Dependence Of Modulus Research Articles

Dependence of the Dynamic Modulus of Soil Deformation on Impact Frequency

Dependence of the Dynamic Modulus of Soil Deformation on Impact Frequency

High-frequency optimally windowed chirp rheometry for rapidly evolving viscoelastic materials: Application to a crosslinking thermoset

Knowledge of the evolution in the mechanical properties of a curing polymer matrix is of great importance in composite parts or structure fabrication. Conventional rheometry, based on small amplitude oscillatory shear, is limited by long interrogation times. In rapidly evolving materials, time sweeps can provide a meaningful measurement albeit at a single frequency. To overcome this constraint, we utilize a combined frequency- and amplitude-modulated chirped strain waveform in conjunction with a homemade sliding plate piezo-operated rheometer (PZR) and a dual-head commercial rotational rheometer (Anton Paar MCR 702) to probe the linear viscoelasticity of these time-evolving materials. The direct controllability of the PZR, resulting from the absence of any kind of firmware and the microsecond actuator-sensor response renders this device ideal for exploring the advantages of this technique. The high frequency capability allows us to extend the upper limits of the accessible linear viscoelastic spectrum and, most importantly, to shorten the length of the interrogating strain signal (OWCh-PZR) to subsecond scales, while retaining a high time-bandwidth product. This short duration ensures that the mutation number (NMu) is kept sufficiently low, even in fast-curing resins. The method is validated via calibration tests in both instruments, and the corresponding limitations are discussed. As a proof of concept, the technique is applied to a curing vinylester resin. The linear viscoelastic (LVE) spectrum is assessed every 20 s to monitor the rapid evolution in the time and frequency dependence of the complex modulus. Comparison of the chirp implementation, based on parameters such as duration of the experiment, sampling frequency, and frequency range, in a commercial rotational rheometer with the PZR provides further information on the applicability of this technique and its limitations. Finally, FTIR spectroscopy is utilized to gain insights into the evolution of the chemical network, and the gap dependence of the evolving material properties in these heterogeneous systems is also investigated.

Приложение биоинспирированных алгоритмов глобальной оптимизации в задаче подбора коэффициентов модели усталостной деградации жесткости композиционного материала

<p>The problem of finding the fatigue characteristics of a material based on the test results of a composite material is considered. The initial data are the properties of the material, load parameters and the tabulated dependence of the elastic modulus on the number of tests performed. A differential mathematical model has been formed that describes the change in the elastic modulus with increasing number of loading cycles. Its parameters are found by approximating the rate of change of the elastic modulus using numerical differentiation formulas of various orders and solving the parametric identification problem. The model coefficients are determined by using a method that simulates the behavior of a swarm of moths, related to bio–inspired global optimization algorithms. A solution to the problem for a specific composite material is given.</p>

Pre-and post-cyclic behavior of soft ground improved by geogrid-encased granular columns considering clogging effect

A triaxial apparatus was utilized to evaluate pre-and post-cyclic behavior of soft ground improved by geogrid-encased granular columns considering clogging effect. The pre-cyclic behavior of specimens showed that the deformation modulus improvement due to the use of a stiffer encasement would be less noticeable in case of clogged granular columns. It was found that during cyclic loading, the use of geogrid encasement will be effective in reducing cumulative settlements and mitigating the liquefaction potential when its tensile stiffness is large enough. Moreover, the post-cyclic behavior of specimens showed that the use of granular columns (whether encased or non-encased) decreased the dependence of the ground deformation modulus on the CSR changes so that the evaluation of the cyclic-induced ground deformation can be done completely independent of the cyclic loading magnitude. It was also found that the use of an encasement with appropriate stiffness played an important role in minimizing the loss of the strength of the ground stabilized by granular columns after experiencing cyclic loads, especially under large earthquakes and after the occurrence of possible liquefaction.

First-principles study on the structure, mechanical and thermodynamic properties of (Ti, Hf, Nb, Ta)C high-entropy carbide ceramics

High-entropy carbide ceramics (HECCs) have demonstrated extraordinary properties and broad application potential. However, the action mechanisms of metallic elements on the properties have not been understood in depth. In this study, the structural stability and the mechanical and thermodynamic properties of (Ti, Hf, Nb, Ta)C HECCs across a broad composition spectrum were systematically analyzed based on the density functional theory and Debye–Grüneisen model. The crystal structure was constructed and validated through experimental testing. The mechanical properties such as elastic moduli, ductility, hardness, and Poisson's and Pugh's ratios were calculated. Furthermore, the temperature dependence of bulk moduli, thermal expansion coefficients, and heat capacities of the HECCs were investigated. To interpret the elastic and toughening mechanisms of non-equiatomic HECCs, the electronic structures were investigated. The results indicate that the HECCs with a single solid solution phase of the FCC rock-salt structure are thermodynamically stable. The HECCs containing higher Nb and Ta contents have greater strength and stiffness, and those containing higher Ti and Hf contents exhibit greater hardness and brittleness than the equiatomic HECC. In addition, non-equiatomic HECCs containing higher Nb and Ta contents have larger bulk moduli and lower linear thermal expansion coefficients, which can be attributed to the stronger covalent interaction among metallic elements and carbon. This study is expected to have an impact on designing ideal HECCs for high-temperature applications under extreme environments.

Characterizing the shear response of polymer-grafted nanoparticles.

Grafting polymer chains to the surface of nanoparticles overcomes the challenge of nanoparticle dispersion within nanocomposites and establishes high-volume fractions that are found to enable enhanced material mechanical properties. This study utilizes coarse-grained molecular dynamics simulations to quantify how the shear modulus of polymer-grafted nanoparticle (PGN) systems in their glassy state depends on parameters such as strain rate, nanoparticle size, grafting density, and chain length. The results are interpreted through further analysis of the dynamics of chain conformations and volume fraction arguments. The volume fraction of nanoparticles is found to be the most influential variable in deciding the shear modulus of PGN systems. A simple rule of mixture is utilized to express the monotonic dependence of shear modulus on the volume fraction of nanoparticles. Due to the reinforcing effect of nanoparticles, shortening the grafted chains results in a higher shear modulus in PGNs, which is not seen in linear systems. These results offer timely insight into calibrating molecular design parameters for achieving the desired mechanical properties in PGNs.

Mechanical properties of VC/ZrC and VC/HfC superlattices

Face-centered cubic transition metal carbides exhibit high melting points and hardness, making them prominent candidates for protective coating applications. Vanadium carbide (VC) has typical characteristics of transition metal carbides. It serves as model material in this study, in which we showcase the effect of superlattice architecture on mechanical properties and fracture toughness. While beneficial effects of superlattice arrangement have been demonstrated for a series of nitride-based coatings, transition metal carbides remain largely unexplored territory. Following density functional theory based ab initio predictions on lattice and shear modulus mismatch, we develop VC/ZrC and VC/HfC superlattice coatings synthesized via pulsed DC sputter deposition. The bilayer periods (Λ) of our fully fcc-structured polycrystalline coatings range between 2–50 nm (indicated by X-ray diffraction, transmission and scanning electron microscopy). The chemical composition is close to 1:1 stoichiometry (from X-ray fluorescence, elastic back-scattering spectrometry and elastic recoil detection analysis). Both superlattice series exhibit a strong dependence of hardness, elastic modulus, and fracture toughness on their bilayer periods, which can only be correlated with the in-plane stress variations for VC/ZrC. The VC/HfC superlattices provide their peak-hardness of 36.0 ± 1.6 GPa for Λ = 6 nm and their peak in fracture toughness of 3.5 ± 0.5 MPa√m for Λ = 10 nm.

Cage-C22 and Cage-C28: Two novel superhard orthorhombic carbon allotropes

In this work, two novel three-dimensional Cage carbon allotropes with all-sp3 and mixed sp2-sp3 hybridized networks, namely, Cage-C22 and Cage-C28 are theoretically predicted by the analysis executed using based on the density functional theory. Cage carbon superhard crystals possess Pmmm (47) symmetry (space group no. 25) which are orthorhombic crystals. The electronic properties, mechanical properties (hardness, elastic anisotropy, elastic modulus, and directional dependence of Young's modulus in GPa), and structural properties for both the carbon phases are systematically investigated and analyzed. The calculated phonon dispersions and elastic coefficients Cij show that Cage carbon allotropes are dynamically and mechanically stable at ambient conditions (0 GPa). To study the mechanical properties of these structures, the (Young's, shear, bulk) modulus were obtained by using the Voigt-Reuss-Hill approximation. The ratios of Emax/Emin as significant ratios of mechanical anisotropy in Young's modulus are greater than that of diamond (1.10) which means that Cage structures show elastic anisotropy. Furthermore, the electronic properties of these two new structures show that Cage-C22 crystal is a direct semiconductor and its gap energy is about 1.5 eV at Z point, while Cage-C28 is a metal because it has zero band gap between valence bands (VB) and conduction bands (CB). The calculated X-ray spectrum patterns show noncrystalline behavior which is derived from its structural complexity, and bond angles and bond lengths are also effective in this matter. The calculated results indicate that these two 3D superhard structures have the required potential for the use of cathode materials in capacitors, electrical and mechanical applications.

Effects of hydrocolloids on mechanical properties, viscoelastic and microstructural properties of starch-based modeling clay

The effects of various hydrocolloids (guar gum, xanthan gum, and carboxymethyl cellulose) on the texture, rheology, and microstructural properties of modeling clay prepared with cassava starch were investigated. Notably, incorporation of 3 % guar gum and 4 % xanthan gum into starch-based modeling clay resulted in enhancements of 94.12 % and 77.47 % in cohesiveness, and 64.70 % and 66.20 % in extensibility, respectively. For starch-based modeling clay with added guar gum and xanthan gum, compared to formulations without hydrocolloids, the linear viscoelastic range exceeded 0.04 %, and the frequency dependence of both maximum creep compliance (Jmax) and storage modulus (G′) was significantly reduced. This indicates a more stable network structure and enhanced resistance to deformation. Results from Fourier Transform Infrared (FTIR) spectroscopy and X-ray diffraction (XRD) confirmed that the physical interactions between starch and various hydrocolloids, along with the addition of these hydrocolloids, inhibited the degradation effect of thermomechanical processing on the crystalline structure of starch. With the addition of guar gum, it is observed that a continuous and dense network structure forms within the starch-based modeling clay, and starch particles are distributed uniformly. In conclusion, hydrocolloids enhances the properties of starch-based modeling clay, introducing an innovative solution to the modeling clay sector.

Characterizing the thickness and temperature dependence of elastic modulus in polymer films using picosecond ultrasonics

Abstract Polymer nanofilms have found extensive applications in fields such as medical science and microelectronics, making the exploration of their mechanical properties highly significant. In this study, we examine the dependency of the out-of-plane elastic modulus of polymer films on both thickness and temperature, utilizing picosecond ultrasonics. Multiple acoustic modes of a polymer film are employed to measure its elastic modulus with heightened precision. Measurements are conducted on samples with different thicknesses and at different temperatures. The results indicate that the modulus of polymer nanofilms strongly depends on both thickness and temperature. For polymethyl methacrylate (PMMA) films with a thickness of less than 81 nm, the modulus determined exhibits a decrement correlating with thickness and is quantifiably inferior to the analogous bulk value. Additionally, as the temperature rises, the elastic modulus declines at clearly varying rates, which are described by two distinct modulus-temperature coefficients.

Local swelling effect of flexible entangled polymer chains in athermal solvents

Solutions of flexible, entangled polymer chains dissolved in athermal solvents have been widely studied; however, the influence of the local swelling effects on the overall dynamics of such systems remains incompletely understood. In this study, we performed coarse-grained simulations to compute the concentration dependence of plateau modulus of such systems. Initially, we examined the concentration dependence of entanglement length, denoted as Ne, through simulations. Our findings revealed a concentration scaling relationship for Ne, demonstrating Ne=AΦ−5/4+B, where A and B are chain length independent constants, and Φ is polymer concentration. To account for the local swelling effects, we employed the concept of blobs to represent the chains confined in athermal solvents. Each blob was characterized by a diameter ξ, a number of connected beads g, and a volume Ωb∼ξ3. Our simulations showed that the blob diameter followed the excluded volume relationship, with ξ∼g3/5. By combining the local swelling effect and the non-zero constant B, we derived a concentration scaling relationship for the plateau modulus G of solutions of flexible polymer chains in athermal solvents: G∼Φ(Ne/g)Ωb∼Φ2.30. This scaling exponent aligns with experimental observations ranging from dilute to highly concentrated systems, as well as our simulations, where values of 2.0–2.3 were observed.

Elastic anomalies across the P21mn→Pnnm structural phase transition in δ-(Al,Fe)OOH

Abstract Hydrogen may be recycled into the Earth's lower mantle by subduction and stabilized in solid solutions between phase H (MgSiO4H2), δ-AlOOH, ε-FeOOH, and SiO2 post-stishovite. In high-pressure oxyhydroxide phases, hydrogen is incorporated following the typical (OHO) sequence, adopting the asymmetric configuration O-H···O that evolves into a symmetric disordered state upon compression. Moreover these iron-/aluminum-bearing oxyhydroxides [δ-(Al,Fe)OOH] present a structural phase transition from P21nm to Pnnm as pressure increases. Here, the single-crystal elasticity of the P21nm phase of δ-(Al0.97,Fe0.03)OOH has been experimentally measured across the P21nm→Pnnm transition up to 7.94(2) GPa by simultaneous single-crystal X-ray diffraction (XRD) and Brillouin spectroscopy at high pressures. The transition appears to be continuous, and it can be described with a second, fourth and six order terms Landau potential. Our results reveal an enhanced unit-cell volume compressibility, which is linked to an increase of the b- and a-axes linear compressibility in the P21nm phase of δ-(Al0.97,Fe0.03)OOH prior to the transition. In addition, we observed the presence of elastic softening in the P21nm phase that mostly impacts the elastic stiffness coefficients c12, c22 and c23. The observed elastic anomalies cause a significant change in the pressure dependence of the adiabatic bulk modulus (KS). These results provide a better understanding of the relation between elasticity, P21mn→Pnnm structural phase transition and hydrogen dynamics in δ-(Al0.97,Fe0.03)OOH, which may be applied to other O-H···O-bearing materials.

Exploration of the mechanical properties of carbon-incorporated amorphous silica using a universal neural network potential

C-incorporated amorphous silica (a-SiOC) is expected to be a significant dielectric film for miniaturized semiconductor devices. However, information on the relationship among its composition, atomic structures, and material properties remains insufficient. This study investigated the dependence of the elastic modulus on the C content in a-SiOC, employing a universal neural network interatomic potential to realize a high-accuracy and high-speed simulation of multicomponent systems. The relationship between elastic modulus and atomic network structures was explored by fabricating 480 amorphous structures through the melt-quenching method without predetermined structure assumptions. The bulk modulus increased from 45 to 60 GPa by incorporating 10% C atoms under O-poor conditions and 20% C atoms under O-rich conditions, respectively. This result is attributed to the formation of denser crosslinking atomic network structures. In particular, the C atoms bonded with the Si atoms with higher coordination under O-poor conditions, whereas they tend to bond with O atoms under O-rich conditions, breaking the SiO2 network. Large C clusters precipitated as the C fraction was increased under O-rich conditions. Gas molecules, such as CO and CO2, were also generated. These results are consistent with reported ab initio calculation results of the formation energies of C defects and gas molecules in SiO2. The findings suggest that realizing O-poor conditions during deposition is crucial for fabricating stronger dielectric films. Therefore, this work contributes to understanding the fabrication of stronger dielectric films and elucidating the underlying mechanism of C cluster formation.

RHEOLOGY OF STRUCTURED LIQUIDS. ADDICTION DYNAMIC MOD-ULES FROM STRAIN AMPLITUDE

A new interpretation is proposed for the dependence of dynamic moduli on the deformation amplitude during shear vibrations occurring at a xed vibration frequency. It is based on a structural rheological model, which includes the kinetic equations for the formation and destruction of particle aggregates under the action of an oscillating shear flow. Rheological equations have been obtained that are able to approximate rheological curves in separate sections with different amplitudes of shear deformation. The possibilities of the new rheological model are shown on the example of two polymer systems filled with solid particles.

Theoretical model for the Frank elastic moduli in the intercalated SmAb phase of bent-shaped dimers

ABSTRACT In our previous works we have shown that the elastic properties of the intercalated SmAb phase formed by bent-shaped dimers are governed by the nematic-like behaviour of the secondary director m that is associated with the projection of the molecular axes of the monomers on the plane of the smectic layer. From the experiment, the corresponding three Frank-like moduli K 11 m , K 22 m and K 33 m related to the secondary director demonstrate the usual behaviour of the Frank moduli of the nematics formed by rod-like molecules: monotonously increase with decreasing temperature. This is contrary to the temperature dependence of the elastic moduli for the primary director of N and NTB phases formed by bent-shaped dimers (for which the bend elastic constant decreases with temperature to zero). However, the values of the Frank-like moduli for SmAb were found to be smaller than their nematic-phase equivalents, and demonstrate a strong and unusual anisotropy, with K 11 m : K 22 m : K 33 m ratio being approximately 30 : 1 : 10. Here we present a theoretical model based on the assumption of the nematic-like order within the smectic layers that provides a qualitative explanation of the experimental results.

Modelling rapid non-destructive test using light weight deflectometer on granular soils across different degrees of saturation

This study introduces an advanced finite element model for the light weight deflectometer (LWD), which integrates contact mechanics with fully coupled models. By simulating LWD tests on granular soils at various saturation levels, the model accurately reflects the dependence of the LWD modulus on dry density, water content, and effective stress. This model addresses and overcomes the limitations of previous finite element models for this specific problem. Simultaneously, this research presents the first experimentally validated fully coupled contact impact model. Furthermore, the research provides a comparative assessment of elastoplastic and nonlinear elastic models and contrasts an enriched node-to-segment method (developed in this study) with the more precise mortar technique for contact mechanics. These comparisons reveal unique advantages and challenges for each method. Moreover, the study underscores the importance of careful application of the LWD modulus, emphasising the need for sophisticated tools to interpret soil behaviour accurately.

Determination of Young’s Modulus of PET Sheets from Lamb Wave Velocity Measurement

BackgroundThe elastic modulus of polyethylene terephthalate (PET) sheets is typically measured through destructive tests that require specific sample preparation and time-consuming testing procedures.ObjectiveTo improve the efficiency of measuring the elastic modulus of PET sheets, research on a non-destructive measurement approach using guided Lamb waves was conducted.MethodsIn this approach, the group velocity of the zero-order symmetric Lamb wave mode (S0 mode) at a single frequency is first measured from PET sheets. The semi-analytical finite element method (SAFEM) is used as the forward model to calculate the corresponding numerical group velocity. Particle swarm optimisation (PSO) is used to update the elastic modulus in the SAFEM model until the numerical group velocity from the model matches the experimental results.ResultsThe results show that measuring the group velocity data at a single frequency is sufficient for elastic modulus measurement while the material thickness can be assumed as a constant, which improves the efficiency of the measurement. The identified modulus differs from the tensile modulus of the material due to the frequency dependence of the elastic modulus. However, this discrepancy could be eliminated by using a linear regression model.ConclusionsThe method mentioned above can achieve non-destructive and efficient measurement of the elastic modulus of PET sheets, which can potentially be applied for in-line quality inspection in PET bottle production processes.

Explaining an anomalous pressure dependence of shear modulus in germanate glasses based on Reverse Monte Carlo modelling

Unlike traditional silicate glasses, germanate glasses often feature non-monotonic variations in material properties (e.g., elastic moduli and glass transition temperature) with varying chemical composition, temperature, and pressure. However, the underlying atomic-scale structural origins remain poorly understood. This is because, in most oxide glasses, the structural changes are quantified through solid-state NMR spectroscopy, but unfortunately the only NMR active germanium isotope (73Ge) has very unfavorable NMR properties. Here, we circumvent this problem by using high-energy X-ray and neutron total scattering coupled with ab initio molecular dynamics simulations as input for Reverse Monte Carlo modeling. In detail, we study the structure and properties of two sodium germanate glasses (10Na2O-90GeO2 and 20Na2O-80GeO2) subjected to permanent densification through hot compression up to 2 GPa at the glass transition temperature. While density as well as Young's and bulk modulus increase with pressure as expected, shear modulus first increases and then decreases slightly at higher pressures. The refined atomistic structure models suggest that the glasses feature a distribution of 4, 5, and 6 coordinated Ge with a majority of 4 and 5 coordinated species. Only minor changes in the Ge–O coordination occur upon hot compression, but a notable transformation of edge- to corner-sharing Ge-polyhedra is found. This anomalous polyhedral packing causes a lower number of angular constraints upon higher pressure treatment, explaining the non-monotonic trend of shear modulus with pressure. We also find that the rings become smaller and less circular upon compression, contributing to the volumetric compaction. These findings may aid the future design of germanate glasses with tailored properties and the general understanding of structure-property relations in oxide glasses.

Temperature-dependent elasticity of DNA, RNA, and hybrid double helices

Nucleic acid double helices in their DNA, RNA, and DNA-RNA hybrid form play a fundamental role in biology and are main building blocks of artificial nanostructures, but how their properties depend on temperature remains poorly understood. Here, we report thermal dependence of dynamic bending persistence length, twist rigidity, stretch modulus, and twist-stretch coupling for DNA, RNA, and hybrid duplexes between 7°C and 47°C. The results are based on all-atom molecular dynamics simulations using different force field parameterizations. We first demonstrate that unrestrained molecular dynamics can reproduce experimentally known mechanical properties of the duplexes at room temperature. Beyond experimentally known features, we also infer the twist rigidity and twist-stretch coupling of the hybrid duplex. As for the temperature dependence, we found that increasing temperature softens all the duplexes with respect to bending, twisting, and stretching. The relative decrease of the stretch moduli is 0.003–0.004/°C, similar for all the duplex variants despite their very different stretching stiffness, whereas RNA twist stiffness decreases by 0.003/°C, and smaller values are found for the other elastic moduli. The twist-stretch couplings are nearly unaffected by temperature. The stretching, bending, and twisting stiffness all include an important entropic component. Relation of our results to the two-state model of DNA flexibility is discussed. Our work provides temperature-dependent elasticity of nucleic acid duplexes at the microsecond scale relevant for initial stages of protein binding.

Theoretical study of kinetic arrest, shear elastic modulus, and yielding in simple biphasic colloidal mixtures.

Based on integrating microscopic statistical mechanical theories for structure and ideal kinetic arrest at the naive mode coupling level, we study dynamic localization, the linear elastic shear modulus, applied stress induced modulus softening, and the absolute yielding of simple biphasic binary mixtures composed of equal diameter hard and attractive spheres. The kinetic arrest map is a rich function of total packing fraction, strength of attraction, and mixture composition. The gel to attractive ideal glass transition, the degree of glass melting re-entrancy, and the crossover boundary separating repulsive glasses from attractive glasses vary with the mixture composition. Exponential and/or apparent (high) power law dependences of the elastic shear modulus on the total packing fraction are predicted with effective exponents or exponential prefactors that are sensitive to mixture composition and location in the kinetic arrest map. An analysis of the effective mean square force on a tagged particle that induces dynamic localization reveals a compensation effect between structural correlations and degree of particle localization, resulting in the emergence of a weaker dependence of the shear modulus on mixture composition at very high attraction strengths. Based on a microrheologically inspired formulation of how external stress weakens particle localization and the shear modulus, we analyze mechanical-induced modulus softening and absolute yielding, defined as a discontinuous solid-to-fluid stress-induced transition that can occur in either one or two steps. Estimates of the corresponding yield strains predict that the binary mixture becomes more brittle with increasing sticky particle composition and/or attraction strength.