Theory Of Rate Processes Research Articles

Degradation of Materials and Products Described with Eyring’s Rate Process Theory

Degradation of Materials and Products Described with Eyring’s Rate Process Theory

Backward erosion piping in geotechnical infrastructure: a rate process perspective

Backward erosion piping (BEP) has been recognised as a major cause of failures in water-retaining structures. However, the fundamental mechanisms controlling the phenomenon are not well understood. This research applies the theory of rate processes to develop a constitutive relationship between energy density of the seepage flow and the erosion rate of soils during the evolution of BEP. The resulting equation is used to analyse four datasets of previously reported experimental observations. The mechanical parameters estimated through the proposed model fall into the ranges of values that were reported in the literature. To validate the proposed approach, the constitutive model was incorporated into a multiphase numerical framework to simulate evolution of BEP in embankment soil and compared with reported experimental observations. The numerical framework with the proposed constitutive model is shown to be capable of reproducing both the observed evolution of local hydraulic gradients and pipe progression in the structure.

On Spontaneous Dispersion as a Cause of Microstratification of Metal Melts.

The phenomenon of spontaneous dispersion is considered as the cause of the microstratification of metal melts. In a microstratification melt, a violation of long-range order in the arrangement of atoms (LRO) is observed, which corresponds to a dispersed particle size of more than 2 nm. Microseparation occurs due to spontaneous dispersion upon contact of liquid and solid metal or the mixing of two liquid metals. The possibility of spontaneous dispersion was assessed using three different criteria: Volmer's cr iterion, Rehbinder's criterion and the diffusion rate criterion. The diffusion rate criterion was obtained on the basis of the theory of rate processes, which describes how diffusing atoms overcome the interphase boundary. It has been established that Al-Sn melts contain colloidal-scale particles (4 nm), and Al-Si and Al-Ge melts contain atomic-scale particles (0.1 nm). For a system with a continuous series of Cu-Ni solid solutions in dispersion (Cu10Ni90-Cu20Ni80), the particle size is 2 nm. The particle size of the ternary eutectic GaInSn in the dispersion (Ga50In50-Ga50Sn50) is 5.6 nm, and the size of immiscible Cu-Fe melts in the dispersion (Cu80Fe20-Cu60Fe40) is 4.8 nm. Long-range order violations (LRO) and the presence of microlayering with colloidal particles larger than 20 nm were observed in the GaInSn ternary eutectic, in the Al-Sn simple eutectic with the preferential interaction of similar atoms, and in Cu-Fe melts with a monotectic phase diagram.

Three-dimensional numerical modeling of the temporal evolution of backward erosion piping

Backward erosion piping (BEP) is a complex degradation mechanism in geotechnical flood protection infrastructure (GFPI) that is still relatively less understood, particularly when considering its time-dependent features. This manuscript presents a novel dual random lattice modeling approach for three-dimensional simulation of BEP, with a focus on its evolution over time. The key novelty of this presented framework is twofold: (1) we propose and incorporate a novel constitutive relationship for computation of time-dependent soil erosion based on the theory of rate processes, and (2) we devise an algorithm for calculation of coupled degradation of the dual lattices for accurate computation of 3-D hydraulic gradients. The constitutive relationship was developed from fundamental granular physics, and brings the potential to provide deeper fundamental physical understanding of the phenomenon. The capabilities of the modeling framework are investigated by comparison with available laboratory experiments which illustrates good agreement in the spatial advancement of piping erosion, pipe progression speeds, as well as the evolution of local gradients. To the best knowledge of the authors, the presented model is the first to be able to capture all of the aforementioned features when simulating BEP.

Effects of Loading Modes on Fatigue Limit Estimation in Terms of Rotating Bending Fatigue and Rate Process Theory

In this study, the influence of loading modes on the fatigue limit estimation of low-to-medium-carbon steels was modeled in terms of the rate process theory proposed by Guennec et al. The axial loading model established in terms of the rate process theory has been shown to be effective for axial loading fatigue, but its applicability to rotating bending fatigue is uncertain. Therefore, low- and medium-carbon steels were tested for rotating bending fatigue, and the fatigue limits obtained were compared with those estimated by the axial loading model established in terms of the rate process theory. However, since the model could not be applied, we propose a new model in which the material parameters of an estimation equation established in terms of the rate process theory are expressed based on Vickers hardness, which was introduced to improve the usability of the model. It was found that there was a discrepancy between the axial load fatigue limit and the rotating bending fatigue limit due to the effect of the loading mode. To solve this discrepancy, the stress index was introduced into the model. The proposed model provides a method for estimating the frequency-dependent fatigue limits for different loading modes.

The empty world - a view from the free volume concept and Eyring's rate process theory.

The many-body problem is a common issue, irrespective of the scale of entities under consideration. From electrons to atoms, small molecules like simple inorganic or organic structures, large molecules like proteins or polymers, nanometer- or micrometer-sized particles, granular matter, and even galaxies, the precise determination or estimation of geometrical locations and momentum energy of individual entities, and interaction forces between these millions of entities, is impossible but unfortunately important for understanding the collective physical properties like mechanical and electrical characteristics of the whole system. Despite foreseeable difficulties and complexities, attempts to estimate "interparticle" forces have never stopped using traditional Newtonian models, quantum mechanical approaches, and density functional theory. In this review, a simple approach integrating the free volume and Eyring's rate process theory is summarized and its application across a wide range of scales from electrons to the universe is presented in a unified manner. The focus is on comparisons between theoretical predictions and experimental results.

Dislocation phenomena described with free volume concept and Eyring's rate process theory.

Dislocation phenomena in solids under simple shear stress are theoretically addressed with the free volume concept and Eyring's rate process theory for obtaining a generic and unified description. The obtained equations do not have any restrictions to specific materials and are compared with various theories and empirical equations like the Hall-Petch and its inverse forms. Moreover, our equations are used to fit experimental data of mechanical properties and dislocation density against grain sizes available in the literature. A good agreement with observations is achieved, indicating that our theoretical framework is sound. Our findings provide a theoretical foundation for the very common dislocation phenomena observed among many solid materials including pure metals, metallic alloys, ceramics, and even geological scale entities, potentially clearing out many inconsistencies and puzzles in the literature.

Influence of particle shape on creep and stress relaxation behaviors of granular materials based on DEM

The creep and stress relaxation behaviors stem from time-dependent changes in the microstructure of granular materials. As a non-negligible inherent granular material characteristic, particle shape plays a significant role on the formation and evolution of microstructure. However, the effects of particle shape on creep and stress relaxation behaviors of granular materials are still open questions. In this study, 3D DEM models based on the rate process theory and superellipsoids are incorporated to simulate the creep and stress relaxation of granular samples with different aspect ratios and blockiness. The results show that the aspect ratio and blockiness of particle have a great effect on creep and stress relaxation. However, the effects of aspect ratio and blockiness on creep and stress relaxation are coupled. Further analysis on contact forces shows the influences of aspect ratio and blockiness on creep mainly come from the contact force ratio. The influences of the aspect ratio and blockiness on stress relaxation mainly arise from the variation of the normal contact force anisotropy of the granular assemblies. The above results provide the tendency and mechanism on the effects of particle shape on creep and stress relaxation of granular assemblies.

A Unified concrete damage model for monotonic loading and fatigue loading

AbstractIn this work, a unified damage model is proposed for describing the mechanical behavior of concrete under monotonic loading and fatigue loading. Based on the micro‐meso stochastic fracture model (MMSF), the multiscale energy dissipation within the microspring is investigated. The rate process theory and a crack hierarchy model are employed to describe the nanocrack growth rate and crack number, respectively. It is found out that the fracture strain of the microspring can be derived from the energy dissipation analysis. The expression of the stochastic damage evolution law is changed to “energy dissipation threshold” instead of “fracture strain.” The new model can describe different damage evolution forms under monotonic and fatigue loading with the same parameters. The mechanisms of different damage evolution laws under different loading modes are analyzed in detail. Finally, a numerical example is presented to verify the proposed model.

A unified stochastic damage model for concrete under monotonic and fatigue loading

This study proposes a unified concrete damage model that can be applied to both monotonic and fatigue loading scenarios. The proposed model adopts the framework of stochastic damage mechanics and considers the micro-spring in the micro-meso stochastic fracture model (MMSF) as an energy dissipation element. To describe the multiscale energy dissipation process of the micro-spring, the rate process theory and a crack hierarchy model are employed. It is found that the energy dissipation threshold is linked to the elastic strain energy of the micro-spring, and the derived fracture strain of the micro-spring in MMSF enables the proposed model to describe the damage evolution laws for both monotonic loading and fatigue loading. The underlying damage mechanisms associated with the two loading processes are analyzed in detail. Additionally, the energy dissipation analysis enables the definition of the corresponding micro-damage to the micro-spring, which leads to the demonstration of the nonlinear properties of the micro-spring's constitutive law. Finally, several numerical examples are presented to validate the model.

Rock shear creep modelling: DEM – Rate process theory approach

Understanding the rock creep behavior is necessary to determine the long-term strength and safety of several geotechnical designs. There are several formulations to study the rock creep; however, most of them do not properly capture the tertiary creep. To overcome such limitation, model improvements have been made and new creep models (e.g., creep models with an associated viscoplastic flow rule) have been proposed. As an alternative, the Rate Process Theory (RPT) has been recently used to study the soil/rock creep behavior. This article expands previous works by analyzing the applicability of the Discrete Element Method (DEM) with RPT implementation to simulate Rock Shear Creep (RSC). To do that, (i) 2D DEM direct shear creep tests under Constant Normal Load (CNL) conditions are used, (ii) DEM specimens are built by a combination of the Flat-Joint Contact Model (FJCM) and the Linear Model (LM), and (iii) the DEM + RPT approach is calibrated by using experimental tests from the literature. DEM results presented here illustrate the suitability of DEM–RPT methodology to reproduce all stages of RSC, including tertiary creep. The effect of the applied shear stress and normal stress on RCS is also analyzed. Finally, the most important novelties of this paper are: (1) the DEM–RPT methodology can be easily calibrated by using a laboratory direct shear creep test; (2) the calibrated DEM models are suitable to analyze the main aspects of RSC; and (3) DEM results qualitatively agree with the overall experimental trend published in the literature.

Steady-state deformation of asphalt concrete

• An expression has been obtained for the steady-state deformation rate of the asphalt concrete. • The steady-state deformation rate depends on the viscosity, a stress, a temperature and an activation energy. • The graphs for “the steady-state deformation rate – a temperature” are similar. • “The stress substitution principle” has been proposed. • The test for creep is an alternative method for determination of the materials viscosity. The steady-state deformation rate of an asphalt concrete is investigated in details within a wide range of a stress variation (from 0.0081 MPa to 3.0 MPa) and a temperature variation (from + 60 °C to −24 °C). A hot dense fine-grained asphalt concrete of type B accepted for the investigation has been prepared with the use of a road viscous bitumen (4.8 % by weight of a dry mineral material) of the grade 100–130 under penetration. The bitumen was produced by the Pavlodar petrochemical plant (Kazakhstan) by the direct oxidation method from an oil of the Western Siberia (Russian Federation). The investigation of the steady-state deformation of the asphalt concrete has been performed by testing of samples (50x50x150 mm) for creep at direct tension. A load and a temperature have been kept as the constant ones from the beginning to the end of testing of all the samples (241 units). The tests of the asphalt concrete samples for creep have been performed in a device, which has been specially invented and assembled. It has been found out that the tested asphalt concrete is deformed under the impact of a constant stress and at a constant temperature during some period in a steady-state regime, i.e. it is deformed with a constant rate; the dependence of a steady-state deformation rate on a stress is described by power function with a high accuracy at all the considered temperatures; a fundamental expression has been obtained which connects the steady-state deformation rate with its viscosity, stress, temperature and activation energy of the viscous deformation; a simplified expression has been obtained for the steady-state deformation rate of the asphalt concrete for the practical use; a similarity has been shown for the dependence of the steady-state deformation rate on a temperature at various stresses in semi-logarithmic coordinates; “the stress substitution principle” has been formulated. The results obtained in this work have shown that the viscous flow and the steady state deformation (steady-state creep) of the elastoviscoplastic materials as the physical phenomena can be explained on the basis of the kinetic theory of liquids (Ya.I. Frenkel) and the theory of rate processes (H. Eyring). The test for the creep can be considered as an alternative method of the experimental determination for the viscosity of the materials.

Theoretical exploration of external pressure impact on superconducting transition temperatures

An external pressure could raise superconducting transition temperatures Tc, which has been experimentally observed but hasn’t been understood systematically. Utilizing superconducting transition temperature equations obtained with Eyring’s rate process theory and free volume concept in our previous work, we have explored how an externally applied pressure could change Tc in this article, under an assumption that the pressure P could change the free volume available for electrons in a system. The electron traveling distance and/or inter-particle spacing between electrons could have a linear, power law, and exponential relationships with pressures, borrowed from the relationship between viscosity and the free volume of molecules for glass liquids. Predicted relationships between Tc and pressures can be used to explain currently observed experimental phenomena such as Tc linearly increasing with pressures, initially slowly increasing and then suddenly jumping to a very high level, or showing skewed saw tooth relationships, etc. Our findings may provide an alternative simple theoretical approach to understand pressure induced superconductivity phenomena, further clearing doubts on many seemingly unrelated experimental observations.

Water in Sugar Electrolytes and Application to Electrodeposition of Superconducting Rhenium

A systematic electrochemical study is carried out on electrolytes with superhigh concentrations of fructose. The effect of fructose concentration on the viscosity and conductivity of electrolyte are determined and analyzed using Walden rule and the theory of rate process. The diffusion rates of proton and cupric cation are calculated from the peak current in cyclic voltammogram on stationary electrode and the limiting current on rotating electrodes. Raman spectroscopy is used to characterize the hydrogen bond network in water and the effect of fructose concentration on such network. Rhenium deposition with different fructose concentrations is studied on rotating disc electrodes. X-ray fluorescence, X-ray diffraction, and four point probe measurements at cryogenic temperature are used to study the deposition rate, crystallographic structure, and superconductivity of film, respectively.

Quantized conductance and superconductivity of twisted graphene and other 2D crystals explained with the Eyring’s rate process theory and free volume concept

Theoretical treatment originally intended to address proton transporting through a 2D (two dimensional) crystal like graphene and hexagonal boron nitride has been borrowed to examine conductivity and superconductivity of single layer, bilayer, trilaye, even multilayer graphene or other 2D crystals. The theory was developed based on the Eyring’s rate process theory and free volume concept under an assumption that protons behave exactly same as electrons, thus obtained equations should hold for electron conduction through a 2D crystal, too. These equations show that at high temperature regions conductivity should be scaled as σ=ν1e2h, similar to fractional/integral quantum Hall effect; while at low temperature regions conductivity should be scaled as σ=ν22eh, similar to Josephson junction effect. At high temperature regions, the parameter α, related to electron packing structure and critical to superconductivity, is canceled out and not present in derived equations, indicating that no superconductivity occurs in high temperature regions. While in low temperature regions, superconductivity should appear at temperature about 5 K or even higher, depending on electron packing structures. The fractional parameter f that can vary from fully close status with f=0 or full open status with f=1 should be controlled by the twisted angles. Our equations predict that superconductivity and insulating states are closely adjacent to each other; ”on” and ”off” superconductivity can be observed periodically when twisted angles are precisely varied from one direction to another. The volume ratio of conduction electrons to the conductive area and thickness play a critical role in superconductivity, implying that varying the area and/or thickness could have similar impact as twisted angle does. Our findings shed new lights on conductivity of stacked graphene or other 2D crystals.

Damage degree evaluation of masonry using optimized SVM-based acoustic emission monitoring and rate process theory

Evaluation of masonry damage is considerably challenging because of the non-homogeneous nature of masonry materials and the rapid attenuation of signals. To this end, a methodology combining qualitative analysis employing support vector machine-based acoustic emission (AE) monitoring and quantitative analysis using AE rate process theory was proposed. In this work, firstly, the propagation attenuation characteristics of the AE amplitude and frequency were studied using pencil-lead break tests. The hybrid PSO-SVM model was employed to automatically identify the damage stages of the AE signals based on the field in-situ axial compression test data. Then, laboratory compression and shear tests on small-scale specimens were performed with AE monitoring. The Boltzmann sigmoidal modified function between relative stress and AE hits was established. Based on qualitative and quantitative analysis, a damage index-based early warning range was proposed, which can help to decide the damage level of masonry structures. The results of this paper can provide some new insight for the analysis of masonry damage.

Research on dynamic splitting damage characteristics and constitutive model of basalt fiber reinforced concrete based on acoustic emission

In order to effectively utilize fiber reinforced concrete in engineering, it is necessary to investigate its mechanical properties and damage characteristics under dynamic tensile loads. This paper studied the effects of loading rate and fiber content on the tensile strength and acoustic emission (AE) characteristics of basalt fiber reinforced concrete (BFRC) in dynamic splitting tests. Brazilian disc splitting tests were carried out on the BFRC specimens with various fiber volume fraction (0%, 0.05%, 0.1%, 0.15%, 0.2%). Then the dynamic splitting AE characteristics were analyzed by means of parameter analysis method. Additionally, the stress–strain curves of BFRC were fitted by the constitutive model modified based on AE rate-process theory. The test results indicate that the tensile strength is enhanced with the increasing loading rate while adding basalt fibers has the same effect. Preferable fiber contents are 0.1% and 0.15%. Then it is found that loading rate and fiber content exert considerable impacts on the AE characteristics. Furthermore, the good fitting results suggest that the mechanics behavior of BFRC under dynamic splitting loads can be well described by the modified constitutive model.

DEM simulation of rock creep in tunnels using Rate Process Theory

The time-dependent (creep) behaviour of rocks affects the safety and stability of tunnels excavated in weak rocks and at great depths. Several theories have been proposed to simulate the creep deformation in rock; i.e., the progressive time-dependent damage that rocks (or other materials) exhibit under constant stress. However, most of these theories do not capture the accelerating strains associated to tertiary creep and leading to rock failure. In this research, the Rate Process Theory (RPT), combined with the Discrete Element Method (DEM), are used to simulate rock creep deformation in deep tunnels. To do that, two-dimensional (2D) DEM tunnel models are built using particles, with their interactions being simulated by a hybrid mixture of the linear and flat joint contact models. The RPT is incorporated into such models by a user-defined Visual C++ script that modifies their friction coefficients during the DEM simulation, depending on the relative velocity between particles. Numerical results show, for the first time, that the joint RPT-DEM approach is able to reproduce all stages of tunnel convergences associated to rock creep, including tertiary creep; and that it can reproduce the rock damage associated to such creep strains.

Discrete Element Modelling of Rock Creep in Deep Tunnels using Rate Process Theory

Rock creep behaviour is a key aspect of many engineering projects, such as deep tunnels in which squeezing problems could occur. Many theories have been published in the literature to reproduce rock creep behaviour; however, most of them are not able to capture the last phase of creep (i.e., tertiary creep, or the accelerating strains that occur prior to failure). In this work, the Distinct-Element Method (DEM) approach is employed, in conjunction with Rate Process Theory (RPT), to simulate the effect of rock creep in deep tunnels. To do that, the DEM models are constructed using particles, whose interactions are simulated with a hybrid mixture of the Flat Joint Contact Model (FJCM) and the Linear Model (LM) contact models; the RPT is implemented into DEM models using a Visual C++ function. Results show that the DEM plus RPT combination can suitably reproduce the tunnel convergences due to rock creep.

DEM study of creep and stress relaxation behaviors of dense sand

The creep and stress relaxation behaviors under the triaxial shearing of an idealized granular soil were studied using the three-dimensional discrete element method, into which the rate process theory was incorporated to enable simulation of these two time-dependent physical processes by a high-performance computing facility. The model was validated by comparing the simulation results with published experimental data. The study is focused on the effects of deviatoric stress during triaxial shearing of the granular soils on their creep and stress relaxation behaviors. In particular, to gain insights into their micromechanical mechanisms, a careful examination was made of the relationship between the shear-strain localizations occurring during creep and triaxial shearing, and the evolution of the contact number, average contact forces, and shear-induced anisotropies during these two time-dependent processes. The results indicate that the deviatoric stress level strongly affects the rates of creep strain and stress relaxation and dictates whether creep rupture will occur. These two time-dependent processes of the granular soil are also found to be isotach, which is evidenced by a unique normalized stress–strain relationship derived from the creep and stress relaxation tests.