• 85uivalent stress=
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Axial stress*oop stress
Radial stress
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Multi linear isotropiResults=
• Pressure is applied for ' y le 4ith ? Dautofrettage .
• 85uivalent stress=
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Axial stress*oop stress
Radial stress
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;on lusion• "he residual stress distribution indu ed in
autofrettaged spheri al
pressure vessels made of A' steels! based on their a tual
behavior in loading and unloading 4as evaluated by numeri
almethod (Bilinear and multilinear analysis).• &t 4as
investigated that usage of isotropi hardening model in
analysis leads to signi# ant overestimation in residual hoop
stress.• "he autofrettage per ent by 4hi h high ompressive and
relatively
lo4 tensional hoop residual stress are simultaneously
attainablenear the inner and outer radii of the vessel 4as introdu
ed as theoptimum per entage of autofrettage.
• &t 4as observed that in the ase of A' spheri al vessel
4ithradius ratio of ! by in reasing autofrettage per ent up to ?
D!the inner ompressive hoop residual stress de reases and the
outer hoop tensional stress gradually in reases (Both in
bilinearand multilinear analysis.
