Simulated Microstructures Research Articles

Snow Equi‐Temperature Metamorphism Described by a Phase‐Field Model Applicable on Micro‐Tomographic Images: Prediction of Microstructural and Transport Properties

AbstractRepresenting snow equi‐temperature metamorphism (ETM) is key to model the evolution and properties of the snow cover. Recently, a phase‐field model describing mean curvature flow evolution on 3D microstructures was proposed (Bretin et al., 2019, https://doi.org/10.1051/m2an/2018075). In the present work, this model is used to simulate snow ETM at the pore scale, considering the only process of moving interfaces by sublimation‐deposition driven by curvatures. We take 3D micro‐tomographic images of snow as input in the model and obtain a time series of simulated microstructures as output. Relating the numerical time, as defined in the model, to the real physical time involves the condensation coefficient α, a poorly constrained parameter in literature. A calibration was performed by fitting simulations to experimental data through the evolution of specific surface area (SSA) of snow under ETM at −2°C. A value of the condensation coefficient was obtained: (9.8 ± 0.7) × 10−4 and was used in all the following simulations. We then show that the calibrated model enables to well reproduce an independent time series of ETM at −2°C in terms of SSA, covariance length, and mean curvature distribution. Finally, the calibrated model was used to investigate the effect of ETM on microstructure and effective transport properties (thermal conductivity, vapor diffusion, and permeability) for four different samples. As an interesting preliminary result, simulations show an enhancement of the structural anisotropy of snow in the case of initially anisotropic microstructures, such as depth hoar. Results highlight the potential of such microscale models for the development of snow property predictions for large‐scale snowpack models.

Interplay of strain and phase evolution of laser powder bed fusion Ti–6Al–4V

While additive manufacturing (AM) provides a method of producing geometrically complex and highly detailed structures, the generation of residual strain in AM processes like laser powder bed fusion (L-PBF) can negatively impact performance-enabling properties. In applications such as orthopedic implants, specific performance windows require optimized microstructures in order to obtain desirable properties from multi-phase alloys like Ti–6Al–4V. This research aims to quantify the microscale origins of strain in L-PBF manufactured Ti–6Al–4V by understanding how strain is distributed at the grain and sub-grain scale, the interplay between phase evolution and strain, and examining post-processing strain relief strategies to control these features. Model spinal cage implants were manufactured from Ti–6Al–4V powder via L-PBF and then subjected to strain relieving heat treatment cycles above and below the Ti–6Al–4V β transus as a function of time and cooling rate. Residual strain was then studied via high resolution electron backscatter diffraction (HR-EBSD), and 2D strain maps with sub-micron resolution were generated for each post-processing state. It was found that macroscale thermal strains decreased with heat treatment time, but additional contributions from phase stabilizing residual strains retained primarily in the α′ grains as lattice distortive strain remained. Additionally, the retention of β phase significantly changed the strain and dislocation distribution while reducing overall residual strain. These results were validated and reinforced with 3D mesoscopic micromechanical modeling of strain behavior across simulated microstructures, confirming that the local lattice dilation of α’ martensite is a primary contributor of microscale strain generation and retention in L-PBF Ti–6Al–4V.

Microstructure simulation and experimental evaluation of the anisotropy of 316 L stainless steel manufactured by laser powder bed fusion

PurposeThe effect of processing parameters on the microstructure of steel produced by laser-based powder bed fusion (LPBF) is a recognized opportunity for property design through microstructure control. Because the LPBF generates a textured microstructure associated with high anisotropy, it is of interest to determine the fabrication plane that would generate the desired property distribution within a component.Design/methodology/approachThe microstructure of 316 L produced by LPBF was characterized experimentally (optical, scanning electron microscopy, glow discharge emission spectrometry and X-ray diffraction), and a finite element method was used to study the microstructure features of grain diameter, grain orientation and thermal parameters of cooling rate, thermal gradient and molten pool dimensions.FindingsThe computational tool of Ansys Additive was found efficient in reproducing the experimental effect of varying laser power, scanning speed and hatch spacing on the microstructure. In particular, the conditions for obtaining maximum densification and minimum fusion defects were consistent with the experiment, and the features of higher microhardness near the component’s surface and distribution of surface roughness were also reproduced.Originality/valueTo the best of the author’s knowledge, this paper is believed to be the first systematic attempt to use Ansys Additive to investigate the anisotropy of the 316 L SS produced by LPBF.

Computing diffraction patterns of microstructures from phase-field simulations

The diffraction pattern of a material contains information not only on the crystal structures of its constituting phases, but also on its mesoscale spatial distributions of phases, grains, and ferroelastic, ferroelectric, and ferromagnetic domains. While diffraction patterns from experiments such as X-ray diffraction are presented in the reciprocal or Fourier space, mesoscale microstructure models such as the phase-field method naturally produce real-space images of spatial distribution of chemical composition, structural, and ferroic domains. Although one could rather readily compute the Fourier amplitudes of chemical and structural domain distributions generated by mesoscale simulations, they only contain information about the length scale and alignment of the real-space chemical and structure domains. Therefore, a direct comparison between diffraction experiments and mesoscale microstructure simulations is not possible. Here, we develop a theoretical approach to directly compute the crystal diffraction patterns of microstructures predicted by phase-field simulations. In particular, we consider five representative examples of microstructure patterns involving purely compositional domains, a single pair of tetragonal twin structures, multiple twin variants in a hexagonal system, ferroelectric polar vortices, and polycrystalline grains. The results are compared with previous experimental observations as well as X-ray diffraction experiments performed in the present study. The theoretical framework allows one to directly connect material microstructures and diffraction patterns predicted from phase-field simulations and the corresponding diffraction patterns from experiments, and thus providing guidance to experimental diffraction characterization and interpretation of microstructures.

Microstructural Modeling and Simulation of a Carbon Black-Based Conductive Polymer-A Template for the Virtual Design of a Composite Material.

Carbon black is the most frequently applied conductive additive in rubber and polymer composites. In this work, we show how a carbon black microstructure in a polymer matrix can be conclusively modeled based on carbon black aggregation as well as an agglomeration mechanism using a state-of-the-art mathematical model. This novel and flexible microstructural modeling method enables us to virtually investigate the morphology of conductive additives within a polymer matrix and can be adapted to many conductive polymer combinations used for different applications. Furthermore, we calculate the electrical conductivity of the composite using a finite volume-based as well as a discrete element-based simulation technique and validate the results with experimental data. Utilizing a novel discrete element method (DEM) modeling technique, we were able to improve calculation times by a factor of 12.2 compared to finite volume method (FVM) simulations while maintaining high accuracy. Using this approach, we are able to predict the required carbon black content and minimize the amount of additive to create a polymer composite with a designated target conductivity.

A facile synthesis of ibandronate modified hydroxyapatite renewable nanomaterials for simultaneous removal of Cu2+/Pb2+ and chlortetracycline: Experimental design and adsorption mechanism study

A simple co-precipitation method was used to synthesize ibandronate nano-functionalized hydroxyapatite (IB-HAP) and used for the removal of Pb2+/Cu2+ and chlortetracycline. The effects of the amount of modifier IB added, the initial concentration and the pH value of the solution on the adsorption effect of heavy metal ions were investigated. When the P atom in IB accounts for 5% of the total phosphorus, the adsorption capacity of IB-HAP was 1565.3 mg/g (Pb2+) and 246.71 mg/g (Cu2+), respectively. By adding heavy metal ions and chlortetracycline (CTC) in different addition sequences, the co-adsorption effect of various pollutants on IB-HAP was studied. According to microstructure analysis and simulation, the adsorption mechanism was studied from a microscopic point of view. It is the first time that modifiers and pollutants were used as central molecules to study the interaction sites and interaction strengths with surrounding molecules in a wholly covered state by Hirshfeld surface analysis. Finally, the desorption experiments showed that IB-HAP had strong regeneration and sustainability. These results showed that IB-HAP was a potential adsorbent, and this study also provided new guidelines and valuable methods for analyzing the mechanism of co-adsorption of heavy metal ions and antibiotics.

Phase-field, dislocation based plasticity and damage coupled model: Modelling and application to single crystal superalloys

In the present work, we propose a novel model coupling phase-field, dislocation density based plasticity and damage. The dislocation density governing equations are constructed based on evolutions of mobile and immobile dislocations. Mechanisms including dislocation multiplication, annihilation, mobile–immobile transfer due to dislocation interactions and block of interfaces are incorporated in the model. Especially, the “swallow-gap” problem surrounding the coarsened second phase, which often appears in dislocation and phase-field coupled simulations, is solved in the present model. Moreover, the phenomenon of dislocation cutting into the second phase during tertiary creep, which has rarely been considered in previous phase-field simulations of single crystal superalloys, is successfully captured in the present model with the coupling of damage. The long range stresses induced by external loading, coherent interface misfit, plastic activity and damage, as well as the short range stresses induced by antiphase boundary, dislocation line tension and forest dislocation trapping are considered in the dynamics of the model. High temperature 〈001〉 creep simulations of single crystal superalloys under 200MPa and 350MPa are conducted using the coupled model and compared with experiments. The results show that simulated phase microstructures, dislocations and creep properties principally agree with experiments during the whole creep stage, in terms of both microscopic and macroscopic features.

Temperature dependence of kinetics pathway of γ′ precipitation in Co-Al-W superalloys: A phase-field study

The expeditious development of novel Co-based superalloys depends on achieving a compressive understanding of the kinetics path way of γ′ precipitates. This paper investigates the temperature dependence of evolution processing and mechanism of γ′ phase in a model Co-9.5Al-9W (at%) alloy using phase-field method. The simulated microstructures during aging at 700, 800 and 900 ℃ show that spherical γ′ quickly changes to cuboidal aged at 900 ℃ while transforms into irregular interconnected morphology at low temperature, which is consistent well with experimental observations. By characterizing the long-range parameters, this irregular γ′ is attributed to the coalescence of adjacent precipitates with the same domain, primarily driven by the decrease of interfacial energy. The temporal evolution of average size of the γ′ precipitates suggests classical Lifshitz-Slyozov-Wagner coarsening at the three temperatures, and the coarsening rate constants K are determined. The temperature dependence of K is clarified by analyzing the thermodynamic driving force and chemical mobility. Additionally, the effects of particle inter-distance, shape and size on γ′ evolution are discussed from the perspective of diffusion potential.

Study on Corrosion Behavior of Simulated Welding Microstructure of Austenitic Stainless Steel

In this paper, the simulated welding structure of austenitic stainless steel is prepared by external heating, and the corrosion resistance of austenitic stainless steel in different areas of heat affected zone (HAZ) is evaluated by means of metallographic structure analysis, electrochemical impedance spectroscopy (EIS) test and equivalent circuit numerical fitting analysis. The result shows that the simulated welding structure of austenitic stainless steel had a growth trend with the increase of heating temperature, but the growth trend is not very obvious. The short thermal process has insufficient driving force for the growth of single-phase austenitic structure. The resulting of product resistance and charge transfer resistance of simulated welding microstructure of austenitic stainless steel is not completely consistent. The simulated welding microstructure of stainless steel shows the tendency of corrosion resistance degradation with the heating temperature increasing, and it has slightly lower when the maximum heating temperature locating at 1000-1100 °C.

Simple Formalisms for the Concept of Heterogeneity in the Porous Electrodes of Lithium-Ion Batteries

The presence of inhomogeneity in the porous electrodes of lithium-ion cells can significantly affect the active material utilization, energy/power density, and ageing dynamics of the cell, among others. 1-4 In Li-ion cells, inhomogeneity is caused by an uneven spatial distribution of the active material, carbon, binder, and electrolyte, or porous electrode micro/nanoscale properties such as the contact resistances, porosity and tortuosity. The existing literature suggests that the heterogeneity could inadvertently be introduced to the electrode with improper combination of design parameters and manufacturing steps, e.g. slurry formulation, thickness, mixing, and drying.5 Important insights into the local microstructure of the porous electrodes have been provided by FIB-SEM,6 X-ray tomography,7 or full simulation of electrode microstructure.8 Little attention has been paid, however, to develop formalisms to quantify the electrode heterogeneity and its correlation to the design parameters, manufacturing steps, and the battery performance.In this presentation, the electrochemical and microstructural characteristics of a large group of NMC111 and NMC622 porous electrodes with different design parameters will be presented and discussed. The experimental data were obtained by preparing porous electrodes of different thickness, porosity, formulation (NMC loading and carbon/binder ratio), and surface chemistry. We spotlight the sensitivity of the energy and power density of the Li|NMC cells to the microstructural indexes including tortuosity, porosity, and effective conductivities. The experimental data were analysed with the help of modeling and simulations to introduce a simplified formalism which expresses the concept of heterogeneity in the porous electrodes of lithium-ion batteries. References H. Hamed, S. Yari, J. D'Haen, FU. Renner, N. Reddy, A. Hardy, M. Safari, “Demystifying Charge Transport Limitations in the Porous Electrodes of Lithium‐Ion Batteries,” Advanced Energy Materials (2020)10 (47), 2002492.S. Yari, H. Hamed, J. D’Haen, MK. Van Bael, FU. Renner, A. Hardy, M. Safari, “Constructive versus Destructive Heterogeneity in Porous Electrodes of Lithium-Ion Batteries,” ACS Applied Energy Materials (2020) 3 (12), 11820-11829. J. Harris and P. Lu, “Effects of Inhomogeneities—nanoscale to mesoscale—on the durability of Li-Ion batteries,” J. Phys. Chem. C, (2013) 117(13). M. Forouzan, B. A. Mazzeo, and D. R. Wheeler, “modeling the effects of electrode microstructural heterogeneities on Li-Ion battery performance and lifetime,” J. Electrochem. Soc., (2018) 165(10). Jaiser, N. Sanchez Salach, M. Baunach, P. Scharfer, and W. Schabel, “Impact of drying conditions and wet film properties on adhesion and film solidification of lithium-ion battery anodes,” Dry. Technol., (2017) 35(15). Kehrwald, P. R. Shearing, N. P. Brandon, P. K. Sinha, and S. J. Harris, “local tortuosity inhomogeneities in a lithium battery composite electrode,” J. Electrochem. Soc., (2011) 158(12). Ebner, D. W. Chung, R. E. García, and V. Wood, “tortuosity anisotropy in lithium-ion battery electrodes,” Adv. Energy Mater., (2014) 4(5). Liu, V. Battaglia, and P. P. Mukherjee, “mesoscale elucidation of the influence of mixing sequence in electrode processing,” Langmuir, (2014) 30(50).

Simulation of Microstructure and Ionic Diffusivity for Leached Cement Pastes

Simulation of Microstructure and Ionic Diffusivity for Leached Cement Pastes

Microstructure-guided deep material network for rapid nonlinear material modeling and uncertainty quantification

Modeling nonlinear materials with arbitrary microstructures and loading paths is crucial in structural analyses with heterogeneous materials with uncertainty. However, it is computationally prohibitive because (1) fine meshes are required to resolve the microstructures for nonlinear simulations, (2) enormous model evaluations are expected to simulate stochastic microstructures and the loading variabilities, and (3) nonlinear material models are generally expensive to solve. In this paper, we present the microstructure-guided deep material network (MgDMN), a deep-learning-based approach to model multi-phase materials and efficiently predict their mechanical response under virtually any loading paths and microstructure definitions considering plasticity. This work is built upon the earlier development of the deep material network (DMN) method for fast predictions of nonlinear homogenized responses of multi-phase materials using linear elastic training data for a predefined microstructure. We extend DMN to MgDMN for any microstructure definition by parameterizing the microstructure space, mapping a small set of DMNs to their respective microstructure parameters, and interpolating the DMNs to generate new models in the microstructure space. The proposed method achieves superb efficiency and accuracy since the interpolated DMNs do not need additional training to predict nonlinear behavior of any new microstructures. We demonstrate our approach via modeling and uncertainty quantification of short fiber reinforced polymer (SFRP) composites. We show that for this dual-phase material, only four base DMNs are needed to predict the nonlinear stress responses for any loading path given any fiber volume fraction, orientation states, and constituent properties as long as the combination is within the microstructure space enclosed by the base models. The accelerated modeling process enables complex structural simulations of heterogeneous materials and nonlinear stochastic analyses with uncertain microstructures, which are essential in computational materials engineering and multiscale modeling. Our research also draws insights into the impact of microstructure uncertainties on linear and nonlinear material behaviors.

A stochastic geometrical 3D model for time evolution simulation of microstructures in SOC-electrodes

An original 3D stochastic geometrical model has been developed to simulate the microstructural evolution of porous solid-oxide cell electrodes made of yttria-stabilized zirconia and nickel. The microstructural change induced by Ni agglomeration has been more specifically simulated. The model is based on random sets and algorithms for solving the linear assignment problem related to the time evolution of one component in the microstructure. The possibility to generate realistic 3D microstructures with the model has been verified by comparing the geometrical characteristics of synthetic microstructures with those extracted from real electrode reconstructions. The ability of the Stochastic Time Evolution Microstructure (STEM) model to generate microstructures with evolving characteristics has been then illustrated and compared to real data obtained on aged electrodes. The error on most of the geometrical characteristics are in general lower than 10%, except in some particular cases, such as the microstructure factor. All the results have then been discussed and suggestions have been proposed for improving the model.

Study of grain boundary orientation gradients through combined experiments and strain gradient crystal plasticity modeling

A combined experimental and strain gradient crystal plasticity framework is presented for studying the development of orientation and misorientation gradients at the grain boundaries during plastic deformation. The regions in the vicinity of prior-deformation grain boundaries experience localized plastic deformation and are referred to as Near Boundary Gradient Zones (NBGZs). Deformed microstructures of an aluminum–magnesium (Al–6wt.% Mg) alloy are studied using Electron Back Scattered Diffraction (EBSD) during progressive tensile deformation. Orientation and misorientation gradients at the prior-deformation grain boundaries are quantified on grain pairs with different combinations of crystallographic orientations. Realistic virtual microstructures are then simulated using a strain gradient crystal plasticity finite element framework to study the evolution of local misorientations, stresses and strains and their correlation with the underlying substructure. The simulated microstructures indicate that the average profiles of the Geometrically Necessary Dislocation (GND) density correlates with the local misorientation, while the average profiles of the Statistically Stored Dislocation (SSD) density correlates with the effective plastic strain in these NBGZs. The combined experimental and modeling analysis reveals that the width (mean with deviation) of the distribution of the length of NBGZs, normalized by the grain size, scales with the initial grain-average Schmid factor. Further, our results also suggest a possibly strong correlation between the length of the NBGZ and the grain size.

Application of computed tomography data–based modelling technique for polymeric low density foams, Part B: Characterization of the mechanical behaviour

The non-linear material behaviour of low density polypropylene foams is investigated under several quasi-static loading conditions with a combined modelling technique based on computed tomography data and Voronoi diagrams. A simulation methodology for determining the linear elastic properties is introduced in Hössinger-Kalteis et al. (2021). In this paper, the methodology is extended regarding the material model, where additionally the non-linear region is considered. The model takes into account property determining microstructural features like orientation-dependent cell wall thicknesses and anisotropic cell shapes. Thus, the anisotropic material behaviour under tension and compression load is estimated for extrusion foams with different densities utilizing the microstructural simulation model. Based on the characterized behaviour under tension and compression, constitutive models are generated. These are implemented in bending test simulations due to lower computational effort. The simulation results are validated with experimental results, which shows that the model gives satisfactory results.

An algorithm for physics informed scan path optimization in additive manufacturing

Site specific microstructure control is a critical research area within the field of additive manufacturing due to its potential to revolutionize part performance. One way to achieve site specific microstructure control is through control of the solidification conditions via the construction of intricate scan paths; however, the search space for such a problem is large. Previous attempts only considered the solidification conditions at the top surface while also requiring either lots of manual-fine tuning or large amounts of computational resources. This paper introduces a general method for scan path optimization which considers the solidification conditions in the bulk of the material without an increase in computational expense. This method consists of three core components:1.A heat transfer model for simulating the temperature field at a given time.2.A surrogate model which takes scan pattern information and temperature data and predicts the solidification conditions of the bulk as well as the meltpool depths for a spot melt.3.A decision algorithm to decide which spot melt should be printed next based on the outputs of the surrogate model.Each of these components can be changed without changing the overall method. Within this paper, this method is applied in the creation of an algorithm containing a semi-analytic heat transfer model to simulate the temperature field, a fully convolutional neural network (FCNN) as the surrogate model, and a greedy decision algorithm. The resulting algorithm produced complex scan patterns which gave strong results for simulated microstructure control.

Multi-scale modeling of shock initiation of a pressed energetic material. II. Effect of void–void interactions on energy localization

Heterogeneous energetic materials (EMs) contain microstructural defects such as voids, cracks, interfaces, and delaminated zones. Under shock loading, these defects offer potential sites for energy localization, i.e., hotspot formation. In a porous EM, the collapse of one void can generate propagating blast waves and hotspots that can influence the hotspot phenomena at neighboring voids. Such void–void interactions must be accounted for in predictive multi-scale models for the reactive response of a porous EM. To infuse such meso-scale phenomena into a multi-scale framework, a meso-informed ignition and growth model (MES-IG) has been developed, where the influence of void–void interactions is incorporated into the overall reaction rate through a function, fv−v. Previously, MES-IG was applied to predict the sensitivity and reactive response of EM, where fv−v was assumed to be a function of the overall sample porosity alone. This paper performs a deeper analysis to model the strong dependency of fv−v on other factors, such as void size and shock strength. The improved model for void–void interactions produces good agreement with direct numerical simulations of the HE microstructures and, thus, advances the predictive capability of multi-scale models of the shock response and sensitivity of EM.

Selective Laser Melting of CuSn10: Simulation of Mechanical Properties, Microstructure, and Residual Stresses

In this study, the evolution of mechanical properties, microstructure, and residual stresses during selective laser melting of CuSn10 components was studied. To provide a proper material model for the simulations, various CuSn10 parts were manufactured using selective laser melting and examined. The manufactured parts were also used to validate the developed model. Subsequently, a sequentially coupled thermal–mechanical FEM model was developed using the Ansys software package. The developed model was able to deliver the mechanical properties, residual stresses, and microstructure of the additively manufactured components. Due to introducing some simplifications to the model, a calibration factor was applied to adjust the simulation results. However, the developed model was validated and showed a good agreement with the experimental results, such as measured residual stresses using the hole drilling method, as well as mechanical properties of manufactured parts. Moreover, the developed material model was used to simulate the microstructure of manufactured CuSn10. A fine-grain microstructure with an average diameter of 19 ± 11 μm and preferred orientation in the Z-direction, which was the assembly direction, was obtained.

Modeling the thermodynamics of the FeTi hydrogenation under para-equilibrium: An ab-initio and experimental study

FeTi-based hydrides have recently re-attracted attention as stationary hydrogen storage materials due to favorable reversibility, good sorption kinetics and relatively low costs compared to alternative intermetallic hydrides. Employing the OpenCalphad software, the thermodynamics of the (FeTi)1−xHx (0 ≤x≤ 1) system were assessed as a key basis for modeling hydrogenation of FeTi-based alloys. New thermodynamic data were acquired from our experimental pressure-composition-isotherm (PCI) curves, as well as first-principles calculations utilizing density functional theory (DFT). The thermodynamic phase models were carefully selected based on critical analysis of literature information and ab-initio investigations. Key thermodynamic properties such as dissociation pressure, formation enthalpies and phase diagrams were calculated in good agreement to our performed experiments and literature-reported data. This work provides an initial perspective, which can be extended to account for higher-order thermodynamic assessments and subsequently enables the design of novel FeTi-based hydrides. In addition, the assessed thermodynamic data can serve as key inputs for kinetic models and hydride microstructure simulations.

Microstructure, Properties, and Numerical Simulation of Semi-Solid Aluminum Alloy under Planetary Stirring Process

In order to solve the problem of insufficient convective heat transfer of uniaxial stirred melt, the temperature field and shear rate of melt under planetary stirring were studied based on CFD simulation. The microstructure and properties of this technology were also experimentally studied. The results show that compared with the uniaxial stirring semi-solid technology, the convective heat transfer ability of aluminum alloy, semi-solid slurry in planetary stirring mode is stronger. In addition, its temperature field can be reduced to the semi-solid range faster and more evenly, which is conducive to a large number of nucleation and improves the nucleation rate. The temperature difference of the whole melt is small, so the preferred direction growth and uniform growth of dendrites are avoided, and the morphology is improved. Properly increasing the revolution and rotation speed of the stirring shaft can refine the grains of semi-solid aluminum alloy parts, improve the grain morphology, and improve the tensile strength. The planetary stirring semi-solid process is very suitable for rheological high-pressure casting.