Shear Band Velocity Research Articles

The dominating dimensionless numbers of adiabatic shear localization

Adiabatic shear is a complex phenomenon involving thermo-mechanical coupled failure mechanisms, which is affected by material properties, loads, and geometries. In this study, four dimensionless numbers which only contain input parameters and can fully reflect the influence of adiabatic shear are determined by reducing the conservation equations of shear localization to dimensionless terms. The dimensional analysis method of adiabatic shear, along with predictive models for the characteristic parameters of adiabatic shear, are systematically provided by revealing the physical significance of the dimensionless numbers. Based on data analysis, a dimensional analysis method of adiabatic shear for multi-physical processes is proposed, which has been successfully applied to explosively-driven metal shells, to realize the prediction and control of adiabatic shear. This study demonstrates that the prediction models of adiabatic shear-band spacing and width can be unified through a relationship involving the Prandtl number, Pr. Furthermore, the classical prediction models of spacing and width are improved based on the experimental data. It is clearly pointed out that the more favorable the formation of shear localization, the smaller the width and spacing of the shear band, which illustrates the influence of material properties and loads on the spatial distribution of shear bands. In addition, a new prediction model for the propagation velocity of the shear band including Pr is proposed by using dimensional analysis. Compared with the classical model, the new model has higher accuracy, and can correctly reflect the influence of loads, material mechanical and thermophysical properties on the shear-band velocity.

Micromechanical response of an electrodeposited NiP metallic glass by pillar compression under extreme conditions

In this work, the mechanical properties of pulse electrodeposited amorphous nickel phosphorous (NiP), with ∼16 wt% P, was investigated for an improved understanding of the deformation behavior of metallic glasses at extreme conditions, particularly at the microscale. Upon decreasing the temperature to sub-ambient, both the yield strength and the shear band density increase. While the change of yield strength with temperature can be well explained by a cooperative shear model, the increase in the number of shear bands can be related to an increase in potential sites for activation of shear transformation zones due to the enhanced structural heterogeneity at lower temperatures. This, however, hinders the percolation of deformation units and leads to a decrease in the shear band propagation speed, from ∼50 nm/s at 295 K to ∼20 nm/s at 195 K. By testing micropillars across seven orders of magnitude in strain rate, a two-stage strain rate sensitivity is observed, from nearly negligible at the quasi-static range (m1 = 0.001 ± 0.002 for 10−3 s−1 to 10−1 s−1) to highly positive at dynamic high strain rate range (m2 = 0.02 ± 0.004 for 1 s−1 to 1000 s−1). This transition implies a change in the yield-controlling process, from the diffusion-assisted relaxation at quasi-static conditions to the rate of energy barrier crossing of shear transformation zones at high strain rates. These findings highlight several distinctive features of microscale metallic glasses, including the reduced shear band velocity at sub-ambient temperature and the two-stage strain rate sensitivity.

A maximum temperature rise model of the shear band in bulk metallic glasses

Based on mechanisms applicable to bulk metallic glasses (BMGs), such as a superposition principle of an instantaneous finite surface heat source temperature field and a flow model about the shear-band velocity, a maximum temperature rise model of shear bands in BMGs was deduced, ΔTmax=σycpΔupl·vSB2πα. The model describes the dependence of the maximum temperature rise on the yield strength and the shear-band velocity in BMGs. It can be calculated that the maximum temperature rise of BMGs is between 1 K ∼ 30 K at room temperature through these two parameters. A critical temperature, TC, of almost 0.8∼0.9Tg is introduced, at T<TC, the change of the yield strength with temperature in BMGs basically conforms a cooperative shear model (CSM), and at T>TC, a significant reduction of the yield strength in BMGs can be attributed to avoiding failure due to localized material softening.

Shear band velocity and activation volume during shear deformation by acoustic emission in a Zr-based bulk metallic glass

An analysis is presented for the shear band velocity of plastic deformation and activation volume of the shear transformation zone (STZ) in a Zr60Cu30Al10 bulk metallic glass (BMG). Compared to the values calculated by the stick-slip model, the values of shear band velocity calculated after optimization by the acoustic emission technique are much larger than those reported previously. Plastic flow in BMGs is found to be described by a power-law correlation between the maximum velocity of the shear band and the strain rates. Combining the free volume theory and the STZ theory, the relationship between the volume change in the STZ and the shear band velocity is derived as Ω=A(27−lnv/l). The value of A, which is a material dependent constant, is 5.43 × 10−3 for the current BMG at room temperature.

Ductile Ni-based bulk metallic glasses at room temperature

In this work, a series of new Ni76-xCoxNb4P16B4 (x = 5, 10, 15, in at.%) bulk metallic glasses (BMGs) with the maximum diameter in the range of 1.2–1.6 mm were prepared by combining fluxing and J-quenching technology. The effects of Co content on glass forming ability (GFA), thermal stability, mechanical properties, serrated-flow behaviors and corrosion performance of the present Ni-based BMGs were systematically investigated. The ranges of Tg and ΔTx are 664–668 K and 21–31 K, respectively. Uniaxial compressive tests revealed that the present Ni-based BMGs have the compressive plastic strain (εp), yield strength (δy), and fracture strength (δf) that range from 16% to 27%, 2.1–2.6 GPa, and 2.2–3.6 GPa, respectively. The unprecedented mechanical properties originate from more icosahedral-like clusters (ILCs) and crystal-like clusters (CLCs) in the present Ni-based BMGs. It is found that the serrated-flow behaviors of the present Ni-based BMGs transition self-organized critical state (SOCs) into chaotic state (Cs) as plasticity decreases. The stick-slip dynamics were used to calculate the average shear-band velocity (ASBV), which shows an increasing trend as the Co content rises from 5 at.% to 15 at.%. Electrochemical measurements in 3.5 wt.% NaCl solution showed that the Ni71Co5Nb4P16B4 BMG has a self-corrosion current density of 3.30 × 10−8 A/cm2 and significantly stronger corrosion resistance than austenite 316L and 304L stainless steel. The present Ni-based BMGs have excellent comprehensive performance, which has great potential for industrial applications.

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.

Microstructure and mechanical behavior evolution of Ti-based bulk metallic glass induced by sub-Tg isothermal annealing

In this study, the effects of sub-Tg isothermal annealing on the microstructure, mechanical and serrated flow behaviors of Ti33Zr30Cu9Ni5.5Be22.5 bulk metallic glass (BMG) were investigated. The change in free volume content of the BMG was characterized according to the structural relaxation enthalpy δHr and the onset structural relaxation temperature Tr, with the results indicating a monotonic decreasing trend of the free volume content with the extension in annealing time. A number of nanocrystals with a size of approximately 4 nm were precipitated on the glassy matrix when the annealing time was extended to 1.0 h, and then the size of these nanocrystals increased with further prolongation of the annealing time. Meanwhile, the room-temperature compressive plasticity of the Ti33Zr30Cu9Ni5.5Be22.5 BMG greatly improved from 1.4% to 4.2%, and the high strength was retained after annealing for 1.0 h, which can be largely attributed to the formation of the nanocrystals with the size of about 4 nm. With the extension of the annealing time, however, the further growth of the nanocrystals resulted in the degeneration of the compressive strength and the plasticity. The serrated rheology analysis revealed that the distribution histogram of the stress drop for the 1.0 h-annealed specimen represented a well characteristic of power-law distribution, whereas the 4.0 h-annealed showed a chaotic dynamics of jerk flow. Furthermore, the 1.0 h-annealed specimen possessed the lower average stress drop (12 MPa), formation energy per unit shear band (254.9 J/m2) and average shear band velocity (1.21 × 10−5 m s−1).

Postfailure Characterization of Shallow Landslides Using the Material Point Method

Although the mechanisms of slope failure caused by rising groundwater have been widely investigated, the kinematic behavior of landslides in the postfailure stage, which contains essential information for hazard mitigation and risk assessment, has not yet been fully studied. Thus, in this study, a series of numerical simulations using the material point method (MPM) were conducted to analyze the kinematic behavior and soil movement of shallow landslides (infinite slope problems). First, the proposed MPM formulation was validated in a full-scale landslide flume test. The simulated results of final slope profile, runout distance, deposit height, shear band development, slope displacement, and velocity accorded with the experimental results, suggesting that the MPM can quantitatively simulate large deformations. A parametric study of shallow slopes with various hydrological conditions and soil hydraulic and soil mechanical parameters was then performed to assess the influence of the aforementioned factors on landslide kinematics. The simulation results indicated that mechanical behavior at the slope toe is complex; the multiple plastic shear bands generated at the slope toe were due to a combination of shearing and compression. The deposition profile of the slopes was significantly influenced by all input parameters. Among the aforementioned parameters, soil cohesion, location of the groundwater table, and saturated soil permeability most greatly affected runout distance in the sensitivity assessment. Soil friction angle had a minor influence on the kinematic behavior of the slope.

Size-temperature equivalence in tensile deformation of metallic glass

Abstract Tensile fracture of irradiation-free metallic glass specimens with diameters ranging from 100 nm to 500 μm is investigated at different temperatures. A gradual change in fracture morphology from vein-pattern to completely smooth fracture surface to necking is observed with decreasing sample size and testing temperature. The size-temperature equivalence in the entire length scale can be described by considering the thermal effects in shear localization of metallic glasses. We construct an empirical model based on the shear band heating and velocity formulations to qualitatively describe the size and temperature effects on the fracture morphology. Our results suggest that the widely reported size-dependent transition from shear-localized to homogeneous flow in metallic glasses is fundamentally different from the high temperature homogeneous viscous flow. The plastic deformation in nanoscale samples is spatially localized in embryonic shear bands, which never mature to the propagation stage due to lack of heat content.

Aspect ratio effects on the serrated flow dynamic of TiZrHfCuNiBe high entropy metallic glass

The effects of aspect ratio on serrated flow dynamic and plasticity of TiZrHfCuNiBe high entropy bulk metallic glass were investigated. With increasing of the aspect ratio, the stress drop time decreases and a ductile-to-brittle transition was observed, which indicates the motion of shear bands will berestricted in the specimens with smaller aspect ratio. Thus, the shear band velocity can be estimated based on the stick-slip dynamics, which enhances with increasing of the aspect ratio, while the critical shear band velocity is almost identical. Therefore, the specimens with larger aspect ratio will achieve the critical shear band velocity faster until fracture. When the aspect ratio is relatively small, the value of shear-band stability index is larger and promotes stable propagation of the shear bands. In addition, the plasticity and serration size are not monotonic correlated. Benefitting from the abundant secondary shear bands and the interactions at various scales, the plastic deformation can be regarded as the self-organized critical state for samples with better plasticity and lower aspect ratio. However, the self-organized critical state will switch to a chaotic state with increasing of the aspect ratio.

Optimum shear stability at intermittent-to-smooth transition of plastic flow in metallic glasses at cryogenic temperatures

The runaway instability of shear bands leads to catastrophic failure of metallic glasses while the link between the shear banding process and the macroscopic plasticity in a quantitative manner in metallic glasses remains a major challenge.Through a series of compression tests at cryogenic temperatures, we found that the plasticity of the metallic glass can attain a maximum value at a critical temperature at which the transition from serrated flow to non-serrated flow occurs on a Zr-based metallic glass at cryogenic temperatures. The transition point corresponds to the lowest shear-band velocity and the most stable state of plastic shearing during deformation. The results provide an insight for understanding the temperature-dependent plasticity of metallic glasses from shear-band dynamics and may help to design the plasticity/ductility of metallic glasses at cryogenic temperatures.

Optimum Shear Stability at Intermittent-to-Smooth Transition of Plastic Flow in Metallic Glasses at Cryogenic Temperatures

The runaway instability of shear bands leads to catastrophic failure of metallic glasses while the links between the shear banding process and the macroscopic plasticity in a quantitative manner in metallic glasses remains a major challenge.Through a series of compression tests at cryogenic temperatures, we found that the plasticity of the metallic glass can attain a maximum value at a critical temperature at which the transition from serrated flow to non-serrated flow occurs on a Zr-based metallic glass at cryogenic temperatures. The transition point corresponds to the lowest shear-band velocity and the most stable state of plastic shearing during deformation. The results provides an insight for understanding the temperature-dependent plasticity of metallic glasses from shear-band dynamics and may help to design the plasticity/ductility of metallic glasses at cryogenic temperatures.

On the Appearance of Scaling in the Time Dependence of the Rate of Shear Processes in a Metallic Glass

A possible explanation of the square scaling observed in the time dependence of the velocity of shear motions in a metallic glass has been proposed. Numerous experiments demonstrating this scaling in the time variation range by four orders of magnitude and in the shear band velocity range by nine orders of magnitude indicate its universality and the possibility of separating mechanisms of strain localization in metallic glasses.

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.

On the shear band velocity in metallic glasses: A high-speed imaging study

Development of localised shear bands (SB) in bulk metallic glassy (BMG) alloys was investigated by a high-speed microscopic imaging technique. The velocities of SBs propagating by a progressive mechanism were found to be in the m/s range. It has been shown that after rapid initiation, the mean SB velocity decays as a function of time t, exhibiting a scaling-like t−n behaviour with n close to 2 over several orders of magnitude.

Effect of heat treatment on adiabatic shear susceptibility in ZK60 magnesium alloy

Adiabatic shear susceptibility was investigated in the ZK60 magnesium alloy by means of the radial collapse of a thick-walled cylinder. The adiabatic shear susceptibility of ZK60 magnesium alloy samples with different heat treated conditions were evaluated in light of their self-organization characteristics of adiabatic shear bands, such as shear- band spacing, shear- band average length, shear- band average propagated velocity. It is shown that the shear- band spacing in the (as-quenched) sample was 5.2mm with the effective strain of 0.72 and 4.72mm with the effective strain of 0.95, one order of magnitude more than that of the peak-aged sample, with shear- band spacing of 0.49mm (εef=0.72) and 0.38mm (εef=0.95), respectively. Calculations indicated that the average velocity of shear band propagates nearly 2.5 times faster in the peak-aged sample (271m/s) than in that of the (as-quenched )sample (105m/s). Experimental results show that the peak-aged sample has higher adiabatic shear susceptibility, due to precipitates and the higher strength of the peak-aged samples.

The Critical Criterion on Runaway Shear Banding in Metallic Glasses.

The plastic flow of metallic glasses (MGs) in bulk is mediated by nanoscale shear bands, which is known to proceed in a stick-slip manner until reaching a transition state causing catastrophic failures. Such a slip-to-failure transition controls the plasticity of MGs and resembles many important phenomena in natural science and engineering, such as friction, lubrication and earthquake, therefore has attracted tremendous research interest over past decades. However, despite the fundamental and practical importance, the physical origin of this slip-to-failure transition is still poorly understood. By tracking the behavior of a single shear band, here we discover that the final fracture of various MGs during compression is triggered as the velocity of the dominant shear band rises to a critical value, the magnitude of which is independent of alloy composition, sample size, strain rate and testing frame stiffness. The critical shear band velocity is rationalized with the continuum theory of liquid instability, physically originating from a shear-induced cavitation process inside the shear band. Our current finding sheds a quantitative insight into deformation and fracture in disordered solids and, more importantly, is useful to the design of plastic/tough MG-based materials and structures.

Yielding and shear banding of metallic glasses

In this study the yielding and subsequent shear banding evolution process of Zr-, Cu-, Fe- and Mg-based metallic glasses (MGs) were investigated using carefully designed cyclic microcompression tests. It was found that yielding starts from a stable plastic flow with a viscosity of the order of 1012Pas, resembling that of the glass transition. This provides critical evidence that yielding is caused by a stress-induced glass transition with internal randomly distributed liquid-like cores get connected. Up to a critical point the liquidized layer penetrates the entire sample with an initiation viscosity of 108Pas, comparable with that of the liquid-like cores. Along the liquid-like layer shear band propagation involves shear band sliding and is succeeded by shear band arrest. Dynamic softening leads to an increase in the velocity of shear band sliding, with resultant shear offset, which can be successfully captured by a linear softening model. Once the elastic energy in the shear band is dissipated its internal structure begins to recover, with the solid-like matrix being reconstructed, resulting in shear band arrest. A simple diagram elucidating the yielding and shear banding dynamics is constructed, which sheds light on the fundamental nature of the deformation mechanisms of MGs.

Assessing the shear band velocity in metallic glasses using a coupled thermo-mechanical model

Shear band (SB) velocity is a key parameter in assessing the dynamic behavior and also deformation mechanisms of metallic glasses. Using a coupled thermo-mechanical model, we calculated the speed of SB propagation in Vitreloy 1 (Zr41.25Ti13.75Ni10Cu12.5Be22.5) under compression at a strain rate of 10 s−1. The propagation of the SB exhibits a non-uniform speed: a rather slow stage followed by a rapid propagation when the SB is close to the sample surface or at failure. The average speed is estimated to be about 100 m/s, while the maximum speed could reach 1400 m/s. The impact of the varying SB velocity on measurement relying on surface detection such as thermographic images, strain gauge, and surface offsets is discussed.

Room-temperature flow in a metallic glass – Strain-rate dependence of shear-band behavior

The rate dependence of serrated flow in amorphous Al 86.8Ni 3.7Y 9.5 has been investigated by nanoindentation. Three samples, containing different initial amounts and distributions of free volume, were used: as quenched, cold rolled and annealed below the crystallization temperature. When the cold-rolled sample is indented at low rates, no new shear bands form, and stable, time-dependent, flow takes place at pre-existing shear bands, well below the glass transition temperature. Aside from instrumental resolution, factors that likely affect serrated flow include the magnitude of the yield drop and the shear-band propagation velocity. The trends we observe are compared with calculations based on the free-volume theory.