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A theory for swaging of discs and lugs

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Abstract

A practical theory for swaging bored holes within plates and cylinders is proposed which can take into account work-hardening in the presence of small plastic strains based upon equivalent stress-strain data. With the appropriate choice of yield function, this theory applies to the swaging of both thin and thick plates under respective plane stress and plane strain conditions. The theory can be adapted further to the autofrettage of open and closed-ended, thick-walled cylinders where similar plane deformations conditions apply. Here swaging refers to the practice in which an oversized plug or sphere is forced into the bore thereby expanding it permanently to leave a residual circumferential compression in the bore material upon removal of the expanding tool. A similar effect results from applying an initial over-pressure to a long thick-walled cylinder in an autofrettage process. Both treatments are employed to enhance the fatigue resistance when the service loading upon the disc or cylinder amounts to a cyclic, circumferential tension within its bore. Strain gauges bonded to the entry face of the plate are used to monitor the circumferential and radial strain distributions both during and after the swaging process. Experimental results presented for swaging of thin and thin annular discs in aluminium alloy show that the measured residual strain distributions concord with the theory for large discs with a 10/1 diameter ratio. The agreement is less satisfactory with the loss in axial symmetry for parallel-sided lugs with a width to hole diameter ratio of 4/1.

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Abbreviations

α :

Plug’s semi-taper.

ε, dε :

Principal strain and strain increment.

ε P :

Equivalent plastic strain.

σ i :

Principal stress.

\(\bar{\sigma}\) :

Equivalent stress.

a,b :

Cylinder inside and outside radii.

A :

Elastic constant.

B :

Flow law constant.

c :

Elastic-plastic interface radius.

E :

Elastic constants.

F :

Axial force.

k :

Shear yield stress.

K :

Cylinder diameter ratio (=b/a).

n :

Hollomon hardening exponent.

p :

Internal pressure.

r :

Disc radius.

\(\bar{S}\) :

Normalised equivalent stress \(=(\bar{\sigma}/Y)\).

Y :

Uniaxial yield stress.

k :

Shear yield stress.

E :

Elastic recovery.

c :

Interface radius.

I :

Initial yield.

M :

Mises-based.

R :

Residual.

i :

Principal directions (i=1,2,3).

r, θ, z :

Cylindrical co-ordinate directions.

T :

Tresca-based.

E,P :

Elastic and plastic strain.

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  1. School of Engineering and Design, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK

    D. W. A. Rees

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Rees, D.W.A. A theory for swaging of discs and lugs. Meccanica 46, 1213–1237 (2011). https://doi.org/10.1007/s11012-010-9377-x

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