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TECHNICAL PAPERS

# Residual Elastic Strains in Autofrettaged Tubes: Variational Analysis by the Eigenstrain Finite Element Method

[+] 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

Gabriel M. Regino

Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK

In the case of elastic–ideally plastic deformation closer analysis of autofrettage in thick tubes shows that plastic strain distribution has the form $ε*(r)=A−D∕r2$. This distribution, however, may also be closely approximated by a parabolic distribution.

J. Appl. Mech 74(4), 717-722 (Aug 15, 2006) (6 pages) doi:10.1115/1.2711222 History: Received September 30, 2005; Revised August 15, 2006

## Abstract

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 a novel analytical approach to the interpretation of residual elastic strain measurements within slices extracted from autofrettaged tubes. The central postulate of the approach presented here is that the observed residual stress and residual elastic strains are secondary parameters, in the sense that they arise in response to the introduction of permanent inelastic strains (eigenstrains) by plastic deformation. The problem of determining the underlying distribution of eigenstrains is solved here by means of a variational procedure for optimal matching of the eigenstrain finite element model to the observed residual strains reported in the literature by Venter, 2000, J. Strain Anal., 35, p. 459. The eigenstrain distributions are found to be particularly simple, given by one-sided parabolas. The relationship between the measured residual strains within a thin slice to those in a complete tube is discussed.

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## Figures

Figure 5

Radial residual elastic strain in specimen C: experimental measurements (markers) and eigenstrain model prediction (continuous curve)

Figure 6

Hoop residual elastic strain in specimen C: experimental measurements (markers) and eigenstrain model prediction (continuous curve)

Figure 7

Eigenstrain profile in specimen B: the distribution determined by variational eigenstrain analysis (markers) and a parabolic fit (dashed curve)

Figure 8

Eigenstrain profile in specimen C: the distribution determined by variational eigenstrain analysis (markers) and a parabolic fit (dashed curve)

Figure 4

Hoop residual elastic strain in specimen B: experimental measurements (markers) and eigenstrain model prediction (continuous curve)

Figure 3

Radial residual elastic strain in specimen B: experimental measurements (markers) and eigenstrain model prediction (continuous curve).

Figure 2

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 that indicates the orientation of the strain component being measured (radial in the present example).

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.

## Errata

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