Random Microstructure Research Articles

Prediction of the cohesive strength for simulating composite delamination by a micro-mechanical model based on random RVE

A three-dimensional micro-mechanical model based on the random RVE is developed to predict the cohesive strengths of all the three delamination modes in unidirectional laminates. The interface RVE with two layers of randomly distributed fibers is established to represent the cohesive layer. Two types of random microstructure corresponding to the square and hexagonal periodic packing are defined. Delamination is assumed to be induced by matrix yield and cracking. The extended linear Drucker–Prager yield criterion and a paraboloidal yield criterion are used to predict the crack initiation in the matrix and compared with the major principal stress criterion. The predicted results show that the cohesive strengths are largely dependent on the type of random microstructure and the random microstructure morphology described by the minimum inter-fiber distance and the fiber alignment angle. Global sensitivity analysis based on a polynomial chaos expansion surrogate model is done to quantify the influence of the geometrical parameters on the variance of the cohesive strengths. Moreover, the predicted cohesive strengths are found to be unequal.

Statistical characterization and reconstruction of heterogeneous microstructures using deep neural network

Heterogeneous materials, whether natural or artificial, are usually composed of distinct constituents present in complex microstructures with discontinuous, irregular and hierarchical characteristics. For many heterogeneous materials, such as porous media and composites, the microstructural features are of fundamental importance for their macroscopic properties. This paper presents a novel method to statistically characterize and reconstruct random microstructures through a deep neural network (DNN) model, which can be used to study the microstructure–property relationships. In our method, the digital microstructure image is assumed to be a stationary Markov random field (MRF), and local patterns covering the basic morphological features are collected to train a DNN model, after which statistically equivalent samples can be generated through a DNN-guided reconstruction procedure. Furthermore, to overcome the short-distance limitation associated with the MRF assumption, a multi-level approach is developed to preserve the long-distance morphological features of heterogeneous microstructures. A large number of tests have been conducted to compare the reconstructed and target microstructures in both morphological characteristics and physical properties, and good agreements are observed in all test cases. The proposed method is efficient, accurate, versatile, and especially beneficial to the statistical reconstruction of 2D/3D microstructures with long-distance correlations.

Numerical investigation of delamination onset and propagation in catalyst layers of PEM fuel cells under hygrothermal cycles

Durability is one of the main obstacles that inhibits the commercialization of polymer electrolyte membrane (PEM) fuel cells for transport applications, in which the microstructure of the catalyst layers (CLs) deteriorates under dynamic loading operation. In this study, CLs’ naturally random porous structure is simplified to be a random three-phase microstructure consisting of ionomers, catalyst agglomerates and pores, and the onset and growth of delamination process between the ionomer and catalyst agglomerate is investigated numerically by considering the catalyst agglomerate as elastic while the ionomer is elasto-viscoplastic, influenced by the cell assembly force arising from the cell clamping and variations in temperature and relative humidity. It is found that increasing clamping stress delays the delamination onset but has marginal effect on delamination propagation. The amplitude of hygrothermal cycles is the dominating factor in delamination and more frequent startup/shutdown of PEM fuel cells alleviates the delamination. Correlation between the rate of plastic strain accumulation in the ionomer and the interface delamination has been observed.

Microscopic Damage Model for Fibrous Composites Considering Randomness in Constituent Materials

For the multiscale damage behaviour simulation of advanced materials with hierarchical and random heterogeneous microstructures such as fibrous composites by finite element method, the mathematical homogenization method has been extended to the stochastic nonlinear multiscale method. A first-order perturbation based stochastic homogenization method was developed to calculate the microscopic strain, as well as the homogenized macroscopic properties considering randomness in the mechanical properties of constituent materials. Based on the calculated stochastic microscopic strain, the damage simulation framework was proposed for fibrous composites. For a demonstrated application, a numerical example of a single short fiber reinforced plastic composite was carried out. The damage propagation in the interphase between fiber and matrix was predicted in a stochastic way considering the physical random parameters for the interphase material model. The influences of the randomness on damage volume fraction and damage propagation of the interphase were discussed.

Nonlinear dielectric properties of random paraelectric-dielectric composites

The challenge of designing new tunable nonlinear dielectric materials with tailored properties has attracted an increasing amount of interest recently. Herein, we study the effective nonlinear dielectric response of a stochastic paraelectric-dielectric composite consisting of equilibrium distributions of circular and partially penetrable disks (or parallel, infinitely long, identical, partially penetrable, circular cylinders) of a dielectric phase randomly dispersed in a continuous matrix of a paraelectric phase. The random microstructures were generated using the Metropolis Monte Carlo algorithm. The evaluation of the effective permittivity and tunability were carried out by employing either a Landau thermodynamic model or its Johnson’s approximation to describe the field-dependent permittivity of the paraelectric phase and solving continuum-electrostatics equations using finite element calculations. We reveal that the percolation threshold in this composite governs the critical behavior of the effective permittivity and tunability. For microstructures below the percolation threshold, our simulations demonstrate a strong nonlinear behaviour of the field-dependent effective permittivity and very high tunability that increases as a function of dielectric phase concentration. Above the percolation threshold, the effective permittivity shows the tendency to linearization and the tunability dramatically drops down. The highly reduced permittivity and extraordinarily high tunability are obtained for the composites with dielectric impenetrable disks at high concentrations, in which the triggering of the percolation transition is avoided. The reported results cast light on distinct nonlinear behaviour of 2D and 3D stochastic composites and can guide the design of novel composites with the controlled morphology and tailored permittivity and tunability.

Random organic nano-textured microstructures formed by photoexcitation for light extraction of blue OLEDs

Organic light-emitting diodes require efficient and inexpensive light extraction methods for applications toward lighting and displays. Here, a facile and effective method for fabricating random organic microstructures for efficient light extraction from blue OLEDs is presented. Simple drop casting of a TCTA and B4PyMPM mixed solution followed by UV curing results in films with irregular-shaped microstructures (DACMs), ideal for light extraction without diffraction patterns. An external quantum efficiency (EQE) of 44.3% is realized by attaching DACMs formed on a polymer film to a blue phosphorescent OLED. The efficiency is improved by 35% compared to a planar device without the light extraction layer, greater than the 22% improvement obtained by using hemispherical-shaped microlens arrays. The method is useful for OLED lighting and potentially in displays because of the simple fabrication method that is applicable to a large area on rigid or flexible substrates, the low material cost, the insolubility of the microstructure in alkyl halide solvents such as chloroform, and the controllability of the structure through the solution process. Furthermore, we fully discuss on the EQE, enhancement ratio and the efficiency of light extraction structure (ELOS). We show that enhancement ratio and ELOS should be obtained using the optimized device structure as the reference device to be useful indicators for the effectiveness of a light extraction structure.

Entropy decay during grain growth

Materials with random microstructure are characterized by additional thermodynamic parameters, entropy and temperature of microstructure. It has been argued that there is one more law of thermodynamics: entropy of microstructure decays in isolated systems. In this paper, we check this assertion experimentally for the process of grain growth. We show that entropy of grain structure decays indeed as expected. We study also the equation of state for microstructure entropy. In general, microstructure entropy should be a function of microstructure energy and the average grain size. We observed that the equation of state degenerates, and there is a universal dependence of microstructure entropy on microstructure energy, at least at the stage of self similar grain growth.

Tailoring ductile-phase toughened tungsten hierarchical microstructures for plasma-facing materials

Biological materials, such as bones, nacre, etc., have been found to exhibit attractive and unique combinations of stiffness, strength and fracture toughness. Research has been conducted in various engineering areas to mimic the naturally hierarchical microstructures or nanostructures of these materials to produce materials with optimum stiffness, high strength and fracture toughness for their intended structural applications. In the same objective, this work applies a multiscale microstructural approach recently developed (J. Nucl. Mater., (2018) 508: 371–384) to investigate the deformation and fracture behavior of ductile phase toughened tungsten (W) materials such as tungsten-nickel/iron (W-Ni/Fe) composites that possess lamellar-like and hierarchical “brick-and-mortar” (BAM) microstructures. First, the approach is used to simulate tensile loading of W-Ni/Fe specimens cut out from hot-rolled W-Ni/Fe plates which possess lamellar-like microstructures. The finite element model of the gage section of the specimen consists of a W-Ni/Fe dual-phase microstructural domain in which the constitutive behaviors of W and Ni/Fe phases are described by an elastic-plastic damage model. The predicted material stress-strain response and crack pattern development as a function of loading are then compared to the corresponding experimental results to determine the constitutive model parameters for W and Ni/Fe. Subsequently, the model parameters are used to analyze W-Ni/Fe BAM microstructures that are artificially created to investigate the effects of microstructural features and morphologies on the composite stress-strain response, damage, and fracture patterns. The modeling shows that regular BAM microstructures that experience bridging mechanism combined with crack penetration across W-phase regions exhibit significantly higher strengths than the rather random lamellar-like microstructures. More significantly, however adjusting the brick’s length-to-height ratio, the BAM microstructure can be designed to allow a more distributed damage zone which leads to increased strength, ductility and fracture energy.

Mechanical properties and deformation mechanisms of gradient nanostructured metals and alloys

Inspired by the gradient structures of biological materials, researchers have explored compositional and structural gradients for about 40 years as an approach to enhance the properties of engineering materials, including metals and metallic alloys. The synthesis of various gradient nanostructured materials, such as gradient nanograined, nanolaminated nd nanotwinned metals and alloys, has provided new opportunities to understand gradient-related mechanical behaviour. These emerging gradient materials often exhibit unprecedented mechanical properties, such as strength–ductility synergy, extraordinary strain hardening, enhanced fracture and fatigue resistance, and remarkable resistance to wear and corrosion, which are not found in materials with homogeneous or random microstructures. This Review critically assesses the state of the art in the field of gradient nanostructured metallic materials, covering topics ranging from the fabrication and characterization of mechanical properties to underlying deformation mechanisms. We discuss various deformation behaviours induced by structural gradients, including stress and strain gradients, the accumulation and interaction of new dislocation structures, and unique interfacial behaviour, as well as providing insight into future directions for the development of gradient structured materials. Gradient nanostructured metals and alloys are an emerging class of materials that exhibit a combination of excellent mechanical properties that are not possessed by their homogeneous counterparts. This Review assesses the fabrication, characterization and deformation behaviour of these materials, as well as the challenges and future directions of the field.

Properties of poly(butylene-co-isosorbide succinate) after blown film extrusion

In this study, the sugar-based monomer isosorbide (IS) was used to improve the properties of poly(butylene succinate) (PBS). The molecular weight of all copolyesters was approximately 100 000 g/mol, and they presented a random microstructure combined with excellent thermal stability. The IS-containing copolyesters were all semicrystalline, and both their crystallinity and crystallization rate decreased with the introduction of the rigid structure of IS into the PBS chain. IS also had an effect on the mechanical properties and gas barrier properties of the copolyesters. Blown films from poly(butylene-co-isosorbide succinate) copolyesters were prepared. The gas barrier and mechanical properties achieved a significant improvement after blowing.

Stochastic micromechanics-based investigations for the damage healing of unsaturated concrete using electrochemical deposition method

The (micro-) cracks or (micro-) voids will lead to the damage of concrete material. A stochastic micromechanical framework is proposed to investigate the damage healing of the unsaturated concrete with the electrochemical deposition method. Stochastic micromechanical representations are presented based on the material’s random microstructures. Differential scheme-based multilevel homogenization procedures are proposed to quantitatively predict the effective properties of the repaired concrete. The probability density functions are obtained for the material’s effective properties with an efficient stochastic simulation framework, which is composed of the univariate approximation for the multivariate function, Newton interpolations and Monte Carlo simulations. Numerical examples are employed to verify the proposed stochastic micromechanical framework, which indicates that the presented framework is computationally efficient and capable of describing the electrochemical deposition method healing process for the unsaturated concrete considering the material’s inherent randomness. Finally, the influences of the saturation degrees and the equivalent aspect ratios on the probabilistic behavior of the repaired concrete are discussed on the basis of the proposed models.

Enhanced Backscattering of a partially coherent field from an anisotropic random lossy medium

The weak localization or enhanced backscattering phenomenon has received a lot of attention in the literature. The enhanced backscattering cone refers to the situation that the wave backscattered by a random medium exhibits an enhanced intensity in a narrow cone around the incoming wave direction. This phenomenon can be analyzed by a formal path integral approach. Here a mathematical derivation of this result is given based on a system of equations that describes the second-order moments of the reflected wave. This system derives from a multiscale stochastic analysis of the wave field in the situation with high-frequency waves and propagation through a lossy medium with fine scale random microstructure. The theory identifies a duality relation between the spreading of the wave and the enhanced backscattering cone. It shows how the cone, its regularity and width relate to the statistical structure of the random medium. We discuss how this information in particular can be used to estimate the internal structure of the random medium based on observations of the reflected wave.

Poisson’s ratio of porous and cellular materials with randomly distributed isometric pores or cells

AbstractThe porosity dependence of Poisson's ratio of materials with random microstructure is investigated via analytical and numerical modeling. It is shown that all analytical models predict porosity independence if the solid Poisson ratio is 0.2 and for low porosities a converging trend toward this value with increasing porosity. From all theory‐based relations, only power‐law and exponential relations allow for auxetic behavior. Numerical calculations on computer‐generated digital microstructures (overlapping and isolated spherical pores, pores between overlapping spherical grains, wall‐based cellular materials/closed‐cell foams, and strut‐based cellular materials/open‐cell foams) confirm the general qualitative trends of the analytical models, although a closer look reveals significant quantitative differences. Cellular materials and foams exhibit similar features as porous materials in general, but lack their converging trend toward values around 0.2. Comparison of our results with the classical Roberts‐Garboczi results shows good agreement, with subtle differences due to the different microstructures generated.

Fourier spectral methods for phase field fracture modelling of CMCs

Numerical homogenization of multiphase brittle materials, such as ceramic matrix composites is obviously a computationally intensive task. Common approach involving multiscale finite element models remains quite limited to scientific applications instead of being a reasonable alternative for analytical constitutive models. Despite the exponential growth of computational resources (known as Moore’s law) numerical complexity of the underlying algorithms is simply too high to ensure proper scaling to millions of elements. One of the approaches in-between continuous and discrete mechanics is the use of fast Fourier transform (FFT). The aim of this paper is to extend FFT-based methodology beyond its usual elastic regime, using mathematical formalism developed earlier for FE by means of variational principles. Governing equations are formulated in the frequency domain and solved iteratively on a parallel system. Well-known computational specifics of the discrete FFT algorithm itself provide uncompromised efficiency and a first, promising step towards truly multiscale mechanical analysis of random microstructures.

An experimental and numerical study on masonry triplets subjected to monotonic and cyclic shear loadings

This paper presents an experimental and numerical study on the mechanical behaviour of masonry triplets subjected to monotonic and cyclic shear loadings. Masonry triplets were constructed with fired bricks bonded together with three different in composition (i.e. cement-to-sand ratios) mortars. Shear tests on triplets show that cyclic loading significantly reduces the peak shear strength (typically around 18%) with respect to monotonic loads, regardless of the mortar composition. The shearing behaviour of the triplets obtained from the experiments were successfully reproduced using an innovative discrete element modelling strategy in which masonry units and mortar were represented by a series of irregular particles (i.e. through Voronoi-shaped particles) with a fictitious random microstructure. Numerical results highlight that cyclic shear strength reduction can be attributed to the progressive formation of cracks in the mortar layers along with the cyclic loading. These observations provide new insight into behaviour of structural masonry and lead to suggestions for improving assessment techniques for masonry structures subjected to combined actions of compression and shear.

Stress intensity factors and crack propagation of metal-ceramic random microstructures

This paper is concerned with the crack analysis of RVE (representative volume element) microstructures of metal-ceramic phase composite. The detailed random RVE microstructure models of metal-ceramic phase composite are generated by a mathematical RMDF (random morphology description functions) micro modeling technology. The dispersion pattern and scale of random microstructure models are controlled by the volume fractions V of base materials and the total number N of Gaussian functions. The stress intensity factors (SIF) and the crack propagation trajectories are evaluated by the interaction integral and predicted by Paris law. These crack characteristics are investigated with respect to the model scale N and the initial crack length, and also compared with those of homogenization models. Through the numerical results, it is observed that both SIFs and crack propagation trajectories are remarkably influenced by the crack length, the model scale N and the dispersion pattern of RVE microstructure.

A Peridynamics-Based Micromechanical Modeling Approach for Random Heterogeneous Structural Materials.

This paper presents a peridynamics-based micromechanical analysis framework that can efficiently handle material failure for random heterogeneous structural materials. In contrast to conventional continuum-based approaches, this method can handle discontinuities such as fracture without requiring supplemental mathematical relations. The framework presented here generates representative unit cells based on microstructural information on the material and assigns distinct material behavior to the constituent phases in the random heterogenous microstructures. The framework incorporates spontaneous failure initiation/propagation based on the critical stretch criterion in peridynamics and predicts effective constitutive response of the material. The current framework is applied to a metallic particulate-reinforced cementitious composite. The simulated mechanical responses show excellent match with experimental observations signifying efficacy of the peridynamics-based micromechanical framework for heterogenous composites. Thus, the multiscale peridynamics-based framework can efficiently facilitate microstructure guided material design for a large class of inclusion-modified random heterogenous materials.

FEA-Net: A physics-guided data-driven model for efficient mechanical response prediction

An innovative physics-guided learning algorithm for predicting the mechanical response of materials and structures is proposed in this paper. The key concept of the proposed study is based on the fact that physics models are governed by Partial Differential Equation (PDE), and its loading/response mapping can be solved using Finite Element Analysis (FEA). Based on this, a special type of deep convolutional neural network (DCNN) is proposed that takes advantage of our prior knowledge in physics to build data-driven models whose architectures are of physics meaning. This type of network is named as FEA-Net and is used to predict the mechanical response under external loading. Thus, the identification of mechanical system parameters and the computation of its responses are treated as the learning and inference of FEA-Net, respectively. Case studies on multi-physics (e.g., coupled mechanical–thermal analysis) and multi-phase problems (e.g., composite materials with random micro-structures) are used to demonstrate and verify the theoretical and computational advantages of the proposed method.

Representative Volume Element for Mechanical Properties of Carbon Nanotube Nanocomposites Using Stochastic Finite Element Analysis

AbstractThe aim of this study is to present a representative volume element (RVE) for nanocomposites with different microstructural features using a stochastic finite element approach. To that end, computer-simulated microstructures of nanocomposites were generated to include a variety of uncertainty present in geometry, orientation, and distribution of carbon nanotubes. Microstructures were converted into finite element models based on an image-based approach for the determination of elastic properties. For each microstructure type, 50 realizations of synthetic microstructures were generated to capture the variability as well as the average values. Computer-simulated microstructures were generated at different length scales to determine the change in mechanical properties as a function of length scale. A representative volume element is defined at a length scale beyond which no change in variability is observed. The results show that there is no universal RVE applicable to all properties and microstructures; however, the RVE size is highly dependent on microstructural features. Microstructures with agglomeration tend to require larger RVE. Similarly, random microstructures require larger RVE when compared with aligned microstructures.

Legendre polynomial-based stochastic micromechanical model for the unsaturated concrete repaired by EDM

A Legendre polynomial-based stochastic micromechanical framework is proposed to quantify the unbiased probabilistic behavior for the unsaturated concrete repaired by the electrochemical deposition method (EDM). By following the authors’ previous works, a deterministic micromechanical model with new multilevel homogenization scheme for the repaired unsaturated concrete is presented based on the material’s microstructures. With the stochastic descriptions for the microstructures of the repaired unsaturated concrete, the deterministic framework is extended to stochastic. The unbiased probabilistic behavior of the repaired concrete is reached by incorporating the Legendre polynomial approximations and the Monte Carlo simulations. The predictions herein are then compared with the available experimental data, existing models and the commonly used probability density functions, which indicate that the presented stochastic micromechanical framework is capable of characterizing the EDM healing process for unsaturated concrete considering the material’s random microstructure. Finally, the statistical effects of the deposition products and unsaturated pores are discussed.