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Shear band

About: Shear band is a research topic. Over the lifetime, 4683 publications have been published within this topic receiving 151316 citations. The topic is also known as: Localization of deformation.


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TL;DR: In this paper, the authors investigated the hypothesis that localization of deformation into a shear band may be considered a result of an instability in the constitutive description of homogeneous deformation.
Abstract: T his paper investigates the hypothesis that localization of deformation into a shear band may be considered a result of an instability in the constitutive description of homogeneous deformation. General conditions for a bifurcation, corresponding to the localization of deformation into a planar band, are derived. Although the analysis is general and applications to other localization phenomena are noted, the constitutive relations which are examined in application of the criterion for localization are intended to model the behavior of brittle rock masses under compressive principal stresses. These relations are strongly pressure-sensitive since inelasticity results from frictional sliding on an array of fissures; the resulting inelastic response is dilatant, owing to uplift in sliding at asperities and to local tensile cracking from fissure tips. The appropriate constitutive descriptions involve non-normality of plastic strain increments to the yield hyper-surface. Also, it is argued that the subsequent yield surfaces will develop a vertex-like structure. Both of these features are shown to be destabilizing and to strongly influence the resulting predictions for localization by comparison to predictions based on classical plasticity idealizations, involving normality and smooth yield surfaces. These results seem widely applicable to discussions of the inception of rupture as a constitutive instability.

2,411 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of microscopic voids on the failure mechanism of a ductile material is investigated by considering an elastic-plastic medium containing a boubly periodic array of circular cylindrical voids.
Abstract: The effect of microscopic voids on the failure mechanism of a ductile material is investigated by considering an elastic-plastic medium containing a boubly periodic array of circular cylindrical voids. For this voided material under uniaxial or biaxial plane strain tension the state of stresses and deformations is determined numerically. Bifurcation away from the fundamental state of deformation is analysed with special interest in a repetitive pattern that represents the state of deformation inside a shear band. Both in the fundamental state and in the bifurcation analysis the interaction between voids and the details of the stress distribution around voids are fully accounted for. Comparison is made with the shear band instabilities predicted by a continuum model of a ductile porous medium. Based on the numerical results an adjustment is suggested for the approximate yield condition in this model of dilatant, pressure sensitive plastic behaviour.

2,021 citations

Journal ArticleDOI
TL;DR: Under unconstrained mechanical loading organized shear band patterns develop throughout the sample, which results in a dramatic increase in the plastic strain to failure, impact resistance, and toughness of the metallic glass.
Abstract: Results are presented for a ductile metal reinforced bulk metallic glass matrix composite based on glass forming compositions in the Zr-Ti-Cu-Ni-Be system. Primary dendrite growth and solute partitioning in the molten state yields a microstructure consisting of a ductile crystalline Ti-Zr-Nb b phase, with bcc structure, in a Zr-Ti-Nb-Cu-Ni-Be bulk metallic glass matrix. Under unconstrained mechanical loading organized shear band patterns develop throughout the sample. This results in a dramatic increase in the plastic strain to failure, impact resistance, and toughness of the metallic glass. PACS numbers: 81.40. – z, 81.05.Kf Zr41.2Ti13.8Cu12.5Ni10Be22.5 (V1) exhibits an exceptional bulk metallic glass (BMG) forming ability that has motivated investigations of its mechanical behavior [1– 3]. This alloy exhibits a 1.9 GPa tensile yield strength, and a 2% elastic strain prior to failure under tensile or compressive loading. However, as in all metallic glasses, V1 specimens loaded in a state of uniaxial or plane stress fail catastrophically on one dominant shear band and show little global plasticity. Specimens loaded under constrained geometries (plane strain) fail in an elastic, perfectly plastic manner by the generation of multiple shear bands. Multiple shear bands are observed when the catastrophic instability is avoided via mechanical constraint, e.g., in uniaxial compression, bending, rolling, and under localized indentation. This behavior under deformation has limited the application of bulk metallic glasses as an engineering material. This Letter presents results for a new class of ductile metal reinforced BMG matrix composites prepared via in situ processing. Under loading, the two-phase microstructure leads to spatial variations in elastic properties as well as the conditions for yielding, the ductile phase having a lower yield strain. The initiation and propagation of shear bands is controlled by the scale and geometry of the ductile phase dispersion with the result that deformation occurs through the development of highly organized patterns of regularly spaced shear bands distributed uniformly throughout the sample. The compositions in the Zr-Ti-Cu-Ni-Be system are compactly written in terms of a pseudoternary Zr-Ti-X phase diagram, where X represents the moiety Be9Cu5Ni4, characteristic of Zr41.2Ti13.8Cu12.5Ni10Be22.5. Results presented here are for alloys of the form Zr1002x2zTixMz1002yXy, where M is an element that stabilizes the crystalline b phase in Ti- or Zr-based alloys. The inset in Fig. 1 shows the x-ray diffraction pattern for the nominal composition Zr75Ti18.34Nb6.6675X25; i.e., an alloy with M Nb, z 6.66, x 18.34, and y 25. The diffraction pattern was obtained with an INEL diffractometer (Co-Ka radiation) on the cross sectioned surface of a 25 g arc melted rod of roughly cylindrical diameter, f 1 cm. The peaks shown [with (hkl) values labeled] are due to the bcc phase. A Nelson-Riley extrapolation yields a lattice parameter a 3.496 A [4]. Upon cooling from the high temperature melt, the alloy undergoes partial crystallization by nucleation and subsequent dendritic growth of the b phase in the remaining liquid. The remaining liquid subsequently freezes to the glassy state producing a twophase microstructure containing b-phase dendrites in a glass matrix. The final microstructure of a chemically etched specimen is shown in the scanning electron microscopy (SEM) image of Fig. 1. SEM electron microprobe analysis gives the average composition for the b-phase dendrites (light phase in Fig. 1) to be Zr 71Ti16.3Nb10Cu1.8Ni0.9. Under the assumption that all of the Be in the alloy is partitioned into the matrix we estimate that the average composition of the amorphous matrix (dark phase) is Zr47Ti12.9Nb2.8Cu11Ni9.6Be16.7. Both are quoted

1,365 citations

Journal ArticleDOI
TL;DR: In this paper, a planar double slip model was proposed to analyze the effect of material rate sensitivity on the formation of conjugate slip bands in planar planar crystal geometries.

1,327 citations

Journal ArticleDOI
28 Feb 2008-Nature
TL;DR: T titanium–zirconium-based BMG composites with room-temperature tensile ductility exceeding 10 per cent, yield strengths of 1.2–1.5 GPa, K1C up to ∼170 MPa m1/2, and fracture energies for crack propagation as high as G1C ≈ 340 kJ’m-2.2 were reported.
Abstract: Metallic glasses have been the subject of intense scientific study since the 1960s, owing to their unique properties such as high strength, large elastic limit, high hardness, and amorphous microstructure. However, bulk metallic glasses have not been used in the high strength structural applications for which they have so much potential, owing to a highly localized failure mechanism that results in catastrophic failure during unconfined loading. In this thesis, bulk metallic glass matrix composites are designed with the combined benefits of high yield strengths and tensile ductility. This milestone is achieved by first investigating the length scale of the highly localized deformation, known as shear bands, that governs fracture in all metallic glasses. Under unconfined loading, a shear band grows to a certain length that is dependent on the fracture toughness of the glass before a crack nucleates and fracture occurs. Increasing the fracture toughness and ductility involves adding microstructural stabilization techniques that prevent shear bands from lengthening and promotes formation of multiple shear bands. To accomplish this, we develop in-situ formed bulk metallic glass matrix-composites with soft crystalline dendrites whose size and distribution are controlled through a novel semi-solid processing technique. The new alloys have a dramatically increased room-temperature ductility and a fracture toughness that appears to be similar to the toughest steels. Owing to their low modulus, the composites are therefore among the toughest known materials, a claim that has recently been confirmed independently by a fracture mechanics group. We extend our toughening strategy to a titanium-vanadium-based glass-dendrite composite system with density as low as 4.97 g/cm3. The new low-density composites rival the mechanical properties of the best structural crystalline Ti alloys. We demonstrate new processing techniques available in the highly toughened composites: room temperature cold rolling, work hardening, and thermoplastic forming. This thesis is a proven road map for developing metallic glass composites into real structural engineering materials.

1,324 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202363
2022159
2021222
2020178
2019156
2018197