Two-dimensional Microstructures Research Articles

Fast reconstruction of multiphase microstructures based on statistical descriptors.

In this paper, we propose a hierarchical simulated annealing of erosion method (HSAE) to improve the computational efficiency of multiphase microstructure reconstruction, whose computational efficiency can be improved by an order of magnitude. Reconstruction of the two-dimensional (2D) and three-dimensional (3D) multiphase microstructures (pore, grain, and clay) based on simulated annealing (SA) and HSAE are performed. In the reconstruction of multiphase microstructure with HSAE and SA, three independent two-point correlation functions are chosen as the morphological information descriptors. The two-point cluster function which contains significant high-order statistical information is used to verify the reconstruction results. From the analysis of 2D reconstruction, it can find that the proposed HSAE technique not only improves the quality of reconstruction, but also improves the computational efficiency. The reconstructions of our proposed method are still imperfect. This is because the used two-point correlation functions contain insufficient information. For the 3D reconstruction, the two-point correlation functions of the 3D generation are in excellent agreement with those of the original 2D image, which illustrates that our proposed method is effective for the reconstruction of 3D microstructure. The comparison of the energy vs computational time between the SA and HSAE methods shows that our presented method is an order of magnitude faster than the SA method. That is because only some of the pixels in the overall hierarchy need to be considered for sampling.

Quantitative characterization of bamboo cortex structure based on X-ray microtomography

Bamboo is a natural fiber composite with layered structure. Millions of years of evolution have endowed bamboo with the most effective structure in nature. The ingenious microstructure provides bamboo with excellent mechanical properties. Bamboo culm is composed of the cortex, a middle layer, and a pith ring. The cortex refers to the area starting from the periphery of the culm wall to the vascular bundles. The present study obtained the two-dimensional (2D) microstructure of bamboo cortex cells by optical microscopy and characterized the three-dimensional (3D) structure through high-resolution X-ray microtomography (µCT). The 2D anatomical parameters of cortex cells were measured to verify the reliability of cortical cell classification in 3D models. Based on the analysis, the bamboo cortex cells were classified into four layers: epidermis layer, hypodermis layer, transitional layer, and parenchyma layer. The total volume of the reconstructed area of interest in μCT was 7.85 × 106 µm3, in which the total pore volume of bamboo cortex was 2.84 × 106 µm3, the average pore volume of bamboo cortex was about 1.54 × 103 µm3. Thus the porosity was 36.1%, and the relative density was 0.639. Studies on bamboo anatomical structure, especially three-dimensional digital characterization, will enrich the bamboo microstructure database. Besides, the three-dimensional structure of the bamboo cortex revealed in this study can provide a reference for optimizing composite material hierarchy and biomimetic design.

Efficiently Integrated Desulfurization from Natural Gas over Zn-ZIF-Derived Hierarchical Lamellar Carbon Frameworks.

Selective removal of carbonyl sulfide (COS) and hydrogen sulfide (H2S) is the key step for natural gas desulfurization due to the highly toxic and corrosive features of these gaseous sulfides, and efficient and stable desulfurizers are urgently needed in the industry. Herein, we report a class of nitrogen-functionalized, hierarchically lamellar carbon frameworks (N-HLCF-xs), which are obtained from the structural transformation of Zn zeolitic imidazolate frameworks via controllable carbonization. The N-HLCF-xs possess the desirable characteristics of large Brunauer-Emmett-Teller surface areas (645-923 m2/g), combined primary three-dimensional microporosity and secondary two-dimensional lamellar microstructure, and high density of nitrogen base sites with enhanced pyridine ratio (17.52 wt %, 59.91%). The anchored nitrogen base sites in N-HLCF-xs show improved accessibility, which boosts their interaction with acidic COS and H2S. As expected, N-HLCF-xs can be employed as multifunctional and efficient desulfurizers for selective removal of COS and H2S from natural gas. COS was first transformed into H2S via catalytic hydrolysis, and the produced H2S was then captured and separated and catalyzed oxidation into elemental sulfur. The above continuous processes can be achieved with solo N-HLCF-xs, giving extremely high efficiencies and reusability. Their integrated desulfurization performance was better than many desulfurizers used in the area, such as activated carbon, β zeolite, MIL-101(Fe), K2CO3/γ-Al2O3, and FeOx/TiO2.

Rational design of hyperelastic semi-linear material and its application to elastic wave control

Incremental elastic wave in a hyperelastic semi-linear (SL) material can be purposely controlled by pre-deformation with help of hyperelastic transformation (HT) theory. However, this material model, assuming a linear stress-strain relation for large deformation, has neither been realized with naturally occurring materials nor through microstructure design. By balancing the stiffness of axial and rotational springs in a hexagonal mass-spring lattice, we propose a lattice prototype to realize the SL material. The performance of the model is systematically verified from static strain energy to wave property on different finitely deformed configurations. Based on this SL lattice, an elastic wave cloak is designed and validated through numerical simulation. This work provides the first two-dimensional (2D) microstructure model for realizing SL material and paves the way for elastic wave control with HT method.

Hard superellipse phases: particle shape anisotropy & curvature.

We report computer simulations of two-dimensional convex hard superellipse particle phases vs. particle shape parameters including aspect ratio, corner curvature, and sidewall curvature. Shapes investigated include disks, ellipses, squares, rectangles, and rhombuses, as well as shapes with non-uniform curvature including rounded squares, rounded rectangles, and rounded rhombuses. Using measures of orientational order, order parameters, and a novel stretched bond orientational order parameter, we systematically identify particle shape properties that determine liquid crystal and crystalline phases including their coarse boundaries and symmetry. We observe phases including isotropic, nematic, tetratic, plastic crystals, square crystals, and hexagonal crystals (including stretched variants). Our results catalog known benchmark shapes, but include new shapes that also interpolate between known shapes. Our results indicate design rules for particle shapes that determine two-dimensional liquid, liquid crystalline, and crystalline microstructures that can be realized via particle assembly.

A homogenised model for flow, transport and sorption in a heterogeneous porous medium

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium. We use homogenisation via the method of multiple scales to systematically upscale a novel problem involving cells of varying area to obtain effective continuum equations for macroscale flow and transport. The equations are characterised by the local porosity, a local anisotropic flow permeability, an effective local anisotropic solute diffusivity and an effective local adsorption rate. These macroscale properties depend non-trivially on the two degrees of microstructural geometric freedom in our problem: obstacle size and obstacle spacing. We exploit this dependence to construct and compare scenarios where the same porosity profile results from different combinations of obstacle size and spacing. We focus on a simple example geometry comprising circular obstacles on a rectangular lattice, for which we numerically determine the macroscale permeability and effective diffusivity. We investigate scenarios where the porosity is spatially uniform but the permeability and diffusivity are not. Our results may be useful in the design of filters or for studying the impact of deformation on transport in soft porous media.

Microstructuring of the end-surface for silver halide polycrystalline fibers to suppress Fresnel reflection

Silver halide polycrystalline infrared fibers (PIR) have unique properties such as excellent transmittance in the spectral range from 3 to 17 µm, while also being highly flexible, non-toxic, and non-hygroscopic. They are used in industry and medicine for CO2-laser power delivery, flexible infrared imaging, and remote process spectroscopy. While PIR fibers possess a quite low attenuation (0.1-0.5 dB/m) in the 8-12 µm range, their total transmittance is limited by significant Fresnel reflections at the fiber end faces due to the high refractive index of silver halide (>2.1). Functionalization of these surfaces with specially designed Anti-Reflective Microstructures (ARMs) enables a striking enhancement of fiber transmittance. In this work, direct imprinting (or embossing) of microstructures to fiber ends and their profiling with a microstructured knife was applied to fabricate such ARMs. The resulting two-dimensional Moth-eye microstructures and one-dimensional microgrooves at the PIR-fiber ends enable to an increase of fiber transmittance in a broadband range of (5-17 µm) as well as to reach up to 20% improvement for PIR-fiber laser cables used for power delivery of CO2-lasers at 10.6 µm.

Shape Measurement Method of Two-Dimensional Micro-Structures beyond the Diffraction Limit Based on Speckle Interferometry

A technique based on speckle interferometry for observing microstructures beyond the diffraction limit by detecting the spatial phase distribution of scattered light from microstructures has previously been reported. In this study, the development of this technique using a two-dimensional method is discussed. In order to observe general two-dimensional images, development of new technology in several stages is required. A two-dimensional filtering technique to reduce the noise component and a two-dimensional integration path to detect the three-dimensional shape of the surface are described in detail. As a first step toward observing complex two-dimensional structures in the future, it is investigated that directional two-dimensional information such as fibrous materials and micro-linear structures can be visually captured and treated as meaningful two-dimensional structures. As a result, it is shown that it is possible to observe fine two-dimensional letters with a line width of 100 nm, which is beyond the diffraction limit of the objective lens, demonstrating the effectiveness of the observation technique for microstructures by phase detection.

Towards accurate prediction for ultra-low carbon tempered martensite property through the cross-correlated substructures

Accurately predicting properties of steels containing martensite by using models based on traditional strengthening mechanisms remains a challenge. In this study, a smart machine learning model possessing two-dimensional microstructure input terminals was developed using high-throughput experiments and machine learning on steels for low-temperature service. An algorithm based on a convolutional neural network enriched with the two-dimensional input terminals increased the prediction accuracy, achieving an average microhardness error of as low as 14.37 HV for the validation set. The improved prediction accuracy is ascribed to the comprehensive strengthening mechanism and coupling of strengthening effects contained in the multifarious input terminals. The information acquisition and cross-correlation of substructures related to strengthening mechanism played an important role. The reported strategy can deepen the cognition of the strengthening mechanism of tempered martensite. It is promising for application to different steels containing tempered martensite.

Phase-field modeling of magnetic field-induced grain growth in polycrystalline metals

A constitutive model for diffuse interface description of magnetic field-induced grain boundary migration in polycrystalline metals is developed based on the laws of thermodynamics. Within this phase field modeling framework, simultaneous minimization of the total grain boundary energy and the stored magnetic energy within grains provides the driving force for grain growth in a polycrystal material exposure to a magnetic field. Using the available experimental data, phase field simulations of magnetic field induced grain growth in bicrystalline zinc and polycrystalline titanium with two-dimensional columnar microstructure are performed and the model is validated by demonstrating a qualitative and quantitative match with experimental data. Using the validated constitutive model, the effects of magnetic field intensity and direction on evolution of microstructure and polycrystalline texture in titanium are investigated. Quantitative simulation results show that under certain magnetic field directions and sufficient magnetic field intensity, the magnetic energy minimizing driving force can overcome the curvature driving force and cause texture evolution towards less magnetic energy grain orientations during annealing. However, magnetic fields with insufficient intensity or improper direction have negligible effect on grain coarsening by nearly normal grain growth. The desired magnetic field direction and intensity are quantitatively presented for cold-rolled and annealed sheet titanium samples.

Toughening of interface networks through the introduction of weak links

The resistance of polycrystalline materials to intergranular fracture depends on the toughness of the interfaces between neighboring grains. Using finite element simulations on model, two-dimensional microstructures, we demonstrate that the steady-state crack growth resistance of a polycrystal that contains exclusively high toughness interfaces is suboptimal: its crack growth resistance may be increased by introducing a minority fraction of weak interfaces at random locations within the interface network. Furthermore, the weaker are these interfaces, the greater is their toughening effect. These weak interfaces toughen the material through crack deflection and branching, nucleation of secondary cracks, and inelastic dissipation within intact interfaces. Our findings suggest that fracture resistance-oriented material development should not aim to eliminate all weak interfaces, but rather judiciously incorporate a low fraction of them.

Design, fabrication and verification of a novel auxetic microstructure using topology optimization

This research presents a numerical method to design a two-dimensional auxetic microstructure with negative Poisson’s ratios. The method is established by combining the finite element method (FEM) with two different optimization procedures called bi-directional evolutionary structural optimization (BESO) and solid isotropic material with penalization (SIMP), respectively. The results show that by choosing any of the two methods of optimization (FEM and BESO or FEM and SIMP), each with a different objective function, it is possible to create microstructures that show negative Poisson’s ratio. In addition, there is a significant resemblance between the results of both optimization methodologies. The final part of this study is to verify the outcome of optimization, both numerically and experimentally using three-dimensional (3D) printing techniques.

Computational evaluation of long-term ravelling susceptibility of Permeable Friction Courses (PFC)

Ravelling is a main distress in Permeable Friction Courses (PFC). This damage process is enhanced by the presence of moisture and ageing, which further reduces the overall durability of the mixtures. This study uses Finite Element (FE) methods to assess long-term ravelling susceptibility of PFC. Different two-dimensional (2D) PFC microstructures were randomly generated through a Microstructure Generator (MG) and Discrete Element (DE) gravimetric methods. These microstructures were located on top of a conventional pavement and subjected to a moving wheel load under different traffic operation conditions. PFC ravelling was assumed to occur at the asphalt mortar located at the stone-on-stone contacts. The linear viscoelastic and fracture properties of the PFC asphalt mortar were experimentally obtained after subjecting the material to long-term ageing conditions and multiple water moisture cycles, which represent several in-service years. Zero thickness Cohesive Zone Elements (CZE) were included within the mortar-mortar contacts of the PFC to better quantify the potential initiation of ravelling. The results show that the ravelling susceptibility of a PFC is drastically affected by the loading conditions (e.g., load magnitude, vehicle breaking over the pavement, vehicle speed) and the environmental and mechanical degradation of the asphalt mortar when subjected to in-service conditions.

An FFT framework for simulating non-local ductile failure in heterogeneous materials

The simulation of fracture using continuum ductile damage models attains a pathological discretization dependence caused by strain localization, after loss of ellipticity of the problem, in regions whose size is connected to the spatial discretization. Implicit gradient techniques suppress this problem introducing some inelastic non-local fields and solving an enriched formulation where the classical balance of linear momentum is fully coupled with a Helmholtz-type equation for each of the non-local variable. Such Helmholtz-type equations determine the distribution of the non-local fields in bands whose width is controlled by a characteristic length, independently on the spatial discretization. The numerical resolution of this coupled problem using the Finite Element method is computationally very expensive and its use to simulate the damage process in 3D multi-phase microstructures becomes prohibitive.In this work, we propose a novel FFT-based iterative algorithm for simulating gradient ductile damage in computational homogenization problems. In particular, the Helmholtz-type equation of the implicit gradient approach is properly generalized to model the regularization of damage in multi-phase media, where multiple damage variables and different characteristic lengths may come into play. In the proposed iterative algorithm, two distinct problems are solved in a staggered fashion: (i) a conventional mechanical problem via a FFT-Galerkin solver with mixed macroscopic loading control and (ii) the generalized Helmholtz-type equation using a Krylov-based algorithm combined with an efficient pre-conditioner. The numerical implementation is firstly validated on simple two-dimensional microstructures, showing identical responses for different spatial discretizations and reproducing a ductility change dependent on the characteristic length. Finally, the robustness and efficiency of the algorithm is demonstrated in the simulation of failure of complex 3D particle reinforced composites characterized by millions of degrees of freedom.

Pore-Scale Modeling of Electrokinetics in Geomaterials

Pore-scale finite-volume continuum models of electrokinetic processes are used to predict the Debye lengths, velocity, and potential profiles for two-dimensional arrays of circles, ellipses and squares with different orientations. The pore-scale continuum model solves the coupled Navier–Stokes, Poisson, and Nernst–Planck equations to characterize the electro-osmotic pressure and streaming potentials developed on the application of an external voltage and pressure difference, respectively. This model is used to predict the macroscale permeabilities of geomaterials via the widely used Carmen–Kozeny equation and through the electrokinetic coupling coefficients. The permeability results for a two-dimensional X-ray tomography-derived sand microstructure are within the same order of magnitude as the experimentally calculated values. The effect of the particle aspect ratio and orientation on the electrokinetic coupling coefficients and subsequently the electrical and hydraulic tortuosity of the porous media has been determined. These calculations suggest a highly tortuous geomaterial can be efficient for applications like decontamination and desalination.

Modeling damage evolution of graphene/aluminum composites considering crystal cracking and interface failure

Graphene is a significant reinforcement in metal matrix composites by virtue of its superior mechanical properties. The cracking of metal crystal and the failure of graphene-metal interface are the main reasons for the decrease of mechanical properties of graphene/metal composites, but the damage mechanism of that is not clear. In this paper, a novel two-dimensional microstructure model of graphene/polycrystalline metal composites is established by a self-developed structure modeling procedure. According to the actual structure of graphene/metal composites, the numbers, sizes, orientations, arrangements of graphene and grain can be controlled respectively. Moreover, by employing the method of combining the crystal plasticity finite element method (CPFEM) and the cohesive zone model (CZM), the damage mechanism of graphene/aluminum (Al) composites on polycrystalline Al matrix, graphene-reinforcement and graphene-Al interface under tensile load is revealed from the mesoscale for the first time, then the effects of graphene morphology and initial microcracks on the failure behavior and overall mechanical properties of graphene/Al composites are fully captured. This study provides a strong theoretical support and inspiration for the construction of graphene/Al composites with excellent properties.

Dye-assembled two-dimensional porous HMX for enhanced energy release and safety performance

The potential practical applications of high-energy 1,3,5,7-tetranittro-1,3,5,7-tetrazocane (HMX) are hindered by their unfavorable safety behavior and sluggish thermal decomposition. This paper proposes dye-assisted assembly of HMX crystals with crystal violet (CV) as soft templates (denoted as CV-HMX). As revealed by the XPS and molecular-dynamics simulations, preferred electrical interactions between HMX and conjugation electrons in planar CV molecular ensure that the resultant CV-HMX has a two-dimensional (2D) microstructure. The BAM impact sensitivity of CV-HMX is 12.5 ​J, higher than that of raw-HMX (5 ​J) and HMX recrystallized from pure water (PW-HMX; 4.5 ​J). Meanwhile, the BAM friction sensitivity of CV-HMX is 320 ​N, also much higher than that of PW-HMX (96 ​N) and raw-HMX (88 ​N). In addition, the decomposition kinetics of CV-HMX is improved due to its large specific surface area and high pore volume. Such dye-template assembly can be applied to a large number of systems, indicating that the method proposed in this work is universal. This work provides synergistic template regulation on morphology and pore structure using general dye-assisted assembly, holding great promises in developing practically viable high energy materials with favorable sensitivity and improved energy release performance.

Random generation of 2D PFC microstructures through DEM gravimetric methods

Computational mechanics has proven to be a useful method to understand and assess the mechanical behaviour and main degradation mechanisms of Porous Friction Courses (PFC) at the microstructural level. However, a common limitation when preparing these models is the difficulty to achieve realistic microstructures. The ideal model to evaluate the mechanical behaviour and the degradation mechanisms of PFCs would use a three-dimensional (3D) geometry of the mixture with realistic aggregate shape, angularity, and gradation. However, these models are computationally expensive and typically related with numerical instabilities. This paper proposes a novel methodology to generate two-dimensional (2D) random PFC microstructures using gravimetric methods through Discrete Element Method (DEM) modelling. The proposed methodology was calibrated to generate coarse aggregates with realistic and controlled morphological properties. The produced 2D microstructures were implemented in the commercial Finite Element Method (FEM) software Abaqus® and, after coating the particles with asphalt mortar, they were used to verify that the microstructures were able to reproduce the mechanical response –measured through the dynamic axial modulus– of an actual PFC mixture tested in the laboratory. The results show that the proposed methodology is able to produce microstructures with the same dynamic modulus than an actual PFC mixture at different loading frequencies. Among other applications, this methodology could be used to estimate the mechanical properties of PFC mixtures or to assess the expected performance and durability of a specific PFC under realistic field conditions.

Micromechanical modelling of pervious concrete reinforced with treated fibres

Pervious concrete has been widely used in parking lots and airport fields. However, excessive cracking and spalling issues of pervious concrete remain a challenge for its adoption in wider applications, since its binding material proportion is low and the use of fine aggregates is nearly zero. When loaded in compression, failure appears first in the weak concrete zone, induced by the random distribution of voids. The process continues until failure of the whole specimen. Fibre-reinforcement delays crack generation and enhances the strength of the host matrix. However, the bonding mechanism between the fibre and concrete matrix is a controversy in the literature. In this study, the influence of polypropylene fibre inclusion on the strength and stiffness of pervious concrete microstructure was studied through delicate interface modelling. Two-dimensional microstructures of pervious concrete were generated using Matlab and Ansys parametric design languages. A cohesive-zone technique was then used to model the interface between fibres and the concrete matrix. Load–displacement plots were thus obtained in Ansys for specimens under compression for various void–fibre percentages and different treated interface properties.

Current divisions and distributed Joule heating of two-dimensional grid microstructures

This paper presents current divisions and distributed Joule heating of two-dimensional (2D) grid microstructures. The current divisions on 2 × 2, 4 × 4, and n × n grid microstructures made of the same conductive beams are analyzed theoretically, and Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL) are employed to determine the current division factors and directions under different voltage input cases. The equivalent resistances and Joule heating power are therefore derived. 2D 2 × 2 grid microstructures made of gold (60 nm in thickness) and those made of near-equiatomic NiTi (850 nm in thickness) for various independent voltage input cases are fabricated by electron-beam evaporation and co-sputtering, respectively. The equivalent resistances of these grid microstructures are measured by four-terminal resistance measurement at ambient conditions, which show a good agreement with the theoretical results. Further investigation on the electrical resistivities of evaporated gold layer (4.85 × 10–8 Ω m) and co-sputtered NiTi (1.23 × 10–5 Ω m) reveals that the influences of scale effect and fabrication process on the resistivity cannot be neglected. As such, it is found to be necessary to consider the materials’ resistivity in the fabricated grid microstructures before their electro-thermal analysis.