Studies of Elastic-Plastic Instabilities

Analyses of plastic instabilities are reviewed, with focus on results in structural mechanics as well as continuum mechanics. First the basic theories for bifurcation and post-bifurcation behavior are briefly presented. Then, localization of plastic flow is discussed, including shear band formation in solids, localized necking in biaxially stretched metal sheets, and the analogous phenomenon of buckling localization in structures. Also some recent results for cavitation instabilities in elastic-plastic solids are reviewed.

Download Full-text

Effects of Crystallographic Texture on Plastic Flow Localization

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.340-341.211 ◽

2007 ◽

Vol 340-341 ◽

pp. 211-216

Author(s):

Mitsutoshi Kuroda

Keyword(s):

Shear Band ◽

Plane Strain ◽

Plastic Flow ◽

Texture Component ◽

Three Dimensional ◽

Cube Texture ◽

Shear Band Formation ◽

Flow Localization ◽

Band Formation ◽

Plastic Flow Localization

In this study, effects of typical texture components observed in rolled aluminum alloy sheets (i.e. Copper, Brass, S, Cube and Goss texture components) on plastic flow localization are studied. The material response is described by a generalized Taylor-type polycrystal model, in which each grain is characterized in terms of an elastic-viscoplastic continuum slip constitutive relation. First, forming limits of thin sheet set by sheet necking are predicted using a Marciniak–Kuczynski (M–K-) type approach. It is shown that only the Cube texture component yields forming limits higher than that for a random texture in the biaxial stretch range. Next, three-dimensional shear band analyses are performed, using a three-dimensional version of M–K-type model, but the overall deformation mode is restricted to a plane strain state. From this simple model analysis, two important quantities regarding shear band formation are obtained: i.e. the critical strain at the onset of shear banding and the corresponding orientation of shear band. It is concluded that the Cube texture component is said to be a shear band free texture, while some texture components exhibit significantly low resistance to shear band formation. Finally, shear band developments in plane strain pure bending of sheet specimens with the typical textures are studied.

Download Full-text

A Mechanism for Shear Band Formation in the High Strain-Rate Torsion Test

Journal of Applied Mechanics ◽

10.1115/1.2897649 ◽

1990 ◽

Vol 57 (4) ◽

pp. 836-844 ◽

Cited By ~ 21

Author(s):

Timothy J. Burns

Keyword(s):

Shear Band ◽

High Strain Rate ◽

Strain Rate ◽

Plastic Flow ◽

Moving Boundary ◽

High Strain ◽

Numerical Study ◽

Torsion Test ◽

Shear Band Formation ◽

Band Formation

A numerical study of a one-dimensional model of the high strain-rate torsion test shows that a moving boundary of rigid unloading, starting from the ends of the thin-walled tubular specimen, is a plausible mechanism for adiabatic shear band formation during the test. Even though the dimensionless thermal diffusivity parameter is very small, the moving boundary is due to heat transfer from the specimen through its ends, which are assumed to be isothermal heat sinks. The mathematical model is based on a physical model of thermoelastic-plastic flow and a phenomenological Arrhenius model for the plastic flow surface. The numerical technique used is the semi-discretization method of lines.

Download Full-text