Two-phase Materials Research Articles

МОДЕЛЮВАННЯ ПОВЕДІНКИ СТРИЖНЯ З ТРИЛІНІЙНОГО ДВОФАЗНОГО МАТЕРІАЛУ З УРАХУВАННЯМ ТЕМПЕРАТУРИ

В роботі сформульовано феноменологічну модель для опису властивостей сплавів із пам’яттю форм та пам’яттю в точці зміни температури. Встановлено, що класичні матеріальні діаграми – це конверт певного сімейства матеріальних діаграм, побудований за певнимизаконами зміни швидкості та розриву фронту деформації. Для використання феноменологічної моделі з метою дослідження двофазних матеріалів з різними модулями пружності розв’язано додаткову задачу, яка пов’язана з розбудовою миттєвої термомеханічної поверхні. В роботі проведено числове дослідження, як результат показано типову залежність для швидкості розповсюдження фазового переходу від часу. Графік залежності має три ділянки. На першій ділянці швидкість дорівнює нулю, а на третій – досягає постійного значення. Між ними міститься ділянка зі змінною швидкістю. В результаті обчислення дотичного модуля на кожному кроці інтегрування за часом інтегральна діаграма матеріалу, побудована в роботі, теж має три характерні ділянки.

Modeling of heterogeneous materials at high strain rates with machine learning algorithms trained by finite element simulations

Great progress has been made in the dynamic mechanical properties of concrete which is usually assumed to be homogenous. In fact, concrete is a typical heterogeneous material, and the meso-scale structure with aggregates has a significant effect on its macroscopic mechanical properties of concrete. In this paper, concrete is regarded as a two-phase composite material, that is, a combination of aggregate inclusion and mortar matrix. To create the finite element (FE) models, the Monte Carlo method is used to place the aggregates as random inclusions into the mortar matrix of the cylindrical specimens. To validate the numerical simulations of such an inclusion-matrix model at high strain rates, the comparisons with experimental results using the split Hopkinson pressure bar are made and good agreement is achieved in terms of dynamic increasing factor. By performing more extensive FE predictions, the influences of aggregate size and content on the macroscopic dynamic properties (i.e., peak dynamic strength) of concrete materials subjected to high strain rates are further investigated based on the back-propagation (BP) artificial neural network method. It is found that the particle size of aggregate has little effect on the dynamic mechanical properties of concrete but the peak dynamic strength of concrete increases obviously with the content increase of aggregate. After detailed comparisons with FE simulations, machine learning predictions based on the BP algorithm show good applicability for predicting dynamic mechanical strength of concrete with different aggregate sizes and contents. Instead of FE analysis with complicated meso-scale aggregate pre-processing, time-consuming simulation and laborious post-processing, machine learning predictions reproduce the stress–strain curves of concrete materials under high strain rates and thus the constitutive behavior can be efficiently predicted.

Machine learning-based accelerated property prediction of two-phase materials using microstructural descriptors and finite element analysis

This study explores the use of supervised machine learning (ML) to predict the mechanical properties of a family of two-phase materials using their microstructural images. Random two-phase microstructures with a diversity of inclusion volume fractions, size distributions, and/or shapes are input into a finite element analysis program to determine the elastic modulus, Poisson’s ratio, and phase stresses. The finite element analysis results establish the “ground truth” to train the supervised ML models. Two-point correlation (TPC) functions and principal component (PC) analysis are applied to the microstructures before training and testing the artificial neural network (ANN) and forest ensemble MLs. The chosen ML methods are found to accurately predict the homogenized elastic properties. Although the PCs for each set of microstructures are unique, recognizable patterns are detected that signify microstructural features that are key to microstructure-based property prediction. This work enables the development of ML algorithms to predict the mechanical properties of complex, multi-phase microstructural composites, based on microstructural images.

Calibration capacity of hot-pressed hydrogen standards for glow discharge optical emission and mass spectrometry

Mixed copper and titanium hydride powder was hot-pressed and characterized by Carrier Gas Hot Extraction, X-Ray Diffraction, Thermal Gravimetric Analysis coupled with Mass Spectrometry, and Scanning Electron Microscopy. The hot-pressed and five conventional samples were applied for calibration of hydrogen in Glow Discharge Optical Emission and Mass Spectrometry. Up to the introduction of 15 ng/s hydrogen the emission yield model is useful in Glow Discharge Optical Emission Spectrometry. A correlation between saturation and even reversal of the emission yield of the spectral lines H121, H486 and H656 and low sputtering rates was found. Hydrogen effects exist for the spectral lines of Cu(II) 219 and Ti(I) 399. In Glow Discharge Mass Spectrometry, a linear dependency of the 1H ion current on the sputtered mass per time exists over the total range of hydrogen content investigated. Hydrogen effects also exist for the sensitivity of 48Ti and 63Cu. The sputtering rate of two-phase materials depends linearly on the sputtered mass per time of one phase, which allows the sputtering rate of two-phase materials with known composition to be predicted.

Investigation of switching uniformity in resistive memory via finite element simulation of conductive-filament formation

Herein, we present simulations of conductive filament formation in resistive random-access memory using a finite element solver. We consider the switching material, which is typically an oxide, as a two-phase material comprising low- and high-resistance phases. The low-resistance phase corresponds to a defective and conducting region with a high anion vacancy concentration, whereas the high-resistance phase corresponds to a non-defective and insulating region with a low anion-vacancy concentration. We adopt a phase variable corresponding to 0 and 1 in the insulating and conducting phases, respectively, and we change the phase variable suitably when new defects are introduced during voltage ramp-up for forming. Initially, some defects are embedded in the switching material. When the applied voltage is ramped up, the phase variable changes from 0 to 1 at locations wherein the electric field exceeds a critical value, which corresponds to the introduction of new defects via vacancy generation. The applied voltage at which the defects percolate to form a filament is considered as the forming voltage. Here, we study the forming-voltage uniformity using simulations, and we find that for typical planar-electrode devices, the forming voltage varies significantly owing to the stochastic location of the initial defects at which the electric field is “crowded.” On the other hand, a protruding electrode can improve the switching uniformity drastically via facilitating the deterministic location of electric-field crowding, which also supported by the reported experimental results.

Prediction of compressive strength of the welded matrix-rock mixture by meso-inclusion theory

As a special and widely distributed geological material, the matrix-rock mixture (block-in-matrix texture) has been worldwide focused on its complex physical and mechanical properties for 25 years. However, the macro-meso mechanical relationship of matrix-rock mixture has not been well clarified so far, leading to the unclear understanding of its mechanical behavior. In this paper, the welded matrix-rock mixture is considered as a two-phase composite material, and a mesoscopic mechanical method is presented for calculating the uniaxial compressive strength (UCS). The influence of volumetric block proportion of rock (VBP) and mechanical contrast of meso components (i.e. UCS ratio (SR) and modulus ratio (MR) of rock to matrix) on the strength and the failure mechanism of the matrix-rock mixture is illustrated by the meso-inclusion theory. To avoid the rock damage in the welded mixture, it is suggested that the SR of rock to matrix should be larger than 1.5 for the low stiffness ratio of rock to matrix (e.g. MR ≤ 5), while for the mixture with high stiffness contrast (e.g. 5 < MR < 100) the SR of rock to matrix should be larger than 2. For the common case of strong rock-weak matrix mixture, the reinforced effect of VBP is positive with the MR of rock to matrix but seems to be insignificant when MR > 100. Meanwhile, the Weibull function is adopted to describe the strength property of the matrix in view of its strength randomness contributing to the matrix-rock mixture. It is shown that the strength evolution of the mixtures can be effectively predicted by the present model considering the Weibull distributed strength of the matrix, based on the comparison with the published experimental data and the discussion of existed empirical formulas.

Numerical simulation of liquefaction phenomenon considering infinite boundary

The response of liquefaction behaviour can be analyzed by incorporating the effects of the transient flow of the pore-fluid through the voids, which requires a two-phase continuum formulation for saturated porous media named ‘mixture theory’. The saturated soil system is modelled as a two-phase material based on the Biot's theory for porous media. Infinite elements have been incorporated in the solution algorithms to simulate infinite boundary. A computer code is developed in FORTRAN 90 considering fully coupled dynamic analysis to determine the responses of pore fluid and soil skeleton of an unbounded saturated sandy layer. The unconditionally stable generalized Newmark-Beta method is employed in the solution algorithm for evaluation of response at each time step. A generalized non-associative plasticity-bounding surface model Pastor–Zienkiewicz Mark III is considered to describe the inelastic behaviour of soils under earthquake loading. A parametric study is conducted to consider the effect of the material nonlinearity of the soil grain on liquefaction behaviour. A significant reduction in displacement and excess pore pressure is observed while considering unbounded domain. The salient feature of the solution algorithm is simulation of build up pore pressure and consequent reduction in mean effective stress. It was also observed that key parameters like permeability, earthquake intensity and shear modulus had significant effect on liquefaction response.

Fracture of thermo-elastic solids: Phase-field modeling and new results with an efficient monolithic solver

Thermally induced cracking occurs in many engineering problems such as drying shrinkage cracking of concrete, thermal shock induced fracture, micro cracking of two-phase composite materials etc. The computational simulation of such a fracture is complicated, but the use of phase-field models (PFMs) is promising as they can seamlessly model complex crack patterns like branching, merging, and fragmentation by treating the crack discontinuity as thin band of diffuse damage. Despite the success of phase-field models there are two major issues in previous PFMs of thermally induced fracture. Firstly, these models, which are mostly based on a PFM using a simple quadratic degradation function without any user-defined parameters, provide solutions that are sensitive to a length scale. Secondly, they are limited to brittle fracture only. As a solution, we extend the phase-field regularized cohesive zone model (PF-CZM) of Wu [JMPS, 103 (2017)], with a rational degradation function dependent on elasticity and fracture related material parameters, to thermoelastic solids. Furthermore, we present a monolithic BFGS algorithm to solve the three-field (displacements, phase-field and temperature) coupling equations altogether. Multiple thermally induced fracture problems, simulated within the framework of the finite element method, are presented with predictions in good agreement with previous findings and experiments. The proposed model is shown to give better performance in capturing the physics of thermally induced fracture: it provides length scale insensitive responses. And the monolithic solver is 4∼5 times faster than the conventional alternating minimization solver.

Evaluation of microstructure and conductivity of two-phase materials by the scanning spreading resistance microscopy (the case of shungite)

The determination of the content of the conducting phase and the assessment of conductivity by microscopic images are interesting for rapid and non-destructive analysis of the electrophysical properties of two-phase (conductor/dielectric) samples during the atomic force microscopy. In this paper we summarized results of the analysis of the conductivity maps of the shungite surface by the method of discretization by applying a square grid with subsequent binary digital processing. Microstructure and conductivity were evaluated by measuring the average length of continuous conductive circuits isolated on the grid. A model was considered that established a unique correspondence (up to normalizing coefficients) between the length of the conductive circuits on the conductivity maps and the integral conductivity of the sample as a whole. An analytical equation was obtained that described such dependence with an accuracy of units of percent. We proposed a method for measuring the integral conductivity of a shungite samples based on an analysis of its binary conductivity map obtained by spreading resistance microscopy. This method can be used to determine the conductivity by surface conductivity mapping for shungite-like two-phase conductor/dielectric systems, and in general, for any two-phase substances where the phases differ in AFM-determined properties.

A crystal plasticity based finite element framework for RVE calculations of two-phase materials: Void nucleation in dual-phase steels

A crystal plasticity based finite element (CPFE) framework is developed for performing representative volume element (RVE) calculations on two-phase materials. The present paper investigates the mechanical response and the evolution of microstructure of dual-phase (DP) steels under uniaxial tensile loading, with a special focus on void nucleation. The spatial distribution and morphology of the ferrite and martensite grains in DP steels are explicitly accounted for by generating three-dimensional RVEs with Voronoi tessellations. The effects of microstructural parameters—the volume fraction, morphology and spatial distribution of the martensite phase, and the grain size and orientation distribution of the ferrite phase—on the initiation and spread of localized plastic deformation (leading to void nucleation) are investigated in detail. The soft ferrite phase is modelled by a local crystal plasticity theory with anisotropic elasticity, and the hard martensite phase by the J2 flow theory with isotropic elasticity. The developed CPFE framework successfully predicts both the overall and the local mechanical response, and is perfectly capable of distinguishing between different void nucleation mechanisms experimentally observed for DP steels.

Multiphysics modeling of the initiating capability of detonators. I. The underwater test

Detonators are explosive devices used for the initiation of secondary explosives in commercial and military applications. They are characterized by their initiating capability, which is a critical factor for their safe and effective use but challenging to assess accurately. In this two-part study, we employ numerical simulations to investigate the blast wave generated by detonators and examine their initiating capability. The first part, presented here, follows the European underwater test of initiating capability, which evaluates detonators in isolation (direct method) and the second part considers detonators placed within a receiving explosive charge (indirect method). In the underwater test, the detonator is ignited inside a water tank and the initiating capability is assessed through pressure measurements in the far field. We employ a multiphysics methodology that allows the use of distinct mathematical models for each component such as two-phase reactive materials, elastic–plastic solids, and inert fluids. The computational implementation is validated against underwater experiments and is employed for the simulation of the blast wave generated by different types of detonators. The initial focus is on the general characteristics of the blast wave and subsequently on the differences between detonators of different shell material and thickness. Results show that the blast wave in the near field is asymmetric and varies significantly between detonators, but these features do not persist in the far field. The underwater test considers only the far field and is thus unable to capture the near field differences, which have a significant impact on the initiation of secondary explosives.

Strength and plasticity of lamellar vs. fibrous eutectic Mg-Al nanocomposites: An in-situ microcompression study

Owing to their low density and high strength-to-weight ratio, Mg alloys are attractive for automotive and aerospace applications. However, the current use of magnesium in the industry is limited due to the low strength and poor formability at ambient temperatures. Two-phase nanostructured materials are a promising solution to improve the mechanical properties of Mg alloys. Depending on processing parameters, either fibrous or lamellar morphologies can be formed via the eutectic transformation. In this work, the mechanical behavior of these two different morphologies were examined by in-situ SEM microcompression tests. The lamellar morphology exhibited a superior combination of strength and plasticity with respect to the fibrous morphology, and both showed superior strength relative to pure Mg, up to five-fold in the former and 12-fold in the latter. However, the higher strength in the fibrous eutectic was obtained at the expense of a low plasticity. According to the HR/TEM analyses of the deformed micropillars, the relatively high plasticity of the lamellar morphology was attributed to the two reasons; on the one hand, high dislocation activity was observed in both α and β phases and resulted in plastic co-deformation of the layers. On the other hand, the α layers played a significant role in restricting the shear instabilities that initiated in the β layers. Such an effect was not observed with the fibrous morphologies, and thus, they failed by cleavage along the closest-packed planes in the β crystal.

Numerical Maximization of the p-Laplacian Energy of a Two-Phase Material

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 17 July 2020Accepted: 23 August 2021Published online: 21 December 2021Keywordsoptimal design, two-phase material, $p$-Laplacian operator, feasible directions method, alternating minimization methodAMS Subject Headings49M05, 49J20Publication DataISSN (print): 0036-1429ISSN (online): 1095-7170Publisher: Society for Industrial and Applied MathematicsCODEN: sjnaam

Mathematical modelling of heat transfer processes in a two-phase material with inclusions in the form of a ball layer absorbing penetrating radiation. 1. Hierarchy of simplified analogs of the heat transfer basic model

Mathematical modelling of heat transfer processes in a two-phase material with inclusions in the form of a ball layer absorbing penetrating radiation. 1. Hierarchy of simplified analogs of the heat transfer basic model

Estimation of the efficiency of destroying hard rocks by composites sintered in the diamond-carbonate system

The purpose of this work is to substantiate the possibility of using a new composite sintered in the "diamond-carbonate" system for equippingdiamond drilling tools with high wear resistance and efficiency of rock destruction. The research technique consisted in establishing the influence of the wear resistance of the cutting edge of the samplesof a superhard composite diamond-containing material on the efficiency of rock destruction, assessed by the granulometric composition of its sludge. Research results. The two-phase superhard composite materials diamond – CaMg(CO3)2 and diamond – SrCO3 were obtained as a result of sintering by the method of impregnation of diamond micropowder with carbonate melts under conditions of a high pressure of 8.0 GPa and a temperature of 2100 °C. Wear resistance of the investigated composite sampleswas determined by based on the results of turning the core of granite from the Korostyshevskoye deposit of the X category of drilling. Determination of the size and shape of particles of granite fragments of the Korostyshevskoye deposit, taken during its destruction was carried out by laser diffraction and digital image analysis using a Microtrac Sync analyzer.The relationship between the degree of its wear of the cutting edge of composite samplesand the energy consumption of rock destruction, the size distribution of particles in the cuttings sample and their specific surface was established after analyzing the results of the study of wear resistance and the nature of their wear. Plates of the diamond–CaMg(CO3)2 composite, which have a higher wear resistance compared to other composites, are characterized by an increase in the proportion of large particles in the cuttings sample and a decrease in the value of their specific surface, which indicates a more rational use of energy, which goes to a greater extent for destruction rock and to a lesser extent for friction and wear. Practical value. The research results allow us to make a conclusion about the advisability of equipping a drilling rock cutting tool with samplesof a diamond–CaMg(CO3)2 composite in order to increase its wear resistance and the efficiency of rock destruction.

Temperature field of a two-phase porous material with penetrating radiation absorbing inclusions in the form of ball layer

Temperature field of a two-phase porous material with penetrating radiation absorbing inclusions in the form of ball layer

The Maximization of the $p$-Laplacian Energy for a Two-Phase Material

We consider the optimal arrangement of two diffusion materials in a bounded open set $\Omega\subset \mathbb{R}^N$ in order to maximize the energy. The diffusion problem is modeled by the $p$-Laplac...

A Three-Dimensional Random Walk Algorithm for Estimating the Chloride Diffusivity of Concrete.

The chloride diffusivity of concrete is an important parameter for assessing the long-term durability of coastal concrete structures. The purpose of this paper is to present a three-dimensional random walk algorithm (RWA) for estimating the chloride diffusivity of concrete. By analyzing the size distribution of aggregates, the equivalent interfacial transition zone (ITZ) thickness is derived in an analytical manner. Each aggregate is combined with the surrounding ITZ to construct an equivalent aggregate model (EAM) and the chloride diffusivity is formulated. It is found that the equivalent ITZ thickness decreases with the increase of practical ITZ thickness and aggregate volume fraction. The aggregate gradation influences the equivalent ITZ thickness to a certain extent. The relative chloride diffusivity of the equivalent aggregate is almost directly and inversely proportional to the equivalent ITZ thickness and the aggregate radius, respectively. The numerical results show that, when the EAM is adopted, the computational time is greatly reduced. With the EAM, concrete can be modeled as a two-phase material and the chloride diffusivity is estimated by applying the RWA. It is shown that, with the increase of mean square displacement and number of Brownian particles, the average chloride diffusivity of concrete approaches a stable value. Finally, through comparison with experimental data, the validation of the RWA is preliminarily verified.

Tangent second-order homogenisation estimates for incompressible hyperelastic composites with fibrous microstructures and anisotropic phases

This work presents new estimates for the effective mechanical response of composites with fibrous microstructures and hyperelastic, anisotropic, incompressible phases. The composites are two-phase materials consisting of aligned cylindrical fibres of circular cross section that are randomly distributed in the transverse plane of the matrix phase. The proposed homogenisation is based on the tangent second-order method proposed by Avazmohammadi and Ponte Castañeda (2013), which utilises variational principles and a suitably chosen “linear comparison material” to provide estimates for effective strain energies of nonlinear materials. To take into account the incompressibility of the fibre phase, we employed an appropriate asymptotic expansion of the fibre deformation field. By doing so, a constraint pressure is identified as the consistent limit of emerging indeterminate forms in the dilatational part of the fibre stress tensor. Furthermore, we performed an asymptotic analysis to obtain regular expressions of the underlying equations in the incompressible matrix limit. While we addressed the general case of incompressible and generally anisotropic phases, we put particular emphasis on composites with transversely isotropic phases whose symmetry axes are collinear with the fibre direction. For such materials, we derived estimates for the effective strain energies in terms of macroscopic strain invariants. In addition, for composites that are described by isotropic phase energies augmented with J4-invariant-based anisotropic terms, which is the case for many biological materials, we show that the anisotropic part of the energy can be easily homogenised by means of a simple Voigt-type average. Moreover, we present closed-form results for composites with isotropic Neo-Hookean phases augmented by transversely isotropic energy contributions. Finally, it is shown that the new estimates correspond to certain exact results under longitudinal shear deformation and that they properly linearise for small strains by recovering the corresponding linear-elastic estimates.

Growth of Titanium Oxide Nanostructures on γ-Аl2О3 by Atomic Layer Deposition

This paper presents results on control over the surface composition, surface structure, and pore texture of core/shell materials, as exemplified by the growth of conformal titanium oxide nanocoatings on γ‑Аl2О3 by atomic layer deposition via sequential and alternating exposure of the alumina to TiCl4 and H2O vapor. The alumina surface and growing titanium oxide layer are shown to influence the characteristics of the forming two-phase material. Increasing the amount of titanium via an increase in the number of deposition cycles leads to a systematic decrease in specific surface area, pore volume, and pore size, which points to conformal pore filling in the starting matrix by a titanium oxide layer. The composition and structure of the titanium oxide coating are influenced by its thickness and the nature of the starting matrix. The coordination state of the titanium oxide in monolayer structures is characteristic of the titanium oxide polyhedra in aluminum titanate. As the distance from the top monolayer to the surface of the matrix (coating thickness) increases, an X-ray amorphous layer is formed in which the oxygen coordination environment of the titanium is similar to that in an anatase-like phase of titanium dioxide.