Digital Microstructures Research Articles

Three-dimensional reconstruction of porous media by fusing multi-grid image features based on extended feature pyramid network

Microstructural analysis of porous media has significant research value in the study of their macroscopic properties. An accurate reconstruction of the digital microstructure model is a prerequisite for understanding their physical properties and transport properties. Deep learning can accurately extract features from training images for a fast and precise reconstruction of porous media. The reconstruction methods based on deep learning have yielded important achievements in the reconstruction of porous media. Aiming at the complex morphology and multi-scale image information of porous media, this paper proposes a generic end-to-end deep learning-based encoder–decoder generative method for the reconstruction of porous media from a single 2D image. This paper designs an extended feature pyramid network encoder to extract image features of different resolutions and different scales, and a generator network incorporating multi-scale image information. Through the training process of the network, the final three-dimensional images that meets certain requirements are generated by means of confrontation. By introducing the loss function of the pattern density function and the loss function of Wasserstein distance with gradient penalty, we constrain the reconstructed 3D structures. Finally, the reconstructed 3D structures and the target 3D structures are visualized to compare their similar morphologies. The morphological parameter indicators of the reconstructed 3D structures were line with those of the target 3D structure. The microstructure parameters of the 3D structures were also compared and analyzed. For complex porous media images, our method can achieve diverse, accurate, and stable 3D reconstruction.

Modelling of the microstructure and thermal conductivity of SiC-bonded diamond materials

Materials with high thermal conductivity are required in a wide range of thermal management applications. Silicon carbide (SiC) bonded diamond materials, which can be produced without pressure, are a possible candidate for such applications. They exhibit thermal conductivities >650 W/(m·K) depending on the diamond content, diamond grain size and residual silicon content. It is difficult to experimentally determine the influence of these factors on the thermal conductivity separately, as changing one of these parameters affects the other parameters. Therefore, a method for generating digital microstructures of SiC- bonded diamond materials was developed and the thermal conductivity was calculated as a function of the grain size These data were compared with real structures.

Stochastic reconstruction and performance prediction of cathode microstructures based on deep learning

The effective properties of lithium-ion battery (LIB) cathode are determined by both the volume fractions of constituents and the morphological features of microstructure. However, it is difficult to establish an accurate quantitative relationship between the macroscopic effective properties and microstructural features. Deep learning techniques, due to their exceptional nonlinear fitting capabilities, have been widely applied in various complex fields. Our study presents a generation scheme of numerous three-dimensional (3D) digital microstructures of cathode, using a deep convolutional neural network (CNN)-based stochastic reconstruction algorithm combining with the scanning electron microscope (SEM) images. The reconstructed samples are substituted with the corresponding finite element (FE) models, and the effective mechanical and electrochemical properties are assessed through the FE-based homogenization theory. Finally, the generated cathode samples and their effective properties are used to train the 3D CNN for performance prediction. This study demonstrates that the deep learning approaches can accurately and rapidly reconstruct the microstructure of cathode and predict their effective properties. Furthermore, the established framework can be extended to other heterogeneous materials.

A fast and flexible algorithm for microstructure reconstruction combining simulated annealing and deep learning

Microstructural analyses of porous media have considerable research value when studying of macroscopic properties,and the accurate reconstruction of a digital microstructure model is an important component of this research. Computational reconstruction algorithms for microstructures have attracted much attention due to their low cost and excellent performance. However, achieving faster and more efficient reconstruction remains a challenge for computational reconstruction algorithms. The bottleneck lies in the computational reconstruction algorithms themselves, which are either too slow (traditional reconstruction algorithms) or not flexible to the training process (deep learning reconstruction algorithms). To address these limitations, we propose a fast and flexible deep learning algorithm using a neural network based on an improved simulated annealing framework (ISAF-NN). The proposed algorithm adopts structural information of the reference image to guide the network design, and uses the description function to extract feature distribution of the reference image as the objective function to complete the network optimization. Benefit from the network structure is simple and flexible, the proposed algorithm can complete training and reconstruction in a short time. By adjusting the input size, the algorithm can also achieve arbitrary sized reconstruction. The proposed algorithm is experimentally applied to several materials to verify its effectiveness and generalizability.

Deep learning enhanced Watershed for microstructural analysis using a boundary class semantic segmentation

The mechanical properties of the materials are determined by the size and morphology of fine microscopic features. Quantitative microstructural analysis is a key factor to establish the correlation between the mechanical properties and the thermomechanical treatment under which material condition has been achieved. As such, microstructural analysis is a very important and complex task within the manufacturing sector. Published standards are used for metallographic analysis but typically involve extensive manual interpretation of grain boundaries, resulting in measurements that are slow to produce, difficult to repeat and highly subjective. Computer vision and the evolution of artificial intelligence in the past decade can offer solutions to such problems. Deep learning and digital image processing techniques allow digital microstructural analysis to be automated using a fast and repeatable method. This paper proposes a novel boundary class semantic segmentation approach (BCSS) to identify each phase of the microstructure and additionally estimate the location of the grain boundaries. The BCSS is then combined with more traditional segmentation techniques based on the Watershed Transform to improve the identification and measurement of each feature within the microstructure using a new, hybrid automated digital microstructure analysis approach. The new method is validated on a published dataset of two-phase titanium alloy microstructure pictures captured using a scanning electron microscope. Measurements match the level of accuracy of accepted manual standards, and the method is demonstrated to be more reliable than other automated approaches. The influence of the subjective nature of manual labelling, required to train the proposed network, is also evaluated.

Estimation of the Porosity of a Bilayered Fibrous Composite Material by Various Methods of Digital Microstructure Processing

Estimation of the Porosity of a Bilayered Fibrous Composite Material by Various Methods of Digital Microstructure Processing

Hierarchical reconstruction of 3D well-connected porous media from 2D exemplars using statistics-informed neural network

The relationships between porous microstructures and transport properties are of fundamental importance in various scientific and engineering applications. Due to the intricacy, stochasticity and heterogeneity of porous media, reliable characterization and modeling of transport properties often require a complete dataset of internal microstructure samples. However, it is often an unbearable cost to acquire sufficient 3D digital microstructures by purely using microscopic imaging systems. This paper presents a machine learning-based technique to hierarchically reconstruct 3D well-connected porous microstructures from one isotropic or several anisotropic low-cost 2D exemplar(s). To compactly characterize the large-scale microstructural features, a Gaussian image pyramid is built for each 2D exemplar. Local morphology patterns are collected from the Gaussian image pyramids, and then they serve as the training data to embed the 2D morphological statistics into feed-forward neural networks at multiple length levels. By using a specially-developed morphology integration scheme, the 3D morphological statistics at different levels can be inferred from the statistics-informed neural networks. Gibbs sampling is adopted to hierarchically reconstruct 3D microstructures by using multi-level 3D morphological statistics, where the large-scale, regional and local morphological patterns are statistically generated and successively added to the same 3D random field. The proposed method is tested on a series of porous media with distinct morphologies, and the statistical equivalence between the reconstructed and the real microstructures is systematically evaluated by comparing morphological descriptors and transport properties. The results demonstrate that the proposed 2D-to-3D microstructure reconstruction method is a universal and efficient approach to generating morphologically and physically realistic samples of porous media.

Microstructure-Sensitive modeling of surface roughness and notch effects on extreme value fatigue response

Fatigue life knockdown due to surface roughness induces local stress concentrations. Physical fatigue experiments are crucial to qualify materials for use but are limited in their capability to examine the mechanisms underlying the fatigue crack formation driving force due to these stress concentrations. Microstructure-sensitive computational models can aid in this regard and are employed in this work to examine the effects of surface roughness in Al 7075-T6. Digital microstructure models are subjected to crystal plasticity finite element method (CPFEM) simulations to examine the combined effects of microstructure and grain scale asperities on the driving force for fatigue crack formation. Following elastic–plastic shakedown, mesoscale volume-averaged fatigue indicator parameters (FIPs) are computed within fatigue damage process zones of grains. An increase in the intensity of realistic surface roughness profiles corresponds accordingly to larger FIPs but it is difficult to precisely interpret the mechanisms and effects of this intensification. We thus parametrically investigate surface asperities that couple with microstructure and lack of constraint on slip at the free surface to describe microstructure-sensitive surface roughness knockdown effects on fatigue resistance. The depth of a single valley (i.e., notch) due to surface roughness is found to be more detrimental to fatigue resistance than the radius (i.e., notch width, not to be confused with notch acuity). We also find that different crystallographic textures, grain morphologies, and number of sampled grains have a limited effect on the depth of influence of these notches.

Influence of tessellation morphology on ultrasonic scattering.

Material properties, such as hardness, yield strength, and ductility, depend on the microstructure of the material. If the microstructural organization can be quantified nondestructively, for example, with ultrasonic scattering techniques, then it may be possible to predict the mechanical performance of a component. Three-dimensional digital microstructures have been increasingly used to investigate the scattering of mechanical waves within a numerical framework. These synthetic microstructures can be generated using different tessellation algorithms that result in different grain shapes. In this study, the variation of ultrasonic scattering is calculated for microstructures of different morphologies for a nickel polycrystal. The ultrasonic properties are calculated for the Voronoi, Laguerre tessellations, and voxel-based synthetic microstructures created by DREAM.3D. The results show that the differences in the two-point statistics and ultrasonic attenuation for different morphologies become more significant at wider size distributions and higher frequencies.

Connectivity aware simulated annealing kernel methods for coke microstructure generation

A vital input for steel manufacture is a coal-derived solid fuel called coke. Digital reconstructions and simulations of coke are valuable tools to analyse and test coke properties. We implement biased voxel iteration into a simulated annealing method via a kernel convolution to reduce the number of iterations required to generate a digital coke microstructure. We demonstrate that voxel connectivity assumptions impact the number of iterations and reduce the normalised computation time required to generate a digital microstructure by as much as 70%.

Characterizing digital microstructures by the Minkowski‐based quadratic normal tensor

For material modeling of microstructured media, an accurate characterization of the underlying microstructure is indispensable. Mathematically speaking, the overall goal of microstructure characterization is to find simple functionals which describe the geometric shape as well as the composition of the microstructures under consideration and enable distinguishing microstructures with distinct effective material behavior. For this purpose, we propose using Minkowski tensors, in general, and the quadratic normal tensor, in particular, and introduce a computational algorithm applicable to voxel‐based microstructure representations. Rooted in the mathematical field of integral geometry, Minkowski tensors associate a tensor to rather general geometric shapes, which make them suitable for a wide range of microstructured material classes. Furthermore, they satisfy additivity and continuity properties, which makes them suitable and robust for large‐scale applications. We present a modular algorithm for computing the quadratic normal tensor of digital microstructures. We demonstrate multigrid convergence for selected numerical examples and apply our approach to a variety of microstructures. Strikingly, the presented algorithm remains unaffected by inaccurate computation of the interface area. The quadratic normal tensor may be used for engineering purposes, such as mean field homogenization or as target value for generating synthetic microstructures.

Influence of cementation on the yield surface of rocks numerically determined from digital microstructures

Digital Rock Physics has reached a level of maturity on the characterisation of primary properties that depend on the microstructure – such as porosity, permeability or elastic moduli – by numerically solving field equations on μCT scan images of rock. After small deformations or at depth though, most rocks eventually reach their limit of elasticity and the complementary plastic properties are needed to describe the full mechanical behaviour. Currently, determination of a rock’s yield surface from its microstructure is often restricted to semi-analytical criteria derived by limit analysis or numerical simulations performed on idealised geometries. Such simplification lacks representativeness, particularly for processes that affect directly the pore-grain interface such as the cementation phenomenon, happening during diagenesis. Eventually, only direct numerical simulation of elasto-plasticity performed on digitalised microstructures can be used to assess the strength of different cemented materials and its evolution with the alteration of the microstructure. In this study, we provide a comprehensive parametric study on the impact of cementation on rock strength for real microstructures of cemented granular materials. Compared to most previous studies, the whole yield surface is determined numerically (using Finite Element Method) in order to assess the influence of cementation for different stress-paths. The previously known tendency of rock to strengthen with increasing cementation volume is verified. New results on the influence of cement property namely Young’s modulus, friction and cohesion on the rock’s yield surface are explored. The envelopes obtained are compared to the ones obtained by experimental data and existing models. The framework presented in this study showcases the wider possibility of determining any rock’s or porous material’s yield surface from its microstructure.

Ultrasonic scattering predictions of two-phase polycrystalline materials based on digital microstructures

Many materials found in nature and used in industry consist of multiple phases, and the mechanical performance of such materials is controlled by their material organization. Ultrasonic scattering is one approach to characterize these microstructures nondestructively. In this presentation, previous ultrasonic scattering theories for two-phase materials are discussed and implemented using discrete synthetic three-dimensional microstructures as a means to assess the material statistics. These models predict the ultrasonic wave speed, attenuation, and diffuse ultrasonic backscatter with respect to the volume fraction and grain size distribution of each constituent. The computational approach is then focused on predictions for samples created using spark plasma sintering (SPS) of Cu and Fe powders with varying volume fractions as well as pure Cu and pure Fe samples. DREAM.3D is used to generate digital synthetics representative of the SPS samples as characterized using electron backscatter diffraction (EBSD). A set of 30 realizations for each volume fraction is used for each to quantify the statistical variations expected. The combined theoretical and computational model is used to study the dependence of ultrasonic wave propagation on the material organization for these two-phase materials. [Work supported by Air Force Research Laboratory (AFRL) under prime contract FA8650-15-D-5231.]

Large set microstructure reconstruction mimicking quantum computing approach via deep learning

Microstructural characterization and reconstruction (MCR) is critical for unearthing processing-structure-property (PSP) links in new materials discovery, design and development. However, the inherent generation of large sets of digital microstructures remains challenging due to the optimization requirements of conventional MCR platforms.In this study, we designed a new framework of MCR mimicking quantum computing (QC) approach to boost the speed of reconstructions. A 2D probabilistic map was utilized as input which contains multi-point correlation functions of the microstructure. The designed framework generates 3D microstructures from the probabilistic map based on a set of parameters calibrated via a deep learning algorithm. Such a framework converts the optimization process of MCR into a parameter extraction process replicating Shor's algorithm. The improved efficiency allows material scientists to build sensible PSP links via simulation and data-mining techniques. This method also demonstrates a potential methodology to achieve quantum supremacy with the aid of deep learning using a classical computer.

Generative Adversarial Networks for Noise Removal in Plain Carbon Steel Microstructure Images

Thermo-mechanical treatments are employed to bring about variety in the quality of metals. These treatments only work when carried out in accordance with appropriate schedules, so as to enable the evolution of metal microstructures in a suitable way. Recently, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">computer-based simulations</i> of these treatments have become hugely desired in the metallurgy industry, due to their time and resource efficiency, and also because they are free from manual experimentation errors. However, such simulations are realizable only with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">digital microstructure images</i> , accessible in proper digitized forms. Taking that into consideration, we propose a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">generative adversarial network</i> architecture for denoising steel microstructure images. Experimental results demonstrate the efficacy of the proposed model in comparison to the contemporary state-of-the-art techniques.

Bounding transverse permeability of fibrous media: a statistical study from random representative volume elements with consideration of fluid slip

In this article, a statistical study on transverse permeability of random fibrous medium is performed. For that purpose, numerous random numerical microstructures are generated with constant or randomly varying fibre radii. Their statistical representativity with respect to experimental data is first briefly discussed. Flow simulations are then performed on these digital microstructures to retrieve their full transverse permeability tensor. The representative volume element (RVE) size is determined by studying convergence of permeability distribution when domain size increases. This allows to characterise the medium isotropy as well as the impact of geometrical randomness on permeability. The approach also integrates Gaussian process regression, that is a Bayesian machine-learning model, to consider variability within interpolation in the proposed permeability predictive model. In addition, this paper considers the impact of fluid slip at liquid/fibre interface on permeability for random fibrous media. An analytical expression is proposed to describe precisely the transition from a no-slip to a free-slip regime. This allows us to propose a probabilistic model that links permeability to both the fibre volume ratio and slip length. This finally yields two bounds for transverse permeability of fibrous media: a first related to statistical scattering and a second purely linked to fluid slip.

Super-resolving material microstructure image via deep learning for microstructure characterization and mechanical behavior analysis

The digitized format of microstructures, or digital microstructures, plays a crucial role in modern-day materials research. Unfortunately, the acquisition of digital microstructures through experimental means can be unsuccessful in delivering sufficient resolution that is necessary to capture all relevant geometric features of the microstructures. The resolution-sensitive microstructural features overlooked due to insufficient resolution may limit one’s ability to conduct a thorough microstructure characterization and material behavior analysis such as mechanical analysis based on numerical modeling. Here, a highly efficient super-resolution imaging based on deep learning is developed using a deep super-resolution residual network to super-resolved low-resolution (LR) microstructure data for microstructure characterization and finite element (FE) mechanical analysis. Microstructure characterization and FE model based mechanical analysis using the super-resolved microstructure data not only proved to be as accurate as those based on high-resolution (HR) data but also provided insights on local microstructural features such as grain boundary normal and local stress distribution, which can be only partially considered or entirely disregarded in LR data-based analysis.

3D pore microstructures and computer simulation: Effective permeabilities and capillary pressure during drainage in Opalinus Clay

The 3D reconstruction of the pore space in Opalinus Clay is faced with the difficulty that high-resolution imaging methods reach their limits at the nanometer-sized pores in this material. Until now it has not been possible to image the whole pore space with pore sizes that span two orders of magnitude. Therefore, it has not been possible to predict the transport properties of this material with the help computer simulations that require 3D pore structures as input. Following the concept of self-similarity, a digital pore microstructure was constructed from a real but incomplete pore microstructure. The constructed pore structure has the same pore size spectrum as measured in the laboratory. Computer simulations were used to predict capillary pressure curves during drainage, which also agree with laboratory data. It is predicted, that two-phase transport properties such as the evolution of effective permeability as well as capillary pressures during drainage depend both on transport directions, which should be considered for Opalinus Clay when assessing its suitability as host rock for nuclear waste. This directional dependence is controlled on the pore scale by a geometric anisotropy in the pore space.

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.

From 2D to 3D: Exploring the validity of two-point correlation functions to study polycrystalline media

Acoustic attenuation in polycrystalline materials is generally formulated using statistical representations of the material in the form of two-point correlation functions. Common formulations assume decoupling of the spatial and tensorial components and invoke analytical forms to represent the spatial correlation function (W(r)). A widely accepted form of W(r) is an exponential expression that employs a single characteristic length to describe the microstructure. More recently, this approach has been extended to include grain size distributions and different grain morphologies. To date, experimental approaches have relied on using 2D micrographs of material sections to obtain the necessary material parameters. However, the accuracy of the 2D statistical parameters relative to the three-dimensional two-point statistics is yet to be validated. In this presentation, we propose an analytical approach to transform 2D image data to 3D volumetric data by extending Wicksell's corpuscle problem to the case of equiaxed grains in polycrystalline materials. We use digital microstructures to evaluate the validity of the transformation for a broad scope of grain size distribution parameters and evaluate the accuracy of the analytical forms of the spatial correlation function. Finally, we study the impact of these approximations on acoustic attenuation.