Temperature Dependence Of Modulus Research Articles

Temperature and strain rate-dependent compression properties of 3D-printed PLA: an experimental and modeling analysis

PurposeThis study aims to investigate the compression characteristics of the 3D-printed polylactic acid (PLA) samples at temperatures below the glass transition temperature (Tg) with varying strain rates and develop a thermo-mechanical viscoplastic constitutive model to predict the finite strain compression response using a single set of material parameters. Also, the micro-mechanical damage processes are linked to the global stress–strain response at varied strain rates and temperatures through scanning electron microscopy (SEM).Design/methodology/approachTg of PLA was determined using a dynamic mechanical analyzer. Compression experiments were conducted at strain rates of 2 × 10–3/s and 2 × 10–2/s at 25°C, 40°C and 50°C. The failure mechanisms were examined using SEM. A finite strain thermo-mechanical viscoplastic constitutive model was developed to analyze the deformations at the considered strain rates and temperatures.FindingsTg of PLA was determined as 55°C. While the yield and post-yield stresses drop with increasing temperature, their trend reverses with an increased strain rate. SEM imaging indicated plasticizing effects at higher temperatures, while filament fragmentation and twisting at higher strain rates were identified as the dominant failure mechanisms. Using a non-linear regression analysis to predict the experimental data, an overall R2 value of 0.98 was achieved between experimental and model prediction, implying the robustness of the model’s calibration.Originality/valueIn this study, a viscoplastic constitutive model was developed that considers the combined effect of temperature and strain rate for FDM-printed PLA experiencing extensive compression. Using appropriate temperature-dependent modulus and flow rate properties, a single set of model parameters predicted the rise in the gap between yield stress and degree of softening as strain rates and temperatures increased.

Temperature-dependent storage modulus of polymer nanocomposites, blends and blend-based nanocomposites based on percolation and De Gennes’s self-similar carpet theories

Temperature-dependent storage modulus of polymer nanocomposites, blends and blend-based nanocomposites based on percolation and De Gennes’s self-similar carpet theories

A hybrid constitutive model of high-damping viscoelastic materials used for vibration control of civil structures

The dynamic mechanical properties of high-damping viscoelastic (VE) materials exhibit significant frequency and temperature dependences in the glass transition zone. However, the current state of VE constitutive models face a challenge in balancing the accuracy, simplicity, and ease of structural dynamic analysis. In this study, a power-law and exponent-law hybrid model is proposed to model the frequency-dependent and temperature-dependent complex modulus of VE materials. The equivalence of hybrid model and existing VE constitutive models is presented. A total of 12 groups of experimental data are collected to validate the accuracy of hybrid model. An efficient numerical method for the hybrid model is proposed and then validated through a viscoelastically damped frame. Results show that the hybrid model is equivalent to two rheological models or fractional derivative models owning to the unshared model coefficients. The hybrid model is superior to the eight-parameter fractional derivative model in predicting the complex modulus over a wide equivalent frequency range. The proposed numerical method performs quite well in calculating seismic responses of proportional and non-proportional damped frames.

Micromechanics-based modeling of temperature-dependent effective moduli of fiber reinforced polymer composites with interfacial debonding

In this paper, the dimensionless debonding length of fiber at various temperatures was obtained based on the maximum shear stress criterion. Then Hill's stress–strain relations were employed to determine the equivalent elastic moduli of the fiber in the debonding zone. Finally, a micromechanics model of temperature-dependent effective moduli of fiber reinforced polymer composites was developed, which is capable of including the effects of interfacial debonding and its evolution with temperature. To validate this model, temperature-dependent effective moduli of several polymer composites were calculated and benchmarked with experimental results extracted from the published literature, demonstrating the validity of the present model. This study offers an efficient method to forecast the temperature-dependent effective moduli, thereby helping to save considerable time and resources by reducing high-temperature testing. Furthermore, parametric studies were conducted to obtain constructive insights into the sensitivity of the debonding length and effective moduli to the material parameters at different temperatures.

Process-induced residual stress in a single carbon fiber semicrystalline polypropylene thin film

During the processing of semicrystalline thermoplastic composites, various models for the prediction of residual stress have been proposed but experimental validation is limited. In this study, a modeling framework is developed to predict the evolution of residual stress in a single carbon fiber embedded in a semicrystalline polypropylene thin film subjected to non-isothermal cooling. Validation is based on in-situ measurement of axial fiber strain after processing using micro-Raman Spectroscopy. A material model for polypropylene (50% equilibrium crystallinity) is presented that incorporates the effects of non-isothermal cooling on crystallinity-dependent resin shrinkage and crystallinity-dependent resin modulus from the amorphous polymer melt to room temperature. The evolution of residual stress is calculated using a finite element (FE) model with a user-developed subroutine incorporating the resin material models. Single-fiber polypropylene films are fabricated using a range of fiber pretension levels to prevent fiber waviness during cooling and to induce a wide range of axial strain levels in the fiber for model validation. The fiber axial strain was measured over the length of the fiber, from the free edge into the bulk, capturing the ineffective length region where strain builds up and plateaus. A good correlation has been obtained between the model results and the in-situ measurements of axial compression strain in the fiber. A key finding was the importance of including temperature-dependent resin modulus and that the contribution of crystallinity shrinkage to residual strain in the carbon fiber is relatively low. The model developed in this study is also compared to residual stress models in the literature which shows the importance of including the effects of crystallization and cooling rate on temperature and crystallinity-dependent modulus and resin shrinkage for accurate predictions.

P-V-T equation of state of boron carbide.

We report the P-V-T equation of state measurements of B4C to 50 GPa and approximately 2500 K in laser-heated diamond anvil cells. We obtain an ambient temperature, third-order Birch-Murnaghan fit to the P-V data that yields a bulk modulus K0 of 221(2) GPa and derivative, (dK/dP)0 of 3.3(1). These were used in fits with both a Mie-Grüneisen-Debye model and a temperature-dependent, Birch-Murnaghan equation of state that includes thermal pressure estimated by thermal expansion (α) and a temperature-dependent bulk modulus (dK0/dT). The ambient pressure thermal expansion coefficient (α0 + α1T), Grüneisen γ(V) = γ0(V/V0)q and volume-dependent Debye temperature, were used as input parameters for these fits and found to be sufficient to describe the data in the whole P-T range of this study. This article is part of the theme issue 'Exploring the length scales, timescales and chemistry of challenging materials (Part 1)'.

Characterisation of temperature and loading rate dependent bond strength on the Bitumen-aggregate interface using direct shear test

The objective of this paper is to characterise the temperature and loading rate dependences of bond strength on the bitumen-aggregate interface. An aggregate-bitumen-aggregate sandwich sample was first employed to quantify its bond strength under four different temperatures (15, 25, 35, and 45 °C) and four levels of loading rate (5, 10, 15, and 20 mm/min) using a strain-controlled direct shear test. Then, a master curve of bond strength on the bitumen-aggregate interface was constructed via the time–temperature superposition principle traditionally used to determine the temperature-dependent complex modulus of polymer-based material (e.g., asphalt biner or mixture). After that, the impacts of temperature and loading rate on interfacial debonding were analysed based on SEM observation of the cracked bitumen-aggregate interface after the direct shear test. Lastly, percentages of cohesive and adhesive debonding at different temperatures were quantified. Results show that the time–temperature superposition principle applies to the quantification of bond strengths of bitumen under different temperatures and loading rates. Based on the comparative analysis of bond strength measured in the direct shear test, its master curve can well reflect the viscoelastic properties of the bitumen-aggregate interface over a wide range of temperatures and loading rates. At 15 °C and 25 °C, the interfacial crack mainly exhibits a combination of cohesive and adhesive debonding; however, at 35 °C and 45 °C, it is dominated by cohesive debonding. This observation is attributable to the fact that as the temperature rises, the chain network of bitumen molecules gets loosened and its kinematic activity enhances, which leads to the debonding between the bitumen molecules when subjected to shear loads and a higher percentage of cohesive failure.

Temperature-dependent elastic constants of thorium dioxide probed using time-domain Brillouin scattering

We report the adiabatic elastic constants of single-crystal thorium dioxide over a temperature range of 77–350 K. Time-domain Brillouin scattering, an all-optical, non-contact picosecond ultrasonic technique, is used to generate and detect coherent acoustic phonons that propagate in the bulk perpendicular to the surface of the crystal. These coherent acoustic lattice vibrations have been monitored in two hydrothermally grown single-crystal thorium dioxide samples along the (100) and (311) crystallographic directions. The three independent elastic constants of the cubic crystal (C11, C12, and C44) are determined from the measured bulk acoustic velocities. The longitudinal wave along the (100) orientation provided a direct measurement of C11. Measurement of C44 and C12 was achieved by enhancing the intensity of quasi-shear mode in a (311) oriented crystal by adjusting the polarization angle relative to the crystal axes. We find the magnitude of softening of the three elastic constants to be ∼2.5% over the measured temperature range. Good agreement is found between the measured elastic constants with previously reported values at room temperature, and between the measured temperature-dependent bulk modulus with calculated values. We find that semi-empirical models capturing lattice anharmonicity adequately reproduce the observed trend. We also determine the acoustic Grüneisen anharmonicity parameter from the experimentally derived temperature-dependent bulk modulus and previously reported temperature-dependent values of volumetric thermal expansion coefficient and heat capacity. This work presents measurements of the temperature-dependent elasticity in single-crystal thorium dioxide at cryogenic temperature and provides a basis for testing ab initio theoretical models and evaluating the impact of anharmonicity on thermophysical properties.

Thermomechanical Characterization and Modeling of NiTi Shape Memory Alloy Coil Spring.

Today, shape memory alloys (SMAs) have important applications in several fields of science and engineering. This work reports the thermomechanical behavior of NiTi SMA coil springs. The thermomechanical characterization is approached starting from mechanical loading-unloading tests under different electric current intensities, from 0 to 2.5 A. In addition, the material is studied using dynamic mechanical analysis (DMA), which is used to evaluate the complex elastic modulus E* = E' - iE″, obtaining a viscoelastic response under isochronal conditions. This work further evaluates the damping capacity of NiTi SMA using tan δ, showing a maximum around 70 °C. These results are interpreted under the framework of fractional calculus, using the Fractional Zener Model (FZM). The fractional orders, between 0 and 1, reflect the atomic mobility of the NiTi SMA in the martensite (low-temperature) and austenite (high-temperature) phases. The present work compares the results obtained from using the FZM with a proposed phenomenological model, which requires few parameters for the description of the temperature-dependent storage modulus E'.

Compatibilized bio-based polybutylene-succinate blended composites filled with surface modified Si3N4 for improved rigidity and thermal performance

In this study, polybutylene succinate was melt blended with polypropylene (PP) to fabricate partially bio-based and miscible composites filled with various loading silicon nitride (Si3N4) particles. Oleic acid and PP-grafted maleic anhydride were used as a functionalizing agent for Si3N4 and as a compatibilizer for polymer blends, respectively. The surface functionalization of the Si3N4 particles enhanced the interfacial adhesion between the filler and the blended polymers, affecting the thermal and mechanical properties of the composites. The thermal conductivity of the composite filled with only 18.6 vol% surface-treated Si3N4 increased by 342% compared to that of the blended polymer. In addition, the surface treatment of Si3N4 significantly improved the Young’s modulus, tensile strength, and thermal stability of the corresponding composites. However, the temperature-dependent storage modulus was unaffected by the surface treatment of Si3N4 and increased as the loading content of the Si3N4 particles increased.

Early melting of tantalum carbide under anisotropic stresses: An ab initio molecular dynamics study

Tantalum carbide (TaC) is an ultrahigh-temperature ceramic binary compound with the highest melting temperature $(3770{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C})$ of its analogues. Combined with high chemical stability, good thermal conductivity, high hardness, etc., it is identified as an excellent refractory material with wide applications in extremely high temperature environments as thermal protection systems for designing sharp leading edges of hypersonic flying vehicles, thrust nozzles of rockets, tank armors, cutting and drilling tools, etc. In this paper, we present striking results from ab initio molecular dynamics simulations, unveiling that anisotropic stresses under uniaxial compression along the [001] direction can reduce the melting temperature of TaC by as much as $700{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$, to within the typical working temperature $(3000{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C})$ in thrust nozzles of rockets. The mechanical strengths of TaC, associated with the peak stresses in full-range stress-strain curves which set the maximum stresses sustainable by TaC under given deformations, are found to be reduced by half as the temperature approaches $3000{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$, displaying a severe deterioration of its plastic mechanical properties at high temperatures in contrast to its elastic properties, represented by the temperature-dependent bulk, Young's, and shear moduli of TaC, which are reduced by about 20% in the same temperature range. These discoveries provide fresh perspectives for understanding the extreme physics of TaC at high temperatures.

Anomalous temperature dependence of modulus in water-cooled beta Ti-Mo-based alloys

The internal friction (Q-1) and relative dynamic modulus (RDM) of the specimens were measured using a multifunctional internal friction apparatus during heating and cooling. DSC (Differential Scanning Calorimetry) experiments were also carried. It is shown that the anomalous temperature-dependence(ATD) of RDM occur only in water-cooled Ti-12Mo alloys with medium Mo contents, being mainly attributed to either α”→ω or α”→ɑ+β transformation during heating. The water-cooled Ti-5Mo alloy possesses α” phase, but it cannot form ωth phase when heated. The Ti-12Mo-2X(where X = 0,Nb,Sn,Fe,Al) alloys have the ATD of RDM since they contain α” and βM phases, which can be transformed into the phases with large modulus such as ɑ, β, causing the RDM to raise with increasing temperature.DSC experiments show the occurrence of the ATD of RDM is accompanied by the phase transformation.

Crystallinity and temperature dependent mechanical properties of Poly(4-methyl-1-pentene)

Crystallinity and temperature dependent modulus in poly(4-methyl-1-pentene) were investigated over a wide temperature range covering glass transition of the amorphous phase. It turns out that the storage moduli of different samples decrease with the increase of crystallinity below Tg. The storage moduli of different samples are the same regardless of crystallinity at around 45 °C where the densities of crystalline and amorphous phases are identical. A model considering parallelly arranged crystalline skeleton and amorphous network allows a decomposition of the measured modulus into moduli of both phases. In addition to the fact that the modulus of amorphous phase in the glassy state is much larger than that of crystalline phase due to a higher density in amorphous phase than that of the crystals, a peculiar positive temperature dependent apparent crystalline phase modulus below Tg was observed. This seemingly anti-intuitive result can be understood by considering the strong constraint of the crystalline phase by the denser amorphous network at lower temperatures due to different thermal expansion coefficients of the two phases.

Investigation of conduction mechanism and UV light response of vertically grown ZnO nanorods on an interdigitated electrode substrate.

Vertically aligned zinc oxide nanorod (ZnO-NR) growth was achieved through a wet chemical route over a comb-shaped working area of an interdigitated Ag-Pd alloy signal electrode. Field-emission scanning electron microscopy images confirmed the formation of homogeneous ZnO-NRs grown uniformly over the working area. X-ray diffraction revealed single-phase formation of ZnO-NRs, further confirmed by energy-dispersive X-ray spectroscopy analysis. Temperature-dependent impedance and modulus formalisms showed semiconductor-type behavior of ZnO-NRs. Two electro-active regions i.e., grain and grain boundary, were investigated which have activation energy ∼0.11 eV and ∼0.17 eV, respectively. The conduction mechanism was investigated in both regions using temperature-dependent AC conductivity analysis. In the low-frequency dispersion region, the dominant conduction is due to small polarons, which is attributed to the grain boundary response. At the same time, the correlated barrier hopping mechanism is a possible conduction mechanism in the high dispersion region attributed to the bulk/grain response. Moreover, substantial photoconductivity under UV light illumination was achieved which can be attributed to the high surface-to-volume ratio of zinc oxide nanorods as they provide high density of trap states which causes an increase in the carrier injection and movement leading to persistent photoconductivity. This photoconductivity was also facilitated by the frequency sweep applied to the sample which suggests the investigated ZnO nanorods based IDE devices can be useful for the application of efficient UV detectors. Experimental values of field lowering coefficient (βexp) matched well with the theoretical value of βS which suggests that the possible operating conduction mechanism in ZnO nanorods is Schottky type. I-V characteristics showed that the significantly high photoconductivity of ZnO-NRs as a result of UV light illumination is owing to the increase in number of free charge carriers as a result of generation of electron-hole pairs by absorption of UV light photons.

Synthesis, morphological, electrical, and conduction mechanism studies of a sodium cerium diphosphate compound.

A NaCeP2O7 compound was successfully synthesized by a high-temperature reaction with the solid-state method. Analyzing the XRD pattern, of the studied compound, confirms the orthorhombic phase with the Pnma space group. The examination of SEM images reveals that the majority of grains are around 500 to 900 nm with a uniform distribution. As for the EDXS analysis, all chemical elements were detected and found in the appropriate ratio. The curves of temperature-dependent imaginary modulus M'' versus angular frequency reveal the presence of one peak at each temperature, proving that the dominant contribution is associated with the grains. The frequency dependence of the conductivity of alternating current is explained using Jonscher's law. The close values of the activation energies obtained from the jump frequency and extracted from the dielectric relaxation of the modulus spectra, as well as from the continuous conductivity imply that the transport takes place by the Na+ ions hopping mechanism. The charge carrier concentration in the title compound has been evaluated and shown to be independent of temperature. The exponent s increases with the increase in temperature; this behavior proves that the non-overlapping small polaron tunneling (NSPT) is the appropriate conduction mechanism model.

High Ionic Conduction and Polarity-Induced Piezoresponse in Layered Bimetallic Rb4Ag2BiBr9 Single Crystals

The emergence of lead-free metal-halide perovskites in modern-day energy research is primarily due to their competent semiconducting and optoelectronic properties, as well as their nontoxicity and improved stability in ambient operating conditions. However, a detailed understanding of ion transport dynamics and the relaxation behavior of these materials is still elusive. In this article, we report on the single-crystal (SC) growth of a bimetallic two-dimensional layered Rb4Ag2BiBr9 and explore its dielectric, piezoelectric, and ferroelectric properties. The dielectric attributes are investigated by studying the temperature-dependent complex impedance, complex electric modulus, and AC conductivity over an extensive frequency range from 4 Hz to 8 MHz. The role of grain and grain boundaries in the effective impedance is established using the Maxwell–Wagner equivalent circuit model from the Nyquist plots. The observed electric modulus spectra are studied using the Havriliak–Nigami and the Kohlrausch–Williams–Watts formalisms to understand the ionic transport and relaxation mechanisms in Rb4Ag2BiBr9. The DC conductivity and relaxation time show Arrhenius-like behavior with the inverse temperature validating the hopping motion of ions. The values of the activation energy required for ion hopping are calculated independently from the relaxation time, hopping frequency, and DC conductivity Arrhenius plots and are in good agreement with a value of 0.47 eV. The scaling of the temperature-dependent conductivity and electric modulus spectra into a single master curve demonstrates the congruence of the ionic conduction and the relaxation phenomena at different temperatures for Rb4Ag2BiBr9. This SC demonstrates decent thermal and ambient stability up to 500 °C and 12 months, respectively. The pristine orthorhombic Rb4Ag2BiBr9 SC shows a piezoelectric amplitude value of ∼564 pm at the maximum applied bias (±10 V), and a saturation polarization of ∼0.14 nC/cm2 estimated from the piezoelectric force microscopy and polarization hysteresis loop measurement, respectively. The ferroelectric and semiconducting attributes of this material can be harnessed for prospective applications as a thin film in designing mechanical energy harvesters as well as functional photoferroelectrics, such as optical switches and ferroelectric photovoltaics.

Novel method and instrument for temperature-dependent tensile test of metallic materials without thermometers.

A novel method for measuring temperature and conducting tensile tests of metallic wires at elevated temperatures is presented. Ohmic heating is used to elevate the sample temperature with a uniform distribution, which could vary from room temperature to its melting point. The temperatures of the wires in steady states are determined by using a heat transfer model without measuring directly by thermometers, which reduces the error introduced by contact temperature measurement or optical pyrometers. This technique for temperature measurement can be applied to measuring temperature-dependent electrical resistivity and conducting temperature-dependent tensile tests of metallic materials. A low-cost instrument was designed to conduct the tensile tests. In this work, temperature-dependent Young's modulus, tensile strength at break, and the steady-state creep rate of 99.994%-pure Pb wires were further determined as applications of the tensile tests. The results show that the proposed method is valid and very useful for conducting temperature-dependent tensile tests of metallic materials.

Dual thermodynamics approach to the temperature dependence of viscoplastic creep durability in graphene-based nanocomposites

The ambient temperature at which creep deformation takes place is known to exert significant influence on the creep durability of graphene-based nanocomposites, but at present no theory could illustrate the underlying microstructural evolution to predict such a phenomenon. In this paper, a novel dual thermodynamics approach in conjunction with a time-temperature superposition principle (TTSP) is established to address this issue. First, temperature-dependent secant moduli are exclusively adopted as the unique homogenization variables shifted through TTSP, and then the time- and temperature-dependent effective stresses inside the matrix are calculated via the principle of equivalent work rate combined with the field-fluctuation method. Next, the dual irreversible thermodynamic processes, including the stress-induced creep damage inside the matrix and the temperature-dependent degradation at the interphase, are introduced through two independent sets of evolution equations. The predicted creep rupture strain and rupture time are calibrated with experiments over a wide range of temperature. It is demonstrated that the creep rupture strain increases with the rise of ambient temperature, while the creep rupture time decreases with it. The onset of creep-damage process also commences earlier at higher temperature. This research can provide a design guidance to assess the damage process and failure of low-dimensional nanocomposites at elevated temperature environment.

Stress Analysis and Q-Factor of Free-Standing (La,Sr)MnO3 Oxide Resonators.

High-sensitivity nanomechanical sensors are mostly based on silicon technology and related materials. The use of functional materials, such as complex oxides having strong interplay between structural, electronic, and magnetic properties, may open possibilities for developing new mechanical transduction schemes and for further enhancement of the device performances. The integration of these materials into micro/nano-electro-mechanical systems (MEMS/NEMS) is still at its very beginning and critical basic aspects related to the stress state and the quality factors of mechanical resonators made from epitaxial oxide thin films need to be investigated. Here, suspended micro-bridges are realized from single-crystal thin films of (La0.7 ,Sr0.3 )MnO3 (LSMO), a prototypical complex oxide showing ferromagnetic ground state at room temperature. These devices are characterized in terms of resonance frequency, stress state, and Q-factor. LSMO resonators are highly stressed, with a maximum value of ≈260 MPa. The temperature dependence of their mechanical resonance is discussed considering both thermal strain and the temperature-dependent Young's modulus. The measured Q-factors reach few tens of thousands at room temperature, with indications of further improvements by optimizing the fabrication protocols. These results demonstrate that complex oxides are suitable to realize high Q-factor mechanical resonators, paving the way toward the development of full-oxide MEMS/NEMS sensors.

Size and displacement combining detection on physics properties of carbon nanotubes using a proposed energy approach

In this paper, a coupling of advanced molecular structural model with energy method is developed to calculate the mechanical properties of single-walled carbon nanotubes (SWCNTs). The energy of a system is expressed by an advanced force field of molecular mechanics. Under the assumption of a small deformation and the principle of minimum potential energy, closed form formations are derived for temperature-dependent Young's modulus, Poisson's ratio, and bulk modulus, which are the functions of the length of C-C bonds and the out-plane displacement. The results show that the effects of tube diameter and out-plane displacement on the elastic properties of carbon nanotubes is significant when the tube diameter is small. Moreover, the principle of force-heat equivalent energy density (FHEED) is applied to describe the strain-dependent energy density of SWCNTs.