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Design and Analysis

An Analytical Solution of Residual Stresses for Shrink-Fit Two-Layer Cylinders After Autofrettage Based on Actual Material Behavior

[+] Author and Article Information
Yuan Gexia

Associate Professor
School of Mechanical and Precision Instrument
Engineering,
Xi’an University of Technology,
Xi’an 710048, China;
Mechanical and Electrical Institute,
Baoji University of Arts and Sciences,
Baoji 721007, China
e-mail:  yuangexia2006@126.com

Liu Hongzhao

Professor
School of Mechanical and Precision Instrument
Engineering,
Xi’an University of Technology,
Xi’an 710048, China
e-mail: Liuhzxalg@163.com

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received May 11, 2011; final manuscript received February 6, 2012; published online November 6, 2012. Editor: G. E. Otto Widera.

J. Pressure Vessel Technol 134(6), 061209 (Nov 06, 2012) (8 pages) doi:10.1115/1.4006121 History: Received May 11, 2011; Revised February 06, 2012

To enhance the pressure capacity and the life of a pressure vessel, different processes such as shrink-fit and autofrettage are usually employed. For autofrettaged and shrink-fit multilayer cylinders, numerical solutions for determining the residual stress distribution have been reported. However, few studies about the analytical method are available. In this study, an analytical solution was presented for shrink-fit two-layer cylinders after autofrettage based on the actual tensile-compressive stress–strain curve of material. The new analytical method accurately predicted a residual stress distribution, and it could be used to design two-layer compound cylinders. In this method, unloading and shrink-fitting were considered as a simultaneous operation for an inner cylinder, allowing for a simple and accurate analysis. Some significant factors were taken into account, including the nonlinear behavior of an original autofrettaged inner layer in the shrink-fitting process and a material’s different unloading behavior at different maximum tensile affects back-yielding. The results of the proposed method were in excellent agreement with the results from the simulation performed by ansys. The results indicated that an increased shrink-fit pressure expanded the back-yielding zone of the inner cylinders, and did not affect the back-yielding zone of the outer cylinders. The optimum percentages overstrain depend on the working pressure when the shrink-fit pressure, cylinder size, and material are defined, and inner and outer cylinders have different optimum percentages overstrain.

Copyright © 2012 by ASME
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Figures

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Fig. 1

General material tensile-compressive stress–strain curve

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Fig. 2

Loading history of inner cylinders

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Fig. 3

Loading history of outer cylinders

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Fig. 4

Force diagram of the unloading and shrink-fitting inner cylinder

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Fig. 5

Bilinear material model

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Fig. 6

Comparison of analytical solution and simulation: (a) inner cylinder and (b) outer cylinder

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Fig. 7

Engineering stress–strain plots of A723-1130 MPa [21]

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Fig. 8

Unloading behavior at four different maximum tensile strains (i.e., 0.01, 0.02, 0.03, and 0.04)

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Fig. 9

Adjustment of the parameters in the unloading curves depending on the maximum strain during tension

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Fig. 10

Residual stresses of Af = 10% for inner cylinder

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Fig. 11

Residual stresses of Af = 50% for inner cylinder

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Fig. 12

Residual stresses of Af = 90% for inner cylinder

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Fig. 13

Residual stresses of Af = 90% for outer cylinder

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Fig. 14

Effective stress curves of two-layer cylinder under pw = 700 MPa

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Fig. 15

Effective stress curves of two-layer cylinder under pw = 880 MPa

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