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Research Papers: Design and Analysis

Thermal Simulation of an Arbitrary Residual Stress Field in a Fully or Partially Autofrettaged Thick-Walled Spherical Pressure Vessel

[+] Author and Article Information
M. Perl

Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

In the case of a sphere under internal pressure Tresca’s yield criterion is identical to that of von Mises.

J. Pressure Vessel Technol 130(3), 031201 (Jun 06, 2008) (5 pages) doi:10.1115/1.2937762 History: Received December 31, 2006; Revised March 28, 2007; Published June 06, 2008

The equivalent thermal load was previously shown to be the only feasible method by which the residual stresses due to autofrettage and its redistribution, as a result of cracking, can be implemented in a finite element (FE) analysis of a fully or partially autofrettaged thick-walled cylindrical pressure vessel. The present analysis involves developing a similar methodology for treating an autofrettaged thick-walled spherical pressure vessel. A general procedure for evaluating the equivalent temperature loading for simulating an arbitrary, analytical or numerical spherosymmetric autofrettage residual stress field in a spherical pressure vessel is developed. Once presented, the algorithm is applied to two distinct cases. In the first case, an analytical expression for the equivalent thermal loading is obtained for the ideal autofrettage stress field in a spherical shell. In the second case, the algorithm is applied to the discrete numerical values of a realistic autofrettage residual stress field incorporating the Bauschinger effect. As a result, a discrete equivalent temperature field is obtained. Furthermore, a FE analysis is performed for each of the above cases, applying the respective temperature field to the spherical vessel. The induced stress fields are evaluated for each case and then compared to the original stress. The FE results prove that the proposed procedure yields equivalent temperature fields that in turn simulate very accurately the residual stress fields for both the ideal and the realistic autofrettage cases.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

The equivalent temperature fields for simulating full or partial ideal autofrettage in a spherical vessel of radii ratio of (b∕a)=1.7

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Figure 2

The residual radial stress component σrrR(r) for ideal autofrettage

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Figure 3

The residual hoop and meridional stress components σθθrR(r)=σφφR(r) for ideal autofrettage

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Figure 4

The equivalent temperature field for simulating full realistic autofrettage in a spherical vessel of radii ratio of (b∕a)=1.7

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Figure 5

The residual radial stress component σrrR(r) for realistic autofrettage

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Figure 6

The residual hoop and meridional stress components σθθrR(r)=σφφR(r) for realistic autofrettage

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