Power-law Expression Research Articles

High-temperature creep behavior and hot-pressing consolidation of NiAl

AbstractThe steady-state creep behavior of NiAl was studied by constant strain-rate tests in the strain-rate regime 1.5 × 10−4≤ ɛ̇ ≤ 1.0 × 10−2s−1.Primary creep of NiAl was investigated at different stresses (10 MPa−40 MPa) in the temperature range from 1200 to 1400°C. The steady-state creep rate was fitted to a temperature-compensated power-law expression ɛ̇ =B(σ/μ)nexp(−Q/RT), from which a stress exponent n≈3.5 and an activation energy Q ≈ 398 kJ/mol were derived, respectively. The obtained activation parameters indicate that dislocation creep dominates the creep behavior of NiAl at temperatures above 1200°C up to 1400°C. The transient creep behavior at 40 MPa could be fitted to a power-law equationε=ε0+btmwithbα σ3:5and 0.52<m<0.68. The creep data of NiAl obtained in this study were utilized for modeling and simulation of the consolidation process of NiAl composites during hot pressing by finite-element analysis.

Deactivation kinetics of γ-Al2O3 catalyst in methanol dehydration to dimethyl ether

The kinetics of deactivation of γ-alumina catalyst in dehydration of methanol to dimethyl ether (DME) was studied using integral method of analysis. A power-law rate expression was used for dehydration reaction and an independent kinetics for catalyst deactivation. Catalytic test runs were performed in a fixed-bed integral reactor in the temperature range of 250–300 °C under kinetically controlled reaction conditions. A second-order independent deactivation kinetics was found to fit experimental conversion-time data accurately. The activation energies of the main reaction and catalyst deactivation were obtained as 121 and −85 kJ/mol, respectively. The apparent negative value of the latter was attributed to a predominant deactivation mechanism via exothermic reversible partial hydration of active γ-alumina phase to the less active boehmite. At higher reaction temperatures, however, this mechanism is ceased at the expense of irreversible sintering of alumina crystallites.

Solar Modulation of Galactic Cosmic-Ray Protons Based on a Modified Force-field Approach

Abstract In this work, a modified force-field approach is established to investigate the long-term solar modulation of galactic cosmic-ray (GCR) protons. In this approach, the solar modulation potential ϕ is assumed to be energy dependent. As ϕ also depends on the local interstellar spectrum (LIS), a new proton LIS model is first presented based on data from Voyager 1 and 2, PAMELA, and AMS-02. Then, a double power-law expression is proposed to model ϕ as a function of proton energy. By fitting to the selected GCR measurements, the solar cycle variation characteristics of parameters in the expression of ϕ are obtained, and these parameters are reconstructed using the sunspot number, the heliospheric current sheet tilt angle, and the polarity of heliospheric magnetic field. Finally, a new analytical predictive model for GCR protons is established. It is shown that the 11 and 22 yr cyclic variations of GCRs are reproduced, and the computed proton intensities are in good agreement with GCR measurements at various energies since 1954.

Shock tube measurements of high-temperature argon broadening and shift parameters for the potassium D1 and D2 resonance transitions

The current study presents a novel approach to determine the spectroscopic line shape parameters of atomic potassium in a controlled laboratory environment and reports the results for temperatures between 1100 – 1900 K. Experiments were conducted in a shock tube using argon as the dilution gas. Potassium was introduced through a precursor, potassium chloride salt, on the surface of a stainless-steel threaded-rod inserted upstream of the measurement plane. The incident shock wave entrained the potassium chloride in the test gas before the reflected shock wave dissociated the compound, producing atomic potassium at ppb levels for spectroscopic studies with tunable diode lasers. This potassium seeding approach was tested over a wide range of temperatures and is readily deployable for other collisional partners and for other absorbing species of alkali metals. The well-resolved absorption features of both the potassium D1 and D2 transitions near 0.77 μm were modeled as Voigt profiles, enabling high-fidelity calculations of the argon broadening coefficients and pressure shift coefficients at various temperatures. The results are presented as temperature-dependent power-law expressions. These correlations will be useful for interpretation of brown dwarf spectra and for the development of remote sensing techniques in high-enthalpy facilities.

A unified description of mechanical and actuation fatigue crack growth in shape memory alloys

The damage tolerance approaches to fatigue rely on fracture mechanics concepts to explicitly account for the fatigue crack growth process. These approaches typically adopt the Paris equation, which relates the crack growth per cycle to the range of variation of the stress intensity factor, ΔK, during cyclic loading by means of experimentally calibrated parameters. Conditions on the validity of a single parameter description of the near crack tip stress and strain fields restrict the applicability of ΔK to fatigue crack growth resistance in Shape Memory Alloys (SMAs) under general thermomechanical loading paths. These conditions are substantially relaxed for the cyclic ΔJ–integral approach, which can achieve similitude over a wider range of loading conditions and geometric configurations. Thus, ΔJ qualifies as a potential unified descriptor of thermomechanical fatigue crack growth resistance in SMAs, an assertion, which is tested in this work for data from both purely mechanical and actuation fatigue crack growth experiments of a high temperature SMA, Ni50.3Ti29.7Hf20. In the latter, compact tension specimens are subjected to thermal cycling under constant load between an upper and a lower cycle temperature that allows for the stable phase to alternate in each cycle. It is shown here that a Paris-type power-law crack growth expression based on the ΔJ-integral can fit fatigue crack growth rate data from both types of experiments with a single set of parameters. This new analysis method for both actuation and mechanical fatigue crack growth rates provides a unified description for fatigue crack growth in SMAs and can allow estimating actuation fatigue crack growth rates, laborious and challenging to measure, from easier to detect mechanical fatigue crack growth rates.

Evaluation of Concurrent Variation in Rain Specific Attenuation and Tropospheric Amplitude Scintillation Over Akure, Southwest Nigeria

Rain constitutes a major limitation to the performance and use of terrestrial and satellite communication systems with operational frequencies greater than 10 GHz. The situation gets further complicated by fast fluctuations in the received signal amplitude due to in homogeneities in atmospheric weather conditions; a phenomenon known as amplitude scintillation. The concurrent evaluation of the two phenomena guarantees a better fade margin determination for the planning of radio communication over any location. This work employs 3 years of in-situ measurement of temperature, humidity, rainfall rate and rainfall amount for the estimation of tropospheric amplitude scintillation and rain specific attenuation over Akure (7.17° N, 5.18° E, 358 m) South West Nigeria. Davis vantage pro weather station at 1-min integration time was used for the measurement and the ITU models for rain specific attenuation (ITU-R P.838-3) and amplitude scintillation (ITU–R 618-13) were employed for the estimation. Time series and statistical analyses of the phenomena show that rain attenuation is the more prominent cause of signal degradation at Ku-band frequencies. Nevertheless, the need to make an extra fade margin allowance of about 0.25 dB due to amplitude scintillation fade subsists to forestall any loss of synchronization on the link. Also, a 3-parameter power-law expression developed for estimating amplitude scintillation fade from rain attenuation performed excellently well, as indicated by average root mean square error (RMSE) and coefficient of determination (R2) values of 0.002151 and 0.8747, respectively.

Anisotropic models with generalized hybrid expansion in Brans–Dicke theory of gravity

The hybrid expansion law (HEL) for average scale factor that yields power-law and exponential-law cosmologies is considered in spatially homogenous and anisotropic Bianchi type-I model in the context of Brans–Dicke (BD) Theory of gravitation. The solutions of the field equations have been calculated by assuming the power-law expression between the average scale factor [Formula: see text] and scalar field ([Formula: see text]). We studied both interacting and non-interacting forms of dark energy and dark matter and obtained respective solutions. The energy density [Formula: see text] decreases with time while energy densities [Formula: see text] increases with time. In both the cases, the physical acceptability and stability of the models are also studied. The coincidence problem in [Formula: see text]CDM model can be ruled out with proper choice of coupling between dark matter (DM) and dark energy (DE). We also discussed the physical behaviors of the derived models with the current observations applied to late-time acceleration and beginning of the universe. In this model, it is observed that our HEL Bianchi type I universe is highly anisotropic in the beginning of universe and becomes isotropic and overlaps with flat [Formula: see text]CDM model at late times.

Catalytic influence of mineral compounds on the reactivity of cellulose-derived char in O2-, CO2-, and H2O-containing atmospheres

The catalytic effects of mineral compounds on the conversion of a biomass-derived char in air- and oxyfuel-related atmospheres were investigated by thermogravimetric analysis at atmospheric pressure. The applied char originated from the hydrothermal carbonization (HTC) of cellulose followed by pyrolysis at 1073 K and subsequent mixing with 20 wt% of minerals by grinding to achieve tight contact. The reactivities of the mineral-loaded HTC chars were evaluated based on isothermal experiments in O2-, CO2-, and H2O-containing atmospheres as a function of their composition applying a magnetic suspension balance. The reactivity sequence K2CO3 > Na2CO3 ≫ Fe2O3 > CaO > MgO ≥ mineral-free was derived consistently for char oxidation in O2/inert as well as for char gasification in diluted H2O and CO2 mixtures. In addition to this qualitative assessment, the kinetic experiments were first modelled based on a simple global nth-order power-law rate expression. Then, the more complex Carbon Burnout Kinetics (CBK/G) model and the PoliMi model were applied. All three modeling approaches enabled a systematic quantification of the catalytic effects and led to a comparable lowering in the apparent activation energy. In combination with the kinetic parameters determined for the mineral-free char, the lowered apparent activation energies specific for the applied mineral and atmosphere facilitate the implementation of catalytic effects on the conversion of biomass-derived char into combustion models.

Simulating transient heat transfer in graphene at finite Knudsen number via the Boltzmann transport equation and molecular dynamics

The phonon Boltzmann transport equation (BTE) with the relaxation time approximation (RTA) scattering model is used to calculate transient temperature profiles in graphene, and the results are compared to analogous molecular dynamics (MD) simulations. For the BTE calculations, the phonon dispersion relation and frequency-dependent scattering rates are obtained from a combination of MD data and semi-empirical power-law expressions for the normal and Umklapp phonon lifetimes. The dimensions and initial temperature conditions of graphene are varied to study the size and temperature dependence of thermal transport physics at the mesoscopic scale. Good quantitative agreement to within 5% is found between the BTE and MD results, over a wide range of temperatures and lengthscales of the temperature variation in the graphene sheet. Small differences are attributed to the inaccuracy of the RTA as applied to graphene, and to neglecting four-phonon scattering in the BTE simulations. The present results may further understanding in applications such as the transient heating of nanoelectronics.

Obtención y análisis de expresiones de cinética química

En este artículo se discute la importancia de los análisis cinéticos. Se habla del tipo de función matemática que conforma una expresión de rapidez de reacción (-RA), en especial en presencia del catalizador; se describe la funcionalidad de (-RA) con la temperatura y concentración. Se describen también varias expresiones de rapidez, como las de la ley de potencia, las expresiones teóricas y las ecuaciones de LHHW. También se habla de los reactores típicos que se usan en el laboratorio y se describen los criterios que pueden utilizarse para desestimar los problemas de transferencia de masa y energía que se presentan comúnmente en las evaluaciones catalíticas.

Salt wedge intrusion modeling along the lower reaches of a Mediterranean river

A three-dimensional numerical model was used to simulate the dynamics of a salt-wedge intruding along the lower Strymon River mouth (northern Greece). The area is microtidal and under the summer increased freshwater demand for irrigation, Strymon outflux at the mouth reduces to near zero. Forcing at boundaries was provided a) from the e-HYPE hydrological model, at the upstream river boundary; b) from the TPXO tidal model, imposed at the open sea boundary, c) from CMEMS for water temperature and salinity open sea profiles, and d) from NOAA-GDAS for meteorological forcing. The model was calibrated with field measurements during summer 2003 and produced fairly reliable results of salt wedge intrusion during summer 2004. The coefficient of determination for salinity reached 0.95; higher correlation was exhibited at the river upstream. Model results underestimated slightly the velocity and salinity along-channel observations. Salt wedge enters the lower river channel in late May 2004, under limited river discharge (< 10 m3/s) and intrudes up to 4.6 km upstream. The wedge length is controlled by the low river flow, the microtidal domain and complex bottom topography. Logarithmic and power law expressions were derived relating saline water intrusion length (L30) and Strymon River discharge from validated model results. Retention time (RT) calculated based on model outputs varies in Strymon salt wedge between 10 and 20 days. Future work includes the operationalization of Strymon salt wedge model to produce reliable salinity and velocity forecasts along the lower channel.

An experimental and first principles DFT investigation on the effect of Cu addition to Ni/Al2O3 catalyst for the dry reforming of methane

The influence of varying Cu atomic ratios in a bimetallic Ni-Cu catalytic system for the CO2 or Dry Reforming of Methane (DRM) is investigated experimentally, in conjunction with ab-initio Density Functional Theory (DFT) and Generalized Power Law Expression (GPLE)-based mathematical modeling approaches. Among the synthesized catalysts, an 8:1 Ni:Cu ratio shows highest activity with stable H2/CO selectivity compared to its monometallic counterpart. Detailed physico-chemical characterization of the catalysts indicate that copper addition minimizes deactivation by forming a Ni-Cu alloy that increases reducibility of the NiO and limits the tendency of the active site toward coke formation. DFT calculations reveal increased energy barrier for carbon adsorption, whilst promoting facile removal of deposited carbon. GPLE analysis of the deactivation profiles suggest coking as the primary deactivation route in monometallic Ni catalyst; although much lesser in extent, deactivation of Ni8Cu1/Al2O3 catalyst is induced by both sintering and coking regimes.

Dynamic modeling and semibatch reactive crystallization of calcium carbonate through CO2 capture in highly alkaline water

A laboratory scale integration of carbon capture and utilization (CCU) technique operating based on highly alkaline aqueous hydroxide sorbents with a semibatch reactive crystallization process of calcium carbonate is presented. The study was conducted with a focus on investigating the kinetics of the crystallization process for CCU applications, where the production of micron-sized calcium carbonate particles occurs by direct addition of CO2-loaded solution to a crystallizer containing calcium chloride.Within this system, the need for high temperature heat consumption above 800 °C (109.4 kJ/mol CO2) for CO2 decomposition from Na2CO3 is avoided by production of value-added chemical from carbonate reach solution. The current set-up enables potential pre-treatment of carbon emission sources due to separate absorption and liquid-liquid crystallization processes. This leads to production of high-purity solid particles in comparison to conventional industrial practices.Experiments were carried out at several operating conditions at ambient temperature and pressure and effect of the absorbent solution concentration on CO2 capture efficiency and subsequently the precipitation yield was analyzed. Based on coupling the standard method of moments approach of the population balance formulation with power-law kinetic expressions, a correlation was extracted between the growth rate constant and feed flow rate for the adopted process. Moreover, characterization of the precipitated sample indicates the vaterite polymorphs of calcium carbonate as the dominant crystals in the pH range of 7.9–10.4. These types of demonstrations could contribute to circular economy processes using waste materials and can be considered as a potential approach toward an efficient carbon capture and valorization technique.

Influence of Assumed Strain Hardening Relation on Plastic Stress-Strain Response Identification From Conical Indentation

Abstract Instrumented indentation tests provide an attractive means for obtaining data to characterize the plastic response of engineering materials. One difficulty in doing this is that the relation between the measured indentation force versus indentation depth response and the plastic stress-strain response is not unique. Materials with very different uniaxial stress-strain curves can give essentially identical curves of indentation force versus indentation depth. Zhang et al. (2019, “Identification of Plastic Properties From Conical Indentation Using a Bayesian-Type Statistical Approach,” ASME J. Appl. Mech., 86, p. 011002) numerically generated “experimental” conical indentation data and showed that using surface profile data and indentation force versus indentation depth data together with a Bayesian-type statistical analysis permitted the uniaxial plastic stress-strain response to be identified even for materials with indistinguishable indentation force versus indentation depth curves. The same form of hardening relation was used in the identification process as was used to generate the “experimental” data. Generally, a variety of power law expressions have been used to characterize the uniaxial plastic stress-strain response of engineering materials, and, of course, the form that gives the best fit for a material is not known a priori. Here, we use the same Bayesian statistics-based analysis but consider four characterizations of the plastic uniaxial stress-strain response and show that the identification of the hardening relation parameters and the associated uniaxial stress-strain response is not very sensitive to the form of the power law strain hardening relation chosen even with data that have significant noise.

Cyclic behavior and strain energy-based fatigue damage analysis of mooring chains high strength steel

This study investigates the low-cycle fatigue behavior of mooring chains high-strength steel grade R4 under different strain amplitudes and strain ratios at room temperature. A fatigue test program has been carried out on small low cycle fatigue specimens cut from large mooring chains. The experimental results characterize the cyclic stress-strain relationship, the mean stress relaxation behavior, and the cyclic plasticity parameters of the material. Strain energy density is correlated with fatigue life through a simple power-law expression and very well represented by Basquin-Coffin-Mansion relationship. Further, a non-linear elastic-plastic material model is calibrated to the experimental stress-strain curves and used for the estimation of energy dissipation in the specimens under applied cyclic loads. The predicted fatigue life using the calibrated material parameters demonstrates a close agreement with the experimental fatigue life. Numerical simulations are carried out to analyze local plastic straining and assess crack initiation at the pit site of corroded mooring chains considering the multiaxial stress state. An energy-based approach is employed to estimate the number of cycles needed for a crack to initiate from an existing corrosion pit.

Intermetallic growth kinetics in gold ball bonds on Al-1%Si-0.5%Cu bond pads at 175∘C

Purpose The purpose of this study is to demonstrate that isothermal intermetallic growth data for gold ball bonds can be non-parabolic with explanations of why deviation from parabolic kinetics may occur. Design/methodology/approach Intermetallic thickness measurements were made at the centre of cross-sectioned ball bonds that were isothermally annealed at 175°C. Intermetallic growth kinetics were modelled with a power law expression(x(t) − x0)2 = α1tα2. The parameters of the power law model were obtained by transformation of the response and explanatory variables followed by data fitting using simple linear regression (SLR). Findings Ball bonds made with 4 N (99.99%Au) and 3 N (99.9%Au) gold wires exhibited two consecutive time regimes of intermetallic growth denoted Regime I and Regime II. Regime I was characterised by reactive diffusion between the gold wire and the aluminium alloy bond pad, during which Al was completely consumed in the formation of Au–Al intermetallics with non-parabolic kinetics. In Regime II, the absence of a free supply of Al to sustain intermetallic growth led to the conclusion that thickening of intermetallics was caused by phase transformation of Au8Al3 to Au4Al. Ball bonds made with 2 N (99%Au) wire also exhibited non-parabolic kinetics in Regime I and negligible intermetallic thickening in Regime II. Research limitations/implications The analysis of intermetallic growth is limited to total intermetallic growth at a single temperature (175°C). Originality/value The value of this study lies in showing that the assumption that only parabolic intermetallic growth is observed in isothermally aged gold ball bonds is incorrect. Furthermore there is no need to assume parabolic growth kinetics because with an appropriate data transformation, followed by fitting the data to a power law model using SLR and with the use of statistical diagnostics, both the suitability of the kinetic model and the nature of the growth kinetics (parabolic or non-parabolic) can be determined.

Vibration analysis of porous magneto-electro-elastically actuated carbon nanotube-reinforced composite sandwich plate based on a refined plate theory

In this article, the free vibration response of sandwich plates with porous electro-magneto-elastic functionally graded (MEE-FG) materials as face sheets and functionally graded carbon nanotube-reinforced composites (FG-CNTRC) as core is investigated. To this end, four-variable shear deformation refined plate theory is exploited. The properties of functionally graded material plate are assumed to vary along the thickness direction of face sheets according to modified power-law expression. Furthermore, properties of FG-CNTRC layer are proposed via a mixture rule. Hamilton’s principle with a four-variable tangential–exponential refined theory is used to obtain the governing equations and boundary conditions of plate. An analytical solution approach is utilized to get the natural frequencies of embedded porous FG plate with FG-CNTRC core subjected to magneto-electrical field. A parametric study is led to fulfill the effects of porosity parameter, external magnetic potential, external electric voltage, types of FG-CNTRC, and different boundary conditions on dimensionless frequencies of porous MEE-FG sandwich plate. It is noteworthy that the numerical consequences can serve as benchmarks for future investigations for this type of structures with porous mediums.

Exponent for the power-law relation between activation energy for dislocation nucleation and applied stress

The strength of defect-free crystalline materials is known to be close to the theoretical strength of the material and is typically governed by the nucleation of dislocations. Dislocation nucleation is controlled by the energy barrier associated with the nucleation process, which is a function of both the temperature and stress. Previous work has suggested that the energy barrier decreases with stress towards zero as a power-law relationship and that there may be an exponent with universal value for nucleation. In this paper, we analyze atomistic simulations and continuum models to determine if such a universal exponent exists. Fitting of all available atomistic data to the power-law expression does not yield evidence of a universal power-law behavior. The examination of continuum models, however, provides particular interesting insight. Sufficiently far away from the athermal limit, the energy barrier decays with an effective exponent greater than one such that both the energy barrier and activation volume decrease. However, very close to the athermal limit, the activation volume diverges, due to a divergent activation area of the dislocation loop, resulting in a limiting exponent around 0.5. The divergent activation volume is a result of including the generalized stacking fault energy and allowing the Burgers vector to go to zero during nucleation. These results further provide insight into strategies for empirically modeling the activation energy and activation volume, because they contradict the idea that the activation volume goes to zero, which is currently assumed in most empirical forms of the activation energy.

Dynamic evolution of the soil pore size distribution and its connection to soil management and biogeochemical processes

Soil properties are determined by a complex arrangement of pores, particles, and aggregates, which may change in time as a result of both ecohydrological dynamics and land management processes. The soil pore size distribution (PSD), which typically is treated as a static component, is a key determinant of soil properties, and its accurate representation has the potential to improve hydrological and crop models. Following previous work by Or et al. (2000), a modeling framework is proposed for the time evolution of the PSD which takes into account processes such as tillage, consolidation, and changes in organic matter. A time-varying power law PSD is obtained as the solution of a special form of transport equation for the PSD, parameterized using data from the literature to capture, in a parsimonious and efficient manner, the changes in the PSD as a result of the soil processes considered. Alterations in soil properties brought about by tillage, consolidation, and organic matter are then discussed. The potential benefit of this method for determining soil properties over the more widely used pedotransfer functions (PTF) is that it allows for the history of the soil, rather than only its present state, to be taken into account when estimating soil properties, and it does so in a physically consistent manner, leading to the widely used power law expression for soil properties with few parameters.

Expanded Discrete and Continuous Bĕlehrádek/Ratkowski Models of Microbial Growth Rates Under Oscillating and Extreme Storage Temperatures

The Bĕlehradek/Ratkowski, also known as the square root model, was originally developed to describe and quantify the temperature dependence of organisms’ growth rate, in terms of a simple power-law expression that contains a threshold growth temperature. The model’s original version implied that the rate rises monotonically with temperature. Therefore it has been modified to account for peak growth at the organism’s optimal temperature, by adding a falling multiplying factor. The modified model has been extended to post-peak growth temperatures, and all the way to where growth turns into thermal inactivation. In principle, the model can also be extended to low temperatures where growth not only ceases, as the original model implies, but turns into mortality, albeit at a much slower pace. The performance of the original and extended model’s versions can be visualized with three freely downloadable interactive Wolfram Demonstrations available on the Internet. The three versions can be combined into a single temperature-dependence model that covers the entire temperature range from lethal cold to death by heat. This combined model can be incorporated into a general dynamic (non-isothermal) growth/mortality model, in the form of a differential rate equation, which can describe oscillations between growth, no growth, and mortality modes during a population’s thermal history. All the Bĕlehradek/Ratkowski model’s variants can be replaced by a single continuous algebraic expression that eliminates the need to have “If statements” in their equations. The continuous version too can be incorporated into a dynamic rate model to describe growth, no growth, and mortality, and transitions between them.