Formation Mechanism Of Bands Research Articles

Quasi-static band gaps in metamaterial pipes with negative stiffness resonators

A novel configuration of periodically supported pipes with negative stiffness resonators (NSRs) at midspans is investigated in this paper. By leveraging the expanded bandwidth and enhanced damping effects offered by the NSRs, as well as the quasi-static (QS) band gaps of periodically supported pipes, this configuration enables the realization of ultrawide QS band gaps. The Floquet-Bloch theorem and Finite Element Method (FEM) are employed to determine the dispersion relationship of the infinite periodic pipe, elucidating the wave propagation characteristics. The band formation mechanism is revealed by conducting a comparative analysis with other systems in which unit cells only comprise periodic supports or NSRs. By analyzing the dispersion relationships, the effects of critical parameters on the transition and interplay between Bragg and local resonance (LR) band gaps are investigated. The results reveal that, with increasing absolute values of the negative stiffness ratio or mass ratio at a constant resonant frequency, the LR band gap created by NSRs eventually transforms into a wide QS band gap. The study further extends to metamaterial pipes of finite length, where FEM simulations are carried out using ANSYS to confirm the physical band-gap properties observed in the periodic systems. The advantage of the wave attenuation bandwidth introduced by NSRs is demonstrated by comparing the results with those obtained by traditional types of resonators. With the same added mass, the system with NSRs exhibits a substantially wider LR band gap than the traditional resonators. Finally, owing to the damping magnification mechanism of NS elements, when a reasonable amount of damping is introduced, the proposed system shows superiority in achieving ultrawide QS band gaps through band-gap merging over pipe systems with suspended resonators.

In-situ compression with acoustic emission detection of high pressure torsion deformed Cu38Zr54Al8 metallic glass micropillars

In-situ compression of Cu38Zr54Al8 metallic glass micropillars in a scanning electron microscope was performed together with continuous acoustic emission recording on samples in the as-cast state and after pre-deformation by high pressure torsion. A size effect was detected in both shear band operation and acoustic emission signal, irrespective of the preliminary deformation. This phenomenon was explained by the size dependent compliance of the pillar/indenter system. Differences between acoustic emission signals from the as-cast and pre-deformed states indicated changes in the shear band formation mechanism due to high pressure torsion. These differences were clear in the elastic regime of the in-situ compression and supported the role of rejuvenation in stabilization of unstable shear bands.

Theoretical study of the void collapse and shear band formation mechanism for β‐HMX

AbstractBased on molecular dynamics simulation, we obtain a shear band formation mechanism for β‐HMX. The shock wave reflected at void face induces rarefaction wave, and the velocity difference between rarefaction wave zone and shock wave zone induces slipping. A set of physical models are developed to describe the wave reflection, shear band expansion and energy dissipation. The orientation angle, face indices, expansion velocity and formation energy of shear bands are calculated. A complete physical picture for shear band formation is obtained.

Kink band formation mechanism in α/β Ti-9Cr two-phase alloy

A combination of experimental and numerical studies was carried out to understand the microstructure and formation mechanism of kink bands in α/β two-phase titanium alloys. A deformation kink band was introduced in a Ti-9Cr alloy after uniaxial compression test. The strength changes of the α and β phases inside and outside the kink band were evaluated by nanoindentation tests. A potential hardening effect was revealed in the α phase inside the kink band, while a possible softening effect was located in the β phase at the kink boundaries. Microstructural examination of the kink band was conducted by electron backscatter diffraction measurement. The crystal rotation axis was found to be perpendicular to both the (0001) basal plane of the α phase and one of the (110) planes of the β phase. The crystallographic features were characterized by transmission electron microscopy observation, revealing a prismatic 〈a〉 slip that occurred during the compression to accommodate the rotations around the c-axis. Nanoindentation tests were performed on an undeformed specimen to calibrate the crystal plasticity model. A crystal plasticity finite element model was developed and {110}β-rotation-type kink bands were reproduced in the simulation and confirmed the prismatic slip activity.

Effect of stress triaxiality on plastic deformation of metallic glasses

Aiming at fabrication of cellular metallic glasses with high mechanical properties, double edge notched samples were designed by orthogonal design method. Compressive tests on those samples were carried out to investigate mechanical responses induced by different notch settings. It was found that the notch tip distance and stress triaxiality are two key factors controlling yield strength and plasticity of notched samples. Besides, free volume theory factoring in hydrostatic stress was incorporated into finite element model to simulate shear band (SB) deformation process for different samples. Combined with experiments, simulations as well as microstructure observations, it was concluded that the notch tip distance effect could be ascribed by transition process between sparsely-intersected and densely-intersected SBs, and the later is the key to plasticity enhancement. Additionally, large stress triaxiality could improve the global plasticity by introducing densely-intersected SBs so as to hinder sample from fracturing along one major SB. The current work could offer useful data in providing direct evidence on fabrication of cellular materials as well as enriching shear band formation mechanism of monolithic metallic glasses.

Closed-form solutions for attenuation peaks and band boundaries of general monocoupled systems

The unit cells connected periodically at a single node with only one degree of freedom is called a monocoupled system. Dispersion relations for such systems are studied widely; however, the analytical solution for salient features of the attenuation band, such as the number of peaks in a band and band merging, have been relatively unexplored. In this paper, a general theory for obtaining the attenuation characteristics of the general monocoupled system from the roots and poles of the rational polynomial of the dispersion relation is developed. The uniqueness of the developed rational polynomial method is that it can predict the attenuation peaks and the possibility of multiple peaks in an attenuation band due to coupling between the different band formation mechanisms in addition to standard band boundaries. The most general monocoupled system has been conceptualized by combining the three mechanisms, namely inertial amplifier, effective negative mass, and effective negative stiffness. This general system is named Inertial Amplifier Negative Mass Negative Stiffness (IANMNS). This designed monocoupled system degenerates into other seven subsystems as special cases, such as the Inertial Amplifier Negative Stiffness (IANS), the Inertial Amplifier Negative Mass (IANM), the Negative Mass Negative Stiffness (NMNS), the Inertial Amplifier (IA), the Negative Stiffness (NS), the Negative Mass (NM) and the Monoatomic system. The closed-form expressions for the peaks in attenuation level and bounds in terms of nondimensional frequency ratio and other governing parameters such as the inertial mass ratio, mass ratios of resonators one (embedded in main chain mass) and two (embedded in inertial mass), frequency ratios of resonators one and two, and angular parameter are derived for the IANMNS and all the other seven subsystems. The conditions for obtaining the double peaks and band merging are defined analytically.

Material Parameters Dependency of Stress-Strain Curve Based on the Crystal Plasticity Finite Element Method Incorporating Non-Crystalline Shear Band Mechanism

The crystal plasticity finite element method (CPFEM) has emerged as an important method for studying materials on a mesoscopic scale. However, a significant obstacle to the application of CPFEM is the numerous material parameters associated with it. This study selected a physics-based CPFEM incorporating the non-crystalline shear band formation mechanism as it can stimulate both work-hardening and strain-softening mechanisms. A three-dimensional smooth specimen model was established to simulate the tensile test. The effects of six fitting crystal plasticity material parameters on the yielding stress, work-hardening behavior, and strain localization behavior are. In addition, the influencing mechanisms are discussed.

Dynamic plastic instability of ring-shaped aluminum alloy with different interface behaviors

Unveiling the rate-dependent shear instability mechanism is essential in evaluating the reliability and safety of materials under dynamic loadings. Herein, the strain rate-dependent plastic instability behaviors of 2A12 aluminum alloy with ring-shaped structure and different surface states were systematically investigated and analyzed. The stress softening was displayed in the stress-strain curves as the loading rate increased to a high level. The lubricated interface will induce the prominent shear instability property, followed by the fine-polished interface and coarse-polished interface. It is revealed that the initial interface state between specimen and bars not only influences the onset strain and the yield strength, but also determines the duration of plastic instability stage. The simulation results also indicated that the shear band runs through the two surfaces with different interface friction coefficients. The minor disturbance under quasi-static loading will be accelerated under dynamic loading owing to the instantaneous rising of local temperature, which eventually causes the observably plastic shear instability. The critical state of shear band formation mechanism and the modeling of the stress-softening stage were then theoretically analyzed and discussed. This work on the dynamic instability behavior of ring-shaped aluminum alloy could provide an insight in understanding the formation of adiabatic shear band with different strain rates and interfaces.

Micro-Crystallographic Analysis of Shear Band Formation Mechanism in Cold Rolled Al-Sc Alloys at Different Precipitation States

The debate on whether the slip in Shear Bands (SBs) is crystallographic or non-crystallographic has continued for decades. In the present study, shear banding in cold-rolled Al-0.2 wt.% Sc alloys with different precipitation states were characterized to elucidate the mechanism of SBs formation and propagation across grain boundaries. The generated SBs are observed only in grains of S {123} and Copper {112} orientation. The orientation of SBs in the S orientation grains is close to R {142} , while the SBs in Copper orientation grains possess an orientation close to D {11 4 4} . This orientation dependency is proven to in tight association with asymmetric slips and local lattice reorientation. A periodic change in the slip systems is accompanied by a periodic change in the lattice orientation between parallel SBs. Through conducting the focussed ion beam (FIB) lift-out method and TEM analysis, the dislocations and slip activation in/around SBs are revealed. The results indicate that a sudden change in the slip path during deformation leads to flow localization, contributing to the formation of SBs. In this process, fine Al3Sc precipitates are characterized to promote the formation of SBs through inhibiting the dynamic recovery. The mechanism of SBs formation is crystallographic as the slip in SBs occurs on {111} planes with local lattice reorientation and the SBs propagation across grain boundaries is also driven by the slip on {111} planes. Furthermore, the effects of SBs on texture evolution are discussed as well.

Age-at-size relationships of the American lobster (Homarus americanus) from three contrasting thermal regimes using gastric mill band counts as a direct aging technique

Direct age determination of crustaceans has remained a long-standing challenge because all calcified structures are shed with each molt. Cuticle bands in the ossicles of the gastric mill have shown promise as age indicators. We validated the one-to-one relationship between known age and number of cuticle bands for 15 hatchery-raised juvenile American lobsters (Homarus americanus). Additionally, we applied this method to 308 lobsters from three contrasting thermal regimes in New England, USA. Band counts matched our expectations of differences in age-at-size across this thermal gradient; lobsters at harvestable size in southern New England were estimated to be 5.5 (±1.5) years old compared with 7.5 (±1.6) years in the Gulf of Maine. We found 81% of our band count estimates of age fell within 2 years of independent, regionally specified growth model estimates of age-at-size for lobster. Notwithstanding remaining uncertainties regarding the mechanism of band formation, our findings indicate the method may provide an independent and direct means to determine the age of individual American lobsters, which will improve estimates of essential life history parameters.

Near-Infrared Spectroscopic Study of Heavy-Metal-Contaminated Loess Soils in Tongguan Gold Area, Central China

Loess soil is a kind of widespread soil type in northwest China. Human engineering activities such as mining have caused numerous problems related to heavy metal pollution in soils, which threaten people’s health. The band formation mechanism of the near-infrared (NIR) spectral features in loess soils forms the theoretical basis for the study of the soil environment by hyperspectral remote sensing. Some NIR features of loess soils will shift because of the variations of the soil composition and microstructure after they adsorb heavy metal cations. In this study, we focused on the heavy metal adsorption of the illite, smectite, and illite–smectite (I/S) mixed layer in loess soils; evaluated the pollution by Nemerow indexing; applied X-ray diffraction (XRD), mid-infrared (MIR) spectral analysis, and inductively coupled plasma mass spectrometry (ICP-MS); and carefully observed the shift behavior of the MIR and NIR features. Then, the NIR bands were assigned to MIR bands according to the vibration behavior. Furthermore, the relationships between the NIR band positions and the six heavy metal cations as well as the Nemerow index were investigated via multiregression and simple linear correlation methods. Finally, the relationship obtained from the experiments was analyzed using the physical and chemical mechanisms of the heavy metal cations in the clay minerals. These findings may benefit the application of NIR and remote sensing techniques for detecting heavy-metal-polluted soils.

Interplay of local resonances and Bragg band gaps in acoustic waveguides with periodic detuned resonators

This letter is concerned with acoustic wave propagation and transmission in acoustic waveguides with periodically grafted detuned Helmholtz resonators. The interplay of local resonances and Bragg band gaps in such periodic systems is examined. It is shown that, when the resonant frequencies of the resonators are tuned close to a Bragg band gap, the behavior of the Bragg band gap can be affected dramatically. Particularly, by introducing appropriately tuned resonators, the bandwidth of a Bragg band gap can be reduced to zero, leading to a very narrow pass band with great wave attenuation performance near both band edges. The band formation mechanisms of such periodic waveguides are further examined, providing explicit formulae to locate the band edge frequencies of all the band gaps, as well as the conditions to achieve very narrow pass bands in such periodic waveguides.

Analysis of an Ultra-Low Frequency and Ultra-Broadband Phononic Crystals Silencer with Small Size

Existing research shows that acoustic BG in a certain frequency range can be realized by installing an expansion chamber on duct system, but the problems of broadband and size limitations at low frequencies remain to be researched. The study of acoustic and elastic wave propagation in artificial periodic structures has received increasing attention for many decades, and the presence of bandgap (BG) in phononic crystals (PCs), which inhibits elastic/acoustic wave propagation within the BG’ frequency range, supplies a new way to control noise and vibrations in duct system. Based on PC theory, a duct silencer backed with a gas–liquid expansion chamber is proposed to enhance the acoustic performance of low-frequency noise attenuation. The transfer matrix method (TMM) is used to investigate the acoustic BG properties. The influences on the BG properties of some key parameters are analyzed, and the band formation mechanism is revealed by the law of energy conservation. The results show that silencers with a small size can effectively attenuate ultra-low frequencies and ultra-broad bands.

Extraordinary Lüders-strain-rate in medium Mn steels

An innovative experimental means based on high-speed digital image correlation (DIC) is employed in this work to investigate the Lüders band formation mechanisms in a medium Mn transformation-induced plasticity (TRIP) steel, allowing precise assessment of local strain rate inside the Lüders band. The stress-controlled instead of conventional strain-controlled mode is adopted during tensile test such that the instantaneous Lüders strain development right under the yield stress can be well captured. A surprisingly high Lüders-strain-rate on the order of 1 s−1 is observed in the tensile test at 25 °C, which is three orders of magnitude above the mean strain rate and about 20 times higher than that obtained in a low-carbon steel. The theoretical analysis shows that the mobile dislocations must be rapidly multiplied so as to support the observed high Lüders-strain-rate. This theoretical viewpoint is confirmed experimentally by transmission electron microscopy (TEM) observations, showing a large number of new dislocations generated in the Lüders band. It is revealed that the martensitic transformation is neither a cause nor a direct effect of Lüders band. Instead, they are two independent events that occur simultaneously. Nevertheless, the martensitic transformation does have the ability to influence a Lüders deformation process when it is involved. It accelerates the Lüders band formation by generating more dislocations and in the meantime raising their velocities, leading to an enhanced Lüders-strain-rate.

Surface composition of pull-apart bands in Argadnel Regio, Europa: Evidence of localized cryovolcanic resurfacing during basin formation

We combine Galileo Solid State Imager (SSI) and Near-Infrared Mapping Spectrometer (NIMS) data to investigate the composition of pull-apart bands in Europa's Argadnel Regio. Using spectral linear mixture modeling employing cryogenic laboratory reference spectra, we find that bands of intermediate age (“grey” bands) are compositionally distinct from bands that are stratigraphically younger (“dark” bands). The grey bands have higher abundances of larger ice grains and lower abundances of hydrated salts than the dark bands; both of these tendencies are statistically significant at the 1% level. The grey and dark bands have similar abundances of hexahydrite, a material which is relatively stable under irradiation; however, the derived abundances of frozen magnesium sulfate brine and of mirabilite, which are more susceptible to fragmentation by radiation, are significantly higher in the dark bands than in the grey bands. These results are consistent with a physical model in which the differences in composition and in ice grain sizes are linked to space weathering and radiolytic processing levels; the grey bands have presumably undergone higher levels of processing, due to being exposed on Europa's surface for a longer period of time. One prominent wedge-shaped band exhibits an anomalous albedo variation across its northern portion, appearing dark in its top third, and grey in its southernmost two-thirds. We find that the dark part of the band has a modeled composition that is in-family with other dark bands, while the grey portion has a modeled composition that is indistinguishable from other grey bands in the study area. Because these variations cannot easily be attributed to the band's formation mechanism (bands open sequentially along a central axis), we surmise that the northern part has been resurfaced, probably in response to the formation of a large topographic basin that cuts through the band. Faulting accompanying basin formation may provide conduits allowing transport to the surface of materials from Europa's interior. We hypothesize that the formation of the basin resulted in fresh cryovolcanic material being deposited across the northern portion of the band, effectively “resetting” its surface age. If, as has been suggested, the giant arcuate basins resulted from an episode of true polar wander, our study may help to more tightly constrain the age of that event within Europa's geologic column.

Microscopical characterization of known postmortem root bands using light and scanning electron microscopy

A postmortem root band (PMRB) is a distinct microscopic feature that is postulated to occur in hair remaining in the follicle during the postmortem interval [1] (Petraco et al., 1998). The scientific validity of this premise has been highlighted in two recent high-profile criminal cases involving PMRBs [2,3] (State of Florida v. Casey Marie Anthony, 2008; People v. Kogut, 2005). To better understand the fundamental aspects of postmortem root banding, the microscopical properties of known PMRBs11In this paper, a known PMRB is defined as a dark elliptical band in a hair (when viewed in transmitted light) in the pre-keratin/keratogenous region of the hair root, which is also confirmed to have been recovered from the tissue of a deceased person during the postmortem interval. This is equivalent to a Stage 2 band as defined by Koch et al [4]. were characterized by light microscopy, and scanning electron microscope (SEM) imaging of microtomed sections of hairs showing root banding. The results from this study show that the appearance of the PMRB may be due to the degradation of the chemically labile, non-keratin intermacrofibrillar matrix (IMM) in the pre-keratin/keratogenous region of anagen hairs. In addition, this degradation is confined to the cortex of the hair, with no apparent damage to the layers of the cuticle. These results could provide valuable information for determining the mechanism of band formation, as well as identify a set of microscopic features that could be used to distinguish hairs with known PMRBs from similarly looking environmentally degraded hairs.

Effect of temperature on kinking failure mode of non-slender glass fiber-reinforced polymer specimens

The kink behavior of non-slender glass fiber-reinforced epoxy prismatic specimens of variable length and fiber volume fraction at temperatures ranging from 25°C to 125°C was investigated. Splitting failure occurred at the glassy state while kinking failure was observed at the glass transition state and buckling with subsequent post-peak kinking at the rubbery state. Kink initiation was caused by the initial imperfections, i.e. the waviness of the unidirectional fibers. Initiation occurred through fiber microbuckling caused by combined compressive and shear stresses at the glass transition state and predominant shear stresses at the rubbery state due to the preceding buckling. The kink band width was narrow at the glass transition state due to the significant compressive stresses and corresponded to the wavelength of the initial fiber waviness. The kink band width at the rubbery state was much wider and corresponded to the band width of the maximum shear stresses at the inflexion points of the buckling shape. The kink band angle depended on the ratio of compressive to shear stresses. The different specimen slendernesses and fiber volume fractions did not influence the kink initiation and kink band formation mechanisms.

Mechanism of macroscopic shear band formation in plane strain compressed fine-grained aluminium

The microstructure and microtexture evolutions during shear banding of very fine grained commercially pure aluminium (AA1050) have been characterized to elucidate the mechanisms of band formation and propagation across layered microstructures and the resulting texture evolution. Samples were pre-deformed in ECAP to 6 passes via route C, then machined and further compressed in a channel-die to form two sets of copper-type macroscopic shear bands (MSBs). The local changes in microstructure and crystallographic orientations were characterized by SEM equipped with a high-resolution EBSD facility. The ECAP-processing led to the formation of a fine-grained structure composed of complementarily oriented layers parallel to the transverse direction and inclined ~20° to the extension direction (ED). During the secondary straining in the channel-die, the layers exhibited two rotation tendencies: (i) a global rotation of the layers towards the compression plane, and (ii) a deflection of layers within narrow areas. The latter increased the layers’ inclination with respect to ED and led to kink-type bands, which are the precursors of MSBs. The mechanism of MSB formation is strictly crystallographic since in all the grains of the sheared zone, the crystal lattice rotated such that one of the {111} slip planes became nearly parallel to the shear plane and the 〈011〉 direction became parallel to the direction of maximum shear. This strain-induced crystal lattice rotation led to the formation of specific MSB components that facilitated slip propagation across the grain boundaries.

Control of sound and vibration of fluid-filled cylindrical shells via periodic design and active control

The wave propagation, vibration transmission and acoustic emission characteristics in the passive and the active periodic shell systems are investigated. A finite element method (FEM) is utilised to conduct the investigation. In the passive periodic shell, two pivotal frequencies (i.e., the cut-off frequency of the periodic shell, and the resonant frequency of flexural vibration of shell ring), which are existed in an arbitrarily high circumferential mode, are found; the frequency range is divided into three regions by these two frequencies. Various band formation mechanisms and the dynamic properties within the three frequency regions are illustrated, with the aid of a series of vibration deformations. Furthermore, an active periodic shell is constructed. Several control methods, such as inverted displacement-, velocity- and acceleration-feedback control strategies, are explored for the active shell. Under these control strategies, the effects of negative stiffness, damping coefficient and mass modulation, can be produced, thus enabling the band gap generable and its characteristics, such as their bandwidth, location and attenuation coefficient, adjustable. The pressure level of the structure-borne sound is also suppressed along the shell within the band gaps.

Flexural wave propagation in beams with periodically attached vibration absorbers: Band-gap behavior and band formation mechanisms

This paper is concerned with flexural wave propagation and vibration transmission in beams with periodically attached vibration absorbers. Such periodic systems feature unique wave filtering characteristics that can find applications in the control of wave propagation in flexural beam structures. The study is performed by using an exact analytical approach based on a combination of the spectral element method and periodic structure theory. Both infinite and finite periodic structures are considered. An explicit expression is provided for the calculation of propagation constants and thus the complex band structures, and it is further developed to examine the effects of various system parameters on the band-gap behavior, including the position, width and wave attenuation performance of all the band gaps. The band formation mechanisms of such periodic systems are explained via both derivations and physical models, yielding explicit equations to enable the prediction of all the band edge frequencies in an exact manner without the need to calculate propagation constants. Based on these equations, explicit formulas are further derived to determine the conditions for the transition and near-coupling between local resonance and Bragg scattering, each being a unique band-gap opening mechanism.