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Research Papers: Design and Analysis

# An Analytical Framework for the Solution of Autofrettaged Tubes Under Constant Axial Strain Condition

[+] Author and Article Information
E. Hosseinian

School of Mechanical Engineering, Sharif University of Technology, P.O. Box 11155-9567, Tehran, Iranehs@mech.sharif.edu

G. H. Farrahi

School of Mechanical Engineering, Sharif University of Technology, P.O. Box 11155-9567, Tehran, Iranfarrahi@sharif.edu

M. R. Movahhedy

School of Mechanical Engineering, Sharif University of Technology, P.O. Box 11155-9567, Tehran, Iranmovahhed@sharif.edu

J. Pressure Vessel Technol 131(6), 061201 (Sep 23, 2009) (8 pages) doi:10.1115/1.3148082 History: Received August 13, 2008; Revised January 20, 2009; Published September 23, 2009

## Abstract

Autofrettage is a technique for introducing beneficial residual stresses into cylinders. Both analytical and numerical methods are used for the analysis of the autofrettage process. Analytical methods have been presented only for special cases of autofrettage. In this work, an analytical framework for the solution of autofrettaged tubes with constant axial strain conditions is developed. Material behavior is assumed to be incompressible, and two different quadratic polynomials are used for strain hardening in loading and unloading. Clearly, elastic perfectly plastic and linear hardening materials are the special cases of this general model. This quadratic material model is convenient for the description of the behavior of a class of pressure vessel steels such as A723. The Bauschinger effect is assumed fixed, and the total deformation theory based on the von Mises yield criterion is used. An explicit solution for the constant axial strain conditions and its special cases such as plane strain and closed-end conditions is obtained. For an open-end condition, for which the axial force is zero, the presented analytical method leads to a simple numerical solution. Finally, results of the new method are compared with those obtained from other analytical and numerical methods, and excellent agreement is observed. Since the presented method is a general analytical method, it could be used for validation of numerical solutions or analytical solutions for special loading cases.

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## Figures

Figure 1

Figure 2

Stresses at peak of 70% autofrettage( plain strain condition)—comparison between analytical method, Huang’s method, and VMP (incompressible material)

Figure 3

Residual stresses (70% autofrettage and plain strain condition)—comparison between analytical method, Huang’s method, and VMP (incompressible material and fixed unloading profile)

Figure 4

Stresses at peak of 70% autofrettage( open-end condition)—comparison between analytical method and VMP(incompressible material)

Figure 5

Residual stresses (70% autofrettage and open-end condition)—comparison between analytical method and VMP (incompressible material and fixed unloading profile)

Figure 6

Stresses at peak of 70% autofrettage( open-end condition)—comparison between analytical method and VMP(compressible material)

Figure 7

Residual stresses (70% autofrettage and open-end condition)—comparison between analytical method and VMP (compressible material and variable unloading profile)

Figure 8

Normalized autofrettage pressure versus normalized axial strain for given percentage overstrain

Figure 9

Normalized autofrettage pressure versus normalized axial force for given percentage overstrain

Figure 10

Normalized axial force versus normalized axial strain for given percentage overstrain

Figure 11

Normalized bore residual hoop stress versus normalized axial strain for given percentage overstrain

Figure 12

Figure 13

Integrand of Eq. 29 versus general radius for different values of normalized axial strains

Figure 14

Residual of Eq. 29 versus normalized axial strain for given percentage overstrain

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