Analysis of the inverse Swift effect using a rate-sensitive polycrystal model

doi:10.1016/0045-7825(93)90050-8

Computer Methods in Applied Mechanics and Engineering

Volume 103, Issues 1–2, March 1993, Pages 291-313

https://doi.org/10.1016/0045-7825(93)90050-8 Get rights and content

Abstract

Complementary to the Swift effect, namely the elongation of specimens during large strain elastic-plastic torsion with free ends, the inverse Swift effect refers to the free twisting of specimens during uniaxial tension after a previous large strain twisting history. In this paper, this intriguing phenomenon in solid cylindrical bars or wires is studied numerically using special purpose finite elements that allow for an accurate and efficient analysis of large strain torsion and simultaneous tension problems. The constitutive model used is a micromechanics polycrystal model based on a large strain crystal plasticity model accounting for rate-sensitive crystallographic slip in face-centered cubic crystals. The description of crystallographic texture development during all stages of the deformation process is inherent in the model. The influence of the material strain-rate sensitivity on the inverse Swift effect is investigated for varying amounts of shear strain imposed during pre-twisting. The simulations are compared with experimental results for copper wires reported in the literature. The marked sensitivity to initial textures as well as a number of constitutive assumptions are discussed in connection with the observed differences between theoretical predictions and experimental observations.

References (29)

K.W. Neale et al.
Large strain shear and torsion of rate-sensitive FCC-polycrystals
Internat. J. Plast.
(1990)
R.J. Asaro et al.
Texture development and strain hardening in rate dependent polycrystals
Acta Metall.
(1985)
D. Peirce et al.
Material rate dependence and localized deformation in crystalline solids
Acta Metall.
(1983)
J.R. Rice
Inelastic constitutive relations for solids: An internal variable theory and its applications to metal plasticity
J. Mech. Phys. Solids
(1971)
R.J. Asaro et al.
Strain localization in ductile single crystals
J. Mech. Phys. Solids
(1977)
S.C. Shrivastava et al.
Equivalent strain in large deformation torsion testing: Theoretical and practical considerations
J. Mech. Phys. Solids
(1982)
K.K. Mathur et al.
On modeling the development of crystallographic texture in bulk forming processes
Internat. J. Plast.
(1989)
E. Van der Giessen et al.
On the effect of plastic spin on large strain elastic-plastic torsion of solid bars
Internat. J. Plast.
(1992)
F. Montheillet et al.
Relation between axial stresses and texture development during torsion testing: A simplified theory
Acta Metall.
(1985)
P. Van Houtte et al.
Considerations on the crystal and the strain symmetry in the calculation of deformation textures with the Taylor theory
Mater. Sci. Engrg.
(1976)

A. Molinari et al.

A self-consistent approach of the large deformation polycrystal viscoplasticity

Acta Metall.

(1987)

H.W. Swift

Length changes in metals under torsional overstrain

Engineering

(1947)

J. Gil-Sevillano et al.

Deutung der Schertexturen mit Hilfe der Taylor-Analyse

Z. Metallkunde

(1975)

S. Harren et al.

Analysis of large-strain shear in rate-dependent face-centered cubic polycrystals: Correlation of micro- and macromechanics

Philos. Trans. Roy. Soc. London Ser.

(1989)

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Analysis of the inverse Swift effect using a rate-sensitive polycrystal model

Abstract

Internat. J. Plast.

Acta Metall.

Acta Metall.

J. Mech. Phys. Solids

J. Mech. Phys. Solids

J. Mech. Phys. Solids

Internat. J. Plast.

Internat. J. Plast.

Acta Metall.

Mater. Sci. Engrg.

Acta Metall.

Length changes in metals under torsional overstrain

Engineering

Deutung der Schertexturen mit Hilfe der Taylor-Analyse

Z. Metallkunde

Analysis of large-strain shear in rate-dependent face-centered cubic polycrystals: Correlation of micro- and macromechanics

Philos. Trans. Roy. Soc. London Ser.