On stress collapse in adiabatic shear bands

Wright, Thomas W.; Walter, J.

doi:10.1016/0022-5096(87)90051-2

Cited by 206 publications

(95 citation statements)

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“…Even though each one of the three materials exhibits softening in the sense that the eective stress decreases with an increase in the eective plastic strain, the initial rate of softening is greatest for the homogeneous WHA alloy. Using perturbation analysis, Wright and Walter (1987) have shown that this initial rate of softening strongly in¯uences the initiation of a shear band. We note that even though values of and in the thermal softening function are same for the Fe±Ni±W particles and the homogeneous WHA alloy, the initial slopes of the softening part of the stress±strain curves are dierent.…”

Section: Computation and Discussion Of Resultsmentioning

confidence: 99%

“…This dierence in behaviors could be due to the fact that for the values of material parameters used, the initial rate of softening is highest for the homogeneous alloy. Wright and Walter (1987) have proposed that the initial slope of the thermal softening function strongly in¯uences the initiation of a shear band. For the rod modeled as a mixture of Fe±Ni±W and W particles, the deformations of softer Fe±Ni±W particles may introduce sucient perturbation to incite localization of deformations at a point on or near the rod's mantle.…”

Section: Discussionmentioning

confidence: 99%

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Adiabatic shear bands in the Taylor impact test for a WHA rod

Stevens

Batra

1998

International Journal of Plasticity

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Section: Computation and Discussion Of Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Adiabatic shear bands in the Taylor impact test for a WHA rod

Stevens

Batra

1998

International Journal of Plasticity

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“…A number of studies of shear band formation caused by thermal softening in metals indicate that strains must be substantial, 10-50%, before shear bands form (6,9,11).…”

Section: Discussionmentioning

confidence: 99%

“…Localization and shear band formation was only observed at average strain rates less than lo00 s-' for the model studied in this work. At sufficiently high strain rate in a metal, above lo5 s-*, Wright and Walter (11) noted that shear band formation was inhibited due to inertial effects. The shear bands observed to form in this work are about two orders of magnitude larger than those in (1 1).…”

Section: Discussionmentioning

confidence: 99%

Shear band formation in plastic bonded explosive (PBX)

Dey

Johnson

1998

AIP Conference Proceedings

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“…1. Shear bands are often precursors to rupture and their study has attracted considerable attention in the mechanics and mathematics literature including experimental works [4,9], mechanical modeling and linearized analysis studies ( [3,8,12,17,19] and references therein), asymptotic analysis [6,18], nonlinear analysis [5,13,14,2], and numerical investigations [16,7,1].…”

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confidence: 99%

Localization and Shear Bands in High Strain-Rate Plasticity

Katsaounis

Tzavaras

2011

Nonlinear Conservation Laws and Applications

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Abstract. This article is devoted to the explanation of the onset of localization and the formation of shear bands in high strain-rate plasticity of metals. We employ the Arrhenius constitutive model and show Hadamard instability for the linearized problem. For the nonlinear model, using an asymptotic procedure motivated by the theory of relaxation and the Chapman-Enskog expansion, we derive an effective equation for the evolution of the strain rate, which is backward parabolic with a small stabilizing fourth order correction. We construct self-similar solutions that describe the self-organization into a localized solution starting from well prepared data.Key words. shear bands, localization, effective equations, self-similarity.1. Introduction. The phenomenon of shear strain localization appears in several instances of material instability in mechanics. It is associated with ill-posedness of an underlying initial value problem, what has coined the term Hadamard-instability for its description in the mechanics literature. It should however be noted that while Hadamard instability indicates the catastrophic growth of oscillations around a mean state, it does not by itself explain the formation of coherent structures typically observed in localization. The latter is a nonlinear effect that will be the center-stage of the present study.The mathematical theory of localization in high strain rate plasticity aims to understand a destabilizing feedback mechanism proposed in [20,3] and deemed responsible for formation of shear band. It poses analytical challenges at the interface of dynamical systems theory and (small viscosity) parabolic regularizations for ill-posed problems. The onset of localization may be decomposed into two stages. At the first stage (a) one aims to determine whether a Hadamard-type instability is at play for a linearized problem. The second stage (b) requires to understand how the Hadamard instability interacts with the nonlinear features of the problem to form a localized coherent state, associated to a shear band. The latter is a challenging problem in the realm of nonlinear analysis. In this survey we draw material from [10,11,1] and focus on the Arrhenius law as a paradigm to describe the sequence of events occurring in the process of localization.

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On stress collapse in adiabatic shear bands

Cited by 206 publications

References 10 publications

Adiabatic shear bands in the Taylor impact test for a WHA rod

Adiabatic shear bands in the Taylor impact test for a WHA rod

Shear band formation in plastic bonded explosive (PBX)

Localization and Shear Bands in High Strain-Rate Plasticity

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