Dependence Of Elastic Modulus Research Articles

High‐Precision Tracking of Sandstone Deformation From Micro‐CT Images

AbstractElastic properties of sandstones can be highly pressure dependent. However, the pressure‐induced deformation of intact sandstones in X‐ray micro‐Computed Tomography (micro‐CT) images are below the resolving power of conventional image analysis methods. Also, most digital rock physics studies of the elastic properties operate with micro‐CT images acquired at ambient pressure. Here, we perform a comprehensive analysis of an intact sandstone sample with pronounced stress‐sensitivity. A purpose‐built X‐ray‐transparent pressure cell enables scanning micro‐CT images at confining pressures of up to 36 MPa. To detect the small pressure‐induced changes from these images, we design an overall deformation detection workflow with slice‐searching technique. We apply this workflow to a set of micro‐CT images of a 2 × 2 × 2 mm sample scanned at several pressures with a voxel size length of ∼1 μm. The results give the static modulus of 2.78 GPa, which is ∼0.5 times of the dynamic modulus derived from ultrasonic measurements. This ratio is consistent with literature data, showing the accuracy of the deformation detection workflow. Images scanned at different pressures are then segmented into two‐phase labels. The porosity change detected from segmented labels is consistent with the value derived from static modulus using poroelastic theory. The two‐phase segmented images are utilized to simulate the elastic properties with a finite element method. Most of the pressure dependency of elastic moduli shown in ultrasonic measurements is caused by closure of compliant pores at grain contacts, which cannot be resolved by the micro‐CT. The accuracy improvement of the estimated elastic properties from images scanned at higher pressures is negligible.

Benchmark polynomials for the porosity dependence of elastic moduli and conductivity of partially sintered ceramics

It is well known that no useful analytical models are available for predicting the porosity dependence of effective properties for partially sintered ceramics with an open (interconnected) pore space where concave pore surfaces are dominating. This does not mean, however, that that the problem of determining the effective properties of partially sintered ceramics does not have a unique solution for a given microstructure. It just means that this solution can be obtained only numerically. In this contribution we report the polynomial fits of our numerical results for the effective elastic moduli (Young’s modulus, shear modulus, bulk modulus) and conductivity (thermal or electrical) for model materials based on the random close packing of monosized spheres. These relations are recommended as benchmark relations for the porosity dependence of the effective properties of partially sintered ceramics.

High-temperature effect on the material constants and elastic moduli for solid rocks

Abstract Thermally coupled constitutive relations are generally used to determine material constants and elastic moduli (Young's modulus and shear modulus) of solid media. Conventional studies on this issue are mainly based on the linear temperature dependence of elastic moduli, whereas analytical difficulties are often encountered in theoretical studies on nonlinear temperature dependence, particularly at high temperatures. This study investigates the thermally coupled constitutive relations for elastic moduli and material constants using the assumption of axisymmetric fields, with applications to geologic materials (marble, limestone and granite). The Taylor power series of the Helmholtz free energy function within dimensionless temperatures could be used to develop the thermally coupled constitutive relations. The thermoelastic equivalent constitutive equations were formulated under the generalized Hooke's law. The material constants of solid rocks were determined by fitting experimental data using axisymmetric stress and strain fields at different temperatures, based on their thermomechanical properties. For these geologic materials, the resultant equivalent elastic moduli and deformations were in good agreement with those from the experimental measurements. Thermal stresses, internal moisture evaporation and internal rock compositions significantly affected the experimental results. This study provides a profound understanding of the thermally coupled constitutive relations that are associated with the thermomechanical properties of solid rocks exposed to high temperatures.

Thermomechanical Homogenization of Corrugated Core Sandwich Structures of Reusable Launch Vehicles

The corrugated core sandwich structure is a potential candidate for the integrated thermal protection system (ITPS) of reusable launch vehicles (RLVs). The sandwich structure can develop a significant thickness-wise thermal gradient during operation, resulting in a temperature-dependent property variation along the cross section as well as thermal stresses. In this work, a homogenization method has been developed that incorporates these effects into the first-order shear deformation plate theory to facilitate thermomechanical structural analysis of RLV components such as wings, fuselage, etc., with the ITPS sandwich panels represented as thick orthotropic plates. The formulation expands the classical plate theory by assuming a polynomial form of thickness-wise temperature variation, as well as a linear dependence of elastic moduli and thermal expansion coefficients on temperature. This expansion introduces unknown constants into the homogenized model that could then be evaluated from unit-cell analyses with periodic boundary conditions and beam analyses of the corrugated core sandwich structure. The accuracy of the homogenized plate has been demonstrated by comparing its response with a full-scale model for a uniform and spatially varying in-plane temperature field. For both cases, a thickness-wise linear temperature variation has been used. The comparisons show that the homogenization approach is reasonably accurate in capturing the midplane deflections as well as stresses on the face sheets. An error of less than 1% could be seen in the maximum midplane transverse deflection for the problem with a spatially varying in-plane temperature field.

First-principles modeling of solute effects on thermal properties of nickel alloys

The effects of Cr and W on high-temperature properties of Ni-based alloys are derived from first-principles calculations combined with a quasi-harmonic Debye model. The modeling procedure integrates all contributions from electronic excitations, magnetic fluctuations and lattice vibrations. The predicted lattice parameter and thermal expansion coefficient agree well with available reference values. The temperature dependence of elastic moduli for Ni-Cr alloys is described satisfactorily. Debye temperature has been calculated to show a strong volume dependence but a weak temperature dependence. A close relationship between the concentration dependence of elastic moduli and the volume dependence of Debye temperature, and thus the vibrational free energy, has been established. Besides, the softening of elastic moduli with increasing temperature is shown to be a result of thermal expansion which mainly comes from lattice vibrations. Therefore, lattice vibrations affect both temperature and concentration dependencies of elastic properties at elevated temperatures. With the help of Labusch–Nabarro model, solid solution hardening caused by Cr and W solutes in Ni has been analyzed. Moreover, the presence of solute atoms increases elastic anisotropy. The effects of Cr or W additions on the thermodynamic properties are found to be small compared to the effect of temperature.

Investigation of pressure dependence of mechanical properties of SbSI compound in paraelectric phase by Ab Initio method

The structural parameters as atomic positions, lattice constants, volume and density were determined using the Quantum Espresso software by geometric optimization at ambient pressure and under hydro static pressure. Using optimized values, elastic constants were calculated. The pressure dependence of elastic modulus (bulk, Young and shear modulus, Poisson ratio), anisotropy, compressibility and Debye temperatures were investigated using the calculated elastic constants. Mechanical stability and ductility/brittleness of the material were evaluated. It was seen that the results obtained were compatible with the existing experimental and theoretical data.

Porosity dependence of elastic moduli of snow and firn

AbstractMeasurements of elastic wave velocities enable non-destructive estimation of the mechanical properties, elastic moduli and density of snow and firn. The variation of elastic moduli with porosity in dry snow and firn is modeled using a differential effective medium scheme modified to account for the critical porosity above which the bulk and shear moduli of the ice frame vanish. A comparison of predicted and measured elastic moduli indicates that the shear modulus of ice in snow is lower than that computed from single crystal elastic stiffnesses of ice. This may indicate that the bonds between snow particles are more deformable under shear than under compression. A partial alignment of ice crystals also may contribute. Good agreement between elastic stiffnesses of the ice frame obtained from elastic wave velocity measurements and the predictions of the theory is observed. The approach is simple and compact, and does not require the use of empirical fits to the data. Owing to its simplicity, this model may prove useful in a variety of potential applications such as construction on snow, interpretation of seismic measurements to monitor and locate avalanches and estimation of density within compacting snow deposited on glaciers and ice sheets.

Electronic origin of the main-group element dependences of elastic moduli in the Ni2Mn-based magnetic shape memory alloys

In this work, the main-group (sp) element dependences of anisotropic elastic moduli, including elastic constants Cij, Young's moduli En, shear moduli Gm, n, Poisson's ratioνm,n and Zener anisotropy index Az, and their correlated electronic origins in the Ni2MnZ (Z = Al, Ga, In, Si, Ge, and Sn) alloys were studied by first-principles calculations. Results show that all the studied alloys are strongly anisotropic. The ratio of E[111] and E[100], which owns the maximum and minimum tension resistance, respectively, is larger than 20 in Ni2MnGa. For the sp element dependence, the mechanical strength-related elastic moduli, such as E111, EH, and GH, show a similar tendency as that of C44. The lattice stability-related elastic moduli, such as Az and ν[110][-110], follow the sp element dependence of tetragonal shear modulus C’. Analyses show that the atomic radius and valence electron number of the sp element are the key parameters to tune C11 and C12 in the studied Ni2Mn-based alloys. One more valence electron of the sp element would lead to an increase of 0.035 Å for the equilibrium lattice parameter. For C44, it is closely related to the electronegativity of the sp element. As for C′, the strength of p-d orbital hybridization between Ni and the sp element plays a decisive role. This work is expected to lay a theoretical foundation for designing advanced Ni2Mn-based magnetic shape memory alloys.

Modeling the Effect of Pressure on the Moduli Dispersion in Fluid‐Saturated Rocks

AbstractLaboratory experiments of ultrasonic velocities of fluid‐saturated rocks are often much higher than the predictions of the Gassmann theory. This difference is usually attributed to the velocity dispersion caused by fluid pressure relaxation between pores of different shapes and orientation. This paper proposes a simple model to characterize pressure and frequency effects on the elastic moduli of fluid‐saturated rocks in a broad frequency range. The proposed model incorporates micromechanics of wave‐induced fluid pressure relaxation at grain contacts (between crack‐like contacts and stiff pores) into pressure dependency of elastic moduli. Previously, the pressure dependency of the velocities or elastic moduli was ascribed to the progressive closure of cracks with the increasing effective pressure and expressed as an integral of crack compliance over the range of aspect ratios. For isolated cracks, this compliance is a function of crack geometry only. For cracks hydraulically connected to stiff pores, this crack compliance can be replaced by a frequency‐dependent solution of the micromechanical problem of fluid pressure relaxation between a single crack and surrounding pores. The resulting equation expresses the bulk and shear moduli of the fluid‐saturated rock as functions of both pressure and frequency. Furthermore, if pressure‐dependent moduli of both dry and fluid‐saturated moduli are known, the aspect ratio distribution can be obtained from the pressure dependency of the dry moduli, and then the saturated moduli can be computed with no adjustable parameters. The model predictions show reasonable agreement with laboratory data measured using ultrasonic and forced oscillation techniques.

Effect of temperature on the fatigue crack growth behaviour of SS316L(N)

Fatigue crack growth (FCG) behaviour of austenitic stainless steel SS316L(N) has been evaluated at different temperatures in the threshold and Paris regimes. Comparison of crack closure corrected data from ASTM tests and the data from constant Kmax test at 300 K brings out the inherent inadequacies of crack closure correction in describing the FCG behaviour. An attempt to describe the temperature effects considering the temperature dependence of elastic modulus and yield strength was not satisfactory. Further analysis to understand the possible role of dynamic strain ageing (DSA) indicated different activation energies in the temperature ranges 623–723 K and 723–823 K, ~80 and 150 kJ mole−1 respectively, pointing to carbon and nitrogen diffusion as the responsible DSA mechanisms.

Elinvar property of cold-rolled NiTi alloy

We tailor the temperature dependence of elastic modulus (TDEM) of polycrystalline NiTi plates by cold rolling up to 60% thickness reduction. In-plane Elinvar property is obtained with a low elastic modulus temperature coefficient of 6.0 × 10−5 K−1 over a temperature range of 192 K. The microstructure mainly consists of approximately equal volume fractions of {111}<uvw>-oriented B2 and {102}<uvw>-oriented B19′ nanocrystals of high thermal stability due to defect pinning and grain refinement. The opposite TDEMs of the two phases can compensate each other and cause the Elinvar behavior. Such mechanism can also be used to obtain Elinvar property for other shape memory alloys.

In-situ reaction synthesis and mechanical properties of quaternary MAX phase (Cr2/3Ti1/3)3AlC2

Bulk quaternary MAX phase (Cr2/3Ti1/3)3AlC2 was synthesized by in-situ reaction/hot pressing method using Cr, Ti, Al, and C powders as starting materials. The involved reaction routes during hot-pressing were determined according to XRD and SEM/EDS analysis results. The possible chemical reactions involved during hot pressing process were proposed. It was revealed that the desired (Cr2/3Ti1/3)3AlC2 was formed via the reaction between intermediate products of ternary MAX Cr2AlC and carbide TiC, providing another path for the preparation of high order MAX phase. Tests of mechanical properties suggested that the Vickers hardness of (Cr2/3Ti1/3)3AlC2 was 5.6 GPa, higher than that of the ternary MAX phase Ti3AlC2. Its flexural and compressive strength were determined to be 493 MPa and 1407 MPa at room temperature, respectively. Flexural strength maintained a relatively high level of 424 MPa up to 1000 °C, about 90% of that at room temperature. The dependence of elastic modulus on increasing temperatures exhibited similar tendency to that of flexural strength. The as-synthesized (Cr2/3Ti1/3)3AlC2, a unique quaternary layered nano-laminated carbide, was a promising high temperature structural material with its attractively comprehensive properties.

Effect of microbial transglutaminase on the mechanical properties and microstructure of acid-induced gels and emulsion gels produced from thermal denatured egg white proteins

In the current study, the impact of microbial transglutaminase (MTGase)-mediated crosslinking on the thermally denatured egg white protein (TD-EWP) made in alkaline pH in relation to their gelling properties of in gel and emulsion gel systems was investigated. Unlike native EWP that was not a good substrate for MTGase due to its compact structure, SDS-PAGE and gel solubility data showed the TD-EWP was sufficiently cross-linked by MTGase. The MTGase significantly (p < 0.05) increased the gel strength, fracture stress, fracture strain, and TPA parameters and decreased the frequency dependence of elastic modulus and stress dependence of creep compliance of TD-EWP gel and emulsion gel samples. The enhanced mechanical properties of the TE-EWP gelled samples treated with MTGase may be suitable for delivering sensitive compounds as well as in fabricating tailored scaffolds in tissue engineering and biomedical products.

Адгезия между жестким индентором и упругим полупространством для несжимаемых градиентных сред с высоким показателем градиентности

Contact problem of cylindrical indenter and graded media with account of adhesion forces between two contacted bodies is considered. Analytical solution of the problem for the case of graded media with power-law dependence of elastic modulus on normal coordinate have been found. The case of uncompressible media with Poisson ratio 1/2 was considered in details. It is shown, that in this case the behavior of system can be qualitatively different from the case of homogeneous media. Influence of roughness of the surface is considered. Surface roughness is presented as axially symmetric “waviness”. The contact of parabolic indenter and a gradient media was considered. Differences from the case of a cylinder is shown.

Temperature Dependence of Elastic Modulus and Internal Friction of Commercial Copper and Copper Alloys with Resonance Method

Temperature Dependence of Elastic Modulus and Internal Friction of Commercial Copper and Copper Alloys with Resonance Method

Design calculation of braided high-temperature composite structures

Following a review of published papers devoted to calculations of braided composite structures, basic requirements for computational models are formulated. A mathematical model intended for design calculations of braided structures of shells of revolution is presented. The dependences for calculating the stiffness, thermal deformation, and strength characteristics of a braided composite material are given depending on the braiding scheme, reinforcement angle, and the current radius of the shell. The relationship between the angle of reinforcement, the thickness of the single-pass layer and the coverage rate of the structure that determines the degree of continuity of the layer is investigated. The features of calculations of structures with a two-axis and three-axis braiding scheme are discussed. Examples of calculations of specific composite structures are given, the dependences of elastic moduli, coefficients of linear thermal expansion and ultimate strengths on the variation of the radius of a typical braided carbon-ceramic composite shell are demonstrated.

Predicting the electrical breakdown strength of elastomers

Elastomers have extensive applications in engineering and industrial fields, such as stretchable electronics and soft robotics. Among the various properties of elastomers, electrical breakdown strength strongly affects their application and design due to safety reason. Nevertheless, measuring and determining the electrical breakdown strength of elastomers is a difficult challenge. This work proposes a general predictor and relation for the electrical breakdown strength of various types of elastomers. Based on configurational mechanics, the proposed predictor captures the stretch dependence, the voltage ramping-rate dependence and the elastic modulus dependence of the breakdown strength through the evolution of defects within the material and can effectively keep track of the variation of the electrical breakdown strength. The proposed predictor and relation can serve as a significant tool for the optimal design of elastomer-based electronics or devices and open new door for improving the electrical breakdown strength of elastomers.

Temperature dependence of elastic moduli in a refractory HfNbTaTiZr high-entropy alloy

The equiatomic HfNbTaTiZr solid solution is currently regarded as a model disordered body-centered cubic high-entropy alloy. Therefore, the temperature dependence of its elastic moduli is of prime importance to improve our understanding of the mechanical properties of this refractory alloy. In this study, the alloy was found to be single phase, fully recrystallized with a slight texture along the normal direction after thermomechanical processing at room temperature. Elastic moduli were determined over the temperature range [293 K-1100 K].

High-temperature dependency of elastic mechanical behavior of two wrought magnesium alloys AZ31B and ZK60A studied by resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) was used to study the elastic mechanical properties and internal friction of two wrought magnesium alloys, AZ31B and ZK60A, from 25 °C to 450 °C. Samples in the rolled, transverse, and normal directions were characterized at 50 °C intervals to determine the temperature dependency of elastic moduli and stiffnesses for each direction. The temperature dependencies represented as, dE/dT, dG/dT, dB/dT, dC11/dT, dC12/dT, and dC44/dT are provided herein. To evaluate the RUS technique for these type of alloys, Young's modulus was also determined by conventional static tension testing and the results were compared. From the same RUS experiment, the internal friction variation with temperature was calculated for both alloys. The linear coefficients of thermal expansion for each direction over the temperature range considered were determined, as they were needed to estimate sample dimension at elevated temperature for the RUS measurements.This study shows that RUS can be a convenient and accurate technique to supply quantitative elastic mechanical data and fill the existing gaps on light metals characterization.

Strain glass in Ti50−xNi35+xCu15 shape memory alloys

Ti-Ni-based shape memory alloys exhibit three types of martensitic structures of B19′ (monoclinic), R (trigonal) and B19 (orthorhombic). So far, the strain glass has been reported in former two martensitic alloys, however, whether it exists in the third one is still unknown. Here, we report a finding of the strain glass in Ti-Ni-Cu B19-martensitic alloys. Our established phase diagram of Ti50−xNi35+xCu15 shows that the strain glass emerges at x ≥ 7, as evidenced by three experimental signatures: (I) invariance of average structure; (II) frequency dependence of elastic moduli at a strain glass transition temperature Tg; (III) formation of nanodomains.