Band Propagation Research Articles

Atomic-scale icosahedral short-range ordering in a rejuvenated Zr-based bulk metallic glass upon deep cryogenic treatment

Tailoring the formation and distribution of loose-packing regions and dense-packing regions in the bulk metallic glasses (BMGs) has long been considered to facilitate macroscopic mechanical properties and break strength-ductility trade-off. Herein, studies on structural heterogeneity caused by the deep cryogenic treatment (DCT) were systematically carried out to not only probe the atomic-scale structure-property relationships but also further understand the deformation mechanisms involving improved plasticity without sacrificing strength on the basis of these experimental results in rejuvenated Zr-based BMGs. The internal stress due to the cooling contraction will activate the atomic motion in weakly bonded regions and meanwhile form perfect icosahedral short-range ordering (ISRO) via containing mobile atoms to become denser geometric configurations. The multiplication and propagation of shear bands are closely associated with their structural features originating from the optimization of perfect icosahedral ordered structures in the rejuvenated glassy matrix. It is believed that these findings are helpful to shed light on the correlations between atomic-scale structural heterogeneity and macroscopic mechanical properties and further provide new possibilities for the development of promising BMGs with strength-ductility synergy.

Transition from softening to hardening related with strain rate in Zr-based metallic glasses

The dynamic deformation and fracture behavior of Zr-based metallic glasses related with strain rate were systematically investigated by dynamic uniaxial compressive tests over a wide range of strain rate. The dynamic fracture strength with the increase of the strain rate shows two stages, i.e., the transition from strain-rate softening to strain-rate hardening. In the first stage, the temperature rise within the shear bands gradually increases due to increasing strain rate. The viscosity in the shear bands greatly reduces and the free volume keeps increasing, which results in the occurrence of strain-rate softening and significantly promotes the propagation of shear bands of Zr-based MGs. However, in the second stage, the increasing temperature in the shear band results in the occurrence of localized crystallization of Zr-based MGs. The shear bands are difficult to extend due the strong interaction between multiple shear bands and dendritic crystal, leading the occurrence of strain-rate hardening.

A unified finite strain gradient-enhanced micropolar continuum approach for modeling quasi-brittle failure of cohesive-frictional materials

In this work, a novel framework for modeling quasi-brittle crack propagation and shear band dominated failure of cohesive-frictional materials like concrete, mortar, rock, tough ceramics, energetic materials, but also granular materials like sands or powders in terms of a unified continuum approach is proposed. It is based on a combination of the gradient-enhanced continuum with gradients of internal variables for representing quasi-brittle cracking, and the micropolar continuum, accounting for the deformation of the microstructure. For developing the gradient-enhanced micropolar framework, the set of balance equations and the kinematic relations are derived, and the constitutive relations are established in a general manner. The framework is formulated in a geometrically exact setting, based on the thermodynamically sound theory of hyperelasto-plasticity, and the numerical implementation by means of the finite element method is discussed. For assessing the approach, realizations of this new approach in terms of constitutive models for particular materials are developed. They are applied to numerical benchmark examples, investigating various loading conditions, and the obtained results are validated by means of a comparison with experiments from the literature.

On the Lüders band formation and propagation in NiTi shape memory alloys

• Both the B19′ martensite and B2 austenite can form Lüders band. • Lüders band initiation strain rate is two orders of magnitude of the applied strain rate. • Lüders band forms with a finite minimum width. • Lüders band propagates with a transition zone half of the band minimum width. • Transition zone local strain rate is more than one order of magnitude of the applied strain rate. Near-equiatomic NiTi shape memory alloys are known to exhibit Lüders-type deformation associated with a stress-induced transformation. Many studies have been conducted in the past mainly focusing on the macroscopic characteristics of the phenomenon and some theories have been proposed in the literature to explain its mechanisms, but some aspects of this phenomenon are still unclear, particularly at the microscopic scale. This study investigated the local strain evolution during the initiation and propagation of Lüders band in a pseudoelastic NiTi alloy during tensile deformation by means of digital image correlation (DIC) analysis. Based on the evidence collected, distinct stages of Lüders band formation and propagation are defined and the corresponding local strain rates are obtained. These local strain rates are much higher than the global strain rate of the testing, giving insight to the mechanism of this phenomenon.

Rare events and disorder control the brittle yielding of well-annealed amorphous solids

We use atomistic computer simulations to provide a microscopic description of the brittle failure of amorphous materials, and we assess the role of rare events and quenched disorder. We argue that brittle yielding originates at rare soft regions, similarly to Griffiths effects in disordered systems. We numerically demonstrate how localized plastic events in such soft regions trigger macroscopic failure via the propagation of a shear band. This physical picture, which no longer holds in poorly annealed ductile materials, allows us to discuss the role of finite size effects in brittle yielding and reinforces the similarities between yielding and other disorder-controlled nonequilibrium phase transitions.

Mapping Shear Bands in Metallic Glasses: From Atomic Structure to Bulk Dynamics.

A deep understanding of the mechanisms controlling shear banding is of fundamental importance for improving the mechanical properties of metallic glasses. Atomistic simulations highlight the importance of nanoscale stresses and strains for shear banding, but corresponding experimental proofs are scarce due to limited characterization techniques. Here, by using precession nanodiffraction mapping in the transmission electron microscope, the atomic density and strain distribution of an individual shear band is quantitatively mapped at 2nm resolution. We demonstrate that shear bands exhibit density alternation from the atomic scale to the submicron scale and complex strain fields exist, causing shear band segmentation and deflection. The atomic scale density alternation reveals the autocatalytic generation of shear transformation zones, while the density alternation at submicron scale results from the progressive propagation of shear band front and extends to the surrounding matrix, forming oval highly strained regions with density consistently higher (∼0.2%) than the encapsulated shear band segments. Through combination with molecular dynamic simulations, a complete picture for shear band formation and propagation is established.

Tensile deformation behaviors of laser powder bed fusion fabricated Al–Mn-Sc alloy with heterogeneous grain structure

The processability of laser powder bed fusion (LPBF) fabricated Al alloys can be significantly improved by the introduction of grain refinement inoculates. However, tensile testing results showed that the fabricated alloys exhibited unusual deformation characteristics, including discontinuous yielding, Lüders elongation and low work hardening behaviors. In this study, the underlying tensile deformation mechanisms of the inoculates modified Al alloys after LPBF processing were elucidated through various characterization techniques, using the recently developed Al–Mn-Sc alloy as an example. It was found that the “extra hardening” effect caused by the fine grain structures promoted the discontinuous yielding behavior, while lack of mobile dislocations within the fine grain regions triggered the Lüders bands propagation. On the other hand, the high initial strain hardening rate contributed to the strong work hardening behaviors of the fabricated alloy with lower fine grain fractions, whereas all alloys with different heterogeneous grain structures proved similar dynamic recovery behaviors at higher strains.

Perspectives of Microstructure Refinement of Aluminum and Its Alloys by the Reciprocating Extrusion (Cyclic Extrusion Compression-CEC).

This paper presents a study on the perspectives of structure refinement of aluminum and its alloys by reciprocating extrusion (cyclic extrusion compression—CEC). The study included Al99.5 and Al99.992 aluminum and AlMg5 and AlCu4Zr alloy. Aluminum and alloys were deformed by reciprocating extrusion (CEC) in the strain range ϕ = 0.42 (1 CEC cycle) to ϕ = 59.8 (67 CEC cycles). After deformation, the structure of the specimens was investigated by optical microscopy (OM) and transmission electron microscopy (TEM), which revealed that the primary mechanism of hardening, over the range of applied strains, was the result of the propagation of shear bands throughout the specimens. The intersection of shear bands was found to divide the volume of the specimens into nano and microvolumes with dimensions limited by the width of the microbands. Due to structure renewal processes such as polygonization and dynamic geometric recrystallization, the formed micro and nano volumes were transformed into nano and micrograins with large misorientation angles. In terms of the occurrence of grain microstructure, a sustained uniform level of hardening was found, which was defined as steady-state flow. The research has shown that the steady state of flow is a result of the competitive interaction between the processes of hardening and structure renewal. The higher the metal purity, the higher the intensity of the structure renewal processes was. The formation of new grains and their growth under dynamic and post-dynamic recrystallization was observed in Al99.992 aluminum, in which high purity of the metal and high strain accumulation caused the growth of new grains at room temperature.

Ductile vs. Brittle Strain Localization Induced by the Olivine–Ringwoodite Transformation

As it descends into the Earth’s mantle, the olivine that constitutes the lithosphere of subducting slabs transforms to its high-pressure polymorphs, wadsleyite and ringwoodite, in the so-called transition zone. These transformations have important rheological consequences, since they may induce weakening, strain localization, and, in some cases, earthquakes. In this study, germanium olivine (Ge-olivine) was used as an analogue material to investigate the rheology of samples undergoing the olivine–ringwoodite transformation. Ge-olivine adopts a ringwoodite structure at pressures ~14 GPa lower than its silicate counterpart does, making the transformation accessible with a Griggs rig. Deformation experiments were carried out in a new-generation Griggs apparatus, where micro-seismicity was recorded in the form of acoustic emissions. A careful analysis of the obtained acoustic signal, combined with an extensive microstructure analysis of the recovered samples, provided major insights into the interplay between transformation and deformation mechanisms. The results show that significant reaction rates cause a weakening via the implementation of ductile shear zones that can be preceded by small brittle precursors. When kinetics are more sluggish, mechanical instabilities lead to transformational faulting, which stems from the unstable propagation of shear bands localizing both strain and transformation. The growth of these shear bands is self-sustained thanks to the negative volume change and the exothermic nature of the reaction, and leads to dynamic rupture, as attested by the acoustic emissions recorded. These micro-earthquakes share striking similarities with deep focus earthquakes, which may explain several seismological observations such as magnitude frequency relations and the occurrence of deep repeating earthquakes and foreshocks.

Effects of structural geometry on the localized deformation of superelastic NiTi sheets

Due to unique reversible martensitic transformation, superelastic NiTi can be strained to several percents and fully recover upon unloading. It is well accepted that superelastic NiTi under primarily tensile deformation is localized rather than homogenous. In this paper, we examine the heterogeneous deformation of superelastic NiTi sheets with various aspect ratios (the ratio of gauge width to gauge length). For the specimens with aspect ratios lower than 2, the deformation at quasi-static loading condition is realized by the nucleation and propagation of a major transformation band. For the specimen with aspect ratio of 4, multiple transformation bands coexist at the loading rate as low as 1 × 10−4/s, and the geometry of the transformation band is no longer well-defined. Finite element analysis indicates that the transition of localized deformation mode is attributable to the enhanced stress biaxiality and stress heterogeneity with the increasing aspect ratio.

Macro-meso fatigue failure characteristics of a bimsoil under multistage cyclic triaxial loads with different frequencies

The dynamic mechanical response of block-in-matrix-soils (bimsoils) is crucial to the long-term stability predication of constructions and building structures made of bimsoils. Although the dynamic failure behaviors of bimsoil under cyclic loads have been widely understood, the influence of loading frequencies on the macro-meso structural deterioration governing localized band propagation have not been well understood. Herein, multistage cyclic triaixal tests and post-test X-ray computed tomography (CT) scanning have been performed on bimsoil with various loading frequencies (f = 0.1 Hz, 0.2 Hz, 1.0 Hz, and 2.0 Hz). The cyclic triaxial tests simulated the behavior of bimsoil material under varied velocities of passing vehicle herein. The macro-meso fatigue failure characteristics were analyzed in terms of stress-strain responses, stiffness degradation, and meso-structural changes. Testing results show that the applied loading frequency alters the coupling degree of soil matrix and rock blocks, and damage develops fully within bimsoil under relatively low loading frequency. In addition, the failure mode of bimsoil changes from bulging failure to shear failure with the increases of loading frequency, and the volumetric deformation is the largest for a bimsoil sample subjected to low loading frequency. Moreover, post-test CT scanning reveals the meso-structural degradation within bimsoil, the multiple interface damage and cracking contribute a lot to the strength, volumetric deformation and failure modes. It is suggested the contact, interlocking, occlusion, and separation among the rock blocks promote the volume dilatancy when subjecting to low loading frequency.

Shear banding and serrated flow behaviors of high toughness Zr61Ti2Cu25Al12 bulk metallic glass under bending

By interrupted three-point bending experiments, the detailed evolutions of shear-banding and serrated flow as well as their correlation of high toughness Z61Ti2Cu25Al12 bulk metallic glass (BMG) under bending were systematically studied. Three stages can be classified during plastic bending of Z61Ti2Cu25Al12 BMG based on the different characteristics of shear-banding and serrated flow behaviors. Moreover, there has a strong correlation between shear-banding and serrated flow at different stages of plastic bending. It is noteworthy that the driving force for shear bands propagation of BMG beam under bending depends on the bending moment, instead of the applied load. Thus, remarkable positive correlations among bending moment, shear band zone height and average load drop of serrations were found during plastic bending. During the progressive propagation of multiple shear bands, intense interactions and competitions among these shear bands have occurred, which manifested by the self-organized criticality behavior from serrated flow dynamics, as well as the very finer irregular striation patterns and uneven fluctuant morphologies which presented on the shear offset surface. The sizeable plastic zone of Z61Ti2Cu25Al12 BMG is very favorable to achieve the greater macroscopic plasticity and lower the risk of fast catastrophic fracture. Thus, Z61Ti2Cu25Al12 BMG is a promising engineering material for structure elements which are naturally subjected to bending load, such as compliant mechanisms and microelectromechanical systems.

The importance of lamellar architecture to obtain ductility in heavily cold-worked pearlitic steels revealed by microbending experiments

In-situ microbending experiments were conducted to understand the effect of composite architecture on the deformation behavior and ductility of heavily cold-worked pearlitic steels. Two extreme architectures were deliberately chosen for this purpose: first, a high-pressure torsion-deformed fully pearlitic steel consisting of a nanolayered lamellar arrangement of ferrite and cementite and second, an even further refined state where this lamellar arrangement is transferred to a carbon-decorated ferritic subgrain structure. Despite the enormous strength of these samples, in-situ microbending experiments reveal an astonishing homogeneous deformation capability of nanostructures – much larger than in uniaxial compression or tension. Plastic strains of up to 20% can be realized without severe failure of the specimens. This outstanding ductility seems to be linked to the inherent strain gradient of the bending beams, hindering early initiation and propagation of shear bands. While this holds true for both tested states, the architecture of the pearlitic steels plays a predominant role in this respect. In case of the lamellar architecture homogenous plastic flow can be realized up to significantly larger plastic strains, while shear band and crack formation occur already at lower plastic strains in case of the carbon-decorated subgrain structure.

Tunable nonreciprocal transmission based on non-Hermitian optical system with magnetic optical materials in a one-dimensional multilayer structure

In this study, a one-dimensional composite structure composed of a PT-symmetric system and magnetic optical (MO) materials is designed. The nonreciprocal propagation of a one-dimensional multilayer structure is investigated both theoretically and numerically based on the transfer matrix theory. Different from the single nonreciprocal frequency in the parity-time (PT) system, two adjacent band gaps are changed into a pair of nonreciprocal bands under the effect of MO materials and a PT system above the PT exceptional point, and extraordinary transmissions are inspired in some nonreciprocal frequencies. At the same time, the nonreciprocal propagation bands can be tuned based on the different choices of external magnetic field directions. Furthermore, with an increase in the gain/loss factor, the two nonreciprocal band gaps both disappear and form two bands with an extraordinary transmission at certain frequencies. Such peculiar properties in the composite structure may have broad potential applications in communication and integration devices.

Molecular dynamics study of fracture and plastic deformation of Cu/Cu64Zr36 crystalline/amorphous composites with a pre-existing void

In this paper, the fracture behavior and damage mechanism of Cu/Cu64Zr36 crystalline/amorphous composites with a pre-existing void are investigated by molecular dynamics (MD) simulation. The results show that the incorporated Cu crystalline phase improves the global plasticity by dislocation slip, effectively avoids catastrophic localization and hinders shear band propagation by controlling the volume ratio of the crystalline/amorphous composite. As the volume fraction of crystalline phase increases, the dislocation density increases, while the degree of strain localization decreases which is associated with homogeneous activation of shear transformation zones (STZs). Numerous dislocation movements and homogeneous STZ activation become the main reason for enhancing the global plasticity of the composites. In addition, the existence of voids changes the distribution of shear strain: the peak shear strain is distributed around the void, where it is most likely to activate dislocation movement and STZ percolation as well as embryonic shear band formation.

Design, fabrication, and characterization of a single-polarization single-mode flexible hollow waveguide for low loss millimeter wave propagation.

A flexible metallic waveguide with elliptical core that achieves single-polarization single-mode (SPSM) propagation at millimeter wave was designed, fabricated, and characterized. In order to achieve SPSM propagation, optimization of the lengths of major/minor axes of elliptical core was conducted to cut off one of the two orthogonally polarized fundamental modes and all high-order modes. A one-meter long hollow elliptical waveguide (HEW) with major/minor axis length of 1.5/2.7 mm was fabricated. The substrate tube was a flexible elliptical polycarbonate (PC) tube, which was fabricated through glass-draw technique. Silver film was then coated on the inner surface of the tube. Simulation results show that the 1.5/2.7 mm HEW maintains SPSM propagation in the frequency band from 66.5 to 114 GHz. The SPSM operation was experimentally discussed in detail at 100 GHz. The measured loss of 2.58 dB/m and the output polarization ratio of 99.9% was obtained after propagating one meter. Furthermore, the waveguide was robust to bending and twisting. The additional loss was as small as 0.2 dB/m even when the waveguide was coiled into a circle. The potential application of HEWs as polarizers was demonstrated by using a 10 cm long waveguide for polarization detection and extinction ratio of 22.3 dB was achieved at 100 GHz.

Topology optimization of soft compressible phononic laminates for widening the mechanically tunable band gaps

Active tuning of frequency bandgaps has received significant attention in the recent past. To this end, soft compressible phononic composites have indicated great promise owing to their capability to undergo large reversible deformations and deformation dependent constitutive properties. In this investigation, we present an optimization framework for arriving at the optimum topology of a two-phase soft compressible phononic composite for maximizing the frequency gap between the first four consecutive frequency bands of longitudinal wave propagation. The laminate is subjected simultaneously to an equal biaxial pre-stretch in the plane perpendicular to the direction of wave propagation and a prestress in the direction of wave propagation. The nonlinear hyperelastic neo-Hookean material model is employed for characterizing the constitutive behavior of the soft compressible laminate phases. The finite element method with Bloch–Floquet theory is employed for finding the band-structure of the infinitely periodic soft laminate. A gradient-based method of moving asymptotes is used to solve the underlying topology optimization problem. In particular, we present the optimum unit cell designs for two separate problems involving maximization of the absolute width of the band gap and that of the relative width of the band gap when compared to that in the un-deformed laminate. Test cases are presented to highlight the effects of the levels of biaxial prestretch and the longitudinal prestress. Our results indicate that a compressional longitudinal prestress and a lateral prestretch have a favorable impact on widening of the frequency band-gaps. The numerical framework and the inferences reported here can find their potential use in the optimal design of soft compressible composites used in acoustic applications.

Stress-induced gradient rejuvenation framework and memory effect in a metallic glass

Rejuvenation of metallic glasses (MGs) brings them in higher-energy states, which improves their mechanical properties. However, how to rejuvenate MGs through a fast and simple approach is still a challenge. In the present work, a nonuniform structure consisting of a center-relaxation region surrounded by an edge-gradient-rejuvenation framework was created in a Zr-based bulk metallic glass (BMG) by lateral elastostatic preloading. Such a nonuniform structure greatly suppresses the rapid propagation of shear bands and has the potential to overcome the inverted relationship between strength and plasticity. More interestingly, we found a stress-induced memory effect, viz., the recovery of relaxation enthalpy during elastostatic loading, which is quite different from the thermal-induced memory effect in previous works. This indicates a certain degree of equivalence between stress and temperature in the dynamics of MGs.

Investigating Shear Bands Propagation in Sands by Using the Developed Elemental-like Direct Shear-faulting Box

Investigating Shear Bands Propagation in Sands by Using the Developed Elemental-like Direct Shear-faulting Box

Fabrication and mechanical property of three-dimensional carbon fiber reinforced Mg-based bulk metallic glass matrix composite

Carbon fiber (CF) reinforced bulk metallic glass matrix composites (BMGMCs) have received widespread attention due to their light weight, but subsequent development is facing urgent challenges of uncontrollable interface reaction and poor plasticity. Here, we report a three-dimensional CF-reinforced Mg-based BMGMC, which significantly improves the microstructure and compressive plasticity by adjusting the pressure infiltration parameters. It has been found that the electroless copper plating improves the wettability of the CF and the melt without inducing the crystallization of the matrix, in spite of the partially dissolving and diffusing of the coating to the matrix. Under a similar infiltration pressure difference, high vacuum conditions are beneficial to reduce the capillary resistance of the porous CF preform, thereby improving the formability of BMGMC. Compression test results prove that the introduction of three-dimensional CF effectively improves the plasticity of the composite material and reduces its brittleness tendency. It can be attributed to the fact that the carbon fibers distributed in different directions effectively bridge the multi-directional cracks and prevent the early rapid shear band propagation. The present work provides meaningful enlightenment for the development of CF-reinforced BMGMC materials.