Multi-particle Unit Cell Research Articles

Quasi-BIC Mode Lasing in a Quadrumer Plasmonic Lattice.

Plasmonic lattices of metal nanoparticles have emerged as an effective platform for strong light–matter coupling, lasing, and Bose–Einstein condensation. However, the full potential of complex unit cell structures has not been exploited. On the other hand, bound states in continuum (BICs) have attracted attention, as they provide topologically protected optical modes with diverging quality factors. Here, we show that quadrumer nanoparticle lattices enable lasing in a quasi-BIC mode with a highly out-of-plane character. By combining theory with polarization-resolved measurements of the emission, we show that the lasing mode has a topological charge. Our analysis reveals that the mode is primarily polarized out-of-plane as a result of the quadrumer structure. The quality factors of the out-of-plane BIC modes of the quadrumer array can be exceedingly high. Our results unveil the power of complex multiparticle unit cells in creating topologically protected high-Q modes in periodic nanostructures.

Cyclic plasticity and creep-cyclic plasticity behaviours of the SiC/Ti-6242 particulate reinforced titanium matrix composites under thermo-mechanical loadings

The purpose of this work is to investigate the cyclic plasticity and creep-cyclic plasticity behaviours of particle reinforced titanium matrix composites (PRTMCs) SiC/Ti-6242, aimed to be used in high temperature applications. The investigation has been conducted upon microstructures that have been taken from a previous study where low-fidelity model-based optimization (LFMBO) has been used to maximise the elastic behaviour of particle reinforced aluminium matrix composites. The effect of the particle spatial distribution, particle fraction volume and number of particles on the shakedown limit, limit load and creep-cyclic plasticity have been explored by direct numerical techniques based on the Linear Matching Method (LMM) framework. The micromechanical approach to modelling and fifteen multi-particle unit cells have been investigated. Under cyclic loading conditions, the structural response of PRTMCs is not trivial and becomes even more significant when high temperature is involved. Hence, the factors that affect the creep and cyclic plasticity of PRTMCs are analysed and discussed, including effects of the applied load level, dwell period and temperature on the composites’ performance. The applicability and accuracy of the proposed direct method has also been verified by the step-by-step analysis.

Failure of glass-microballoons/thermoset-matrix syntactic foams subject to hydrostatic loading

Abstract This study focuses on a lightweight syntactic foam constituted by an epoxy matrix filled with polydispersed Glass Microballoons (GMs) up to 0.75 volume fraction. We present experimental results on hydrostatic loading which demonstrate the possibility of different failure modes depending on whether the surface of the composite is painted/coated or not. In order to explain this surprising behaviour, we propose a three-dimensional Finite Element (FE) micromechanical model. First, we develop a cubic MultiParticle Unit Cell (MPUC) which includes 100 randomly placed GMs and accounting for their polydispersion, in terms of both size and radius ratio. This model is validated by subjecting it to effective uniaxial stress and comparing its predictions of the elastic moduli with experimental findings and an analytical homogenisation technique. Second, towards modelling failure, we implement a structural criterion proposed by our group, which posits that any GM undergoes brittle failure when its average elastic energy density reaches a critical value. We then utilise our measurements of the effective strength under uniaxial compressive stress to identify different critical values for selected types of GMs. Third, on the basis of the MPUC, we reach our goal by developing a larger FE model, including 300 GMs, which enables the study of the stress diffusion from the external surface through an appropriately thick layer of composite, under macroscopic uniform pressure. This micromechanical model allows us to demonstrate the influence of the paint/coating on the syntactic foam failure mode through a detailed analysis of the collapsed GMs and the matrix stress state.

Hybridization of Lattice Resonances.

Plasmon hybridization, the electromagnetic analog of molecular orbital theory, provides a simple and intuitive method to describe the plasmonic response of complex nanostructures from the combination of the responses of their individual constituents. Here, we follow this approach to investigate the optical properties of periodic arrays of plasmonic nanoparticles with multiparticle unit cells. These systems support strong collective lattice resonances, arising from the coherent multiple scattering enabled by the lattice periodicity. Due to the extended nature of these modes, the interaction between them is very different from that among localized surface plasmons supported by individual nanoparticles. This leads to a much richer hybridization scenario, which we exploit here to design periodic arrays with engineered properties. These include arrays with two-particle unit cells, in which the interaction between the individual lattice resonances can be canceled or maximized by controlling the relative position of the particles within the unit cell, as well as arrays whose response can be made either invariant to the polarization of the incident light or strongly dependent on it. Moreover, we explore systems with three- and four-particle unit cells and show that they can be designed to support lattice resonances with complex hybridization patterns in which different groups of particles in the unit cell can be selectively excited. The results of this work serve to advance our understanding of periodic arrays of nanostructures and provide a methodology to design periodic structures with engineered properties for applications in nanophotonics.

Analysis of the specific properties of glass microballoon-epoxy syntactic foams under tensile and flexural loads

Syntactic foam samples of varying volume fractions were fabricated using glass microballoons (GMB) as the filler in an epoxy matrix. The tensile and flexural properties of the foams were obtained from experiments for microballoon volume fractions up to 0.5. Special attention was given to their specific (per unit density) properties which established the means to compare materials of different densities. Even though the actual properties of the foams show a decreasing trend due to the hollow nature of the fillers, the specific properties, especially the specific modulus, show an increase in the 0.3 to 0.5 microballoon volume fraction regime. The foams were also analyzed numerically by creating a suitable representative volume element (RVE) and analyzing it using a commercial software. The RVE was a multi-particle unit cell having microballoons in the same size distribution and volume fraction as the foam itself. The effective overall properties were obtained over it and compared with the experimental results.

Numerical simulation of the influence of particle clustering on tensile behavior of particle-reinforced composites

The spatial distribution of reinforcement particles significantly influences the tensile behavior of particle-reinforced composites. In this study, the role of particle clustering on the macroscopic and microscopic behavior of these composites in the absence of damage was numerically investigated. An infinite material containing a periodic distribution of clustered, elastic, spherical particles was modeled using a unit cell approach. Three types of multi-particle unit cells were simulated with different arrangements of clustered particles as well as different cluster densities. The uniaxial stress–strain curves in tension were compared with the curves obtained from single-particle unit cell simulations. It was shown that clustering of particles increases the plastic strain accumulated in the matrix and slightly increases the work hardening rate. More importantly, it was observed that while the influence of the particle distribution on the overall behavior of the composite was not significant in uniaxial tension, the maximum principal stress inside the particles is acutely sensitive to the particle cluster morphology.

Predicting elastic modulus of particle filled composites

A multi-particle unit cell model of PMMA/ATH composite with different volume fractions was employed to study the influence of interphase properties and inter-particle distance on elastic modulus. The model constitutes amorphous polymer matrix, rigid fillers and interphase between filler and matrix. Polymer matrix was modelled using a thermodynamically consistent dual-mechanism viscoplastic model, whereas fillers were assumed as linear elastic. In numerical simulations, the interphase between filler and matrix was modelled through a user defined interphase model and matrix material was modelled through a user defined material model.

Influence of filler content and interphase properties on large deformation micromechanics of particle filled acrylics

Large deformation response of alumina trihydrate (ATH) filled poly(methyl metacrylate) PMMA over a wide temperature range was investigated. A multi-particle unit cell model of PMMA/ATH composite with different volume fractions was employed to study the influence of interphase properties and interparticle distance. The model constitutes of amorphous polymer matrix, rigid fillers and interphase between filler and matrix. Polymer matrix was modeled using a thermodynamically consistent dual-mechanism viscoplastic model, whereas fillers were assumed as linear elastic. In numerical simulations, the interphase between filler and matrix was modeled through a user defined interphase model and matrix material was modeled through a user defined material model. Damage evolution in PMMA/ATH at large deformations due to particle debonding was studied based on a critical stress criterion. Composite elastic modulus results from finite element analysis of unit cell model were compared with analytical model predictions (Mori–Tanaka, Eshelby, Lielens models) at different temperatures for various volume fractions of fillers. The influence of interphase characteristics, interparticle distance and temperature on large deformation response of PMMA/ATH was examined through multi-particle unit cell model.

Effects of particle shape on the macroscopic and microscopic linear behaviors of particle reinforced composites

A systematic comparison of inhomogeneity shape effects on the linear elastic, thermoelastic and thermal conduction responses of particle reinforced composites is carried out. For this purpose, multi-particle unit cells that contain randomly positioned and, where applicable, oriented, identical particles having the shapes of spheres, regular octahedra, cubes or regular tetrahedra, respectively, and a volume fraction of 20% are employed. The macroscopic moduli and microscopic responses, such as phase averages, as well as phase-level standard deviations and distribution functions of the microfields are evaluated and compared to analytical estimates. The results indicate the presence of relatively small but consistent effects of the particle shape on the effective behavior of particulate composites. Effects on the microscopic stress and flux fields are predicted to be more pronounced.

Modeling of nano-reinforced polymer composites: Microstructure effect on Young’s modulus

A computational numerical-analytical model of nano-reinforced polymer composites is developed taking into account the interface and particle clustering effects. The model was employed to analyze the interrelationships between microstructures and mechanical properties of nanocomposites. An improved effective interface model which is based on Mori–Tanaka approach and includes the nanoparticle geometry and clustering effects was developed. A program code for the automatic generation of two-dimensional multiparticle unit cell models of nanocomposites and finite element meshes on the basis of “grid method” algorithm was developed in the ABAQUS Scripting Interface. In the computational studies, it was observed that the elastic modulus increases with the increasing the aspect ratio of nanoparticles. The thickness and properties of effective interface layers and the shape and degree of particles clustering have strong influence on the mechanical properties of nanocomposite.

TENSILE PROPERTY AND CRACK PROPAGATION BEHAVIOR OF TUNGSTEN ALLOYS

In situ SEM experimental system is employed to investigate the mechanical characteristics and the fracture behavior of 91W–6.3Ni–2.7Fe tungsten alloys. The crack initiation and propagation of tungsten alloys under tensile loadings are examined. Multi-particle unit cell models containing the microstructure characteristics of tungsten alloys are established. Fixed-point iteration method is firstly used for the multi-particle unit cell's boundary condition. By adopting the method, real displacement constrained conditions are applied on the multi-particle unit cell models. The mechanical and fracture behaviors of tungsten alloys under tensile loading are simulated. The effects of tungsten content, particle shape, particle size, and interface strength on the mechanical properties of tungsten alloys are analyzed. The relationship between the mechanical behaviors and the microstructure parameters is studied. A good agreement is obtained between the experimental results and the numerical predictions, verifying the rationality of the FE models using the fixed-point iteration method.

Nanoreinforced polymer composites: 3D FEM modeling with effective interface concept

A computational study of the effect of structures of nanocomposites on their elastic properties is presented. The special program code for the automatic generation of 3D multiparticle unit cells with/without overlapping, effective interface layers around particles is developed for nanocomposite modeling. The generalized effective interface model, with two layers of different stiffnesses and the option of overlapping layers is developed here. The effects of the effective interface properties, particle sizes, particle shapes (spherical, cylindrical, ellipsoidal and disc-shaped) and volume fraction of nanoreinforcement on the mechanical properties of nanocomposites are studied in numerical experiments. The higher degree of particle clustering leads to lower Young’s modules of the nanocomposites. The shape of nanoparticles has a strong effect on the elastic properties of the nanocomposites. The most effective reinforcement is cylindrical one, followed by ellipsoids, discs, and last, spheres. Ideally random oriented and correlated microstructures lead to the same average Young moduli, yet, the standard deviation of Young modulus for correlated microstructure is nearly 4 times of that for fully random orientation case.

Numerical simulation on tensile property of TiC particle reinforced titanium matrix composite

Samples of TiC particle reinforced titanium matrix composite (TP‐650) containing 10 vol.‐% of TiC fabricated by pretreatment melt process have been tested in quasi‐static and dynamic tension at different strain rates from 10−4 to 103 s−1, and the mechanical properties have been compared with those of the unreinforced matrix alloy. homogenization theories for periodic microstructures and the fixed point iteration method for multiparticle unit cell’s boundary conditions are introduced to investigate the mechanical characteristics of the TiC reinforced titanium matrix composites (TP‐650). Finite element models containing some microstructure characteristics of the TP‐650 composites are established. The relationship between the mechanical behaviours and the microstructure parameters was studied.

Multi-Particle Unit Cell Models for Particulate-Reinforced Titanium Matrix Composites

Fixed point iteration method for multi-particle unit cell’s boundary condition is presented. On the basis of this method, the macroscopic effective material parameters can be obtained from a microscopic point of view. Multi-particle unit cell models containing some important microstructure characteristics of TP-650 titanium matrix composites are established. The real displacement constrained conditions are applied on the multi-particle unit cell using this method, and the mechanical properties and fracture behaviors of the composites under tensile loading are simulated. A good agreement was obtained between the experimental results and the numerical predictions, which verifying the rationality of the FE models based on fixed point iteration method.

Effect of pore distribution on the statistics of peak stress and overall properties of porous material

This paper addresses the effect of pore distribution on the overall properties and local stress fields in a porous material. Thermal and elastic fields in materials with uniform microstructure are compared with those of materials containing distinguishable clusters of circular or elliptic shape. The numerical simulation combines multipole expansion of local fields with the multi-particle unit cell method. Our work demonstrates that statistics of the peak stresses follow Gumbel’s rule derived for statistics of extreme values and are directly related to statistics of nearest neighbors. Based on this correspondence, an analytical expression for statistics of maximal stresses in a porous material with arbitrary microstructure is constructed in terms of porosity and statistics of minimal distances between the nearest neighbors. At the same time, the numerical analysis indicates that overall elastic constants and thermal (or electrical) conductivity are almost insensitive to the actual distribution of pores – uniform or with distinguishable pore clusters – at least in the examined interval of porosity (up to 50%).

Fracture Behavior of Particle Reinforced Metal Matrix Composites

SEM experimental system was employed to investigate the fracture behavior of particle reinforced metal matrix composites (91%wt tungsten alloys) by in-situ experiments. The fracture patterns of tungsten alloys under tensile loading were examined. Multi-particle unit cell models containing some important microstructure characteristics of tungsten alloys were established. By using fixed point iteration method, the displacement constraint conditions were applied on the multi-particle unit cell and the mechanical properties of tungsten alloys under tensile loadings were simulated. Comparison of the experimental results and the numerical predictions shows a good agreement between them, verifying the rationality of the FE models using the fixed point iteration method.

Effect of interfacial bonding on uniaxial ratchetting of SiC P/6061Al composites: Finite element analysis with 2-D and 3-D unit cells

The effect of interfacial bonding state between particulate and metal matrix on the ratchetting of SiC particulate reinforced 6061Al alloy composites (i.e., SiC P/6061Al composites) in uniaxial cyclic stressing at room temperature was discussed by numerical simulation using a finite element code ABAQUS. In simulation, axi-symmetrical two-dimensional (i.e., 2-D) mono-particle and three-dimensional (i.e., 3-D) multi-particle unit cells were employed, respectively. The ratchetting of un-reinforced matrix alloy was addressed by an elasto-plastic constitutive model with nonlinear kinematic hardening rule, and the particulates were assumed as elastic. Two kinds of interfacial layers were inserted into the unit cells between particulate and matrix, i.e., elastic and elasto-plastic interfacial layers previously employed by Kang et al. [G.Z. Kang, Q. Gao, Composites A 33 (2002) 657–667] in the numerical simulation for monotonic tensile behavior of short fiber reinforced metal matrix composites. Finally, the ratchetting of T6-treated SiC p/6061Al composites was simulated by using 3-D multi-particle unit cell and suitable interfacial property parameters. It is shown that the simulated results are closer to the corresponding experiments than those obtained with assumption of perfect interface. Simultaneously, some microscopic deformation features in the composites and their evolution rules were also revealed by the numerical simulation. Some significant conclusions are obtained, which are useful to establish a constitutive model to describe the ratchetting of the composites.