scholarly journals Emergence of Shear Bands in Confined Granular Systems: Singularity of the q-Statistics

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 862 ◽  
Author(s):  
Léo Viallon-Galiner ◽  
Gaël Combe ◽  
Vincent Richefeu ◽  
Allbens Picardi Faria-Atman
Keyword(s):  
Shear Band ◽  
Granular Media ◽  
Experimental Validation ◽  
Scaling Law ◽  
Shear Bands ◽  
Percolation Cluster ◽  
Granular Systems ◽  
Original Approach ◽  
Exact Point ◽  
Confined System

The statistics of grain displacements probability distribution function (pdf) during the shear of a granular medium displays an unusual dependence with the shear increment upscaling as recently evinced (see “experimental validation of a nonextensive scaling law in confined granular media”). Basically, the pdf of grain displacements has clear nonextensive (q-Gaussian) features at small scales, but approaches to Gaussian characteristics at large shear window scales—the granulence effect. Here, we extend this analysis studying a larger system (more grains considered in the experimental setup), which exhibits a severe shear band fault during the macroscopic straining. We calculate the pdf of grain displacements and the dependency of the q-statistics with the shear increment. This analysis has shown a singular behavior of q at large scales, displaying a non-monotonic dependence with the shear increment. By means of an independent image analysis, we demonstrate that this singular non-monotonicity could be associated with the emergence of a shear band within the confined system. We show that the exact point where the q-value inverts its tendency coincides with the emergence of a giant percolation cluster along the system, caused by the shear band. We believe that this original approach using Statistical Mechanics tools to identify shear bands can be a very useful piece to solve the complex puzzle of the rheology of dense granular systems.

scholarly journals Emergence of Shear Bands in Confined Granular Systems: Singularity of the $q$-Statistics

2018 ◽  
Author(s):  
Léo Viallon-Galiner ◽  
Gaël Combe ◽  
Vincent Richefeu ◽  
Allbens Atman Picardi Faria
Keyword(s):  
Shear Band ◽  
Probability Distribution Function ◽  
Shear Bands ◽  
Percolation Cluster ◽  
Granular Systems ◽  
Singular Behavior ◽  
Q Value ◽  
Original Approach ◽  
Exact Point ◽  
Confined System

The statistics of grain displacements probability distribution function (pdf) during the shear of a granular medium displays an unusual dependence with the shear increment upscaling as recently evinced [Phys. Rev. Lett.  115 238301 2015]. Basically, the pdf of grain displacements has clear nonextensive ($q$-Gaussian) features at small scales but approaches to Gaussian characteristics at large shear window scales -- the granulence effect. Here, we extend this analysis studying a larger system (more grains considered in the experimental setup) which exhibits a severe shear band fault during the macroscopic straining. We calculate the pdf of grain displacements and the dependency of the $q$-statistics with the shear increment. This analysis have shown a singular behavior of $q$ at large scales, displaying a non-monotonic dependence with the shear increment. By means of an independent image analysis, we demonstrate that this singular non-monotonicity could be associated with the emergence of a shear band within the confined system. We show that the exact point where the $q$-value inverts its tendency coincides with the emergence of a giant percolation cluster along the system, caused by the shear band. We believe that this original approach using Statistical Mechanics tools to identify shear bands can be a very useful piece to solve the complex puzzle of the rheology of dense granular systems.

Development of shear bands in annular shear granular flows

2002 ◽  
Vol 759 ◽  
Author(s):  
Payman Jalali ◽  
Mo Li
Keyword(s):  
Shear Rate ◽  
Shear Band ◽  
Granular Media ◽  
Shear Bands ◽  
Granular Flows ◽  
Area Fraction ◽  
Entire System ◽  
Local Properties ◽  
System Characteristics ◽  
Solid Area

ABSTRACTUsing hard-disk simulations of relatively dense packs of mono-sized system in an annular Couette geometry the formation of dilute regions inside the granular media, namely shear bands, are investigated. The results represent the influence of entire system characteristics such as solid area fraction and shear rate on the development of shear bands as well as the local properties of grains that cause them to participate in the formation of a shear band. Moreover, simulations have been performed for binary-sized system, which revealed that the formation of such diluted shear bands is unlikely.

scholarly journals Experimental Validation of a Nonextensive Scaling Law in Confined Granular Media

2015 ◽  
Vol 115 (23) ◽  
Author(s):  
Gaël Combe ◽  
Vincent Richefeu ◽  
Marta Stasiak ◽  
Allbens P. F. Atman
Keyword(s):  
Granular Media ◽  
Experimental Validation ◽  
Scaling Law

scholarly journals On the nucleation and growth of kink and shear bands

2013 ◽  
Vol 371 (1993) ◽  
pp. 20120431 ◽  
Author(s):  
G. W. Hunt ◽  
T. J. Dodwell ◽  
J. Hammond
Keyword(s):  
Shear Band ◽  
Granular Media ◽  
Numerical Solutions ◽  
Shear Banding ◽  
Shear Bands ◽  
Nucleation And Growth ◽  
Critical Force ◽  
Periodic State ◽  
Similarities And Differences ◽  
Force Dipole

Similarities and differences between the phenomena of kink banding in compressed layered structures and shear banding in compressed granular media are explored. Simple models are introduced for both, and the focus is directed onto how they can nucleate from the perfectly flat state. A convincing scenario is found for each in which a mode develops from an initial bifurcation into a periodic state, followed by rapid localization under falling load, while retaining decaying but wavy tails. At a certain lower critical load, the tails lose their waviness, and the expected form of the kink or shear band appears. In each case, good numerical evidence is provided for the existence of this form of behaviour. A second potential instability for the layered case is also explored, linked to the appearance of a critical force dipole that overcomes bending stiffness locally at some point along the length. This mode, which should appear with non-wavy decaying tails at the lower of the two critical loads mentioned earlier, proves somewhat elusive. Evidence is found for its existence in the linearized approximation to the layered model, but the search for numerical solutions to the underlying nonlinear equation is hindered by a shortage of suitable boundary conditions.

scholarly journals An Insight into Amorphous Shear Band in Magnetorheological Solid by Atomic Force Microscope

Materials ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4384
Author(s):  
Mohd Aidy Faizal Johari ◽  
Asmawan Mohd Sarman ◽  
Saiful Amri Mazlan ◽  
Ubaidillah U ◽  
Nur Azmah Nordin ◽  
...  
Keyword(s):  
Stress Relaxation ◽  
Shear Band ◽  
Shear Bands ◽  
Test Duration ◽  
Phase Imaging ◽  
Force Microscopy ◽  
Atomic Force ◽  
The Matrix ◽  
Relaxation Stress ◽  
Band Deformation

Micro mechanism consideration is critical for gaining a thorough understanding of amorphous shear band behavior in magnetorheological (MR) solids, particularly those with viscoelastic matrices. Heretofore, the characteristics of shear bands in terms of formation, physical evolution, and response to stress distribution at the localized region have gone largely unnoticed and unexplored. Notwithstanding these limitations, atomic force microscopy (AFM) has been used to explore the nature of shear band deformation in MR materials during stress relaxation. Stress relaxation at a constant low strain of 0.01% and an oscillatory shear of defined test duration played a major role in the creation of the shear band. In this analysis, the localized area of the study defined shear bands as varying in size and dominantly deformed in the matrix with no evidence of inhibition by embedded carbonyl iron particles (CIPs). The association between the shear band and the adjacent zone was further studied using in-phase imaging of AFM tapping mode and demonstrated the presence of localized affected zone around the shear band. Taken together, the results provide important insights into the proposed shear band deformation zone (SBDZ). This study sheds a contemporary light on the contentious issue of amorphous shear band deformation behavior and makes several contributions to the current literature.

Plastic Deformation-Induced Nanocrystalline Aluminum in Al-Based Amorphous Alloys

1993 ◽  
Vol 321 ◽  
Author(s):  
H. Chen ◽  
Y. He ◽  
G. J. Shiflet ◽  
S. J. Poon
Keyword(s):  
Plastic Deformation ◽  
Amorphous Alloy ◽  
Shear Band ◽  
Thin Layer ◽  
Ball Milling ◽  
Direct Observation ◽  
Amorphous Alloys ◽  
Shear Bands ◽  
Amorphous Ribbons ◽  
Nanocrystalline Aluminum

ABSTRACTWe report the first direct observation of crystallization induced in the slipped planes of aluminum based amorphous alloys by bending the amorphous ribbons. Nanometer-sized crystalline precipitates are found exclusively within a thin layer (shear band) in the slipped planes extending across the deformed amorphous alloy ribbons. It is also found that the nanocrystalline aluminum can be produced by ball-Milling. It is likely that local atomic rearrangements within the shear bands create the nanocrystals which appear after plastic deformation.

Dynamic Failure Mechanisms in Beryllium-Bearing Bulk Metallic Glasses

1998 ◽  
Vol 554 ◽  
Author(s):  
David M. Owen ◽  
Ares J. Rosakis ◽  
William L. Johnson
Keyword(s):  
Crack Initiation ◽  
Shear Band ◽  
Metallic Glasses ◽  
Impact Loading ◽  
High Speed ◽  
Failure Mechanisms ◽  
Shear Bands ◽  
Dynamic Crack ◽  
Dynamic Failure ◽  
Asymmetric Impact

AbstractThe understanding of dynamic failure mechanisms in bulk metallic glasses is important for the application of this class of materials to a variety of engineering problems. This is true not only for design environments in which components are subject to high loading rates, but also when components are subjected to quasi-static loading conditions where observations have been made of damage propagation occurring in an unstable, highly dynamic manner. This paper presents preliminary results of a study of the phenomena of dynamic crack initiation and growth as well as the phenomenon of dynamic localization (shear band formation) in a beryllium-bearing bulk metallic glass, Zr41.25Ti13.75Ni10Cu12.75Be22.5. Pre-notched and prefatigued plate specimens were subjected to quasi-static and dynamic three-point bend loading to investigate crack initiation and propagation. Asymmetric impact loading with a gas gun was used to induce dynamic shear band growth. The mechanical fields in the vicinity of the dynamically loaded crack or notch tip were characterized using high-speed optical diagnostic techniques. The results demonstrated a dramatic increase in the crack initiation toughness with loading rate and subsequent crack tip speeds approaching 1000 m s−1. Dynamic crack tip branching was also observed under certain conditions. Shear bands formed readily under asymmetric impact loading. The shear bands traveled at speeds of approximately 1300 m s−1 and were accompanied by intense localized heating measured using high-speed full-field infrared imaging. The maximum temperatures recorded across the shear bands were in excess of 1500 K.

scholarly journals A Constitutive Model for Locally Drained Shear Bands in Globally Undrained Dense Sand

2019 ◽  
Vol 92 ◽  
pp. 16005
Author(s):  
Hansini Mallikarachchi ◽  
Kenichi Soga
Keyword(s):  
Shear Band ◽  
Constitutive Model ◽  
Bifurcation Analysis ◽  
Shear Bands ◽  
Constitutive Relationship ◽  
Excess Pore Pressure ◽  
Biaxial Compression ◽  
Compression Tests ◽  
Equilibrium Equations ◽  
Dense Sand

When saturated granular materials which are dilative in nature are subjected to the undrained deformation, their strength increases due to the generation of negative excess pore pressure. This phenomenon is known as dilative hardening and can be witnessed in saturated dense sand or rocks during very fast loading. However, experimental evidence of undrained biaxial compression tests of dense sand shows a limit to this dilative hardening due to the formation of shear bands. There is no consensus in the literature about the mechanism which triggers these shear bands in the dense dilative sand under isochoric constraint. The possible theoretical reasoning is the local drainage inside the specimen under the globally undrained condition, which is challenging to be monitored experimentally. Hence, both incept of localisation and post-bifurcation of the saturated undrained dense sand demand further numerical investigation. Pathological mesh dependency hinders the ability of the finite element method to represent the localisation without advanced regularisation methods. This paper attempt to provide a macroscopic constitutive behaviour of the undrained deformation of the saturated dense sand in the presence of a locally drained shear band. Discontinuation of dilatant hardening due to partial drainage between the shear band and the adjacent material is integrated into the constitutive model without changing governing equilibrium equations. Initially, a classical bifurcation analysis is conducted to detect the inception and inclination of the shear band based on the underlying drained deformation. Then a post-bifurcation analysis is carried out assuming an embedded drained or partially drained shear band at gauss points which satisfy bifurcation criterion. The smeared shear band approach is utilised to homogenise the constitutive relationship. It is observed that the dilatant hardening in the saturated undrained dense sand is reduced considerably due to the formation of shear bands.

Hot Deformation and Dynamic Recrystallization in Titanium Aluminide

2018 ◽  
Vol 941 ◽  
pp. 1391-1396 ◽  
Author(s):  
Nitish Bibhanshu ◽  
Satyam Suwas
Keyword(s):  
Shear Band ◽  
Dynamic Recrystallization ◽  
Titanium Aluminide ◽  
Volume Fraction ◽  
Shear Bands ◽  
Hot Workability ◽  
Compression Tests ◽  
Electron Backscattered Diffraction ◽  
Gamma Titanium Aluminide ◽  
Z Contrast

The hot workability of gamma titanium aluminide alloy, Ti-48Al-2V-2Nb, was assessed in the cast condition through a series of compression tests conducted over a range of temperatures (1000 to 1175 °C) and at the strain rate of 10 S-1. The mechanism of dynamics recrystallization has been investigated from SEM Z-contrast images and from the Electron backscattered diffraction EBSD as well. It has been observed that volume fraction of the recrystallized grains increases with increasing the deformation temperature. The major volume fraction of the recrystallized grains was observed in the shear band which was forming at an angle 45 ̊ with respect to the compression direction. The mechanism of breaking of the laths and the region of the dynamic recrystallization were also investigated from the SEM Z-contrast image and EBSD. The dynamic recrystallization occurred in the region of the broken laths and shear bands. The breaking of the laths was because of the kinking of the lamellae. The shear band, kinked lamellae and dynamic recrystallized region where all investigated simultaneously.

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