Polycrystal microstructures, with their distinct physical, chemical, structural and topological entities, play an important role in determining the effective properties of materials. Particularly for computational studies, the well-known Voronoi tessellation technique is regularly used for obtaining microstructures. Standard Voronoi tessellations, however, exhibit statistics that are generally far removed from those in real microstructures. Nevertheless, such tessellations can be optimized to obtain certain key features and statistics seen in real microstructures. In this work, we develop the open-source software package OptiMic that enables the generation of optimized microstructures for both finite element as well as atomistic simulations. OptiMic allows for both monodispersive grains as well as irregular grains obtained currently via Voronoi tessellations. These initial microstructures can then be optimized to reflect desired statistical features. A key feature of the tool is that it gives the user extensive control on the optimization process via customizable cost functions. The software currently performs tessellations with the Voronoi method and can be easily extended to include other methods like grain-growth, phase-field etc.
Faces-classes of grains, often referred to as topological features, largely dictate the evolution of polycrystalline microstructures during grain growth. Realising these topological features is generally an arduous task, often demanding sophisticated techniques. In the present work, a distinct machine-learning algorithm is extended for the first time to comprehend the topological distribution of the grains constituting a polycrystalline continuum. This regression-based object-detection approach, besides significantly reducing human-efforts and ensuring computational efficiency, predicts the fa…
Unraveling impacts of polycrystalline microstructures on ionic conductivity of ceramic electrolytes by computational homogenization and machine learning
Various machine learning models have been used to predict the properties of polycrystalline materials, but none of them directly consider the physical interactions among neighboring grains despite such microscopic interactions critically determining macroscopic material properties. Here, we develop a graph neural network (GNN) model for obtaining an embedding of polycrystalline microstructure which incorporates not only the physical features of individual grains but also their interactions. The embedding is then linked to the target property using a feed-forward neural network. Using the magne…
Experiments, theory and atomistic simulations show that finite triple junction mobility results in non-equilibrium triple junction angles in evolving polycrystalline systems. These angles have been predicted and verified for cases where grain boundary migration is steady-state. Yet, steady-state never occurs during the evolution of polycrystalline microstructures as a result of changing grain size and topological events (e.g., grain face/edge switching - "$T_1$" process, or grain disappearance "$T_2$" or "$T_3$" processes). We examine the non-steady evolution of the triple junction angle in th…
We present a fast algorithm for generating Laguerre diagrams with cells of given volumes, which can be used for creating RVEs of polycrystalline materials for computational homogenisation, or for fitting Laguerre diagrams to EBSD or XRD measurements of metals. Given a list of desired cell volumes, we solve a convex optimisation problem to find a Laguerre diagram with cells of these volumes, up to any prescribed tolerance. The algorithm is built on tools from computational geometry and optimal transport theory which, as far as we are aware, have not been applied to microstructure modelling befo…
Polycrystalline diamond films with systematic change in microstructure that varies from microcrystalline to nanocrystalline structure are synthesized on Si by hot filament chemical vapor deposition. The morphology and structural properties of the grown diamond films are analyzed using field emission scanning electron microscope (FESEM), atomic force microscope (AFM), X-ray diffraction and Raman spectroscopy. The average roughness and grain size of the diamond films decrease with increase in CH4 to H2 ratio from 0.5 to 3 %. Also, structural disorder in these diamond films increases with decreas…
Systematic experimental and theoretical research on the role of microstructure and interface thermal resistance on the thermal conductivity of the PbTe-CoSb3 bulk polycrystalline composite is presented. In particular, the correlation between the particle size of the dispersed phase and interface thermal resistance (R_{int}) on the phonon thermal conductivity (κ_{ph}) is discussed. With this aim, a series of PbTe-CoSb_3 polycrystalline composite materials with the different particle sizes of CoSb_3 was prepared. The structural (XRD) and microstructural analysis (SEM/EDXS) confirmed assumed chem…
We employ physics-informed neural networks (PINNs) to quantify the microstructure of a polycrystalline Nickel by computing the spatial variation of compliance coefficients (compressibility, stiffness and rigidity) of the material. The PINN is supervised with realistic ultrasonic surface acoustic wavefield data acquired at an ultrasonic frequency of 5 MHz for the polycrystalline material. The ultrasonic wavefield data is represented as a deformation on the top surface of the material with the deformation measured using the method of laser vibrometry. The ultrasonic data is further complemented …
Many time-dependent deformation processes at elevated temperatures produce significant concurrent microstructure changes that can alter the mechanical properties in a profound manner. Such microstructure evolution is usually absent in mesoscale deformation models and simulations. Here we present an integrated full-field modeling scheme that couples the mechanical response with the underlying microstructure evolution. As a first demonstration, we integrate a fast Fourier transform-based elasto-viscoplastic (FFT-EVP) model with a phase-field (PF) recrystallization model, and carry out three-dime…
We present an overview of the electrical, mechanical, and thermal properties of polycrystalline graphene. Most global properties of this material, such as the charge mobility, thermal conductivity, or Young's modulus, are sensitive to its microstructure, for instance the grain size and the presence of line or point defects. Both the local and global features of polycrystalline graphene have been investigated by a variety of simulations and experimental measurements. In this review, we summarize the properties of polycrystalline graphene, and by establishing a perspective on how the microstruct…
The mechanical properties of polycrystalline metals are governed by the interaction of defects that are generated by deformation within the 3D microstructure. In materials that deform by slip, the plasticity is usually highly heterogeneous within the microstructure. Many experimental tools can be used to observe the results of slip events at the free surface of a sample; however, there are only a few methods for imaging these events in the bulk. In this article, the imaging of bulk slip events within the 3D microstructure are enabled by the combined use of X-ray diffraction contrast tomography…
Digital image correlation of laser-ablated platinum nanoparticles on the surface of a polycrystalline metal (nickel-based superalloy Rene 88DT) was used to obtain the local strain behavior from an in situ scanning electron microscope tensile experiment at room temperature. By fusing this information with crystallographic orientations from EBSD, a subsequent analysis shows that the average maximum shear strain tends to increase with increasing Schmid factor. Additionally, the range of the extreme values for the maximum shear strain also increases closer to the grain boundary, signifying that gr…
The purpose of this work is the development of an artificial neural network (ANN) for surrogate modeling of the mechanical response of viscoplastic grain microstructures. To this end, a U-Net-based convolutional neural network (CNN) is trained to account for the history dependence of the material behavior. The training data take the form of numerical simulation results for the von Mises stress field under quasi-static tensile loading. The trained CNN (tCNN) can accurately reproduce both the average response as well as the local von Mises stress field. The tCNN calculates the von Mises stress f…
We present a combined phase field and cohesive zone formulation for hydrogen embrittlement that resolves the polycrystalline microstructure of metals. Unlike previous studies, our deformation-diffusion-fracture modelling framework accounts for hydrogen-microstructure interactions and explicitly captures the interplay between bulk (transgranular) fracture and intergranular fracture, with the latter being facilitated by hydrogen through mechanisms such as grain boundary decohesion. We demonstrate the potential of the theoretical and computational formulation presented by simulating inter- and tr…
The description of distributions related to grain microstructure helps physicists to understand the processes in materials and their properties. This paper presents a general statistical methodology for the analysis of crystallographic orientations of grains in a 3D Laguerre tessellation dataset which represents the microstructure of a polycrystalline material. We introduce complex stochastic models which may substitute expensive laboratory experiments: conditional on the Laguerre tessellation, we suggest interaction models for the distribution of cubic crystal lattice orientations, where the …
Many physical systems can be modeled as large sets of domains "glued" together along boundaries - biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic crystals meet along grain interfaces. Each class of microstructures results from a complex interplay of initial conditions and particular evolutionary dynamics. The statistical steady-state microstructure resulting from isotropic grain growth of a polycrystalline material is canonical in that it is the simplest example of a cellular microstructure resulting fro…
A microstructure-based model that accounts for the effect of grain size has been developed to study the effect of grain size on the fatigue life of Inconel 718 alloys. The fatigue behavior of two alloys with different grain size was determined by means of uniaxial cyclic deformation tests under fully-reversed deformation ($R_\varepsilon$ = -1) at 400$^\circ$C in the low cycle fatigue regime. The model was based in the determination of the fatigue indicator parameter (based on the local crystallographic strain energy dissipated per cycle) by means of computational homogenization of a representa…
We investigate the hot cracking susceptibility and creep resistance of three versions of a nickel-based superalloy with different contents of boron, carbon and zirconium fabricated by laser powder bed fusion. Crack-free and creep resistant components are achieved for alloys with boron, carbon and no zirconium. We then rationalize this result by evaluating how boron, carbon and zirconium are distributed at grain boundaries in the as-built and heat-treated microstructures of an alloy containing all these elements. Observations are conducted by scanning and transmission electron microscopy, and a…
Deformation heterogeneities within microstructures of polycrystalline shape memory alloys (SMAs) during superelastic stressing are studied using both experiments and simulations. In situ X-ray diffraction, specifically the far-field high energy diffraction microscopy (ff-HEDM) technique was used to non-destructively measure the grain-averaged statistics of position, crystal orientation, elastic strain tensor and volume for hundreds of austenite grains in a superelastically loaded nickel-titanium (NiTi) SMA. This experimental data were also used to create a synthetic microstructure within a fin…
The evolution of interfaces is intrinsic to many physical processes ranging from cavitation in fluids to recrystallization in solids. Computational modeling of interface motion entails a number of challenges, many of which are related to the range of topological transitions that can occur over the course of the simulation. Microstructure evolution in a polycrystalline material that involves grain boundary motion is a particularly complex example due to the extreme variety, heterogeneity, and anisotropy of grain boundary properties. Accurately modeling this process is essential to determining p…
A microstructure-sensitive fatigue life prediction framework based on CP-FFT is proposed to study SLM fabricated Hastelloy-X. The microstructure enters in the model through the shape, size and orientation distributions of grains in the RVEs, which are generated from experimental EBSD data. The framework has been applied to specimens built in two different directions with different polycrystalline microstructures and is able to accurately predict their fatigue life, using just two experiments for calibration. The model reproduces the better fatigue performance found experimentally at high stres…
Particle pinning during grain growth -- A new analytical model for predicting the mean limiting grain size but also grain size heterogeneity in a 2D polycrystalline context
An original thermodynamically consistent large strains-based multiphase phase-field (PF) approach of Ginzburg-Landau type is developed for studying the grain boundary (GB)-induced martensitic transformations (MTs) in polycrystalline materials at the nanoscale considering the structural stresses within the interfaces. In this general PF approach, N independent order parameters are used for describing the austenite (A)<->martensite (M) transformations and N(>1) martensitic variants, and another M independent order parameters are considered for describing M(>1) grains in the polycrystalline sampl…
In this work we computationally study the effect of microstructure on saturation magnetostriction of Terfenol-D (Tb$_{0.27}$Dy$_{0.73}$Fe$_{2}$) by means of Finite Element Method. The model is based on the equilibrium magnetoelastic strain tensor at magnetic saturation, and shows that the crystal orientation might play a more significant role on saturation magnetostriction than the morphology of the grains. We also calculate the dependence of saturation magnetostriction on the dispersion angle of the distribution of grains in the oriented growth crystal directions $<011>$ and $<111>$, finding …
An optimization procedure determining the ideal configuration at the microstructural level of ferroelectric (FE) materials is applied to maximize piezoelectricity. Piezoelectricity in ceramic FEs differ significantly from that of single crystals because of the presence of crystallites (grains) possessing crystallographic axes aligned imperfectly. The piezoelectric properties of a polycrystalline (ceramic) FE is inextricably related to the grain orientation distribution (texture). The set of combination of variables, known as solution space, which dictates the texture of a ceramic is unlimited …
The structure and chemistry of grain boundaries (GBs) are crucial in determining polycrystalline materials' properties. Faceting and solute segregation to minimize the GB energy is a commonly observed phenomenon. In this paper, a deposition process to obtain pure tilt GBs in titanium (Ti) thin films is presented. By increasing the power density, a transition from polycrystalline film growth to a maze bicrystalline Ti film on SrTiO$_3$ (001) substrate is triggered. All the GBs in the bicrystalline thin film are characterized to be $Σ$13 [0001] coincident site lattice (CSL) boundaries. The GB pl…
Interactions between grain boundaries and domain walls were extensively studied in ferroelectric films and bicrystals. This knowledge, however, has not been transferred to polycrystalline ceramics, in which the grain size represents a powerful tool to tailor the dielectric and electromechanical response. Here, we relate changes in dielectric and electromechanical properties of a bulk polycrystalline Pb(Zr0.7Ti0.3)O3 to domain wall interactions with grain boundaries. Samples with grain sizes in the range of 3.9 - 10.4 micrometers were prepared and their microstructure, crystal structure, and di…
Scale-free phase-field approach (PFA) at large strains and corresponding finite element method (FEM) simulations for multivariant martensitic phase transformation (PT) from cubic Si I to tetragonal Si II in a polycrystalline aggregate are presented. Important features of the model are large and very anisotropic transformation strain tensor $\varepsilon_{t}=\{0.1753;0.1753; -0.447\}$ and stress-tensor dependent athermal dissipative threshold for PT, which produce essential challenges for computations. 3D polycrystals with 55 and 910 stochastically oriented grains are subjected to uniaxial strai…
In this paper, impedance spectroscopy study was performed to establish the electrical property and microstructure relations of the as-deposited and post-annealed polycrystalline CCTO films prepared on Pt/Ti/SiO2/Si (100) substrates by pulsed-laser deposition (PLD). Our results demonstrated that the as-deposited polycrystalline CCTO film was made of insulating grain boundaries with semiconducting grains, indicating that the high-dielectric-constant is attributed to the barrier layer capacitor (BLC) effects. The simple resistor-capacitor (RC) equivalent circuit and the modified constant phase el…
Microstructure reconstruction has been an essential part of computational material engineering to reveal the relationship between microstructures and material properties. However, finding a general solution for microstructure characterization and reconstruction (MCR) tasks is still challenging, although there have been many attempts such as the descriptor-based MCR methods. To address this generality problem, the denoising diffusion models are first employed for the microstructure reconstruction task in this study. The applicability of the diffusion-based models is validated with several types…
Interfacial segregation can stabilize grain structures and even lead to grain boundary complexion transitions. However, understanding of the complexity of such phenomena in polycrystalline materials is limited, as most studies focus on bicrystal geometries. In this work, we investigate interfacial segregation and subsequent complexion transitions in polycrystalline Cu-Zr alloys using hybrid Monte Carlo/molecular dynamics simulations. No significant change in the grain size or structure is observed upon Zr dopant addition to a pure Cu polycrystal at moderate temperature, where grain boundary se…
This study investigates the effect of ZrB$_2$ additions on the microstructure, thermal stability, and thermo-mechanical wear behaviour of polycrystalline diamond. Following high-pressure high-temperature (HPHT) sintering, the ZrB$_2$-PCD material showed a full conversion of the binder phase to cobalt-boride (Co2B and Co$_{23}$B$_6$) phases. In-situ PXRD and TEM vacuum annealing experiments observed that the onset of bulk graphitisation occurred above $1000^{\circ}C$ for the ZrB$_2$-PCD material, compared to $850^{\circ}C$ for the STD-PCD material. The ZrB$_2$-PCD tools showed excellent thermo-…
We examine room-temperature magnetic relaxation in polycrystalline Fe films. Out-of-plane ferromagnetic resonance (FMR) measurements reveal Gilbert damping parameters of $\approx$ 0.0024 for Fe films with thicknesses of 4-25 nm, regardless of their microstructural properties. The remarkable invariance with film microstructure strongly suggests that intrinsic Gilbert damping in polycrystalline metals at room temperature is a local property of nanoscale crystal grains, with limited impact from grain boundaries and film roughness. By contrast, the in-plane FMR linewidths of the Fe films exhibit d…
A continuum theory based on thermodynamics has been developed for modeling diffusional creep of polycrystalline solids. It consists of a coupled problem of vacancy diffusion and mechanics where the vacancy generation/absorption at grain boundaries is driven by grain boundary dislocations climb. The model is stated in terms of general balance laws and completed by the choice of constitutive equations consistent with classical non-equilibrium thermodynamics. The kinetics of diffusional creep is derived from physically-based mechanisms of climb of dislocations at grain boundaries, thus introducin…
Polycrystalline samples with nominal composition of Ba(Fe1-xIrx)2As2 (x=0.10, 0.15, and 0.20) were investigated by means of X-ray diffraction (XRD), scanning electron microscopy (SEM), electrical resistivity, and magnetization measurements. XRD and SEM results showed that almost single phase samples were obtained. Bulk superconductivity with TC~28 K was observed in the x=0.10 sample. TC~28 K is the highest superconducting critical temperature among the reported data for electron-doped AFe2As2-type (A=Ca, Sr, and Ba) superconductors. The upper critical field Hc2(0) reaches as high as 65 T for t…
We investigate the formation of stress hotspots in polycrystalline materials under uniaxial tensile deformation by integrating full field crystal plasticity based deformation models and machine learning techniques to gain data driven insights about microstructural properties. Synthetic 3D microstructures are created representing single phase equiaxed microstructures for generic copper alloys. Uniaxial tensile deformation is simulated using a 3-D full-field, image-based Fast Fourier Transform (FFT) technique with rate-sensitive crystal plasticity, to get local micro- mechanical fields (stress a…
This work is a natural extension of the authors previous work, Multiple scattering theory for heterogeneous elastic continua with strong property fluctuation, theoretical fundamentals and applications, which established the foundation for developing multiple scattering model for strongly scattering heterogeneous elastic continua. In this work, the corresponding multiple scattering theory for polycrystalline materials with randomly oriented anisotropic crystallites is developed. As applications in ultrasonic nondestructive evaluation, we calculated the dispersion and attenuation coefficient of …
VN-GraphGG: von Neumann--Mullins--based graph grain growth simulation
The Hong Kong University of Science and Technology（香港科技大学）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；Wuhan University（武汉大学）；HKUST Shenzhen-Hong Kong Collaborative Innovation Research Institute（香港科技大学深圳-香港协同创新研究院）
A variant of the U-Net convolutional neural network architecture is proposed to estimate linear elastic compatibility stresses in a-Zr (hcp) polycrystalline grain structures. Training data was generated using VGrain software with a regularity alpha of 0.73 and uniform random orientation for the grain structures and ABAQUS to evaluate the stress welds using the finite element method. The initial dataset contains 200 samples with 20 held from training for validation. The network gives speedups of around 200x to 6000x using a CPU or GPU, with signifcant memory savings, compared to finite element …
Quantifying uncertainty associated with the microstructure variation of a material can be a computationally daunting task, especially when dealing with advanced constitutive models and fine mesh resolutions in the crystal plasticity finite element method (CPFEM). Numerous studies have been conducted regarding the sensitivity of material properties and performance to the mesh resolution and choice of constitutive model. However, a unified approach that accounts for various fidelity parameters, such as mesh resolutions, integration time-steps, and constitutive models simultaneously is currently …
A growing number of shock compression experiments, especially those involving laser compression, are taking advantage of in situ x-ray diffraction as a tool to interrogate structure and microstructure evolution. Although these experiments are becoming increasingly sophisticated, there has been little work on exploiting the textured nature of polycrystalline targets to gain information on sample response. Here, we describe how to generate simulated x-ray diffraction patterns from materials with an arbitrary texture function subject to a general deformation gradient. We will present simulations …
