Temperature Dependence Of Elastic Modulus Research Articles

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.

Elinvar effect in Ti50-xNi41Co9Nbx shape memory alloys

Based on the observation of Elinvar effect in non-magnetic Co doped TiNi alloys, we added a small amount of Nb to Ti50Ni41Co9 alloy with low Co content to regulate the phase transformation behaviors and induce Elinvar effect. The effects of Nb content on the phase transformation behaviors and the temperature dependences of elastic moduli of Ti50-xNi41Co9Nbx shape memory alloys were investigated. The Ti50Ni41Co9 alloy was found to exhibit only the B2→R phase transformation during cooling and RS decreased gradually with the increase of Nb content. As the Nb content increased to 1.5 at.%, the B2→R phase transformation was suppressed and converted to a continuous transformation over a broad temperature range, which accompanied with the electric resistivity abnormally increased and the appearance of some bright “particle”-like dots during cooling. The temperature dependence of elastic modulus also decreased with the increase of Nb content. As a result, Ti48.5Ni41Co9Nb1.5 alloy showed the Elinvar effect over a wide temperature range from 304 °C to 35 °C, which could be attributed the success to the gradual modulus softening caused by the continuous transformation compensated the normal modulus hardening of matrix.

Molecular Dynamics Simulations of DGEBA/OSC Epoxy Composites for Improving Heat-Resistance and Elastic Modulus

Thermal and mechanical properties of DGEBA/OSC epoxy composite polymers composed of both bisphenol A diglygde ether (DGEBA) and alicyclic epoxy resin (OSC) as co-polymerization monomers and 3,3-diaminodiphenyl sulfone (DDS) as curing agent are evaluated and investigated by molecular dynamics (MD) simulations, in which NPT ensembles and annealing cycles in a wide temperature range are utilized for modeling the thermodynamic equilibrium systems and heating processes. Glass transition and thermal-decomposition temperatures are calculated by linear fitting on the temperature dependence of elastic modulus, cohesive energy, fractional free-volume (FFV). It is verified that the two DGEBA/OSC epoxy composite can effectively improve the thermal and mechanical performances of epoxy polymer, in which DGEBA/OSC(1:1) epoxy composite are most significant of promoting mechanical stiffness and render a elevated glass transition temperature by 28 K and thermal-decomposition temperatures by 91 K, the two DGEBA/OSC epoxy composite are capable of efficiently reduce fractional free volume by 4.4% and 8.6% for DGEBA/OSC(3:1) and DGEBA/OSC(1:1) epoxy composite respectively, which is in consistent with the lower rotation amplitudes of crosslinking bonds for DGEBA/OSC composite EP polymers that vdW interaction forces between molecular-chains can be promoted by OSC co-polymeric blocks to inhibit thermal motions of EP molecular-chains.

Temperature effects on the structure and mechanical properties of vapor deposited a-SiO2

Amorphous silica (a-SiO2) exhibits unique thermo-mechanical behaviors that set it apart from other glasses. However, there is still limited understanding of how this mechanical behavior is related to the atomic structure and to the preparation conditions of a-SiO2. Here, we used electron beam (e-beam) physical vapor deposition (PVD) to prepare a series of a-SiO2 films grown at different substrate temperatures and then combined molecular simulations with Positronium Annihilation Lifetime Spectroscopy and nanoindentation experiments to establish relations among processing, structure, and mechanical response of the films. Specifically, we found that increase in the growth temperature leads to increase in the elastic moduli and hardness of the films. The relative porosity in the films also increases while the a-SiO2 network itself becomes denser, resulting in an overall increase in density despite increased porosity. In addition, we found that the a-SiO2 films exhibit the same anomalous temperature dependence of elastic modulus as bulk a-SiO2. However, the rate of increase in the elastic modulus with the measurement temperature was found to depend on the density of the a-SiO2 network and therefore on the growth temperature. Our findings provide new insights into the influence of the atomic network structure on the anomalous thermomechanical behavior of a-SiO2 and in turn guidance to control the mechanical properties of a-SiO2 films.

Effect of thermo-oxidative ageing on the thermo-mechanical responses of 3D braided carbon fiber/epoxy composites during high-speed impact

By developing a thermo-mechanical coupled model, we quantitatively analyzed the effect of thermo-oxidative ageing on the temperature, thermal strain and thermal stress histories of braided composites during high-speed impact. We also considered temperature dependence of elastic modulus during impact in this model. The proposed model was first applied to the unaged composites, then the results were compared to the impact responses captured by the split Hopkinson bar and the high-speed camera. The comparisons of the experimental and numerical results show that the proposed model could capture the adiabatic temperature rise, stress-strain responses and failure process of braided composites during high-speed impact. The validated model was subsequently employed to thermo-oxidative aged composites. Results show that the temperature rise, thermal strain and thermal stress all depend on the mechanical properties of resin, and they decreased with the increase of ageing temperature since the performance of resin is compromised by thermo-oxidation ageing. The change of resin performance after ageing leads to the change in the temperature rise during impact, so the stiffness of composites will decrease in varying degrees after ageing.

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.

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.

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.

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

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].

A novel method for characterizing temperature-dependent elastic modulus and glass transition temperature by processing the images of bending cantilever slender beams at different temperatures

We propose a novel method for estimating the elastic modulus of several materials by processing the bending image of cantilever material sheets. The calculated results (tested for five samples) were consistent with data obtained by direct measurement using a tensile strength device. By placing the cantilever sheets in an environment inside of which the temperature could be controlled, we were able to obtain the temperature dependence of elastic modulus. We identified a drastic drop of elastic modulus at a certain temperature and assumed this temperature corresponds to glass transition temperature. We also introduced an equation for describing the elastic modulus around that critical temperature and were able to estimate the glass transition temperature for all tested polymer materials. Surprisingly, the estimated glass transition temperatures conform to data obtained by direct measurement using a DTA device. Since the elastic modulus changes suddenly around the glass transition temperature, the proposed method might be more accurate than measurement using a DTA device where the glass transition temperature corresponds to the location of a weak peak at the DTA curve. This is the first attempt for estimating the glass transition temperature of polymer based on bending of cantilever slender beam, and seems to be the simplest method. The method is very potential for developing new equipment for determining the glass transition temperature of polymeric materials.

Coda wave interferometry during the heating of deep geothermal reservoir rocks

Coda wave interferometry (CWI) is a high-resolution technique that aims at tracking small changes in a diffusive medium from the time correlation of seismic waveforms. CWI has been widely used in recent years to monitor the fine-scale evolution of fault zones and more recently of deep reservoirs. However, to provide a quantitative interpretation of the reservoir, direct modeling of physical effects like the influence of temperature on seismic wave scattering is required to investigate temperature effects from measurements of velocity changes. Here, we propose to quantify the impact of thermo-elastic deformation on CWI measurements by comparing experimental results obtained from a previous study on Westerly Granite to a numerical approach based on two combined codes (SPECFEM2D and Code_Aster) for modeling wave propagation in complex media during thermo-elastic deformation. We obtain two major results. First, we show that multiple reflections on the boundaries of our simplified numerical sample reproduce well the wave scattering properties of the experimental granitic sample characterized by a complex mineral assembly and a large set of microcracks. We based our comparison on the wave diffusion model that describes both the experimental and numerical samples (similarity in energy density function and mean free path). We also show that both samples share a similar thermo-elastic behavior, but only after the second heating and cooling cycle. Second, the stretching technique used for CWI measurements on both samples reveals reversible time shifts correlated with the thermo-elastic deformation of the sample. However, the influence of thermo-elastic deformation is different between our numerical proxy and the experimental sample. We discuss the role of irreversible deformation (e.g., microcracking) for the observed discrepancy by introducing temperature dependence of elastic moduli in the model. These results suggest that there are open perspectives to monitor thermal strain in geothermal reservoirs using CWI.

Thermodynamic Analysis of Polymer Gel Elasticity

Elastomer and polymer gel have a three-dimensional polymer network structure and the characteristic of being soft and well extended (rubber elasticity). Many researches on rubber elasticity have been carried out mainly with elastomer since 1950's. Entanglement of network chains dominates the physical properties because elastomer contains almost no solvent, thus it is difficult to investigate the correlation between the structure and the physical properties in detail. On the other hand, polymer gel is a dilute system coexisting with solvent, thus it is possible to design various network structures with controlled entanglement. Recently, we developed Tetra-PEG gel, which is formed by AB-type polycondensation of tetra-armed prepolymers. Tetra-PEG gel has a highly homogeneous network structure, which is suitable for verifying the theory of polymer gel. In the previous study, Phantom network model, which is a rubber elasticity model, was verified. Phantom network model assumes that the crosslinks fluctuate with deformation, and elastic modulus (G) is described as G = ξk B T Here, k B is the Boltzmann constant, T is absolute temperature, and ξ is the number densities of independent cycles surrounded by the mesh chain. In tree-like approximation, ξ can be calculated from polymer concentration, polymer molecular weight, and connection probability between prepolymers. This equation indicates that one cycle has the influence of the thermal energy k B T on the elasticity. As a result of the verification using Tetra-PEG gel, it was confirmed for the first time in the world that the connection probability dependence of the elastic modulus and the calculated ξ (ξ th) was the same. This indicates that Phantom network model can describe the elasticity of polymer gel. However, the polymer concentration (C) dependence of them was different as shown in Figure 2. Here, the polymer concentration was normalized by the overlapping concentration (C*). The polymer concentration is a concept inherent to polymer gel, and it has not been considered so much in conventional researches. Therefore, we returned to thermodynamics, which is the origin of rubber elasticity models, and experimentally verified it. The elastic modulus from Helmholtz free energy is described as the following equation. G = U” + S”T The first term (U”) is referred to as energy elasticity, and the second term (S”T) as entropy elasticity. From this equation, it is shown that elastic modulus can be separated into energy elasticity and entropy elasticity by measuring temperature dependence of elastic modulus. Classical rubber elasticity theory ignores the energy elasticity and predicts that the elastic modulus is proportional to temperature (G ~ T). It has been experimentally confirmed that the proportional relationship is roughly correct in the case of elastomer. On the other hand, the elastic modulus of Tetra-PEG gel was not proportional to temperature, and the negative energy elasticity whose value cannot be ignored was measured (Figure 1). This result may indicate an essential difference between elastomer and polymer gel. Therefore, we further investigated the energy elasticity and entropy elasticity using Tetra-PEG gel with various network structures. When only the connection probability was changed, energy elasticity was proportional to entropy elasticity (U”~ S”T). Since in previous study it was shown that the connection probability dependence of the elastic modulus and ξ was the same, we found that the dependence of the entropy elasticity and the energy elasticity was also the same as ξ. Furthermore, the entropy elasticity had the same polymer concentration dependence as ξ, which shows that the entropy elasticity follows Phantom network model except the value. Therefore, this result also shows the different concentration dependence of the elastic modulus and ξ is derived from the energy elasticity (Figure 2). In the poster presentation, I will talk about the cause of energy elasticity and the effect of solvent quality of polymer gel, too. Figure 1

Temperature Dependence of Elastic Moduli for NaCl

Temperature Dependence of Elastic Moduli for NaCl

Mechanical Strength Evaluation of YSZ, GDC and LSCF under SOFC Operating Conditions

1. Introduction For designing SOFC with high mechanical reliability, it is necessary to analyze stress state of cells and stacks under various operating conditions. Based on this concept, our group has attempted to construct multiscale model which can simulate elastic and inelastic deformation and fracture probability with consideration of electro-chemical, thermal and mechanical properties of constituent materials. In this study, we focus on strength of SOFC materials including 8YSZ electrolyte, 10GDC barrier layer and LSCF6428 cathode which are well-known as brittle materials. Their elastic properties and fracture strengths are evaluated as a function of temperature. 2. Experiments Evaluation of elastic and fracture properties Mechanical strength evaluation is performed by Small Punch (SP) tests. The tests were performed on a universal testing machine (INSTRON 5565). The circular specimens were simply supported at the circumferential edge of an alumina tube and subjected to a concentrated load at their center position. The load was applied through a puncher at a crosshead speed of 0.05 mm/min until a final failure occurred. The load-line deflection of the specimens was measured by monitoring the movement of an Al2O3 rod of which one end is made in contact with the bottom surface of the sample, and the position of the other end is monitored using a laser displacement transducer. The elastic modulus ESP and fracture stress σf_SP were calculated using the following equations : ESP = f(t/a)[3a 2(1-ν)(3+ν)P/4πδt 3], σ f_SP =Pmax (1+ν)[0.485ln(a/t)+0.52+3/2π(1+ν)]/t 2, where Pmax is the load applied by the puncher, δ is the load-line deflection, t is the thickness of the specimen,n is Poisson’s ratio, a is the radius of the load support, and f(t/a) is a correction factor of the specimen thickness for the thin plate theory given by the following equation: f(t/a)=1.5136(t/a)2+0.0162(t/a)+0.9962. The elastic modulus ESP was computed from the linear slope of the load versus load-line deflection records (P/δ), and the fracture stress σf_SP was calculated from the peak load Pmax . Sample preparation Commercial powders of 10 mol% gadolinia doped ceria (10GDC) was obtained from Shin-Etsu Chemical Co., Ltd.(Tokyo, Japan) and La0.6Sr0.4Co0.2Fe0.8O3-δ (LSCF6428) from Noritake Co.,Ltd.(Nagoya, Japan). The 10GDC and LSCF6428 powders were uniaxially pressed to f10mm disc-shape with pressure 100 MPa and then with a cold isostatic press (CIP) at 170 MPa. After that, 10GDC green samples were sintered at 1550˚C for 6 hours with 5˚C/min heating rate and 2˚C/min cooling rate. LSCF6428 green samples were sintered at 1300˚C for 6 hours with the same heating and cooling rates. As a SP test specimen, sintered discs were polished to a uniform thickness about 0.5mm by mechanical polishing. One side of the pellet was mirror-polished with a diamond paste of 3mm. 8 mol % Y2O3stabilized zirconia (8YSZ) plates of 7×7×0.5 mm with one side polished were supplied by Japan Fine Ceramic Co., Ltd (Sendai, Japan). We performed ten experiments for respective materials at selected temperature between R.T. and 800˚C in air. Average and standard deviation of elastic moduli and scale and shape parameters of fracture stress based on Weibull distribution were calculated from experimental results at each temperature. Scale parameter means fracture stress at fracture probability 63.2% and, shape parameter indicates the degree of dispersion of fracture stress on Weibull distribution. Lager shape parameter means the dispersion of fracture stress is smaller, and the strength stability is higher. 3. Result and discussion The temperature dependences of elastic moduli and scale and shape parameters of 8YSZ, 10GDC and LSCF6428 are shown in Fig.1 (a), (b). For 8YSZ, elasticity, scale and shape parameters showed minimum at 400˚C. It means decrease of elasticity and fracture stress of 8YSZ is accompanied by increase in the dispersion of fracture stress. For 10GDC, both elasticity and scale parameter decreased up to 200˚C, and gradually increased with further increase in temperature. It should be noted that shape parameter increased with temperature increasing. It shows that the strength stability increased with temperature. For LSCF6428, elasticity once dropped between 200˚C and 400˚C, increased with further heating up to 800˚C. Scale parameter tendency is similar to 10 GDC, but the strength stability of both is switched at 600˚C. In this way, the quantitative characterization of the strength stability in 8YSZ, 10GDC and LSCF6428 are evaluated with their fracture stress and elasticity. Figure 1

Role of the Temperature Dependence of Elastic Modulus in the Basic Characteristics of Giant Magnetically Induced Deformation of Ferromagnetic Martensite

Role of the Temperature Dependence of Elastic Modulus in the Basic Characteristics of Giant Magnetically Induced Deformation of Ferromagnetic Martensite

Elastic Moduli in Cadmium Selenide Doped with Chromium

Temperature dependence of elastic moduli , , and the latter for the piezo-active and non-piezo-active versions, have been measured in the interval of 4 - 180 K at 28 - 262 MHz in a CdSe: Cr2+ crystal. Anomalies below 40 K have been found for all the moduli, except . The interpretation of the results has been carried out involving the Jahn-Teller effect and relaxation between the equivalent distortions of the tetrahedral CrSe4 centers.

Moduli Determination at Different Temperatures by an Ultrasonic Waveguide Method

A novel ultrasonic waveguide based technique for measuring the moduli of elastic isotropic material as a function of temperature using ultrasonic guided wave modes is presented here. This technique can be utilized for measuring Young’s modulus (E) and Shear Modulus (G) of multiple material using the guided ultrasonic L(0, 1) and T(0, 1) wave modes respectively over a wide range of temperatures (demonstrated here from room temperature to 1200 °C). The specimens used in the experiments here have special embodiments (for instance, a bend) at one end of the waveguide and an ultrasonic guided wave generator (transducer) at the other end for obtaining reflected signals in a pulse-echo mode. The far end of the waveguides with the embodiment is kept inside a heating device such as a temperature-controlled furnace. The time of flight difference (δTOF) were used to measure the moduli at different temperatures. Several materials were tested and the comparison between literature values and measured values were found to be in agreement, for both elastic moduli (E and G) measurements, as a function of temperature. This technique provides significant reduction in time, effort and cost over conventional means of measurement of temperature dependence of elastic moduli.

Temperature Dependence of Elastic Moduli of Inorganic Adhesives with 3 Types of Binders

Temperature Dependence of Elastic Moduli of Inorganic Adhesives with 3 Types of Binders