Shear Band Instabilities Research Articles

The size-dependence of compressive mechanical properties and serrated-flow behavior of Ti-based bulk metallic glass

In this work, the size-dependence on the compressive mechanical and serrated-flow behaviors of Ti-based bulk metallic glass (BMG) was systematically investigated. The results demonstrated that the compressive plasticity of the BMGs was greatly improved from 1.0 ± 0.6% to 2.4 ± 0.5% with the specimen diameter reducing from 4 to 2 mm, while the fracture strength decreased from 2070 ± 40 to 1870 ± 31 MPa, indicating a trend of smaller and softer characteristics. Meanwhile, the Weibull distribution analysis of the strength and plasticity indicated that when the specimen diameter was increased from 2 to 4 mm, the Weibull strength modulus (mσ) decreased from 83.5 to 46.6 and the Weibull plasticity modulus (mε) decreased from 0.70 to 0.36, revealing a more discrete distribution of both the strength and the plasticity with the increase in diameter. The average shear-band velocity (ASBV), which was calculated based on the stick–slip dynamics, indicated an increasing trend with the increase in specimen diameter, while the shear-band instability index (SBI) presented a similar increasing trend. Meanwhile, the serrated-flow analysis revealed that the BMG specimen with smaller size possessed a lower average stress drop and a larger Weibull modulus of stress drop, which is the substantial cause for the considerable malleability in smaller specimen. Moreover, the fitting result for the cumulative probability distributions of the stress drop indicated that the stress drops in smaller specimens exhibit better coincidence.

Evolution of microstructures and properties leading to layer instabilities during accumulative roll bonding of Fe[sbnd]Cu, Fe[sbnd]Ag, and Fe[sbnd]Al

Bi-metallic laminates (bcc/fcc) containing Fe and either Cu, Ag, or Al were processed by cold accumulative roll bonding (ARB). The evolving microstructures and properties were measured using optical microcopy, electron backscatter diffraction (EBSD), and nano-indentation up to and beyond when layer instabilities are observed. The evolution of layer morphology, grain size, bulk texture, layer dependent texture, and layer dependent hardness is found to be both material dependent and layer location dependent. Ultimately, the evolving difference in layer hardness between Fe and the fcc metal resulting from the microstructure evolution causes the formation of layer instabilities with the FeAl exhibiting layer pinch-off at a total strain of 2.2, the FeAg developing shear band instabilities at a strain of 3.2, and the FeCu developing shear band instabilities at a strain of 4.5. These finding indicate that once the evolving strength ratio approaches two, processing changes, such as annealing or warm rolling, that improve the strength ratio or materials’ capacity for work hardening are necessary for further processing without layer instabilities.

Controlling shear band instability by nanoscale heterogeneities in metallic nanoglasses

Strain localization during plastic deformation drastically reduces the shear band stability in metallic glasses, ultimately leading to catastrophic failure. Therefore, improving the plasticity of metallic glasses has been a long-standing goal for several decades. In this regard, nanoglass, a novel type of metallic glass, has been proposed to exhibit differences in short and medium range order at the interfacial regions, which could promote the formation of shear transformation zones. In the present work, by introducing heterogeneities at the nanoscale, both crystalline and amorphous, significant improvements in plasticity are realized in micro-compression tests. Both amorphous and crystalline dispersions resulted in smaller strain bursts during plastic deformation. The yield strength is found to increase significantly in Cu–Zr nanoglasses compared to the corresponding conventional metallic glasses. The reasons for the mechanical behavior and the importance of nanoscale dispersions to tailor the properties is discussed in detail.Graphic

Dispersion of rigid line inclusions as stiffeners and shear band instability triggers

A dispersion of stiff and thin (‘rigid line’) inclusions (RLIs) in a matrix material may result beneficial for stiffening in the elastic range, but might be detrimental to strength, as material instabilities may be triggered by inclusions when the matrix is brought to a viscoplastic-damaging state. This dual role of RLIs is investigated by means of the embedded reinforcement model. Validated against available analytical predictions, this numerical model is employed to assess the roles of RLIs’ orientation, interaction, volume fraction, and distribution, considering up to 1500 inclusions. When the matrix material deforms inelastically, RLIs produce stress concentrations that promote the nucleation of shear bands. These are characterized at collapse for many distributions of RLIs, showing that their effects range from almost negligible to a disrupting alteration of the dominant failure mechanism. In the latter case, it is shown that the dominant shear bands can be fragmented by RLIs into a mosaic of tiny localization bands. These results offer new insights into energy dissipation mechanisms of reinforced materials, as they are promoted or inhibited by the interactions of rigid line inclusions.

A new continuum model for viscoplasticity in metallic glasses based on thermodynamics and its application to creep tests

In this study, we developed a new continuum model for the time-dependent plasticity of metallic glasses based on the laws of thermodynamics. In this model, the free energy of a material point is formulated as not only the local strain state but also the local atomic concentration (or the free volume). Atomic kinetics, controlled by the gradient of the chemical potential, is linked directly with the plastic deformation by a new plastic flow rule. Finite element implementation of our model is validated through the classical uniaxial tension and simple shear tests in which the shear band instability and shear-dilatation phenomena are reproduced. Applied to the creep of Cu-Zr metallic glass, our model captures the transition of two distinct power laws for the creep strain rate vs. applied stress relations around a critical stress. These two power laws, below and above the critical stress, correspond to two different diffusion mechanisms activated by the thermal energy gradient and strain energy gradient, respectively. At last, we carry out a linear perturbation analysis to explain the origin of the critical stress as well as its dependence on the sample size.

Mechanical Behaviors of Ultrafine-Grained Ti-6Al-4V Alloy During Compression at Various Strain Rates

Ultrafine-grained (UFG) Ti-6Al-4V alloy with average grain sizes of 305, 430, and 669 nm was fabricated by high-energy ball-milling and spark plasma sintering. The mechanical behaviors of consolidated titanium alloy with different grain sizes were studied under uniaxial compression at the quasi-static strain rate of 1 × 10−3 s−1 and high strain rates ranging from 0.5 × 103 to 2.9 × 103 s−1. Shear bands can be observed in specimens tested under quasi-static and dynamic condition. It is discovered that when the grain size decreases, the flow stress increases and shear band instability takes place at lower strains. The flow stresses of UFG titanium alloy with different grain sizes demonstrate similar dependence on the strain rate when the strain rate ranges from 1 × 10−3 to 0.5 × 103 s−1. However, the strain rate sensitivity m dramatically increases at higher strain rates and is reduced with the decrease of grain size. It is considered that the propensity for adiabatic shear banding $$ \chi_{\text{ASB}} $$ during dynamic compression is increased with the reduction of grain size because of the improved yield strength as well as the diminished strain rate sensitivity.

Criticality at a Finite Strain Rate in Fluidized Soft Glassy Materials.

We study the emergence of critical dynamics in the steady shear rheology of fluidized soft glassy materials. Within a mesoscale elastoplastic model accounting for a shear band instability, we show how additional noise can induce a transition from a phase separated to homogeneous flow, accompanied by critical-like fluctuations of the macroscopic shear rate. Both macroscopic quantities and fluctuations exhibit power law behaviors in the vicinity of this transition, consistent with previous experimental findings on vibrated granular media. Altogether, our results suggest a generic scenario for the emergence of criticality when shear weakening mechanisms compete with a fluidizing noise.

Dynamics of shear band instabilities in cutting of metals

We study the dynamics of flow instability and shear localization in cutting using direct high-speed imaging and low melting point alloy as a model material system. The onset of instability and departure from steady laminar flow is triggered by nucleation of shear band at the tool tip and subsequent propagation towards the free surface. The stress at the onset of shear band formation is found to be constant and a physical characteristic of the material. The shear band velocity and inhomogeneous strain field arising from the banding are quantitatively characterized using an image correlation method.

Effect of temperature on the fracture surface morphology of Ti- and Zr-based bulk metallic glasses: exploring correlation between morphology and plasticity

According to previous studies on the fracture surface morphologies of bulk metallic glasses, the stable crack growth region width and vein pattern size increase with the plasticity at room temperature. In the present work, the fracture surface morphologies of Ti- and Zr-based bulk metallic glasses bent over a wide temperature range (0.1–0.8 glass transition temperature) are systematically analyzed. According to our finding, the stable crack growth region width increases while the vein pattern size decreases as the ductility improves by varying temperature. This observation is in contrast to the common thought that the ductility is proportional to the stable crack growth region width and vein pattern size simultaneously. Moreover, the vein pattern size and shear offset width are found to be almost equal at a specific temperature. Furthermore, smaller vein pattern size and shear offset width reduce shear band instability and, consequently, enhance the ductility.

The mechanism of shear-band blocking in monolithic metallic glasses

The catastrophic failure of shear bands along a dominant shear plane has fatally hampered wide potential applications of metallic glasses. In this study, the blocking of shear bands in monolithic metallic glasses was investigated using an atomic force microscope together with a nanoindenter. At sites of the interaction of two shear bands, if the height of the secondary band is less than that of the pre-existing primary one, the propagation of the secondary band will be blocked, which could lead to the stabilization of glasses. The mechanism of the blocking was explained from the gap of the driving energy between the interactive bands. In addition, from the acceleration of the decreasing rate of the shear offset, it's revealed that more energy can be dissipated at sites of the interaction. These quantitative results provide a mechanistic understanding on the propagation and suppression of shear bands at the nanoscale, as well as a theoretical base to design metallic glasses with promoted plasticity by suppressing the shear band instability.

Combined stability analysis of phase-field dynamic fracture and shear band localization

Dynamic fracture of metals is a fascinating multiphysics-multiscale problem that often results in brittle and/or ductile fracture of structural components and under high strain rates may also suffer from shear banding. While fracture events are mostly driven by tensile loading, shear bands are driven by shear heating caused by inelastic deformations and associated with high temperature rise. These processes are characterized by different failure modes with distinct spatial and temporal scales.A recent unified model developed by the authors attempts to capture dynamic fracture and shear banding failure modes using implicit, mixed finite element formulations. In this model, fracture is modeled with a novel phase field formulation coupled to a set of equations that describe shear bands. While fracture is governed by a strong length-scale that propagates with a fast time scale, shear bands are dominated by a weak length-scale and propagate slower.In this work, we analyze the physical stability of both failure modes and their interaction using a linear perturbation method. The analysis provides insight into the dominant failure mode and can be used as a criterion for mesh refinement.Several numerical results with different geometries and a range of strain rate loadings demonstrate that the stability criterion predicts well the onset of failure instability in dynamic fracture applications.For the example problems considered, if a fracture instability precedes shearbanding, a brittle-like failure mode is observed, while if a shear band instability is initiated significantly before fracture, a ductile-like failure mode is expected. In any case, fracture instability is stronger than a shear band instability and if initiated will dominate the response.

Electromechanical instabilities in fiber-constrained, dielectric-elastomer composites subjected to all-around dead-loading

In this work we investigate the possible development of instabilities in a certain class of dielectric-elastomer composites (DECs) subjected to all-around dead electromechanical loading. The DECs consist of a dielectric elastomer matrix phase constrained to plane strain deformations by means of aligned, long, rigid dielectric fibers of elliptical cross-section that are also aligned but randomly distributed in the transverse plane. Two types of instabilities are considered: loss of positive definiteness (LPD), and loss of strong ellipticity (LE). LPD simply corresponds to the loss of local convexity of the homogenized electroelastic stored-energy function for the DECs and can be of two types depending on the resulting instability modes. When the modes are aligned with the ‘principal’ solution, the instability corresponds to a maximum in the nominal electric field, possibly followed by snapping behavior. Alternatively, when the modes are orthogonal to the principal solution, the instability corresponds to a bifurcation from the principal solution. The LE, on the other hand, corresponds to LPD of the electromechanical acoustic tensor and manifests itself by the onset of highly localized shear band instabilities. Our results show that the stability, as well as the type of instability (when stability is lost), of the DECs depends sensitively on the loading conditions and is also affected by the microstructure of the DECs (i.e. the volume fraction of the fibers and their aspect ratio). In particular, it is found that the non-aligned LPD instabilities typically precede aligned LPD and LE instabilities, especially for in-plane isotropic microstructures, but aligned (limit load) LPD and LE instabilities are also possible for composites with anisotropic microstructures. In this context, it should be noted that the possible development of non-aligned LPD bifurcation instabilities appears to have been ignored by prior work. Fortunately, however, such instabilities can usually be avoided by orienting the long (in-plane) axis of the fibers parallel to the tensile stress direction and orthogonal to the applied electric field.

Numerical study of shear band instability and effect of cavitation on the response of a specimen under undrained biaxial loading

This paper presents an extension of the local second gradient model to multiphasic materials (solids particles, air, water) and including the cavitation phenomenon. This new development was made in order to model the response of saturated dilatant materials under deviatoric stress and undrained conditions and possibly, in future, the behavior of unsaturated soils. Some experiments have showed the significance of cavitation for the hydromechanical response of materials. However, to date and as far as we are aware, no attempt was made to implement the cavitation as a phase change mechanism with a control of pore pressure. The first part of the results section explores the effects of permeability, dilation angle and loading rate on the stability of shear bands during a localization event. The reasons underlying the band instability are discussed in detail, which helps defining the conditions required to maintain stability and investigating the effects of cavitation without parasite effect of materials parameters or loading rate. The model showed that, if a uniform response is obtained, cavitation triggers localization. However, in case of a localized solution, cavitation follows the formation of the shear band, with the two events being quite distinct.

Onset of irreversibility and chaos in amorphous solids under periodic shear

A fundamental problem in the physics of amorphous materials is understanding the transition from reversible to irreversible plastic behavior and its connection to yield. Currently, continuum material modeling relies on phenomenological yield thresholds, however in many cases the transition from elastic to plastic behavior is gradual, which makes it difficult to identify an exact yield criterion. Here we show that under periodic shear, amorphous solids undergo a transition from repetitive, predictable behavior to chaotic, irregular behavior as a function of the strain amplitude. In both the periodic and chaotic regimes, localized particle rearrangements are observed. We associate the point of transition from repetitive to chaotic behavior with the yield strain and suggest that at least for oscillatory shear, yield in amorphous solids is a result of a "transition to chaos."

Shear bands as growing instabilities in viscoanelastic media with memory

In this paper we investigate the critical conditions under which a small perturbation in an homogeneous continuum can possibly grows into a shear band instability. In particular, we analyze from a thermodynamical viewpoint the phenomenon of shear bands in viscoanelastic media with memory. It is emphasized, in the scientific literature, that the specific adopted rheology strongly affects the results so that a special attention has to be paid, also for engineering purposes, to the accuracy of the rheological model. Several well-known rheological model (for instance the so called Maxwell or Jeffreys media) are particular cases of the general model we adopt in the paper to analyze shear bands. Instability conditions, giving rise to shear bands formation, are obtained by introducing small perturbations around an homogeneous deformation into the system of differential equations governing the problem of homogeneous deformations in the considered continuous medium; as a result a non-homogeneous linear dynamical system is obtained whose stability is analyzed. A research perspective in view of a possible comparison with experimental results is proposed; in particular the simple methodology proposed in the paper should be applied in view of using the phenomenon of the initiation of shear bands to calculate the thermomechanical coefficients of real materials.

Granular segregation in narrow rotational drums with different wall roughness: Symmetrical and asymmetrical patterns

The axial segregation of granular flows in rotating drums is closely correlated to the material properties and side-wall friction. In this study, experimental work with two different types of sidewall roughness is performed to characterize the frictional effect of the side walls. In one case both walls are smooth and in the other each sidewall has a different roughness. The evolution of the Rayleigh-instability core inside the granular assembly varies with the aspect ratio of the drums. By increasing the Froude number, the axial banding expands with increasing side-wall roughness. The asymmetrical banding stripe is enhanced by the differential frictional roughness on either side wall. Axial segregation is driven by both the variation in the size ratio of the mixtures and the drum geometrical parameters. We performed experiments to investigate the wall friction of dry granular segregation in the rotary drum. The results show that increasing rotational speed, aspect ratio, and changing the wall friction, have significant influences on the segregation phenomenon of mixed granular matter due to the side-wall shear band and Rayleigh-like instability. ► A new asymmetrical pattern on axial plane is observed in the study. ► The asymmetrical axial segregation is sensitive to the side-wall friction. ► The widespread coarse region causes an axial convection on the granular surface.

Effect of Size and Aspect Ratio on the Mechanical Properties of ZrAlNiCuNb Metallic Glass

Abstract The effects of size and aspect ratio (height/diameter ratio) of the specimen on the mechanical properties of a Zr 56 Al 10.9 Ni 4.6 Cu 27.8 Nb 0.7 metallic glass have been investigated by uniaxial compression tests and scanning electron microscope (SEM) observations. The results show that the metallic glass with smaller size and lower aspect ratio shows an enhanced plasticity due to larger amount of free volume formed during casting. The shear-band instability index (SBI) is introduced to explain the effects of the size and aspect ratio on the plasticity of the metallic glass. Stable propagation of shear bands can be achieved for the specimen with small size and low aspect ratio, resulting in a size and aspect ratio dependance of plasticity.

Cooperative shear and catastrophic fracture of bulk metallic glasses from a shear-band instability perspective

The morphology of the fracture surfaces of a bulk metallic glass (BMG) tested under compression was systematically studied. Experimental results showed that the fracture surface always comprises two kinds of zones, starting with a relatively smooth zone followed by the second zone with vein patterns. It implies strongly that the plastic deformation of BMGs always starts with a cooperative shear. The following catastrophic fracture characterized by the vein patterns may or may not occur, depending on the magnitude of this shear, which is controlled by the sample size and machine stiffness. This phenomenon was interpreted based on the temperature rise resulting from the work done during the cooperative shear. It revealed that for small samples, the shear is so small that the temperature increase is insignificant, accounting for the extensive serrated flow, while the temperature increase in samples beyond a critical size is sufficiently high so that the temperatures are higher than the glass transition temperature or even the melting temperature, leading to catastrophic fracture.

An instability index of shear band for plasticity in metallic glasses

Catastrophic failure along a dominant shear band sets the limit on how much plasticity can be achieved in metallic glasses (MGs) under uniaxial compression. Here we show that this instability process is governed by a single system parameter, called the shear-band instability index (SBI), which is proportional to sample size and inversely proportional to machine stiffness. We provide extensive experimental proof of this concept by conducting a series of tests with a range of controlled values of sample size and machine stiffness. The theory of SBI has led us to a more comprehensive understanding of the mechanisms of plastic deformation in MGs via simultaneous operation of multiple shear bands versus a single dominant one. This concept provides a theoretical basis to design systems which promote plasticity/ductility in MGs by suppressing or delaying shear-band instability.

Suppression of the shear band instability during plastic flow of nanometer-scale confined metallic glasses

The shear band instability that occurs during plastic deformation of metallic glasses limits the application of these high-strength materials. We show that this instability can be suppressed in nanometer-scale metallic glasses constrained by ultrafine crystalline layers. Free-standing Cu/amorphous Pd0.77Si0.23 multilayers consisting either of 10∕90nm glass/Cu or 100∕100nm glass/Cu were deformed to layer thickness reductions greater than 75% by cold rolling or bending, respectively. Transmission electron microscopy showed uniform reduction in the layer thickness with no shear band formation in the amorphous layers. The mechanisms that allow homogeneous codeformation of metallic glasses with nanoscale crystalline layers at high stresses are discussed.