Instability of plastic flow in the directions of pure shear: I. Theory

Chakrabarti, A.K.; Spretnak, J. W.

doi:10.1007/bf02672293

Cited by 60 publications

(6 citation statements)

References 8 publications

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“…The plot in Figure 6(c) shows the evolution of eq as a function of progressing microdamage. The character of this curve is in agreement with the experimental results obtained by Chakrabarti and Spretnak (1975).…”

Section: Uniaxial Tension For An Isothermal Processsupporting

confidence: 91%

The Numerical Analysis of the Intrinsic Anisotropic Microdamage Evolution in Elasto-Viscoplastic Solids

Glema

Łodygowski

Sumelka

et al. 2008

International Journal of Damage Mechanics

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The objective of the present article is to show the formulation for elastic-viscoplastic material model accounting for intrinsic anisotropic microdamage. The strain-induced anisotropy is described by the evolution of the intrinsic microdamage process — defined by the second-order microdamage tensor. The first step of the possibility of identification procedure (calibration of parameters) are also accounted and illustrated by numerical examples.

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Section: Uniaxial Tension For An Isothermal Processsupporting

confidence: 91%

The Numerical Analysis of the Intrinsic Anisotropic Microdamage Evolution in Elasto-Viscoplastic Solids

Glema

Łodygowski

Sumelka

et al. 2008

International Journal of Damage Mechanics

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“…Due to heat flow considerations, adiabatic instabilities normally occur at very large (ballistic) strain rates, much larger than those examined here. [15] When adiabatic instabilities were previously observed in AISI 4340 steel at moderate strain rates, they were allowed by the very low strain hardening slope of the quenched and tempered steel, [16,17] whereas in the present steel, the strain hardening is comparatively higher. Moreover, due to the same heat flow considerations, adiabatic instabilities should be favored by increasing strain rates, [15] whereas in the present case, the opposite holds.…”

Section: Discussionmentioning

confidence: 96%

“…Chakrabarti and Spretnak [15] showed that PLs (other than necking) as a general rule can occur when the following constitutive equation is satisfied: @r @e de þ @r @ _ e d_ e þ @r @T dT 0…”

Section: Discussionmentioning

confidence: 99%

Plastic Localization Phenomena in a Mn-Alloyed Austenitic Steel

Scavino

D’Aiuto

Matteis

et al. 2010

Metall Mater Trans A

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A 0.5 wt pct C, 22 wt pct Mn austenitic steel, recently proposed for fabricating automotive body structures by cold sheet forming, exhibits plastic localizations (PLs) during uniaxial tensile tests, yet showing a favorable overall strength and ductility. No localization happens during biaxial Erichsen cupping tests. Full-thickness tensile and Erichsen specimens, cut from as-produced steel sheets, were polished and tested at different strain rates. During the tensile tests, the PL phenomena consist first of macroscopic deformation bands traveling along the tensile axis, and then of a series of successive stationary deformation bands, each adjacent to the preceding ones; both types of bands involve the full specimen width and yield a macroscopically observable surface relief. No comparable surface relief was observed during the standard Erichsen tests. Because the stress state is known to influence PL phenomena, reduced-width Erichsen tests were performed on polished sheet specimens, in order to explore the transition from biaxial to uniaxial loading; surface relief lines were observed on a 20-mm-wide specimen, but not on wider ones.

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“…The deformation field in the gage section of the specimen on applying a uniaxial tensile load is described as plane stress/plane strain. The extent of these states depends on the width to thickness ratio of the specimen (13). The results of Valkonen indicate that the above steel shows a multiple-n type behavior.…”

Section: Introductionmentioning

confidence: 90%

Deformation behavior of a alpha brass in plane stress/plane strain

Sundaram

Rodriguez

Santiago

1994

Scripta Metallurgica et Materialia

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IntroductionGenerally a simple power law ~ = K E" (where K and n are empirical constants called the strength coefficient and the work hardening coefficient respectively) is used to describe plastic stress-strain dependence of deformable metals (1,2). This equation was employed by Low (3) to describe the uniaxial tensile behavior of an annealed 70/30 brass. The slope of the corresponding double logarithmic true stress-true strain plot gives a single value of n. However, this fit is not always adequate. Geil and Carwile (4) reported a deviation in the linearity of the double logarithmic plot for steel. Two sets of K and n values were used to describe the stress-strain relationship in a spheroidized hypo-eutectoid steel by Wilson and Konnan (5). Various reasons, such as grain size effects, cementite particle distribution, cell formation, stacking fault energy, etc. were proposed to rationalize the double-n behavior (6-9). Ollilainen reported a triple-n behavior for a decarburized steel (10).A study by Valkonen (11) of the mechanical behavior of a Clausing specimen was carried out for an AISI 1090 spheroidized steel. A good dimensional description of the Clausing specimen is given elsewhere (12). Fig. 1 shows the geometry and dimensions of the specimen. The deformation field in the gage section of the specimen on applying a uniaxial tensile load is described as plane stress/plane strain. The extent of these states depends on the width to thickness ratio of the specimen (13). The results of Valkonen indicate that the above steel shows a multiple-n type behavior. Three slope discontinuities were presented in the double logarithmic true stress vs. true strain plot. Concurrently, five slope discontinuities were presented in a "unified" plot of the double logarithmic engineering stress vs. true strain plot. Various reasons, relating to both material and constitutive properties, were hypothesized as to the appearance of these discontinuities. Saturation back stress at second phase carbide particles soon after yielding, self-development of a lateral constraint, the nucleation and growth of incipient shear bands etc. were given as plausible reasons.Although the observation of multiple-n behavior has been previously reported in many cases (4-11), it has not found wide acceptance, probably because of a lack of concrete experimental evidence. This work was undertaken in order to investigate further the presence of these slope discontinuities and determine possible reasons for their appearance. 70/30 c~ brass was chosen as the test material, ct brass also shows a propensity for the formation of shear bands. The Clausing specimen was chosen because of its plane stress/plane strain deformation field, its familiarity with the current investigators and its amenability, because of geometry and size, to be tested in smaller capacity mechanical testing machines. Exoerimental ProcedureThe Clausing specimens were machined from a 50.8 mm by 50.8 mm cross-section hot rolled 70/30 cx brass bar. The specimens were machined in such a way tha...

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Instability of plastic flow in the directions of pure shear: I. Theory

Cited by 60 publications

References 8 publications

The Numerical Analysis of the Intrinsic Anisotropic Microdamage Evolution in Elasto-Viscoplastic Solids

The Numerical Analysis of the Intrinsic Anisotropic Microdamage Evolution in Elasto-Viscoplastic Solids

Plastic Localization Phenomena in a Mn-Alloyed Austenitic Steel

Deformation behavior of a alpha brass in plane stress/plane strain

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