Logarithmic Creep Rate Research Articles

A microindentation two-fold creep model for characterizing short- and long-term creep behavior of a cement paste

Owing to the micrometric size of the probed volume and the minute duration of a test, microindentation provides a unique tool to characterize the non-aging creep properties of a cement paste in hygral equilibrium. Microindentation techniques have been emerging as rapid technique to characterize the logarithmic creep rate of cement pastes. The objective of this study is to develop the analytical microindentation solutions of modern creep models, such as Microprestress-Solidification theory (MPS), Generalized Kelvin-Voigt model (GKV), and a recent microindentation two-fold creep model (M2C), which considers viscoelastic strain in series with a viscous flow strain of which viscosity is exponentially dependent on the viscous flow deformation, to provide a rapid calibration method.To minimize the effect of residual clinker, a cement paste with a water-to-cement ratio of 0.42 was cured for one year before testing. Subsequently, a microindentation grid of both creep and relaxation tests was carried out by employing a spherical tip at low penetration depth to reduce inelastic deformation. The microindentation analytical solutions of the aforementioned creep models were developed and its dual relaxation response was numerically developed. Microindentation creep and relaxation tests were employed to calibrate and validate the creep parameters, respectively. While microindentation allowed identifying the parameters of the considered creep models in a satisfactory manner, the implemented M2C creep model permitted to gain insight into the two-fold basic creep mechanism from a microindentation perspective.

A closer look at the temperature effect on basic creep of cement pastes by microindentation

While several works have investigated the effect of temperature on concrete creep, the effect of thermal activation on the multiple creep mechanisms is not fully understood. This work aims at investigating the thermal effect on the creep rate of cement pastes with different water-to-binder ratios (w/b) by microindentation technique.Firstly, several results of compression creep tests, which are available in open literature, were compared showing that the uniaxial creep modulus Cu is lower at greater temperature within a temperature range of 20–80 °C. Then, several microindentation creep tests were carried out on cement pastes with different w/b ratios (from 0.2 to 0.6) at a constant temperature ranging from 20 °C to 60 °C and at a constant relative humidity of 30%. All the microindentation creep curves exhibited a logarithmic creep compliance J=(1/Ci)log(t/τ+1) with a clear influence of the w/b ratio. Surprisingly, the effect of the temperature on the indentation contact creep modulus Ci was rather negligible, with the only minor exception of the cement paste with high w/b=0.6. Finally, creep tests were reanalyzed by assuming an Arrhenius equation for the characteristic time τarr rather than for the creep modulus Cu. Eventually, the presented microindentation creep results along with the reanalysis of existing macroscopic data suggest that temperature accelerates the kinetics of basic creep without affecting the the long-term logarithmic creep rate of basic creep.

Duality between Creep and Relaxation of a Cement Paste at Different Levels of Relative Humidity: Characterization by Microindentation and Analytical Modeling

Recent studies have showed that microindentation techniques allow assessing the logarithmic creep rate of a cement paste in good correlation with the long-term creep rates measured by compressive tests at macroscopic scale. After having applied microindentation techniques to characterize the effect of relative humidity (RH) on both the creep and relaxation behavior of a cement paste, the objective of this work is to analyze the duality between creep and relaxation curves by means of the analytical models which are currently employed in open literature. First, large grids of creep and relaxation microindentation tests were carried out on a cement paste sample in hygral equilibrium at different levels of RH. Thus, the results were modeled by a viscoelastic model by considering different creep functions (logarithmic and power-law) and corrective terms for initial plasticity under loading. The presented results provide new insights to understand the duality between creep and relaxation rates of a cement paste measured at micrometer scale, especially considering the possible plastic effect.

Quantum Mechanical Tunneling of Dislocations: Quantization and Depinning from Peierls Barrier

Theories of Mott and Weertmann pertaining to quantum mechanical tunneling of dislocations from Peierls barrier in cubic crystals are revisited. Their mathematical calculations about logarithmic creep rate and lattice vibrations as a manifestation of Debye temperature for quantized thermal energy are found correct but they can not ascertain to choose the mass of phonon or “quanta” of lattice vibrations. The quantum mechanical yielding in metals at relatively low temperatures, where Debye temperatures operate, is resolved and the mathematical formulas are presented. The crystal plasticity is studied with stress relaxation curves instead of logarithmic creep rate. With creep rate formulas of Mott and Weertmann, a new formula based on logarithmic profile of stress relaxation curves is proposed which suggests simultaneous quantization of dislocations with their stress, i.e., and depinning of dislocations, i.e., , where is quantum action, σ is the stress, N is the number of dislocations, A is the area and t is the time. The two different interpretations of “quantum length of Peierls barrier”, one based on curvature of space, i.e., yields quantization of Burgers vector and the other based on the curvature of time, i.e., yields depinning of dislocations from Peierls barrier in cubic crystals, are presented. , i.e., the unitary operator on shear modulus yields the variations in the curvature of time due to which simultaneous quantization, and depinning of dislocations occur from Peierls barrier in cubic crystals.

Vortex creep down to 0.3 K in superconducting Fe(Te,Se) single crystals

We report on a study of the vortex creep in Fe${}_{1+\ensuremath{\delta}}($Te${}_{x}$Se${}_{1\ensuremath{-}x}$) single crystals ($x=0.5$ and $0.4$) down to 0.28 K ($\ensuremath{\sim}{T}_{c}/50$) and up to ${\ensuremath{\mu}}_{0}{H}_{a}=2$T. The relaxation of the current density [$J(t)$] has been measured during 20 hours and the decay of $J(t)$ can be well described by a $J(t)\ensuremath{\propto}{[ln(t/{t}_{0})]}^{\ensuremath{-}1/\ensuremath{\mu}}$ law. We show that the relaxation exponent $\ensuremath{\mu}$ tends towards 0 for $T<2$K and ${\ensuremath{\mu}}_{0}{H}_{a}<0.1$T [i.e. $J(t)\ensuremath{\rightarrow}{({t}_{0}/t)}^{\ensuremath{\alpha}}$] and increases for increasing $T$ and/or ${H}_{a}$. Our measurements strongly suggest that the logarithmic creep rate $R=\ensuremath{-}dln(J)/dln(t)$ remains finite at zero temperature (${R}_{|T\ensuremath{\rightarrow}0}\ensuremath{\rightarrow}2$%) and hence that quantum creep plays a dominant role in the relaxation process at low temperature. A maximum is observed in both the temperature and field dependence of $R(t=100\text{s},T,{H}_{a}),$ which can be associated to a crossover from a single vortex (one-dimensional) to a bundle (three-dimensional) creep regime.

Variability of tissue mineral density can determine physiological creep of human vertebral cancellous bone

Creep is a time-dependent viscoelastic deformation observed under a constant prolonged load. It has been indicated that progressive vertebral deformation due to creep may increase the risk of vertebral fracture in the long-term. The objective of this study was to examine the relationships of creep with trabecular architecture and tissue mineral density (TMD) parameters in human vertebral cancellous bone at a physiological static strain level. Architecture and TMD parameters of cancellous bone were analyzed using microcomputerized tomography (micro-CT) in specimens cored out of human vertebrae. Then, creep and residual strains of the specimens were measured after a two-hour physiological compressive constant static loading and unloading cycle. Creep developed (3877±2158με) resulting in substantial levels of non-recoverable post-creep residual strain (1797±1391με). A strong positive linear correlation was found between creep and residual strain (r=0.94, p<0.001). The current results showed that smaller thickness, larger surface area, greater connectivity of trabeculae, less mean tissue mineral density (TMD, represented by gray levels) and higher variability of TMD are associated with increasing logarithmic creep rate. The TMD variability (GLCOV) was the strongest correlate of creep rate (r=0.79, p<0.001). This result suggests that TMD variability may be a useful parameter for estimating the long-term deformation of a whole vertebral body. The results further suggest that the changes in TMD variability resulting from bone remodeling are of importance and may provide an insight into the understanding of the mechanisms underlying progressive failure of vertebral bodies and development of a clinical fracture.

Vortex avalanches in the noncentrosymmetric superconductorLi2Pt3B

We investigated the vortex dynamics in the noncentrosymmetric superconductor ${\text{Li}}_{2}{\text{Pt}}_{3}\text{B}$ in the temperature range 0.1--2.8 K. Two different logarithmic creep regimes in the decay of the remanent magnetization from the Bean critical state have been observed. In the first regime, the creep rate is extraordinarily small, indicating the existence of an unconventional very effective pinning mechanism. At a certain time, a vortex avalanche occurs that increases the logarithmic creep rate by a factor of about 5 to 10 depending on the temperature. This may indicate that certain barriers against flux motion are present and they can be opened under increased pressure exerted by the vortices.

Relaxation of thermo-remanent magnetization in Fe–Cr GMR multilayers

The time decay of the thermo-remanent magnetization (TRM) in Fe–Cr giant magnetoresistive (GMR) multilayers has been investigated. The magnetization in these multilayers relaxes as a function of time after being cooled in a small magnetic field of 100 Oe to a low temperature and then the magnetic field is switched off. Low-field ( < 500 Oe ) magnetization of these samples has shown history dependence. This spin-glass-like behavior may originate from structural imperfections at the interfaces and in the bulk. We find that the magnetization relaxation is logarithmic. Here the magnetic viscosity is found to increase first with increasing temperature, then it reaches a maximum around T g , and further it decreases with increasing temperature. This behavior is different from that of conventional spin glasses where the logarithmic creep rate is observed to increase with temperature. The dynamical effects of these multilayers are related to the relaxation of thermally blocked superparamagnetic grains and magnetic domains in the film layers.

Low Temperature Properties of Crumb Rubber Modified Binders

ABSTRACT This paper presents a study to evaluate low temperature rheological properties of crumb rubber modified binders and the impact of the rubber particle size and content on such properties. Three sizes of the crumb rubber (0.18 mm, 0.425 mm and 2.0 mm), a control (0 percent) and two levels of crumb rubber content (12 percent and 24 percent) were used with four asphalt binders. The measured rheological properties consisted of creep stiffness (St) and logarithmic creep rate (m). Results showed that: increasing the crumb rubber content decreased the creep stiffness which improves thermal cracking resistance. The impact of crumb rubber content on the m-value was very highly inconsistent. The crumb rubber size did not have a significant effect on the low temperature properties. Any effect of the size of the crumb rubber on the resistance to thermal cracking was dependent on the asphalt binder type. The analysis of the data generated in this experiment showed that some combinations of crumb rubber size and content can either improve or jeopardize the PG low temperature grade of the asphalt binder.

Low Temperature Properties of Crumb Rubber Modified Binders

ABSTRACT This paper presents a study to evaluate low temperature rheological properties of crumb rubber modified binders and the impact of the rubber particle size and content on such properties. Three sizes of the crumb rubber (0.18 mm, 0.425 mm and 2.0 mm), a control (0 percent) and two levels of crumb rubber content (12 percent and 24 percent) were used with four asphalt binders. The measured rheological properties consisted of creep stiffness (St) and logarithmic creep rate (m). Results showed that: increasing the crumb rubber content decreased the creep stiffness which improves thermal cracking resistance. The impact of crumb rubber content on the m-value was very highly inconsistent. The crumb rubber size did not have a significant effect on the low temperature properties. Any effect of the size of the crumb rubber on the resistance to thermal cracking was dependent on the asphalt binder type. The analysis of the data generated in this experiment showed that some combinations of crumb rubber size and content can either improve or jeopardize the PG low temperature grade of the asphalt binder.

Structure and properties of poly(vinyl chloride)‐triallyl cyanurate plastisols

AbstractTriallyl cyanurate (TAC) has been used as a reactive plasticizer to promote the high‐temperature creep resistance of poly(vinyl chloride) (PVC) plastisols. The resultant crosslinked structure is characterized using gel content and swell ratio measurements as well as Fourier transform infrared spectroscopy. The crosslinking reaction was initiated using peroxide. The effect on the network structure of using a free radical scavenger in the formulation has also been studied. The gel yield and crosslink density in the gel increase with increasing TAC concentration in the plastisol, while the grafted PVC fraction and the residual unsaturation of TAC behave in the opposite way. Introduction of TAC into the plastisol promotes creep resistance at high temperatures, and the logarithmic creep rate was found to decrease linearly with increasing crosslink density.

Measurement of flux creep in Bi 2Sr 2CaCu 2O 8 using electron spin resonance

Flux creep and susceptibility in a Bi 2Sr 2CaCu 2O 8 polycrystalline sample were measured using an electron spin resonance probing technique. The sample was decorated with two tiny free radical probes the signals of which superimposed at an applied field B r for T > T c . For T < T c the signals split: one shifted up-field to an applied field B a1 > B r and the other shifted down-field to an applied field B a2 < B r . The susceptibility χ was shown to be given by B a1 B a2 − 1 for ellipsoidal samples. As flux crept into or out of the sample, the shifts of the probe signals changed accordingly. When the sample was zero-field cooled and then subjected to an applied field of 330 mT the susceptibility was found to depend on the temperature as follows: χ ≈ − 0.015(1 − 0.026 T) for 18⩽ T ⩽ 31K; and χ ≈ − 0.005(1 + 0.11 T) for 31 ⩽ T ⩽ 90K. The abrupt change at 31 K is attributed to the onset of significant intergranular current. The dimensionless normalized logarithmic creep rate, s, peaked at a value of 0.077 at 21 K. The zero-kelvin intergranular critical current density, estimated from the Bean model and shift data, was 3.2 × 10 3 A cm −1 for T ⩽ 31 K. The pinning potential was approximately constant (0.08) between 18 and 36 K.

Temperature and stress effects in the creep of aramid fibers under transient moisture conditions and discussions on the mechanisms

AbstractIn a previous study, a mechanosorptive phenomenon in poly(p‐phenylene terephthalamide) fibers was reported. In this article, the mechanosorptive creep mechanism of aramid fibers and the temperature and stress influences on the mechanosorptive creep behavior of aramid fibers are addressed. Test results indicate that logarithmic creep rates and the mechanosorptive effects increase with temperature. The creep activation energies of the fibers tested are: 20 kJ/mole for the cyclic moisture condition, 4.4 kJ/mole for a high equilibrium moisture condition (RH = 95%), and 7.8 kJ/mole for a low equilibrium moisture condition (RH = 5%). Increase in stress may increase the logarithmic creep rates but may reduce the mechanosorptive effect. Aramid fibers contain hydrogen bonds between rodlike crystallites oriented at small angles relative to the fiber axis. Transient moisture conditions may cause slippage of hydrogen bonded elements and result in accelerated crystallite rotations due to breakage of hydrogen bonds, thus causing increases in logarithmic creep rate. The obtained activation energies and the reduction in fiber elastic compliance due to creep deformation support the proposed mechanisms. © 1992 John Wiley &amp; Sons, Inc.

The magnetization studies of cast-annealing Bi 1.5Pb 0.28Sr 1.72Ca 2.0Cu 3.5O y ceramic sample

The sample with nominal composition Bi1.5Pb0.28Sr1.72-Ca2.0Cu3.5Oy was prepared by cast-annealing method and identified to contain almost pure 110K phase from X-ray powder diffraction pattern. The A.C. magnetic susceptibility and the Meissner diamagnetic magnetization in various magnetic fields were measured as the functions of temperature down to 77K. With the increase of the field the magnitude of D.C. magnetic susceptibility Xdc is found to be reduced and Xdc transition is significantly broadened. The magnetization curve demonstrates that the present ceramic sample is a weak-pinning type-II superconductor as a whole. The slope of (-4 M) versus magnetic field shows that the value of the diamagnetic volume fractions of the whole sample and the superconducting grains is 34.5% and 18.5%, respectively, which means existence of great shielding effect from weak-link networks. Flux creep was detected at nitrogen temperature and studied directly by the magnetization measurement as a function of time in various constant magnetic fields. The result indicates that in weaker fields the magnetization changes logarithmically in time. The logarithmic creep rate is found to rise gradually as applied field is increased until the magnetic field exceeds the magnetization peak field. In higher field, however, the logarithmic dependence of flux creep on time can no longer be found.

A test of the generalized theory of visco-elasticity in London Clay

Dynamic soil moduli can be deduced from the velocity of shear waves measured in situ. However, soil moduli vary with time and strain magnitude. A correction for time dependence, based upon a relationship between the quality factor Q and the logarithmic creep rate from generalised visco-elasticity theory, can be determined directly from laboratory tests. Details are given of the experimental apparatus whereby a drained or undrained sample of London Clay was subjected to fluid pressures applied to flexible membranes on each face so that the three principal stresses can be applied independently. Transducers used to measure the small strains similar to those expected under a foundation were directly read by a computer which controlled the entire operation. Individual stress or strain-rate paths could be programmed for each stage of the test. Hysteresis measurements were made using sinusoidal loading and were repeated after an interval of a few weeks for a range of times between 8 minutes and 24 hours. Experimental results confirmed theoretical relationships between the slope of the logarithm of strain against the logarithm of time for a step load and the inverse of the quality factor from hysteresis measurements. (TRRL)

Observation of thermally activated flux motion in weak link structures

We have measured the time rate of magnetic flux motion through an array of weak links present in the wall of a hollow cylinder of ceramic YBa 2 Cu 3 O 7 . We observe a logarithmic time dependence of the magnetic field in the center of the tube with an applied field of 28 Oe at 75K. Analysis of the logarithmic creep rate with a standard phenomenological model yields an activation energy of ∼ 1.55 eV for the motion of Josephson vortices through the weak links in the structure.

The effects of damping on the interpretation of geophysical measurements

Measurements of damping in situ as a function of strain are described. Three different methods were used: hammer damping, resonance of an embedded pipe and hysteresis due to cyclic loading. All three methods show distinct values of damping in boulder clay which indicate clearly that anelastic behaviour must be taken into account. There is some evidence that damping is dependent on time as well as strain. When moduli derived from shear wave velocities are used to calculate settlements of loaded pads corrections involving time dependence proportional to damping are required. Theoretically the logarithmic creep rate at a given strain is proportional to (2/nXl/β)- These measurements were used to produce two class A predictions of the time-dependent settlement of loaded pads that were within 20% of the observed values. Suitable viscoelastic models are considered. L'article décrit des mesures d'amortissement in situ en fonction de la déformation. On a utilisé trois méthodes différentes, c'est-à-dire l'amortissement d'un mouton, la résonance d'un tuyau enrobé et l'hystérésis due au chargement cyclique. Les trois méthodes donnent des valeurs différentes pour l'amortissement dans l'argile à blocaux, ce qui indique clairement qu'il faut tenir compte du comportement inélastique. Il apparaît que l'amortissement dépend du temps aussi bien que de la déformation. Lorsque des modules déterminés à partir des vitesses d'onde de cisaillement sont employés pour calculer les tassements des supports chargés, il faut apporter des corrections qui prennent en compte une dépendance du temps proportionnelle à l'amortissement. Théoriquement la vitesse logarithmique de fluage pour une déformation donnée est proportionnelle à (2/π)(1/Q)- Ces mesures ont été utilisées pour produire deux prédictions de classe A du tassement des supports chargés en fonction du temps qui correspondaient aux valeurs observées à 20% près. L'article présent des modèles viscoélastiques corrects.

The determination of ductile creep rupture tim for orthotropic sheets and cylindrical shells

Equations describing the deformation of orthotropic materials for which a logarithmic creep rate in the form of a power function of the stresses are obtained. These equations are then used for the determination of the ductile creep rupture time of orthotropic sheets and cylindrical shells in biaxial tension. They can also be used in superplastic orthotropic metal forming calculations.

Flux Creep in Type-II Superconductors

We have made measurements of the evanescent decay of the irreversible magnetization induced by magnetic cycling of solid superconducting cylinders in order to elucidate the mechanisms of Anderson's thermally activated flux-creep process. A superconducting quantum interferometer device coupled to the creep specimen by a superconducting flux transformer made possible observations of flux changes with a resolution of one part in ${10}^{9}$. The general applicability of Anderson's theory of flux creep was confirmed and the results were analyzed to show that: (1) The total flux in the specimen changed logarithmically in time, i.e., $\ensuremath{\Delta}\ensuremath{\varphi}\ensuremath{\propto}\frac{\mathrm{ln}t}{{t}_{0}}$. (2) The logarithmic creep rate $\frac{d\ensuremath{\varphi}}{d\mathrm{ln}t}$ is proportional to the critical current density ${J}_{c}$ and to the cube of the specimen radius. (3) The logarithmic creep rate appears to be only weakly temperature-dependent because a proportionality to $T$ is nearly compensated by the proportionality to ${J}_{c}$, which decreases as $T$ increases. (4) The creep process is a bulk process that is not surface-limited (in this case). (5) Flux enters and leaves the surface in discrete events containing from about one flux quantum up to at least ${10}^{3}$ flux quanta. (6) On departing from the critical state to a subcritical condition, the creep process tends to remain logarithmic in time, but the rate is decreased exponentially by decreasing $T$ and is decreased extremely rapidly by backing off of the applied field from the critical state. (7) At magnetic fields $H&lt;{H}_{c1}$ on the initial magnetization curve, no flux creep was observed, but the logarithmic creep rate showed a modest increase above ${H}_{c1}$ and a broad rise as $H$ approached ${H}_{c2}$. The creep process is characterized by a dimension parameter $\mathrm{VX}$ consisting of a flux bundle volume $V$ and pinning length $X$, and by an energy ${U}_{0}$, both of which are supposed to be material-sensitive parameters characteristic of the irreversible processes. These parameters were determined from the experiments. Bundle volumes $V\ensuremath{\approx}{10}^{\ensuremath{-}12}$ ${\mathrm{cm}}^{3}$ and energies ${U}_{0}\ensuremath{\approx}1$ eV were found, indicating that groups of fluxoids must be pinned and must move cooperatively. The results are found compatible with a recent model for flux pinning that includes these cooperative effects.