Elastic Softening Research Articles

Elasticity and viscosity of BaO[sbnd]TiO2[sbnd]SiO2 glasses in the 0.9 to 1.2Tg temperature interval

In spite of the potential applications of glasses in the BaOTiO2SiO2 (BTS) system, the mechanical properties of these glasses were little studied so far. Several centimeters large batches of glasses along the 0.3BaOxTiO2(0.7−x)SiO2 composition line were prepared. Their creep behavior and elastic moduli were investigated as a function of x (from x=0 to x=0.3). Titanium increases the atomic packing density as well as the volume density of energy and so do the elastic moduli. An excellent agreement is found between the elastic softening index (α) and the liquid fragility (m) (according to Angell's concept [1]). Nevertheless, as TiO2 is added the glass-forming liquid becomes more “fragile”. The explanation might lie in the structural similarity between the fresnoite crystal and the glass structure consisting of island-like SiTi rich units surrounded by barium-rich channels. These islands would contribute to the increase in rigidity whereas the Ba-rich channels, acting as a lubricant, would make the viscous flow more temperature sensitive.

Rigid proteins and softening of biological membranes-with application to HIV-induced cell membrane softening.

A key step in the HIV-infection process is the fusion of the virion membrane with the target cell membrane and the concomitant transfer of the viral RNA. Experimental evidence suggests that the fusion is preceded by considerable elastic softening of the cell membranes due to the insertion of fusion peptide in the membrane. What are the mechanisms underpinning the elastic softening of the membrane upon peptide insertion? A broader question may be posed: insertion of rigid proteins in soft membranes ought to stiffen the membranes not soften them. However, experimental observations perplexingly appear to show that rigid proteins may either soften or harden membranes even though conventional wisdom only suggests stiffening. In this work, we argue that regarding proteins as merely non-specific rigid inclusions is flawed, and each protein has a unique mechanical signature dictated by its specific interfacial coupling to the surrounding membrane. Predicated on this hypothesis, we have carried out atomistic simulations to investigate peptide-membrane interactions. Together with a continuum model, we reconcile contrasting experimental data in the literature including the case of HIV-fusion peptide induced softening. We conclude that the structural rearrangements of the lipids around the inclusions cause the softening or stiffening of the biological membranes.

Probability analysis of the fire structural resistance of aluminium plate

An experimental and numerical study into the intrinsic scatter in the fire structural resistance of aluminium plate supporting tension loads is presented. Small-scale simulated fire structural tests performed on two aluminium alloys (AA5083 and AA6061) show for the first time a large amount of scatter in the tensile deformation rate and rupture stress. Multiple simulated fire tests conducted under identical heat flux exposure and tensile load conditions reveal scatter in the softening behaviour of the two aluminium alloys; there is large variability in the deformation rate, rupture stress and time-to-rupture, particularly at low stresses when creep dominates the softening process. Finite element analysis (incorporating elastic, plastic and creep softening effects) and elevated temperature material testing reveals that the scatter is caused mainly by variability in creep properties such as creep activation energy. A probability density function is used to quantify the scatter in the creep activation energy, and the finite element model using Monte Carlo simulations computes the scatter in the fire structural resistance of aluminium, which is not possible with existing deterministic models.

Exotic Ground State and Elastic Softening under Pulsed Magnetic Fields in PrTr2Zn20 (Tr = Rh, Ir)

To investigate a field-induced level crossing of the ground-state doublet in PrTr2Zn20 (Tr = Rh, Ir), we performed ultrasonic measurements in pulsed magnetic fields applied along the [110] and [001] directions and analyzed the results in the framework of the strain-susceptibility approach. Above 40 T for H || [110], we observed an elastic softening of the transverse modulus (C11 − C12)/2 corresponding to the ground-state doublet. In both compounds the softening is followed by a minimum at about 47 T at low temperatures. We predict the presence of a new field-induced phase boundary in PrTr2Zn20 at this field with two possible cases. The magnetic field of the minimum cannot be explained by only the quadrupole interaction.

Intrinsic stress mitigation via elastic softening during two-step electrochemical lithiation of amorphous silicon

Recent experiments and first-principles calculations show the two-step lithiation of amorphous silicon (a-Si). In the first step, the lithiation progresses by the movement of a sharp phase boundary between a pristine a-Si phase and an intermediate LiηSi phase until the a-Si phase is fully consumed. Then the second step sets in without a visible interface, with the LiηSi phase continuously lithiating to a Li3.75Si phase. This unique feature of lithiation is believed to have important consequences for mechanical durability of a-Si anodes in lithium ion batteries, however the mechanistic understanding of such consequences is still elusive so far. Here, we reveal an intrinsic stress mitigation mechanism due to elastic softening during two-step lithiation of a-Si, via chemo-mechanical modeling. We find that lithiation-induced elastic softening of a-Si leads to effective stress mitigation in the second step of lithiation. These mechanistic findings allow for the first time to quantitatively predict the critical size of an a-Si anode below which the anode becomes immune to lithiation-induced fracture, which is in good agreement with experimental observations. Further studies on lithiation kinetics suggest that the two-step lithiation also results in a lower stress-induced energy barrier for lithiation. The present study reveals the physical underpinnings of previously unexplained favorable lithiation kinetics and fracture behavior of a-Si anodes, and thus sheds light on quantitative design guidelines toward high-performance anodes for lithium ion batteries.

Phase field modeling of lithium diffusion, finite deformation, stress evolution and crack propagation in lithium ion battery

Mechanical degradation under cyclic charging and discharging has been the one of the most important bottlenecks for the developments of lithium ion batteries. Understanding of stress evolution process of anode during cycling is a way to deeply understand the mechanical degradation. In this paper, a phase field model (PFM) coupling lithium diffusion, finite deformation, stress evolution with crack propagation is established. Then the model is applied to spherical silicon particle to explore the stress evolution with taking account of finite deformation, elastic softening and plastic flow. The numerical results show that small deformation model and finite deformation model provide different stress states especially when the anode undergoes a large volumetric expansion. Elastic softening has not a significant effect on stress evolution in spherical particle. Plastic flow decreases the magnitude of stress, and deeply changes the stress evolution, making the hoop stress near the particle surface to become positive during charge process, indicating the particle surface is subjected to tensile hoop stress.

Finite-thickness cohesive elements for modeling thick adhesives

A new cohesive element formulation is proposed for modeling the initial elastic response, softening, and failure of finite-thickness adhesives. By decoupling the penalty stiffness of the cohesive zone model formulation and the physical adhesive modulus, the new formulation ensures proper dissipation of fracture energy for opening and shear loading modes and mixed-mode loading conditions with any combination of elastic and fracture material properties. Predictions are made using the new element formulation for double cantilever beam, end-notched flexure, mixed-mode bending and single lap joint specimens with varying adhesive thicknesses. Good correlation between all predictions and experimental results was observed.

Molecular dynamics simulations of plasticity and cracking in lithiated silicon electrodes

First-principle calculations have provided critical insights into the deformation behavior of lithiated silicon electrodes in high-capacity lithium ion batteries, but quantitative interpretations have been limited by the size scales of these calculations. Here, we show that large-scale molecular dynamics (MD) simulations, based on the modified embedded atom method (MEAM) potential, are capable of describing the elastic softening and plastic behavior of LixSi alloys. In particular, our MD simulations at 0 K correctly reproduce the stress–strain response of LixSi alloys from Density Functional Theory (DFT) calculations across all Li concentrations, while matching the corresponding yield strength data from existing experiments at 300 K. Results from these MD simulations reveal a sharp transition in the atomic-scale plasticity mechanisms for LixSi with increasing Li content: from the breaking of Li–Si bonds at x<1, to the breaking of Li–Li bonds at x>1. The associated transition in the fracture behavior from brittle to ductile is due to the high stretchability of Li–Li bonds compared to Li–Si and Si–Si bonds.

Elastic softening in Fe7C3 with implications for Earth's deep carbon reservoirs

AbstractIron carbide Fe7C3 has recently emerged as a potential host of reduced carbon in Earth's mantle and a candidate component of the inner core, but the equation of state of Fe7C3 is still uncertain, partly because the nature of pressure‐induced magnetic transitions in Fe7C3 and their elastic effects remain controversial. Here we report the compression curve of hexagonal Fe7C3 in neon medium with dense pressure sampling and in comparison with pure iron in the same loading. The results revealed elastic softening between 7 GPa and 20 GPa, which can be attributed to noncollinear alignment of spin moments in a state between the ferromagnetic and paramagnetic phases, as expected for Invar‐type alloys. The volume reduction associated with the softening would enhance the stability of Fe7C3 in the deeper part of the upper mantle and transition zone. As a result of subsequent spin crossover at higher pressures, Fe7C3 at inner core conditions likely occurs as the nonmagnetic phase, which remains a candidate for the major component of the Earth's central sphere.

Elastic and anelastic relaxations accompanying relaxor ferroelectric behaviour of Ba6GaNb9O30 tetragonal tungsten bronze from resonant ultrasound spectroscopy

Abstract Tetragonal tungsten bronze (TTB) structures offer some promise as lead-free ferroelectrics and have an advantage of great flexibility in terms of accessible composition ranges due to the number of crystallographic sites available for chemical substitution. The ferroic properties of interest are coupled with strain, which will be important in the context of stability, switching dynamics and thin film properties. Coupling of strain with the ferroelectric order parameter gives rise to changes in elastic properties, and these have been investigated for a ceramic sample of Ba6GaNb9O30 (BGNO) by resonant ultrasound spectroscopy. Room temperature values of the shear and bulk moduli for BGNO are rather higher than for TTBs with related composition which are orthorhombic at room temperature, consistent with suppression of the ferroelectric transition. Instead, a broad, rounded minimum in the shear modulus measured at ~1 MHz is accompanied by a broad rounded maximum in acoustic loss near 115 K and signifies relaxor freezing behaviour. Elastic softening with falling temperature from room temperature, ahead of the freezing interval, is attributed to the development of dynamical polar nanoregions (PNRs), whilst the nonlinear stiffening below ~115 K is consistent with a spectrum of relaxation times for freezing of the PNR microstructure.

Phase transformations and indications for acoustic mode softening in Tb-Gd orthophosphate

At ambient conditions the anhydrous rare earth orthophosphates assume either the xenotime (zircon) or the monazite structure, with the latter favored for the heavier rare earths and by increasing pressure. Tb0.5Gd0.5PO4 assumes the xenotime structure at ambient conditions but is at the border between the xenotime and monazite structures. Here we show that, at high pressure, Tb0.5Gd0.5PO4 does not transform directly to monazite but through an intermediate anhydrite-type structure. Axial deformation of the unit cell near the anhydrite- to monazite-type transition indicates softening of the (c1133 + c1313) combined elastic moduli. Stress response of rare-earth orthophosphate ceramics can be affected by both formation of the anhydrite-type phase and the elastic softening in the vicinity of the monazite-phase. We report the first structural data for an anhydrite-type rare earth orthophosphate.

Origin of the c-axis ultraincompressibility of Mo2GaC above about 15 GPa from first principles

The mechanical properties and structural evolution of Mo2GaC are calculated by first-principles under pressure. Our results unexpectedly found that the c axis is always stiffer than a axis within 0–100 GPa. An ultraincompressibility of c axis within 15–60 GPa is observed, with a contraction of about 0.2 Å, slightly larger than that of a axis (0.14 Å). The abnormal expansion of c axis and the fast decrease in a axis above about 15 GPa and 70 GPa failed to induce the structural instability, whereas such behavior caused the elastic softening in many mechanical quantities. The shrinkage anomaly of c axis is closely reflected by the internal coordinate (u) shift of Mo atom as it shows three different slopes within 0–15 GPa, 20–60 GPa, and 70–100 GPa, respectively. The longest Mo-Mo bond is responsible for the unusual shrinkage of c-axis under pressure as they experience nearly identical pressure dependences, whereas the a axis presents certain response with the variation of C-Mo bond particularly at 70 GPa. The electronic properties are investigated, including the energy band and density of states, and so on. At G point of K-M line, the energy decreases at 10 GPa first and increases at 30 GPa subsequently, the critical point is at about 15 GPa, with respective values of −0.17 of 0 GPa, −0.18 of 10 GPa, −0.16 of 15 GPa, and −0.13 of 30 GPa, respectively. This alternative energy change of G point, which is the symmetry center of the rhombic parallelogram of Ga atoms and the midpoint of the two bonded Mo atoms, convincingly reveal the origin of the anomalous ultraincompressibility of c axis as the Mo-Mo bond length shrinkage has to overcome the increasing energy barrier height. The Mo-Mo bond population and the electronegativity investigations of the Mo atom further reveal the most likely origin of the ultraincompressibility of c axis. This interesting result expects further experimental confirmation as this is the first nanolaminate ceramics compound presenting quite low-pressure axial ultraincompressibility.

Effectiveness of shock absorber device for damage mitigation of curved viaduct with steel bearing supports

This paper presents a numerical evaluation of the effectiveness of shock absorber devices installed between roller bearing and stopper in reducing viaduct damage. The effectiveness of thickness and types of shock absorber devices on mitigating viaduct damage is investigated accordingly. The thickness of shock absorber devices is from 0cm to 8cm, with increment of 2cm. The viaduct seismic performance is evaluated for five cases based on the thickness of shock absorber devices. In addition, three cases are studied based on the different design parameters of shock absorber devices. The three cases include viaducts with strain hardening, elastic, and strain softening shock absorber devices. Moreover, the pounding forces between roller bearing and stopper, pier damage, displacement of superstructures, relative displacement between two decks, and bending moment–curvature relationship at the pier base are evaluated. Results show that the application of thick shock absorber devices on viaducts can significantly mitigate viaduct damage. The strain softening shock absorber devices plays a more important role in reducing viaduct damage.

Influence of the Bi 6s 2 lone electron pair on elastic properties of monoclinic Bi4B2O9

Abstract The coefficients of thermal expansion and the complete set of elastic stiffness coefficients of monoclinic Bi4B2O9 were determined as functions of temperature employing dilatometry and, respectively, a combination of resonant ultrasound spectroscopy and the plate resonance technique. Thermal expansion as well as elasticity of Bi4B2O9 exhibit a pronounced anisotropy, with the directions of the maximum longitudinal elastic stiffness and of the minimal longitudinal thermal expansion running almost parallel to [1̅02]. Further, between 100 K and 535 K the principal axes system of the linear thermal expansion rotates by more than 30° around the 2-fold symmetry axis. The deviations from Cauchy-relations show a similar behavior. Both, the anisotropy and the temperature induced changes of the investigated properties are mainly controlled by the stereochemically active Bi 6s 2 lone electron pairs. At room temperature their Wang–Liebau vectors possess preferred components within a plane that runs almost perpendicular to [1̅02]. A systematic analysis of the elastic behavior of bismuth oxides using the quasi-additivity rule for elastic S-factor reveals a general trend: With decreasing relative amount of Bi2O3 the Bi3+ cations tend to align their stereochemically active lone electron pairs in planes or eventually in one direction. With respect to the elastic behavior of the compound the alignment of the easliy deformable lone electron pairs is unfavorable and causes an elastic softening.

Effect of Intrinsic Ripples on Elasticity of the Graphene Monolayer.

The effect of intrinsic ripples on the mechanical response of the graphene monolayer is investigated under uniaxial loading using molecular dynamics (MD) simulations with a focus on nonlinear behavior at a small strain. The calculated stress-strain response shows a nonlinear relation through the entire range without constant slopes as a result of the competition between ripple softening and bond stretching hardening. For a small strain, entropic contribution is dominant due to intrinsic ripples, leading to elasticity softening. As the ripples flatten at increasing strain, the energetic term due to C–C bonds stretching competes with the entropic contribution, followed by energetic dominant deformation. Elasticity softening is enhanced at increased temperature as the ripple amplitude increases. The study shows that the intrinsic ripple of graphene affects elasticity. This result suggests that a change of ripple amplitudes due to various environmental conditions such as temperature, and substrate interactions can lead to a change of the mechanical properties of graphene. The understanding of the rippling effect on the mechanical behavior of 2D materials is useful for strain-based ripple manipulation for their engineering applications.

Structural and vibrational properties of single crystals of Scandia, Sc2O3 under high pressure

We report the results of single-crystal X-ray diffraction and Raman spectroscopy studies of scandium oxide, Sc2O3, at ambient temperature under high pressure up to 55 and 28 GPa, respectively. Both X-ray diffraction and Raman studies indicated a phase transition from the cubic bixbyite phase (so-called C-Res phase) to a monoclinic C2/m phase (so-called B-Res phase) at pressures around 25–28 GPa. The transition was accompanied by a significant volumetric drop by ∼6.7%. In addition, the Raman spectroscopy detected a minor crossover around 10–12 GPa, which manifested in the appearance of new and disappearance of some Raman modes, as well as in softening of one Raman mode. We found the bulk modulus values of the both C-Res and B-Res phases as B0 = 198.2(3) and 171.2(1) GPa (for fixed B′ = 4), respectively. Thus, the denser high-pressure lattice of Sc2O3 is much softer than the original lattice. We discuss possible mechanisms that might be responsible for the pronounced elastic softening in the monoclinic high-pressure phase in this “simple” oxide with an ultra-wide band gap.

Elastic softening of leucite and the lack of polar domain boundaries

Elastic properties of leucite have been investigated using resonant ultrasound spectroscopy over a temperature range from 300 to 1400 K. According to these measurements, elastic moduli soften by ~50% at the Ia 3 d-I 41/ acd ferroelastic transition temperature T c1 = 940 K relative to the value at 1400 K. A second softening is observed at T c2 = 920 K, corresponding to the structural change from the space group I 41/ acd to I 41/ a . These elastic anomalies are analyzed in a simple model under the assumption that the transitions observed at T c1 and T c2 can be approximated by a single pseudoproper ferroelastic transition. The two phase transitions are accompanied by a single peak in mechanical damping attributed to the high mobility of twin walls in the intermediate phase followed by pinning in the low-temperature phase. To determine whether twin walls in tetragonal leucite are polar, resonant piezoelectric spectroscopy and second harmonic generation measurements were performed, but no evidence of polarity was found.

Atomistic mechanism of elastic softening in metallic glass under cyclic loading revealed by molecular dynamics simulations

Metallic glasses (MGs) have a great potential for structural applications due to their high strength; however, they soften under cyclic loadings and exhibit low fatigue endurance limits. To understand the softening mechanism, molecular dynamics simulations were carried out to study the Cu50Zr50 MG within the nominal elastic regime, which clearly show that the quasi-static elastic modulus of the MG softens with either the decreasing cyclic frequency or increasing stress amplitude. Through the extensive analysis of the atomic trajectories, we found the complex elastic softening behavior is related to the activation of string-like liquid-like sites and atomic bond breaking in the cyclically deformed amorphous structure. Our current finding provides a quantitative insight into the atomistic mechanism of damage in MGs under cyclic loadings, also shedding light on the important mechanisms for fatigue damage initiation in amorphous solids.

Softening of stressed granular packings with resonant sound waves.

We perform numerical simulations of a two-dimensional bidisperse granular packing subjected to both a static confining pressure and a sinusoidal dynamic forcing applied by a wall on one edge of the packing. We measure the response experienced by a wall on the opposite edge of the packing and obtain the resonant frequency of the packing as the static or dynamic pressures are varied. Under increasing static pressure, the resonant frequency increases, indicating a velocity increase of elastic waves propagating through the packing. In contrast, when the dynamic amplitude is increased for fixed static pressure, the resonant frequency decreases, indicating a decrease in the wave velocity. This occurs both for compressional and for shear dynamic forcing and is in agreement with experimental results. We find that the average contact number Zc at the resonant frequency decreases with increasing dynamic amplitude, indicating that the elastic softening of the packing is associated with a reduced number of grain-grain contacts through which the elastic waves can travel. We image the excitations created in the packing and show that there are localized disturbances or soft spots that become more prevalent with increasing dynamic amplitude. Our results are in agreement with experiments on glass bead packings and earth materials such as sandstone and granite and may be relevant to the decrease in elastic wave velocities that has been observed to occur near fault zones after strong earthquakes, in surficial sediments during strong ground motion, and in structures during earthquake excitation.

The kinetic fragility of liquids as manifestation of the elastic softening.

We show that the fragility m , the steepness of the viscosity and relaxation time close to the vitrification, increases with the degree of elastic softening, i.e. the decrease of the elastic modulus with increasing temperature, in a universal way. This provides a novel connection between the thermodynamics, via the modulus, and the kinetics. The finding is evidenced by numerical simulations and comparison with the experimental data of glassformers with widely different fragilities (33 ≤ m ≤ 115), leading to a fragility-independent elastic master curve extending over eighteen decades in viscosity and relaxation time. The master curve is accounted for by a cavity model pointing out the roles of both the available free volume and the cage softness. A major implication of our findings is that ultraslow relaxations, hardly characterised experimentally, become predictable by linear elasticity. As an example, the viscosity of supercooled silica is derived over about fifteen decades with no adjustable parameters.