Shear Banding Phenomenon Research Articles

How to catch a shear band and explain plasticity of metallic glasses with continuum mechanics

Capturing a shear band in a metallic glass during its propagation experimentally is very challenging. Shear bands are very narrow but extend rapidly over macroscopic distances, therefore, characterization of large areas at high magnification and high speed is required. Here we show how to control the shear bands in a pre-structured thin film metallic glass in order to directly measure local strains during initiation, propagation, or arrest events. Based on the experimental observations, a model describing the shear banding phenomenon purely within the frameworks of continuum mechanics is formulated. We claim that metallic glasses exhibit an elastic limit of about 5% which must be exceeded locally either at a stress concentrator to initiate a shear banding event, or at the tip of a shear band during its propagation. The model can successfully connect micro- and macroscopic plasticity of metallic glasses and suggests an alternative interpretation of controversial experimental observations.

Shear banding as a dissipative structure from a thermodynamic viewpoint

Granular materials are now known to be an illustration of complex materials as they display emergent macroscopic properties when loaded. An initially homogenous response can bifurcate into a heterogeneous one with the appearance of a rich variety of structured kinematical patterns. The shear banding that ensues illustrates a symmetry-breaking transition with multiple choices of macroscopic behaviours, a common feature of dynamical complex systems. Even though the phenomenon has been studied for decades, this regime transition remains mostly mysterious in geomaterials, with no convincing arguments that could link it to the underlying microscopic mechanisms. The paper investigates this issue by invoking the fundamental minimum entropy production theorem established by Prigogine in the past century to seek any connection with the second-order work theory in the mechanics of failure. A general equation linking the derivatives of the entropy of a mechanical system to the second-order work is thus inferred, which leads to a thermodynamic interpretation of bifurcations in the failure behaviour of granular materials under a given loading. This is verified through discrete element simulations that highlight the fundamental role played by the elastic energy stored within a granular material before a bifurcation occurs, which also corresponds to a minimization of the entropy production. The analysis suggests a new interpretation of the intriguing shear banding phenomenon as a bifurcation with the emergence of ordered dissipative structures germane to nonequilibrium thermodynamics of open systems.

Strain fields as local probe for X-ray diffraction tomography: Non-destructive reconstruction of shear band paths in metallic glasses

Shear bands are nanoscale topologically complex planar shear defects mediating plasticity in metallic glasses and a complete understanding of the shear banding phenomenon requires their three-dimensional characterization; however, we have been unable to tomographically and not-destructively reconstruct the path of shear bands inside a sample until now as X-ray absorption (or phase contrast) tomography is currently unable to distinguish shear bands from the surrounding matrix. Here, we overcome this limitation using the strain field generated by shear bands in the adjacent material as a local probe for X-ray diffraction tomography. This strain field is the analogue of the contrast agents used in conventional clinical tomography, allowing us to non-destructively reconstruct the shear band paths within the glassy specimens. Tomography is based on collecting a series of projections recorded at different angles while the specimen is rotated about a single axis. In this work, we first use full-angle tomography (reconstruction based on projections collected over 360°), which allows reconstructing the paths in excellent detail revealing features of shear banding that are not accessible to other analytical tools. A dataset with missing angles (projections over less than 360°) degrades the reconstruction but opens the door to in-situ measurements during deformation.

Thixotropic constitutive modeling of shear banding by boundary-induced modulus gradient in lamellar gel networks

To predict the complex rheology and shear-rate inhomogeneities of lamellar gel networks, we propose a simple thixotropic constitutive model with an elastoplastic stress and a smoothly decreasing modulus near a solid boundary, motivated by the analysis of the effect of confinement and shear flow on lamellae orientation near surfaces. We show that the model qualitatively captures the important features of the lamellar gel shear rheology observed in experiments [Datta et al., J. Rheol. 64(4), 851–862 (2020)]. These include thixotropic shear thinning that is intermediate between constant viscosity and constant stress, a power-law slow creep under small constant shear stress and abrupt transition to fast creep at higher stress, as well as partial recovery of strain upon stress removal. In addition, the model correctly predicts a gap-dependent rheology and roughly predicts the amplitude dependence of storage and loss moduli in oscillatory tests despite having only a single thixotropic time constant. Most importantly, the introduction of the modulus gradient enables the model to predict the unique shear-banding phenomenon of lamellar gel networks wherein a thin, fast-shearing band exists near the boundary that widens only slowly with increased apparent shear rate until a very high rate is reached, while the bulk moves as a plug [Datta et al., J. Rheol. 64(4), 851–862 (2020)]. We discuss the influence of a lower modulus near the boundary and its possible origin in the underlying lamellar structure of the material.

Computational Analysis of Shear Banding in Simple Shear Flow of Viscoelastic Fluid-Based Nanofluids Subject to Exothermic Reactions

We investigated the shear banding phenomena in the non-isothermal simple-shear flow of a viscoelastic-fluid-based nanofluid (VFBN) subject to exothermic reactions. The polymeric (viscoelastic) behavior of the VFBN was modeled via the Giesekus constitutive equation, with appropriate adjustments to incorporate both the non-isothermal and nanoparticle effects. Nahme-type laws were employed to describe the temperature dependence of the VFBN viscosities and relaxation times. The Arrhenius theory was used for the modeling and incorporation of exothermic reactions. The VFBN was modeled as a single-phase homogeneous-mixture and, hence, the effects of the nanoparticles were based on the volume fraction parameter. Efficient numerical schemes based on semi-implicit finite-difference-methods were employed in MATLAB for the computational solution of the governing systems of partial differential equations. The fundamental fluid-dynamical and thermodynamical phenomena, such as shear banding, thermal runaway, and heat transfer rate (HTR) enhancement, were explored under relevant conditions. Important novel results of industrial significance were observed and demonstrated. Firstly, under shear banding conditions of the Giesekus-type VFBN model, we observed remarkable HTR and Therm-C enhancement in the VFBN as compared to, say, NFBN. Specifically, the results demonstrate that the VFBN are less susceptible to thermal runaway than are NFBN. Additionally, the results illustrate that the reduced susceptibility of the Giesekus-type VFBN to the thermal runaway phenomena is further enhanced under shear banding conditions, in particular when the nanofluid becomes increasingly polymeric. Increased polymer viscosity is used as the most direct proxy for measuring the increase in the polymeric nature of the fluid.

Recreating the shear band evolution in nanoscale metallic glass by mimicking the atomistic rolling deformation: a molecular dynamics study.

Rolling processes are extensively used to induce network of shear bands (SBs) in the bulk metallic glasses, which in turn enhances the overall plasticity of the specimen. However, the atomic-level understanding of shear band formation/propagation mechanism during mechanical processing is still limited. In this perspective, we have developed a molecular dynamics (MD) simulation model to recreate the rolling deformation process and investigate the SB formation in Cu-Zr metallic glass (MG) specimen. Results have shown that dense and concentrated primary SBs along with secondary branching are formed during cryo-rolling, whereas a scattered and thicker SBs are formed during hot rolling process. Meanwhile, Voronoi cluster analysis revealed that the high five-fold symmetry clusters tend to decrease, while the crystalline-like cluster increases during the hot rolling process. These findings from the study are in good agreement with previous experimental studies substantiated in literature, which shows that the model correctly predicts the shear-banding phenomenon.

Bulk and interfacial modes of instability in channel flow of thixotropic-viscoelasto-plastic fluids with shear-banding

We carry out a linear stability analysis of the generalised BMP model, which incorporates the shear-banding phenomenon into flows of thixotropic-viscoelasto-plastic fluids: common behaviours observed in wormlike micellar solutions. We introduce a new dimensionless parameter governing shear-banding, and find that when a flow is unstable in the absence of shear-banding, this parameter has a stabilising effect. Above a critical value of the shear-banding parameter, shear bands appear in the flow gradient direction. Here two different modes of instability are observed: a bulk mode (which is the same as that seen in the absence of shear banding) and an interfacial mode. We found that the former dominates over the latter at low values of the shear-banding parameter, but the interfacial instability becomes dominant at very high values of the parameter. In particular, the interfacial modes are more unstable in flows where the low shear band has almost constant viscosity. The two modes of instability depend on different material timescales: interfacial modes become more dangerous if the interface location is near the channel wall, which is seen when the structural relaxation time is much larger than that of plasticity, while bulk modes (as seen in previous work) are highly unstable if the timescale of viscoelasticity is much longer than both those of plasticity and thixotropy.

Modelling of Shear Banding in Plane Couette Flow of Non-linear Viscoelastic Fluids

We investigate shear banding phenomena in the plane Couette flow of viscoelastic fluids.The viscoelastic fluids are modelled viathe Giesekus constitutive equations with stress diffusion. The nonlinear and coupled systems of equations, comprising the momentum equation and the constitutive equations, are solved numerically using semi-implicit finite difference methods. Theeffects of the fluid parameters on the flow variables are also investigated. Under certain values of the material parameters, we observe formation of shear bands in plane Couette flow.

Benchmark solutions of the stabilized computations of flows of fluids governed by the Rolie-Poly constitutive model

Recent studies demonstrate that flow induced non-uniformities of concentration can trigger shear banding in the flow of certain viscoelastic fluids. These studies show that the driving mechanisms for such shear banding are related to the coupling of the polymer stresses to an inhomogeneous concentration profile. The Rolie-Poly (RP) viscoelastic constitutive model has been used in such studies since it has been comprehensively subjected to extensive experimental validation with regards to shear banding and has the demonstrated ability to accurately express the rheology of polymer solutions for a wide range of strain rates. The primary aim of this work is to develop an efficient computational methodology that could be used to accurately simulate the flow of complex fluids governed by the Rolie-Poly constitutive equation. The development of such a computational platform is crucially important for the purposes of our follow up studies on the computational analysis of shear banding phenomena by coupling polymer stress with inhomogeneous concentration profile. Our numerical algorithms will be based on the finite volume method (FVM) and will be implemented on the open source software package OpenFOAM®. In this paper, we will present both validation results as well as new benchmark results from our FVM based OpenFOAM® numerical solver for flow of fluids governed by the Rolie-Poly constitutive model. We use two well-known benchmark problems, the lid-driven cavity flow and the 4:1 planar contraction flow problems. In order to stabilize the numerical algorithm at high Weissenberg numbers, we employ either of two stabilization techniques; the Discrete Elastic Viscous Stress Splitting (DEVSS) technique as well as the Log-Conformation Reformulation (LCR) methodology. Validation of our results is done by comparing our (stabilized) numerical results, against data from existing literature. The numerical results obtained for the contraction flow using the LCR stabilization approach are in good agreement with the existing literature for a wider range of Weissenberg numbers. The DEVSS method shows a good agreement only for lower Weissenberg numbers. For the lid-driven cavity flow, good agreement with the existing literature is observed for low Weissenberg numbers using either of the two stabilization techniques.

Progressive failure and scale effect of anchor foundations in sand

Progressive failure is considered one of the least understood classical problems in geomechanics, gaining considerable attention in foundation related problems. However, the transformation of model test results to prototype is so much complex (scale effect). This paper highlights a FE ideology for evaluation of the response of shallow circular anchor foundations in sands with sophisticated strain hardening-softening behaviour. In these soils, the progressive failure can occur because of the non-mobilization of pinnacle strength of soil on potential failure surface and softening behaviour of soils. The presented paradigm allows this failure phenomenon to be properly evaluated by using a non-associated elastoplastic constitutive model coupled with explicit dynamic relaxation method considering yield surface as the MC material model and the potential surface is the smooth DP model having shear band effect. The FE results are compared with experimental outcomes to assess the reliability. Numerical model well-predicted the experimental stress-strain data points from element tests very closely. The scale effect is deliberated due to the progressive failure with shear banding phenomenon, which is remarkable with the increase of embedment and predominant in the sand of higher density. The peak resistance factor and settlement are presenting a decreasing trend with the increase of foundation width.

Granular scale responses in the shear band region

The essence of macroscopic shear band phenomena is the cumulative cooperation of granular scale particle rearrangements. In this work, we report an experimental study to present the granular scale properties as the shear band is generated in a confined granular material with soft boundaries. The photoelastic experimental technique is applied to illuminate the force chain network in our experiments. Particle scale stresses are extracted from the photoelastic response. Meanwhile, other particle scale performances like displacements and rotation are also detected. According to the distribution of particle scale volumetric strain, the shear band region and the state of bifurcation are well defined. We find that pressure inside of each particle does not have a clear correlation with the shear band region. Conversely, the local density variation and particle rotation have strong correlation with the shear band region.

The investigation of shear banding polymer solutions in die extrusion geometry

This computational study investigates the shear banding phenomenon of semidilute entangled polymer solutions in an extrusion flow. A recently developed nonequilibrium thermodynamic two-fluid model in which shear banding is associated with stress-induced migration was employed. The interfoam solver of the viscoelastic package RheoTool v.2.0, an open-source toolbox based on OpenFOAM v.4.0, was utilized to solve the free-surface flow problem. The PIMPLE algorithm was used for the pressure-velocity coupling, and the convection terms were discretized using the high-resolution scheme CUBISTA. We gradually increased the uniform inlet velocity to reach the shear banding regime. As observed for the Giesekus model, the extrudate swell ratio initially decreases from the Newtonian case with increasing Deborah number. However, the slope’s subsequent increase is reduced, which may be due to both the impact of shear banding and the use of a single set of relaxation times. The velocity profiles in the die change from parabolic to plug-like while entering into the shear banding regime. At the die exit region where the die wall meets the free surface, the material’s boundary condition is changed from the no-slip surface to free surface, which leads to uniform velocity and stress profiles at the downstream. The polymers are pushed toward the wall in the low-shear-rate regime where Fickian diffusion is dominant. The trend in the shear banding regime is the opposite where the stress-induced migration is dominant. An important observation is that the shear banding effect on the polymer concentration is minor compared to the significant changes occurring in the die expansion region. We suggest using a broader spectrum of relaxation times in future mixed-flow calculations.

Evaluation of mechanical and thermal properties of modified epoxy resin by using acacia catechu particles

Abstract In the current study, the epoxy/amine system is reinforced by the biodegradable Acacia Catechu (AC) particles on 0.5, 1.0, 1.5 and 2.0 wt (wt.) %. The AC/epoxy composites were characterized by Fourier transform infrared (FTIR) spectroscopy, thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), scanning electron microscope (SEM), and mechanical properties. The increased hydrogen bonding for the AC/epoxy composites was observed by FTIR spectroscopy and DSC study confirmed the improved conversion of epoxy after the AC particles addition. 14% increase in the flexural strength and 94% improved impact strength were recorded on only 1.0 wt. % AC addition due to change in morphology and crosslink density. Moreover, slightly improved thermal stabilities were also recorded due to the aromatic tannin phenol structures of AC particles. The glass transition temperature values for AC/epoxy composites were observed at 143 and 148 °C by DSC and DMA, respectively; the decline in the values can be dedicated to the flexible segment of AC particles. The SEM analysis demonstrated shear banding phenomena between particles and matrix.

Experimental and numerical investigation on shear banding during nanomachining of an amorphous glassy polymer

This paper discusses the shear banding phenomenon which took place during nanomachining of an amorphous glassy polymer. The nanomachining were carried out with varying machining conditions (depth of cut, machining speed), and the morphologies of the machined surfaces were characterized using atomic force microscopy. The experiments reveal the occurrence of shear band as the critical machining condition is reached. The shear banding was rationalized by the effect of adiabatic heating during machining. Finite element modelling of nanomachining was conducted using an existing elastic-viscoplastic model for this polymer, which accounts for the adiabatic heating due to plastic dissipation. The simulation was then compared with the experiment. It shows that the simulation can capture the main features of shear banding in nanomachining, indicating that the machining is controlled by a localized deformation mechanism. This work can be helpful in optimizing the processing parameters to improve the surface quality of optical products.

Distinguishing dynamic and static yield stress of fresh cement mortars through thixotropy

The dynamic and static yield stress of fresh cement mortar were measured in a rotational rheometer with a vane geometry using shear rate and shear stress-controlled protocols, respectively. Through a shear rate-controlled steady-state protocol, the equilibrium flow curve is measured and fitted with the Bingham model to obtain dynamic yield stress. A negative slope in the equilibrium flow curve, shear banding and stick-slip phenomena are observed and discussed. Through a stress-controlled creep-recovery protocol, viscosity bifurcation behavior is captured and static yield stress is marked as the creep stress when the bifurcation occurs. Finally, the discrepancy between dynamic and static yield stress is tied to thixotropy.

Indentation-Induced Shear Band Formation in Thin-Film Multilayers

We report an exploratory investigation into the cause of shear band formation in multilayer thin-films subject to nanoindentation. The material system considered here is composed of alternating aluminum (Al) and silicon carbide (SiC) nanolayers, atop a silicon (Si) substrate. Finite element models are developed in an attempt to reproduce the shear banding phenomenon observed experimentally. By introducing strain softening into the material model for the hard SiC layers, shear bands can be seen to emerge from the indentation site in the finite element analysis. Broad implications, along with possible directions for future work, are discussed.

Adiabatic shear bands localization in materials undergoing deformations

We consider the adiabatic shear banding phenomenon in composite materials undergoing the high speed shear deformations. The mathematical model of adiabatic shear banding in thermo-visco-plastic material is given. New two step numerical algorithm which is based on the Courant-Isaacson-Rees scheme that allows one to simulate fully localized plastic flow from initial stage of localization is proposed. To test this numerical algorithm we use three benchmark problems. The testing results show the accuracy and efficiency of proposed algorithm. The features of adiabatic shear bands formation in composites are studied. The existence of characteristic depth of localization in composites is shown. Influence of initial temperature distribution on the processes of adiabatic shear bands formation in composites is considered.

Analysis of shear banding phenomena in non-isothermal flow of fluids governed by the diffusive Johnson–Segalman model

This article investigates phenomena associated with shear banded flows of viscoelastic fluids in both pipe flow and coaxial annular flow. We in particular computationally analyze the effects of stress diffusion, non-isothermal flow conditions and annular gap size on the shear stress path selection (and the selected shear stress value) in shear banded flow of viscoelastic fluids described by the non-local Diffusive Johnson–Segalman (DJS) constitutive model. The DJS model is one of such constitutive models which allows us for a non-zero inter-facial layer between regions of high and low shear rates within the flow field. Temperature effects due to polymer orientation changes, entropic effects (resulting from stress work), conduction heat transfer, Arrhenius chemical kinetics as well as the influence of slip and related frictional heating on the wall are all accounted for. The time dependent model formulated to capture gap effect in the axial annular flow problem (under certain values of the relevant parameters), reduces to the system of equations governing a pipe flow setup. Semi-implicit finite difference methods are employed for the solution process of the coupled nonlinear time dependent partial differential equations governing the flow problem. We discuss with graphical representations the effect of temperature, stress diffusion, wall slip, suction/injection and annular gap size on the related shear rate path selection phenomena for certain material parameter values.

Effect of cohesion on shear banding in quasistatic granular materials.

Cohesive powders have widely different bulk behavior due to their peculiar interactions. We use discrete element simulations to investigate the effect of contact cohesion on the steady state flow of dense powders in a slowly sheared split-bottom Couette cell, which imposes a wide stable shear band. The intensity of cohesive forces can be quantified by the granular Bond number (Bo), namely the ratio between maximum attractive force and average force due to external compression. We find that the shear banding phenomenon is almost independent of cohesion for Bond numbers Bo<1, however for Bo≥1 cohesive forces start to play an important role, as both width and center position of the band increase. Inside the shear band, the mean normal contact force is independent of cohesion and depends only on the confining stress. In contrast, when the behavior is analyzed focusing on the eigendirections of the local strain rate tensor, a dependence on cohesion shows up. Forces carried by contacts along the compressive and tensile directions are symmetric about the mean force (larger and smaller respectively), while the force along the third, neutral direction follows the mean force. This anisotropy of the force network increases with cohesion, just like the heterogeneity in all (compressive, tensile and neutral) directions.

Rheological properties of micro-/nanofibrillated cellulose suspensions: Wall-slip and shear banding phenomena

The rheological properties of enzymatically hydrolyzed and TEMPO-oxidized microfibrillated/nanofibrillated cellulose (MFC/NFC) aqueous suspensions were investigated in oscillation and steady-flow modes and were compared with the morphology of the studied materials. The flow instabilities, which introduce an error in the rheological measurements, were discovered during flow measurements. A wall-slip (interfacial slippage on the edge of geometry tools and suspension) was detected at low shear rates for two types of NFC suspensions while applying cone-plate geometry. A roughening of the tool surfaces was performed to overcome the aforementioned problem. Applying to TEMPO-oxidized NFC, a stronger suspension response was detected at low shear rates with higher values of measured shear stress. However, a shear banding (localization of shear within a sample volume) became more pronounced. The use of serrated tools for enzymatically hydrolyzed NFC produced lower shear stress at the moderate shear rates, which was influenced by water release from the suspension.