Single Shear Band Research Articles

Designs and mechanical responses of 3D-printed Ti6Al4V porous structures based on triply periodic minimal surfaces with different iso-values

With the increasing applications of additive manufacturing in orthopaedic implants and numerous designs of porous structures available, there is a strong need and opportunity to optimize the structure designs for improved bone integration. Here we created a unique group of sheet structures based on triply periodic minimal surface (TPMS) by varying the iso-value and systematically examined how iso-value influences the mechanical performance of sheet diamond TPMS structures compared to the Octet truss structure. Four iso-values (C) 0, 0.25, 0.5, and 0.75 were designed for sheet Diamond (OSD) TPMS with varying porosity, and Ti6Al4V powder bed fusion was used to produce the porous structures. Compressive tests revealed that iso-value C significantly affected mechanical performance, and interestingly, the impact was porosity-dependent. At high relative density (>0.25), OSD0 (C = 0) displayed the highest elastic modulus and yield strength, whereas at low relative density (<0.25), OSD0.5 showed the highest among all OSD structures. Regarding failure mechanisms, OSD0, OSD0.25, and OSD0.75 showed a mixed domination of stretching and bending, while OSD0.5 was predominantly stretching-dominated. Finite Element Analysis (FEA) found that local yielding initiated at cell nodes upon loading, followed by surface bending and the formation of single or multiple shear bands near the cell nodes. This work demonstrated the feasibility of improving the mechanical performance of porous TPMS structures by simple adjustments in their governing trigonometric functions, serving as a starting point to customize porous structures for specific applications.

Dynamic mechanical response and constitutive model of (Ti37.31Zr22.75Be26.39Al4.55Cu9)94Co6 high-entropy bulk metallic glass

In this work, the mechanical response and fracture characteristics of (Ti37.31Zr22.75Be26.39Al4.55Cu9)94Co6 high-entropy bulk metallic glass (HE-BMG) were investigated in detail over a wide range of strain rates (10−4–105 s−1). The HE-BMG exhibited a negative strain rate sensitivity under uniaxial compression, with the strength showing more significant rate dependence under dynamic conditions. The shear band behavior translated from the dominance of multiple shear bands propagations under quasi-static compression to the rapid propagation of a single shear band to form cracks under dynamic compression. Under dynamic loading, the shearing velocity increased along an arc-shaped displacement path, and the local stress state on the shear fracture surface shifted from compressive-shear to tensile-shear, accompanied by changes in fracture morphologies. The spall strength of HE-BMG decreased as flyer impact speed increased, while the long-term dependence of spall strength on strain rate may be positive. With the increase of impact speed, the main microstructural features of the spalling surface translated from flat regions accompanied by dimples to cup-cone structures. Furthermore, the complete parameters of the Johnson–Holmquist II (JH-2) model for HE-BMG were obtained based on experimental data. Numerical simulations of planar impact, penetration, and hypervelocity impact are in good agreement with experimental results, demonstrating the validity of the JH-2 model parameters. The current work has important guiding value for the application of HE-BMG in space debris protection.

Active failure mechanisms and earth pressure of narrow backfill behind retaining structures

Through a series of model tests accomplished by particle image velocimetry analyses, this study presents the visualisation of the displacement field of narrow soil behind retaining structures under translational mode. The progressive development of failure mechanisms and active earth pressure are measured in the process of tests. Finite-element limit analyses are additionally carried out to investigate and verify the ultimate failure mechanism and active earth pressure acting on retaining structures. Furthermore, this study carried out analyses on the development of failure mechanisms and active earth pressure with different aspect ratios, inclinations of the existing structure and backfill surface surcharge. A reasonable agreement was observed between experimental and numerical results. With an increase in backfill spacing, the failure mechanism of backfill turns from reflective shear bands into a single shear band, and the earth pressure exerted on the retaining structure increases.

Assessment of shear band evolution using discrete element modelling

PurposeThe objective of this paper is to quantitatively assess shear band evolution by using two-dimensional discrete element method (DEM).Design/methodology/approachThe DEM model was first calibrated by retrospectively modelling existing triaxial tests. A series of DEM analyses was then conducted with the focus on the particle rotation during loading. An approach based on particle rotation was developed to precisely identify the shear band region from the surrounding. In this approach, a threshold rotation angle ω0 was defined to distinguish the potential particles inside and outside the shear band and an index g(ω0) was introduced to assess the discrepancy between the rotation response inside and outside shear band. The most distinct shear band region can be determined by the ω0 corresponding to the peak g(ω0). By using the proposed approach, the shear band development of two computational cases with different typical localised failure patterns were successfully examined by quantitatively measuring the inclination angle and thickness of shear band, as well as the microscopic quantities.FindingsThe results show that the shear band formation is stress-dependent, transiting from conjugated double shear bands to single shear band with confining stress increasing. The shear band evolution of two typical localised failure modes exhibits opposite trends with increasing strain level, both in inclination angle and thickness. Shear band featured a larger volumetric dilatancy and a lower coordination number than the surrounding. The shear band also significantly disturbs the induced anisotropy of soil.Originality/valueThis paper proposed an approach to quantitatively assess shear band evolution based on the result of two-dimensional DEM modelling.

Inhibition Behavior of Edge Cracking in the AZ31B Magnesium Alloy Cold Rolling Process with Pulsed Electric Current

To solve the edge crack problem of AZ31B magnesium alloy cold rolling, a strong pulsed electric current was introduced to the cold rolling process. The influence of intensity, frequency, width of pulsed electric current and other parameters on edge cracking of AZ31B magnesium alloy plate cold rolling was analyzed based on the principle of a single variable. According to the experimental results, the assistance of pulsed electric current cut down edge cracking and the inhibition effect increased obviously with larger current parameters. When the parameters of pulsed electric current reached 4800 A, 500 Hz, 50 μs, zero edge cracking was achieved. Statistics of edge cracks, rolling load change, and microstructure analysis showed that the current thermal effect was not obvious and non-thermal effect played a more important role in the rolling process under pulse electric current. Edge cracks initiate at the shear bands. The addition of pulse current increases the number of shear bands and presents a blanket structure. Therefore, the amount of strain experienced by a single shear band decrease, which has a positive effect on inhibiting the formation of edge cracks. Furthermore, electroplastic rolling refines the grains and weakens the basal plane. As the current parameter increases, the hardness of the magnesium strip decreases and the yield and tensile strengths increase.

Exploring the structural and spatial evolutions of contact networks in granular systems via the image-based recognition technique

Contact network, a mesoscale structure of granular matters, can be specified as numerous contact loops that are sensitive to changes in loading and deformation. The mechanical behaviors of granular matters can be reflected by the structural and spatial characteristics of contact loops, yet surprisingly little is known about the spatial issue. To overcome this deficiency, several indexes are proposed to quantify the spatial distribution of contact loops, and the image-based recognition technique, an alternative technique to the Delaunay triangulation method, is developed to extract contact loop information from contact network images. Furtherly, three numerical specimens with different initial densities are compressed biaxially to explore relationships between macro-mechanical behaviors and meso-structures of contact networks. The structural evolution of contact networks is most active in the dense specimen, and the conversion of low- and high-order loops leads to macroscopic volumetric dilatancy. Additionally, the distribution of high-order loops along boundaries proves the existing conclusion that strong contacts developed more near the loading boundary. Limited by the inter-locking effect in low-order loops, even the micro-slips developing also cause a significant weakening in network homogeneity. Contrarily, the evolution from multiple slip bands to the single shear band has little effect on the network homogeneity.

New double surface constitutive model of intermittent plastic flow applied to near 0 K adiabatic shear bands

One of the most interesting phenomena that occur in ductile materials strained in the proximity of absolute zero are the adiabatic shear bands. In the stainless steels, massively used to construct superconducting magnets, their occurrence can be detected by various techniques, including magnetometric methods (feritscope). Formation of adiabatic shear bands is strictly correlated to the occurrence of the intermittent plastic flow (IPF), characteristic of stainless steels strained in liquid or superfluid helium. Evidence for the occurrence of the phase transformation during nucleation and formation of the shear bands in the proximity of absolute zero is for the first time given. The rate of shear bands propagation along the sample as well as the amount of secondary phase is measured. In order to describe the intermittent plastic flow, novel double surface model has been developed. It includes type Huber-Mises-Hencky yield surface, and new recovery surface reflecting the lower bound for the stress oscillations. The yield surface can move and expand due to nonlinear mixed (kinematic and isotropic) hardening, resulting from the phase transformation, whereas, the recovery surface remains constant. The serrations occur between the yield surface and the recovery surface, with the yield surface coming back to its initial position after each serration. Each serration corresponds to formation of single shear band there, where the easy slip planes are available, and the mechanism of anchoring the shear bands by the secondary phase is explained. New double surface model has been correlated to the experimental data and applied to explain stress oscillations during the regular stage of the intermittent plastic flow, when the shear bands gradually cover the gauge length of the sample.

Mechanical properties, failure mechanisms, and scaling laws of bicontinuous nanoporous metallic glasses

Molecular dynamics simulations are employed to study the mechanical properties of nanoporous CuxZr1-x metallic glasses (MGs) with five different compositions, x = 0.28, 0.36, 0.50, 0.64, and 0.72, and porosity in the range 0.1 < ϕ < 0.7. Results from tensile loading simulations indicate a strong dependence of Young's modulus, E, and Ultimate Tensile Strength (UTS) on porosity and composition. By increasing the porosity from ϕ = 0.1 to ϕ = 0.7, the topology of the nanoporous MG shifts from closed cell to open-cell bicontinuous. The change in nanoporous topology enables a brittle-to-ductile transition in deformation and failure mechanisms from a single critical shear band to necking and rupture of ligaments. Genetic Programming (GP) is employed to find scaling laws for E and UTS as a function of porosity and composition. A comparison of the GP-derived scaling laws against existing relationships shows that the GP method is able to uncover expressions that can predict accurately both the values of E and UTS in the whole range of porosity and compositions considered.

Effect of Ag substitution for Ti on the deformation behaviors of in-situ Ti-based bulk metallic glass composites

Four Ti53−xZr20Nb10Cu5Be12Agx (x = 0, 1, 3 and 5 at.%) bulk metallic glass composites (BMGCs) with various size, volume fraction and morphology of in-situ crystal phase were prepared by the arc-melting method. The shear bands extensions under strain of 5% and 20% were observed to explore the contributions of in-situ crystal phase on the deformation behaviors. The results showed that addition of Ag element significantly increased the glass forming ability. When Ag addition increased from 0 to 5 at.%, the volume fraction of in-situ crystal phase decreased from 74.5% to 38.3%, the morphology transformed from the dense cluster to the spotted shape, resulting in the decrease of dendrites span length (L) and the increase of dendritic arm spacing (DAS). The size, volume fraction and morphology of in-situ crystal phase had great influence on the initiation and extensions of shear bands. In the in-situ BMGCs, the crystal phases with the appropriate size, volume fraction and morphology were conducive to the initiation of multiple shear bands and could effectively restrain the expansion of single shear band, improving the plasticity, and the in-situ BMGCs with Ag element of 3 at.% exhibited the highest plasticity of 17.9%.

Shear instability in heterogeneous nanolayered Cu/Zr composites

Ultrastrong nanolayered metallic composites are usually subjected to low ductility due to plastic instability during deformation. Here we investigated the shear instability of a newly designed heterogeneous nanolayered Cu/Zr composites by microindentation. The heterogeneity in size was generated by inserting a few thin Cu-Zr bilayers with an individual layer thickness of 2.5 - 10 nm into the interface region of the Cu/Zr layered composites with an individual layer thickness of 100 nm. The microindentation tests showed that multiple shear bands appeared in the heterogeneous composite with one bilayer, whereas only a single shear band was formed in that with two or three bilayers. Most importantly, the layer strain in the multi-shear band region is much smaller than that in the single-shear band area. For example, the strain of the 100 nm layers within the shear band in the composite with one 10 nm bilayer could reach as low as 2.8, which was less than half of that in the composite with three 10 nm bilayers, i.e., 6.1. These findings demonstrated that strain delocalization can be achieved through shear band multiplication if an appropriate number of thin bilayers were used as interlayers in the 100 nm Cu/Zr composites. Besides, compared with the homogeneous composite with an individual layer thickness of 100 nm and the bimodal composite which is composed of alternating one 100 nm Cu-Zr bilayer and two 10 nm Cu-Zr bilayers, the heterogeneous composite with one bilayer displayed a higher strength (2.15 GPa) and a favorable resistance to strain localization.

Deformation and Failure Mechanism of Weakly Cemented Mudstone under Tri-Axial Compression: From Laboratory Tests to Numerical Simulation

The success of the water-preserved mining technology is closely related to the stability of the aquiclude and the aquifer, in particular, which is made of weakly cemented rock mas. This paper starts with the tri-axial compression tests on the mudstone specimens obtained from the Ili mining area, followed by the systematic numerical simulation via the Particle Flow Code (PFC) program, aiming at obtaining an in-depth understanding of the response of weakly cemented mudstone under tri-axial compression loading state. The main outcomes obtained from this research indicated that: (1) the behavior of weakly cemented mudstone is closely sensitive to the confining pressure. As the confining pressure increases, both the peak strength and plastic deformation capacity of weakly cemented mudstone will be enhanced; (2) the main feature of weakly cemented mudstone after tests is its centrosymmetric “Z” shape, mainly attributed to the progressive separation of the particle element of mudstone; (3) the behavior of weakly cemented mudstone either in terms of the axial stress-axial strain or the failure mode is sensitive to the confining pressure. If the applied confining pressure is lower than 5 MPa, the micro-cracks are in the form of the single shear band, whereas the tested specimens will tend from brittle shear to plastic shear associated with the “X” shear when the confining pressure is higher than 5 MPa; and (4) The failure of weakly cemented mudstone is mainly attributed to the continuous expansion and penetration of internal microcracks under compression. The brittle failure mode of weakly cemented mudstone tends to ductile failure with the increase of confining pressure. The main contribution of this research is believed to be beneficial in deepening the understanding of the mechanics of weakly cemented mudstone under tri-axial compression and providing the meaningful reference to the practical application of water-preserved mining in the Ili mining area.

Research on Taylor impact fracture behavior of ZrCuAlNiNb amorphous alloy

Under argon conditions, the Taylor impact test for ZrCuAlNiNb amorphous alloy with impact velocity range of 78.9-155 m/s was carried out, the failure fracture process of the material was recorded by high-resolution high-speed photography, and the fractured samples after fracture were recovered. The microscopic morphology of the section was observed by scanning electroscope, and the fracture behavior of the material at different impact speeds was analyzed. ZrCuAlNiNb amorphous alloy breaks from a single main shear band under low-speed impact to a multi-shear band break at high speed (≥ 150 m/s), and several secondary shear straps are formed along the axial direction of the sample. Its complex force leads to a variety of fractured forms, and dynamic temperature rise aggravates the thermal softening effect of the material. ZrCuAlNi crystal alloy is transmitted by axial cracks, which cause the crystal alloy to fracture under the interaction of multiple cracks, and the fractured morphology presents a river-like cleavage fracture. The study of the mechanical properties of ZrCuAlNiNb amorphous alloys and their failure behavior provide theoretical guidance and experimental basis for the application of ZrCuAlNiNb amorphous alloys.

Synchrotron 4D X-Ray Imaging Reveals Strain Localization at the Onset of System-Size Failure in Porous Reservoir Rocks

Understanding the mechanisms of strain localization leading to brittle failure in reservoir rocks can shed light on geomechanical processes such as porosity and permeability evolution during rock deformation, induced seismicity, fracturing, and subsidence in geological reservoirs. We perform triaxial compression tests on three types of porous reservoir rocks to reveal the local deformation mechanisms that control system-size failure. We deformed cylindrical samples of Adamswiller sandstone (23% porosity), Bentheim sandstone (23% porosity), and Anstrude limestone (20% porosity), using an X-ray transparent triaxial deformation apparatus. This apparatus enables the acquisition of three-dimensional synchrotron X-ray images, under in situ stress conditions. Analysis of the tomograms provide 3D distributions of the microfractures and dilatant pores from which we calculated the evolving macroporosity. Digital volume correlation analysis reveals the dominant strain localization mechanisms by providing the incremental strain components of pairs of tomograms. In the three rock types, damage localized as a single shear band or by the formation of conjugate bands at failure. The porosity evolution closely matches the evolution of the incremental strain components of dilation, contraction, and shear. With increasing confinement, the dominant strain in the sandstones shifts from dilative strain (Bentheim sandstone) to contractive strain (Adamswiller sandstone). Our study also links the formation of compactive shear bands with porosity variations in Anstrude limestone, which is characterized by a complex pore geometry. Scanning electron microscopy images indicate that the microscale mechanisms guiding strain localization are pore collapse and grain crushing in sandstones, and pore collapse, pore-emanated fractures and cataclasis in limestones. Our dynamic X-ray microtomography data brings unique insights on the correlation between the evolutions of rock microstructure, porosity evolution, and macroscopic strain during the approach to brittle failure in reservoir rocks.

Numerical analysis of surface foundation subjected to strike–slip faulting: model boundaries, pre-softening volumetric response, parametric study

The paper investigates strike-slip fault rupture propagation through dense sand and its interaction with surface foundations, employing 3D finite element (FE) modelling. Two soil constitutive models (implemented in Abaqus through user subroutines) are employed for this purpose: (i) a recently developed simple yet efficient model with a Mohr–Coulomb yield criterion, which incorporates post-yield isotropic frictional hardening and softening (MC–HS model); and (ii) the basic version of the more sophisticated hypoplastic model for sand. Both models are calibrated on the basis of monotonic triaxial compression tests (and an additional oedometer test for the hypoplastic model), conducted as part of this study. The numerical predictions are comparatively assessed against centrifuge model test results. In accord with the centrifuge model tests, the free-field analyses with the MC-HS model reveal a complex fault pattern at the ground surface, consisting of Riedel (R) shears. These are the surficial manifestation of complex 3D structures of helicoidal geometry, attributed to the spatial variation of shear stresses within the overburden soil due to the imposed bedrock offset. The development of R shears is primarily controlled by the pre-softening volumetric soil response in monotonic compression and soil dilation. The latter is underestimated by the basic hypoplastic model, thus predicting the formation of a single straight shear band instead of R shears. A parametric study is conducted employing the validated MC-HS model, exploring fault rupture–soil–foundation interaction. Foundation response is shown to be sensitive to the surficial fault pattern (R shears vs. single fault trace), but the mechanism (rotational vs. translational) and foundation distress are not affected to the same extent. A two-step design strategy is outlined, requiring a free-field analysis to capture the surficial fault pattern, followed by a minimum of four interaction analyses, varying the fault-normal and fault-parallel foundation location.

Synergetic toughening mechanism of spherical α-La phases and micron-sized AlLa3 intermetallic in La-based bulk metallic glass composite

A La74Al14Cu6Ni6 bulk metallic glass matrix composite (BMGMC) with in situ spherical α-La phases and micron-sized AlLa3 intermetallic compounds is prepared by adjusting the processing parameters and presents a good combination of high strength and plasticity. Compared with conventional single α-La dendrite-reinforced La74Al14Cu6Ni6 BMGMCs that have a low fracture strength and plasticity, the obtained composite shows a significant plastic strain of 17% and a high fracture strength of 566 MPa. The results show that the formation of ductile bulky spherical α-La phases and hard AlLa3 intermetallic compounds can effectively hinder the rapid propagation of single shear band, and the synergistic effect of the two phases accounts for the significant increase in plasticity. Furthermore, in situ formed AlLa3 intermetallic compounds with a hardness of 238 HV, which has strong interaction with multiple shear bands, dramatically improve the fracture strength of the composite.

Investigation of the effect of cementing ratio on the mechanical properties and strain location of hydrate-bearing sediments by using DEM

This study investigates the strain location and particle-scale contact properties of methane hydrate-bearing sediments with different cementing ratios λ through adopting discrete elements method (DEM). In this paper, a new numerical samples preparation technique that can reflect the real microstructure of methane hydrate-bearing sediments based on the nucleation and growth mechanism of methane hydrate is proposed, and a new hydrate bonding model that can consider the coupling effects of temperature and pore pressure is established. Then a series of biaxial shear tests in which flexible particle membrane boundaries are adopted to capture inhomogeneous deformation on the methane hydrate-bearing sediments with different cementing ratios are carried out to provide new insight on the formation and development of shear bands and the evolution of particulate-scale information inside hydrate-bearing sediments. The simulation results show that the increase of hydrate cementing ratios λ results in enhanced strength and volumetric dilatancy of hydrate-bearing sediments. The different hydrate cementing ratio creates several important differences about strain location modes of bond breakage, contact force chains, particles displacement and rotation, local void ratio, local coordination number, and local volumetric strain with the samples of lower cementing ratio exhibit two shear bands while the samples of higher cementing ratio exhibit single shear band. The main mechanical behaviors of hydrate-bearing sediments are controlled by three microscopic contacts (sand-sand contacts, sand-pore-filling hydrate contacts, and sand-cementation hydrate).

Mechanical properties of Cu50Zr50 amorphous/B2-CuZr crystalline composites studied by molecular dynamic method

The effects of uniformly distributed spherical B2-CuZr crystal particles on the mechanical properties of Cu50Zr50 amorphous alloy were studied. With the increasing of the radius of B2-CuZr particles, the yield strength of nanocomposites decreases first and then increases. In this study, the material shows the best comprehensive mechanical properties when the radius of B2-CuZr particle is 2.3 nm, corresponding volume fraction is 29.1%. Compared with the Cu50Zr50 amorphous alloy, multiple shear bands were formed in the Cu50Zr50 amorphous/B2 crystalline composites during compression. Analysis of the deformation mechanism show that the amorphous-crystalline interfaces play the key role in this process. B2-CuZr particles retard the rapid expansion and propagation of the single shear band, and it makes the nanocomposites have the better plasticity than the Cu50Zr50 amorphous alloy.

Interaction between parallel shear bands in a metallic glass

We present molecular dynamics simulations in a large CuZr metallic glass sample that allows the linking of the structural properties of a single shear band to the presence of other subsequently forming parallel shear bands. In a closely controlled study, we observe that the subsequent formation of parallel shear bands restores the disrupted icosahedral matrix in the core of previously formed shear bands, i.e., the shear-band core structure is partially relaxed to the original bulk level. The relaxation caused by the interaction between shear bands also manifests in a reduction of the potential energy and in an eventual return of previous plastic regions called shear transformation zones.

Study of shear behavior of granular materials by 3D DEM simulation of the triaxial test in the membrane boundary condition

This paper studies the shear behavior of granular materials by using a three-dimensional (3D) discrete element method (DEM) simulation of the triaxial test. The experimental triaxial tests were conducted on glass beads samples for verification. DEM simulations of the triaxial test were carried out in the membrane boundary condition consisting of 37,989 membrane particles. A new method that divides the irregular sample shape into two parts of cones and parts of three-dimensional simplexes is used to follow the volume change of irregular deformation of samples. The free rotatable upper platen is considered during the shearing process, which influences the shear behavior of samples especially in the residual stage and formations of a single shear band or X-shape shear band. The confining pressures have been demonstrated to influence the rotation angle and angular velocity of the upper platen. Moreover, the timing of replacing a rigid wall boundary condition with the membrane boundary condition is investigated, which affects the porosity of samples before shearing and the mechanical strength. The DEM model in the membrane boundary condition reflects well the evolution of irregular sample deformation and shear band in the shearing process. From the perspective of micro structures, the normal force decreases and the tangential stress increases during the shearing stage. This study greatly improves the accuracy of DEM simulations of the triaxial test in the membrane boundary condition.

Hardened core of bilayer shear bands in a Zr-based metallic glass

Bilayer shear bands with a spacing of hundreds of nanometers were prepared in a Zr-based metallic glass. Elastic properties of the bands were detected using a contact-resonance atomic force microscope. Compare with an elastic modulus reduction in each single shear band, the core of the bilayer shear bands is hardened. One possible reason for the forming of the bilayer shear bands is the load releasing and position adjustment during the severe plastic deformation process. Our results reveal a new plastic deformation mechanism of the shear bands in the form of layer by layer, and provide a promising strategy to control the stability of shear bands and enhance the plasticity of metallic glasses.