Two-phase Material System Research Articles

A design technique for transforming statically designed phononic crystals and metamaterials into multifunctional, programmable active acoustic meta-devices

The active tuning of the bandgaps induced by the acoustic metamaterials has sparked significant interest among researchers. It opens up possibilities for programmable, multifunctional acoustic meta-devices. The static design of acoustic metamaterials, however, has limited automation capabilities, particularly for controlling sound propagation through the elastic solids. Designing acoustic metamaterials with fluid as the host medium, specifically air, significantly reduces these constraints. Given this observation, the present work demonstrates a novel design technique that transforms a Phononic Crystal (PnC) into an Active Acoustic Meta-device (AAMD). The designed AAMD has been demonstrated as programmable and multi-functional. It functions as an acoustic barrier over around 94% of the applied frequency sweep (a.f.s)., 300–3500 Hz. As an acoustic transmitter, it magnifies acoustic energy over around 50% of the a.f.s. Similarly, it functions as an acoustic switch over 100% of the a.f.s. This metadevice distinguishes itself by solely utilizing a two-phase material system and employing basic design elements, rather than common resonating elements, such as Helmholtz resonators or softer coatings.

Prediction of the elastic modulus of LLDPE/CNT nanocomposites by analytical modeling and finite element analysis

In the present work, the effective elastic modulus of carbon nanotube (CNT) polymer nanocomposites has been evaluated through micromechanics modeling and finite element analysis (FEA). In the micromechanics model, the inherent trend of CNTs to aggregate is taken into account, considering a two-phase material system, that of the matrix with the finely dispersed CNTs and the inclusions, involving agglomerated CNTs and matrix material. A new model is proposed for the elastic stiffness evaluation of the two phases and the elastic stiffness of the nanocomposite, introducing two aggregation parameters. It was proved that this analysis was rational and operative. The same aggregation concept has been investigated using FEA, and a comparative study between the two procedures was performed. Furthermore, an additional treatment with FEA was performed, based on a three-phase model, including the matrix, the CNTs and the interphase. A parametric analysis has been executed and a comparison with experimental data of linear low density polyethylene (LLDPE)/CNT nanocomposites has been performed.

Application of sonochemical processing to LSC(La0.6Sr0.4CoO3)/SDC(Sm2O3-doped CeO2) composite cathodes for solid oxide fuel cells involving CeO2-based electrolytes

Nanocrystalline Sm2O3-Doped CeO2 (SDC) powders were synthesized in a single- and two-phase material system by using sonochemical processing with high-frequency agitation. The synthesized SDC nanocrystalline powders were used to coat the mixed-conducting La0.6Sr0.4CoO3 (LSC) cathode materials. The combined synthesis processing allows the artificial coating of the LSC materials with the ionic-conducting SDC electrolyte. The electrochemical polarizations of the SDC/LSC composites are characterized using a geometrically constricted contact between the ionic probe and the SDC/LSC composites. The lowest cathode polarization was obtained for the LSC (85wt%)/SDC (15wt%). The lowest electrode polarization is believed to result from the high density of the triple-phase boundaries when the constituent phases are interconnected in a 3-dimensional manner.

Nanocrystalline silicon embedded in silicon suboxide synthesized in high-density inductively coupled plasma

A two-phase material system of nanocrystalline silicon (nc-Si) embedded in a dielectric matrix of silicon suboxide (SiOx) is fundamentally and technologically significant for the photonic and photovoltaic device such as light emission diode and solar cells. nc-Si in amorphous SiOx has been synthesized by means of the low-frequency (460 kHz) inductively coupled plasma (LFICP) of SiH4 + CO2 + H2 without the common route of high hydrogen dilution. The chemical composition, microstructures and optical properties of the complex material system are tuned by the reactive gas flow rate ratio of CO2/SiH4. nc-Si embedded in amorphous SiOx due to the phase separation are observed by means of SEM and TEM characterization tools. The crystalline volume fraction in nc-SiOx:H is determined by the density of the embedded nc-Si particles and the occurrence of the a-SiOx encapsulating shell layer. The bond configuration analysis shows the concurrent oxygenation and dehydrogenation process with the incorporation of oxygen. The underlying mechanism in forming the two-phase complex material system and the phase evolution with the reactive gas flow rate ratio are discussed in terms of the unique features of the utilized high-density LFICP.

Level set topology optimization of problems with sliding contact interfaces

This paper introduces a topology optimization method for the design of two-component structures and two-phase material systems considering sliding contact and separation along interfaces. The geome...

Gradient-based adaptive discontinuity layout optimization for the prediction of strength properties in matrix–inclusion materials

The prediction of strength properties of engineering materials, which in general are time dependent due to chemical and deterioration processes, plays an important role during manufacturing and construction as well as with regard to durability aspects of materials and structures. On the one hand, the speed of production processes and the quality of products may be significantly increased by improved material performance at early ages. On the other hand, the life time of materials and structures can be enlarged and means of repair and maintenance can be optimized.For determination of strength properties of materials, an extension of the discontinuity layout optimization (DLO) towards an iterative adaptation of the underlying mode of discretization (nodes and discontinuities) is proposed in this paper. This technique yields an improved representation of the underlying failure mechanism (thus, avoiding interlocking in consequence of the chosen discontinuity layout) at reduced computational costs. The performance of the proposed DLO method is assessed by the re-analysis of problems with available analytical solution and finally applied to upscaling of strength properties considering, in a first step, two-phase material systems representing matrix–inclusion morphologies.

Modeling thermal shock damage in refractory materials via direct numerical simulation (DNS)

In this paper, a computational investigation on thermo-mechanically induced damage in refractory materials resulting from severe thermal shock conditions is presented. On the basis of an idealized two-phase material system, molten aluminium thermal shock tests 1 are computationally modeled by means of direct numerical simulations (DNS). The interfacial and bulk damage evolution within the material are described by thermo-mechanical cohesive zones and continuum damage mechanics (CDM), respectively. Reported experimental results 1 are used to identify the parameters of the model. Furthermore, a parametric study is carried out to investigate the relative significance of various microstructure parameters in the context of thermal shock response.

A computational study on the effective properties of heterogeneous random media containing particulate inclusions

The effective elastic modulus and conductivity of a two-phase material system are investigated computationally using a Monte Carlo scheme. The models contain circular, spherical or ellipsoidal inclusions that are either uniformly or randomly embedded in the matrix material. The computed results are compared with the applicable effective medium theories. It is found that the random distribution, geometric permeability and particle aspect ratio have non-negligible effects on the effective material properties. For spherical inclusions, the effective medium approximations agree well with the simulation results in general, but the analytical predictions on void or non-spherical inclusions are much less reliable. It is found that the results for overlapping and non-overlapping inclusions do not differ very much at the same volume fraction. The effect of particle morphology is also investigated by modelling prolate and oblate ellipsoidal inclusions.

Error Estimates for Full Discretization of a Model for Ostwald Ripening

We analyze certain finite element schemes for a family of systems consisting of a Cahn–Hilliard equation coupled with several Allen–Cahn type equations, which are related to a model proposed by Fan and Chen for the evolution of Ostwald ripening in two-phase material systems. We obtain error bounds both for a semidiscrete (in time) scheme and a fully discrete scheme.

Numerical simulation of microstructural evolution of ceramic tool materials

The preparation of ceramic tool materials includes powdering, forming, hot-press fabrication and machining process, and the sintering is a key process, which governs the mechanical properties of the ceramic tool materials as well as the components and content. However, the sintering is a very complicated process. With the rapid development of the computer simulation technology and the computational material science, modeling and numerical simulation of ceramic sintering process become a novel way to investigate the sintering process on the micro- or macro-scale. Monte Carlo Potts’ model is widely applied to simulate the solid-phase sintering process of ceramics. Because of no assumption of the particle shape, the model can be properly used to simulate the mass-transport mechanisms. In this paper, a new Monte Carlo Potts’ model is proposed to investigate the single- and two-phase material systems, which is based on the Potts’ model of the description of the single-phase sintering without the presence of pores. The new simulation algorithm has been utilized to simulate the microstructural evolution in the single- and two-phase ceramic tool material sintering process with considering the presence of pores. Different types of interface, different types of grain boundary energy, initial grain size, the composition content, the initial pore size and the content of pore are considered in the new simulation algorithm. It is found from simulation results that the pore and the phase-two can pin the matrix phase and decrease the growth rate of matrix phase during the microstructural evolution, which has been invalidated by the experiment. The second-phase particle is useful for the refinement of matrix grain. The high rate of grain growth is disadvantage of the pore exhalation. The simulation results are consistent with the experiment results.

Impedance modelling of two-phase solid-state ionic conductors. Part I—theoretical model and computer simulations

An equivalent circuit model is introduced to account for the impedance properties of solid state ionic conductors, composed of two distinct phases. The model is developed on the basis of physical arguments, regarding the micrometer-scale structure of the two-phase material system and the comparison of different possible equivalent circuit representations. The final equivalent circuit reduces to two simpler circuits, suitable for fitting experimental impedance spectra. Computer simulations are provided to demonstrate the non-Arrhenius behaviour, which is observed in the temperature dependence of the ohmic elements of the equivalent circuits used for data analysis. This complex dual-slope behaviour of the Arrhenius plot is in agreement with the predictions of the model. Finally, with the aid of mathematical calculations and illustrated by computer simulations, a modified Arrhenius plot evaluation procedure was developed to derive correctly the electrical properties of the individual constituent phases from impedance measurements.

Dynamic plasticity and fracture in high density polycrystals: constitutive modeling and numerical simulation

Presented is a constitutive framework for modeling the dynamic response of polycrystalline microstructures, posed in a thermodynamically consistent manner and accounting for finite deformation, strain rate dependence of flow stress, thermal softening, thermal expansion, heat conduction, and thermoelastic coupling. Assumptions of linear and square-root dependencies, respectively, of the stored energy and flow stresses upon the total dislocation density enable calculation of the time-dependent fraction of plastic work converted to heat energy. Fracture at grain boundary interfaces is represented explicitly by cohesive zone models. Dynamic finite element simulations demonstrate the influences of interfacial separation, random crystallographic orientation, and grain morphology on the high-rate tensile response of a realistic two-phase material system consisting of comparatively brittle pure tungsten (W) grains embedded in a more ductile matrix of tungsten–nickel iron (W–Ni–Fe) alloy. Aspects associated with constitutive modeling of damage and failure in the homogenized material system are discussed in light of the computational results.

Numerical modelling of localized fracture of inelastic solids in dynamic loading processes

The main objective of the paper is the investigation of adiabatic shear band localized fracture phenomenon in inelastic solids during dynamic loading processes. This kind of fracture can occur as a result of an adiabatic shear band localization generally attributed to a plastic instability implied by microdamage and thermal softening during dynamic plastic flow processes. By applying ideas of synergetics it can be shown that as a result of instability hierarchies a system is self-organized into a new shear band pattern system. This leads to the conclusion that inelastic solid body considered during the dynamics process becomes a two-phase material system. Particular attention is focussed on attempt to construct a physically and experimentally justified localized fracture theory that relates the kinetics of material failure on the microstructural level to continuum mechanics. The description of the microstructural damage process is based on dynamic experiments with carefully controlled load amplitudes and duration. The microdamage process has been treated as a sequence of nucleation, growth and coalescence of microcracks. The microdamage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature and history-dependent, non-linear process. The theory of thermoviscoplasticity is developed within the framework of the rate-type covariance material structure with a finite set of internal state variables. The theory takes into consideration the effects of microdamage mechanism and thermomechanical coupling. The dynamic failure criterion within localized shear band region is proposed. The relaxation time is used as a regularization parameter. Rate dependency (viscosity) allows the spatial differential operator in the governing equations to retain its ellipticity, and the initial-value problem is well-posed. The viscoplastic regularization procedure assures the unconditionally stable integration algorithm by using the finite element method. Particular attention is focused on the well-posedness of the evolution problem (the initial–boundary value problem) as well as on its numerical solutions. Convergence, consistency and stability of the discretized problem are discussed. The Lax equivalence theorem is formulated and conditions under which this theorem is valid are examined. Utilizing the finite element method and ABAQUS system for regularized elasto–viscoplastic model the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body at nominal strain rates ranging over 103−104 s−1 is presented. A thin shear band region of finite width which undergoes significant deformation and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. Numerical results are compared with available experimental observation data. © 1997 John Wiley & Sons, Ltd.

Dispersed-phase martensitic transformation controlled deformation behavior of two-phase metallic materials

A constitutive model which describes transformation plasticity accompanying stress-assisted martensitic transformation in two-phase material systems consisting of a stable matrix and a transforming dispersed phase is developed. The model consists of two parts: (a) a transformation thermodynamics/kinetics law describing the evolution of the transformed fraction of dispersed particles and (b) a constitutive law describing plastic flow resistance of the evolving three-phase (matrix phase, dispersed parent phase, dispersed product phase) composite material. The model is constructed in such a way that it can be readily implemented in a finite element program suitable for the analysis of boundary value problems. The model is used to analyze the uniaxial tensile behavior of the two-phase gamma Ti-A1 matrix/beta (Ti-A1-V-Fe) phase system in order to rationalize an experimentally observed nearly 100% increase in tensile ductility of the material due to the martensitic transformation in the beta phase. The model is also used to study the uniaxial tensile behavior of beta/alpha two phase Ti-10V-2Fe-3A1 (wt.%) alloy characterized by a sigmoidal stress-strain curve. A reasonably good agreement is obtained between the model predictions and the experimental data.