Residual Elastic Strains in Autofrettaged Tubes: Elastic–Ideally Plastic Model Analysis

[+] Author and Article Information
Alexander M. Korsunsky

Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UKalexander.korsunsky@eng.ox.ac.uk

J. Eng. Mater. Technol 129(1), 77-81 (Jun 05, 2006) (5 pages) doi:10.1115/1.2400267 History: Received September 10, 2005; Revised June 05, 2006

Autofrettage is a treatment process that uses plastic deformation to create a state of permanent residual stress within thick-walled tubes by pressurizing them beyond the elastic limit. The present paper presents explicit analytical formulas for residual elastic strains within the tube wall derived on the basis of the classical elastic–ideally plastic solution. Then the problem is addressed of rational interpretation of the radial and hoop residual elastic strains measured at a fixed number of points. To this end, the mismatch between the experimental measurements and theoretical predictions of the residual elastic strains is represented in the form of quadratic functional, J, the minimum of which is sought in terms of the problem parameters, namely, the material yield stress, σY, and the radial position of the elastic-plastic boundary, c. It is shown that J shows an approximately parabolic variation in terms of either parameter when the other is fixed, and that therefore the global minimum of J can be readily found. This procedure is implemented and applied to a set of experimental data on neutron diffraction measurements (Venter, A.M., de Swardt, R.R., and Kyriacou, S.,2000, J. Strain Anal., 35, pp. 459–469). In conclusion, further applications of this family of interpretation approaches are discussed.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 6

The comparison between the measured and predicted residual elastic strains (experimental data of (8)). Continuous curves correspond to the predictions, whereas the markers indicate experimental results.

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Figure 7

Illustration of the shape of the surface defined by the function J=J(c,σY) over the (c,σY) plane

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Figure 5

A possible arrangement of autofrettaged tube slices with respect to the incident and diffracted beams. The dashed lines indicate the incident and diffracted beams; the arrow shows the scattering vector indicates the orientation of the strain component being measured (radial in the present example).

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Figure 4

Elastic–ideally plastic model predictions for residual elastic strains

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Figure 3

Elastic–ideally plastic model predictions for stress distributions after unloading

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Figure 2

Elastic–ideally plastic model predictions for stress distributions under maximum internal pressure loading

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Figure 1

Schematic illustration for the description of axisymmetric deformation of a thick-walled tube of internal radius a and external radius b under internal pressure p. Parameter c indicated the radius of the elastic-plastic boundary, and q is the pressure transmitted across this interface.




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