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The design of shell-infill structures has been a focal point in the topology optimization community due to their advantages in energy absorption characteristics, strength-to weight ratio and bucking resistance. This paper introduces a phase field-based topology optimization method for designing shell-infill structures. Interface-related issues can be easily addressed through the phase field function. A coupled topology optimization process is proposed to establish the connection between the shell and infill, facilitating the generation of optimized structures. The shell thickness, infill pattern and infill volume percentage, can be naturally controlled by different model parameters. Additionally, multiscale phase field topology optimization integrates the numerical homogenization method to evaluate the effective elasticity matrix of the microstructural infill. The approach is introduced for a uniform, periodical microstructure layout in the infill region, thereby achieving superior mechanical properties. Numerical results indicate the effectiveness of the proposed method in the design of both 2D and 3D shell-infill structures. [ABSTRACT FROM AUTHOR]

The interface of atmospheric plasma spray (APS) thermal barrier coatings (TBCs) is highly irregular and rough, while their microstructure is porous and extremely uneven. This complexity leads to intricate patterns during the growth of thermally grown oxide (TGO), the distribution and evolution of the generated stress, as well as the initiation and expansion of cracks. Along these lines, in this work, a phase-field theory considering both the thermal gradient strain and TGO growth was established to thoroughly investigate the interface oxidation cracking in TBCs. More specifically, a two-dimensional geometric model of APS TBCs was established, incorporating real interface morphology and microstructure. Numerical simulations and experiments were also conducted to study the temperature and stress distribution, as well as the underlying mechanism of interface cracking during the service of TBCs. The results indicated that at high temperatures, the bottom temperature of the top coating (TC) layer with a porosity of 3.1% and a thickness of 200 μm was approximately 5 °C lower than that of the TC layer without porosity. Compared to the ideal model without pores, the model considering the real microstructure, with the presence of microcracks in the TC, makes it easier for the normal stress in the TGO at the peak region to be released. The inter-lamella cracks (Type A) in the TC near the peaks initiated earliest, followed by the creation of inter-lamella cracks at other locations, accompanied by the appearance of lamella-fracture cracks (Type B), inter-lamella to interfacial cracks (Type C), inter-lamella to TGO cracks (Type D), and internal TGO cracks (Type E). The coalescence of all these types of cracks will ultimately lead to coating failure. • A global assignment method which can describe real microstructure of porous material. • A interfacial delamination model of TBCs with a real microstructure was developed. • The initiation, propagation and coalescence laws of interface cracks were obtained. • Five types of interface cracks could be found in the simulation results. [ABSTRACT FROM AUTHOR]

In addition to orientation degree, grain microstructure also greatly affects ferroelectric performance of a textured ceramic. Accordingly, simulation that can well describe the microstructure evolution is highly desired for understanding the grain growth behavior. A modified formulation was recently developed based on the phase field method for the oriented growth of grains. The objective of this study was to investigate the effect of grain boundary energy anisotropy on the microstructure evolution of textured ferroelectric ceramics. It was found that the grain boundary energy anisotropy had a significant influence on the size distribution and shape of grains. As the degree of grain boundary energy anisotropy decreased, grain growth was accelerated and the shape changed from strip to equiaxial grains. The various microstructures could be achieved by regulating grain boundary energy anisotropy under an initial particle size distribution condition. This work gives a guide for the preparation of textured ferroelectric ceramics with a target microstructure. [ABSTRACT FROM AUTHOR]

The previous study of the authors on a phase field method for modelling progressive failure in multi-phase materials is further extended in this study to capture microscopic failure processes in composite laminates. The auxiliary phase field model for the regularization of material interface is re-formulated. In the computational model, a small part of the model is built from microscopic length scale to explicitly consider the microstructure of the material while the other area is built from macroscopic length scale to improve the efficiency. Cohesive elements are employed to link the two mesh parts with different length scales and also to capture the intralaminar failure. The existing ABAQUS subroutine "UEL" has been rewritten for the present study due to the introduction of cohesive elements and a BFGS solver is used to improve the iteration stability. The thickness effect of a thin ply made laminate is considered and the crack suppression effect is investigated. [ABSTRACT FROM AUTHOR]

In phase field methods for fracture, versatility is acquired at the cost of the addition of a new parameter, a length scale parameter. The length scale parameter affects notch sensitivity, which in cellular materials is typically related to lengths of the material microstructure. Here, the relation between this length scale parameter and observable microstructural lengths of a cellular material is investigated numerically, specifically lengths derived using statistical geometry of random Voronoi tessellations. It is found that the fracture load of a homogeneous continuum model (i.e. a macroscopic model) coincides with that of a microstructured model if the length scale parameter is chosen to be the same in both models, while approximate macroscale stiffness and energy release rate are obtained by scaling the properties of the microstructured model with powers of the relative density. The correlation between the micro- and macroscale models is best when the length parameter is chosen as approximately two to three times the average cell size of the microstructure, depending on the relative density – which is also equal to approximately eight times a critical defect length of the Voronoi tessellation, regardless of relative density – as the microstructured material then behaves more like a continuum. If the length scale parameter needs to be smaller than twice the cell size or five times the critical length, the crack path is sensitive to features in the microstructure, and continuum modelling of the porous material cannot be advised. [ABSTRACT FROM AUTHOR]

Materials with certain heterogeneous microstructures have been shown to hold a synergistic combination of strength and ductility. In this study, we demonstrate novel transformation pathways for creating such heterogeneous microstructure in Ti-alloys by integrating thermodynamic databases with phase field simulations. The results show that the concentration modulations at different length scales produced by (a) precursory spinodal decomposition in the parent phase and (b) interdiffusion in multi-layers having different alloy compositions can generate effectively hierarchical and gradient α + β two-phase microstructures, with a mixture of fine α precipitate regions and α precipitate-free-zones or coarse α precipitate regions. The novel microstructures produced include "inverted globular α" bi-modal microstructures and gradient microstructures with controlled spatial gradients in particle size and number density of α precipitates. This study may shed light on how to design novel hierarchical and gradient two-phase microstructures with tunable size and density of precipitates as well as the length scale of their spatial heterogeneity for desired properties. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Tailoring the microstructural design of a metastable two-phase Ti-Cr dental implant alloy with the optimal quantity of Cr-rich LAVES structure requires an integration of computation with informatics. This research introduces a stepwise process for generating alloy microstructure data using the phase field method, followed by sparsification and tensor computation techniques to reconstruct a microstructural informatics database for Ti-Cr alloy. This results in a significant 28-fold reduction in data size. Characterized by inpainting accuracies of 94.38% (Tucker decomposition) and 90.38% (Canonical Polyadic), the Tucker method is declared as the superior one in preserving microstructural elastic deformation information. The findings suggest that tensor computation methods present a robust strategy for accurately reconstructing complex microstructures, offering valuable insights for the digital manufacturing of Ti-Cr dental implant alloy. • Cr-rich LAVES structure has preferred elasto-chemical properties. • Phase field method can quantify the area proportion of metastable phases in Ti-Cr alloy. • CP and Tucker decompositions for tensor reconstruction. • High degree of sparsity favors microstructure reconstruction. • Tensor ensured data portabilization by 28 folds. [ABSTRACT FROM AUTHOR]

Different methods are developed for simulation of microstructural evolution in metals and alloys subject to Laser Additive Manufacturing. The Monte Carlo (MC) method is combined with a new proposed two scales strategy for simulation of the solidification and the subsequent solid-state phase transformation in Ti–6Al–4V.The Cellular Automaton (CA) method shows its higher efficiency in comparison with MC method. Moore neighbor type with energy barrier is recommended for the CA simulation of grain growth of Al 6061. The phase field (PF) model shows that different temperature gradients lead to different columnar grains in different layers of Ti–32wt.%Nb. The computed structures are related to experimental observations. [ABSTRACT FROM AUTHOR]

• Nc Cu film with more natural GBs is created by phase field method for the MD. • Yong's moduli and flow-stress for PFM are larger due to the high fraction of twinning. • Large deformation of curved GBs in PFM results in reducing the stress-concentration. The phase field method is used to create the nanocrystalline (nc) copper film with more physical and natural grain boundaries (GBs) for molecular dynamics (MD) simulation. The results show that the average flow-stress and ductility for the phase field model (PFM) is larger than that for the regular-hexagonal model (RHM) due to large fraction of twinning in the PFM during the tensile deformation. Multiple twins are generated by the evolution of stacking faults (SFs). But, the conversion rate (hexagonal-close-packed (HCP) → twinning boundaries (TBs)) for the PFM is smaller than that for the RHM because the deformation can be mediated by the curved GBs of PFM to reduce the stress-concentration. [ABSTRACT FROM AUTHOR]

Drastic reduction in the diameter of the Cu-filled through silicon via (TSV) leads to the TSV feature size becoming comparable with the grain size in the Cu filler, and accordingly Cu grain characteristics strongly influence thermo-mechanical behavior and Cu protrusion of the TSV due to the elastic anisotropy of Cu, which poses new emerging issues and challenges for reliability analysis of the TSV. In this paper, a 2-D phase field model is combined with a finite element model to study comprehensively and quantitatively the grain morphology characteristics, thermo-mechanical behavior and Cu protrusion in a typical Cu-filled TSV structure, while considering the mechanical property anisotropy of Cu. Results show that Cu grains with different orientations make distinct contributions to the deformation behavior of the Cu filler which undergoes three stages of deformation, that is, elastic, elasto-plastic, and plastic as temperature increases, consequently resulting in the anisotropic thermo-mechanical behavior of the Cu-filled TSV and the dependence of Cu protrusion on the average grain size of the Cu filler. Moreover, both the average von Mises stress and equivalent plastic strain of the Cu filler decrease with the increase in Cu grain size, and the average von Mises stress in fine grains is higher than that in coarse grains. Furthermore, Cu protrusion decreases with the increase of the average size of Cu grains. However, for limited grains in the Cu-filled TSV, the average von Mises stress, equivalent plastic strain, and Cu protrusion increase with an increase in the average size of Cu grains. [ABSTRACT FROM AUTHOR]

The construction of a homogeneous medium equivalent to a heterogeneous one under quasi-brittle fracture is investigated in the case of non-separated scales. At the microscale, the phase field method to fracture is employed. At the scale of the homogeneous medium, another phase field model either isotropic or anisotropic, depending on the microscale crack length and on the underlying microstructure, is assumed. The coefficients of the unknown phase field model for the homogeneous model are identified through the mechanical response of a sample subjected to fracture whose microstructure is fully described and estimated numerically. We show that the identified models can reproduce both the mechanical force response as well as overall crack paths with good accuracy in other geometrical configurations than the one used to identify the homogeneous model. Several numerical examples, involving cracking in regular lattices of both hard particles and pores, are presented to show the potential of the technique. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Phase-field model perfectly describes the experimental morphology evolution. • LLDPE modified asphalt shows the slowest coarsening process and best stability. • Low crystalline, high MFI and branched PE promote the swelling and interaction. • The stability calculated from simulation is well agreed with experimental result. Abstract Phase behavior is crucial to multi-phase materials, which intensively affects macro-performance of materials. Polymer modified asphalt is a typical multi-phase material and widely applied in paving industry. This paper presents the fundamental understanding of phase behavior and hot storage characteristics of polyethylene (PE) modified asphalts. The influence of polymer structure on phase behavior was studied by experimental and numerical approaches. Experimentally, four typical PE modified asphalts were selected to prepare thin film slides of asphalt, which were subjected to isothermal annealing and observed under fluorescence microscopy (FM). The morphology evolutions were evaluated by statistical size distribution. Storage stability was further evaluated by tube test. Numerically, microstructure evolutions and storage stability were described by phase field method. The results showed that the scope of PE phase size distribution becomes wider during annealing. Linear low-density PE shows a relative slow separation. Phase-field model perfectly describes the experimental microstructure evolution. Polyethylene structural parameters significantly affect the phase behavior. Lower crystalline, higher melt flow index (MFI) as well as more branched molecule promotes the swelling of PE particle and the interaction of constituents. Moreover, differences in density and viscosity between PE and asphalt greatly accelerate the separation in the vertical direction. [ABSTRACT FROM AUTHOR]

In this study, the microstructure evolution of the Inconel 718 alloy fabricated by selective laser melting (SLM) was investigated by a phase field model. The temperature gradient and the solidification velocity were first calculated from a finite element thermal model of SLM and then used as the input of the phase field model to simulate the microstructure growth with time. The influences of the build height and laser beam scanning speed on the microstructure evolution were studied and evaluated. The results show that the columnar dendritic arm spacing values estimated from the phase field simulations are comparable to experimental and analytical results. With the increase of the build height, the dominated values of thermal gradient and cooling rate decreased first and then slightly increased at the top end of the manufacturing process. The microstructural evolution along the build height agreed well with the experimental test. In addition, with the increase of the laser beam scanning speed, the dominant temperature gradient increased to a certain value and then decreased, and the direction of the maximum temperature gradient tended to be parallel to the part build direction. Moreover, the temperature gradient affects the dendrite growth significantly, a greater temperature gradient resulting in a higher growth speed. [ABSTRACT FROM AUTHOR]

The unfrozen water content and its distribution are of importance to the macro mechanical behaviors of frozen soil. In this study, the phase field method was used to deeply investigate and model the evolution of the microstructure of different saturated soils during the freezing process. Particle size distribution and freezing point depression were considered in the simulation of freezing of the soil. The soil freezing characteristic curves of the soil with different particle sizes were well predicted by the phase field method. Moreover, the unidirectional freezing test was used to validate the proposed method. The simulation results successfully predicted the inhibition effect of soil particles on the spread of pore ice during the cooling process. A series of mesoscale characteristics can be well simulated, such as unfrozen water film, retardation effect of soil particles, nonhomogeneous freezing front, and isolated ice and unfrozen water. Our results provide a deeper insight into the freezing process of porous media, including the formation of pore ice, and the movement of the freezing front on a mesoscale. [ABSTRACT FROM AUTHOR]

The misorientation angle between the preferred crystalline orientation and the temperature gradient influences both the incubation time and the average wavelength of any initial instability during the planar growth stage, as well as the dendrite growth direction and the primary dendrite arm spacing during the subsequent epitaxial growth stage. The solidification microstructure gradually changes from normal or tilted dendrites to a seaweed-like structure as the misorientation angle increases. The simulation of the initial wavelength, primary dendrite arm spacing and interface morphology are in general agreement with the experimental observations. [ABSTRACT FROM AUTHOR]

The phase field (PF) method provides a valuable means of predicting radiation induced microstructure evolution of domains ranging roughly from 100 nm to 100 μm in size and for lengths of time ranging from microseconds to years, depending on the rate of diffusion. In this work we summarize how to apply the PF method to modeling radiation damage. We begin by summarizing the PF method, and discuss the numerical solution of the PF equations. We then summarize approaches for representing the free energy of defects within a material. Next, three PF approaches for representing extended defects are discussed: the Wheeler, Boettinger, and McFadden model, the Kim, Kim, Suzuki model, and the Grand Potential model. We use a simple 1D void growth problem to compare the predictions of these models, as well as their computational expense. We end by describing how defect generation, recombination and annihilation at sinks can be described by the PF method, as well as discussing modifications required to model nucleation. [ABSTRACT FROM AUTHOR]

Abstract: Multilayer energy‐storage ceramic capacitors (MLESCCs) are studied by multiscale simulation methods. Electric field distribution of a selected area in a MLESCC is simulated at a macroscopic scale to analyze the effect of margin length on the breakdown strength of MLESCC using a finite element method. Phase field model is introduced to analyze the dielectric breakdown mechanism of MLESCC at a mesoscopic scale. The microstructure of selected area is generated through voronoi tessellation random construction routine containing core‐shell‐structured dielectric materials. The effects of margin length, shell permittivity, and shell volume fraction on the breakdown strength of MLESCC are respectively studied. Results indicate that the breakdown strength of MLESCC can be enhanced by adopting larger margin lengths, or by increasing the shell permittivity or volume fraction. [ABSTRACT FROM AUTHOR]

Shape memory alloys (SMAs) are a class of metallic smart materials which possess pseudoelasticity (PE) and shape memory effect (SME), depending on the ambient temperature. The unique thermomechanical properties of SMAs originate from the temperature-induced as well as stress-induced martensitic transformations (MTs). Former research work has shown that the thermomechanical properties of polycrystalline SMAs are grain size and rate dependent. In order to explore the physical mechanisms behind this phenomenon, a phase field (PF) model is developed in this paper to study the microstructure evolution and the thermomechanical responses of polycrystalline SMAs under dynamic loadings. The inertial effect, the latent heat release and conduction during the phase transformation are simultaneously considered. The grain boundary energy change during the phase transformation is also accounted for in the PF model. Numerical simulations are then conducted to study the temperature-induced MT as well as the stress-induced martensite reorientation of nanocrystalline SMAs with different grain sizes. The influences of the grain size, the latent heat effect and the loading rate on the microstructure evolution process and the stress–strain curves are systematically discussed. [ABSTRACT FROM AUTHOR]

[Display omitted] • The possibility of martial microstructure evolution by artificial intelligence has been demonstrated. • Predictive Recurrent Neural Network (PredRNN) model can predict the microstructure evolution quickly and accurately. • A detailed analysis of the model's performance indicated that the model parameters were optimized. • The quantitative and qualitative comparisons show that the trained PredRNN model can predict the output sequence accurately. • The model inference test demonstrates that it can predict the microstructure evolution quickly and accurately. Prediction of microstructure evolution during material processing is essential to control the material properties. Simulation tools for microstructure evolution prediction based on physical concepts are computationally expensive and time-consuming. Therefore, they are not practical when either there is an urgent need for microstructure morphology during the process or there is a need to generate big microstructure datasets. Essentially, microstructure evolution prediction is a spatiotemporal sequence prediction problem, where the prediction of material microstructure is difficult due to different process histories and chemistry. We propose a Predictive Recurrent Neural Network (PredRNN) model for the microstructure prediction, which extends the inner-layer transition function of memory states in LSTMs to spatiotemporal memory flow. As a case study, we used a dataset from spinodal decomposition simulation of FeCrCo alloy created by the phase-field method for training and predicting future microstructures by previous observations. The results show that the trained network predicts quantitatively accurate microstructure morphologies while it is several orders of magnitude faster than the phase field method. [ABSTRACT FROM AUTHOR]

Phase field method was employed to investigate the effect of the applied temperature gradient on the microstructure evolution for the binary Ni–Cu alloy during the solidification process. As a comparison group, the isothermal solidification and the non-isothermal solidification taking into account the effect of latent heat were simulated at the same time. Simulation results showed that temperature distribution could greatly influence dendrite morphology, concentration distribution and tip velocity. Under the applied temperature gradient, a cone shape of dendrite, instead of the normal dendrite with four symmetric arms, could be found easily. The growth rate of dendrite and the segregation of concentration field increased with the increasing temperature gradient. This model was able to give a clear outlook for the influence of temperature gradient on the dendrite morphology and help a better design for the microstructure control in the field of direct chill casting. [ABSTRACT FROM AUTHOR]

Two-phase microstructure calculated by Phase Field calculations is perturbed by Gaussian filtration processes to produce a series of deteriorated images. Fourier spectral analysis is, then, performed on the resultant images to derive information of spatial distribution of phases consisting of the microstructure. It is shown that Fourier spectrum is correlated with characteristic length involved in the microstructure. By inverting a particular spectrum peak, one can estimate the spatial distribution of a particular phase. [ABSTRACT FROM AUTHOR]

Because the heterogeneity of microstructure has significant effects on the material properties of ultrafine interconnects, it should be quantified, to facilitate high-fidelity prediction of reliability. To address this challenge, a method based on autocorrelation and singular value decomposition is proposed for quantitative characterization of microstructure. The method was validated by developing a quantitative relationship between reported microstructure and tensile strength for SnAgCuRE solders reported in the literature. The method was used to study the effects of size and geometry in ultrafine Sn37Pb interconnects on microstructure and von Mises stress, which were obtained simultaneously by coupling a phase-field model with an elastic mechanical model. By use of this method the degree of heterogeneity of the microstructure in relation to preferred growth directions of the phases was quantified by use of a scalar microstructure index. It was found that microstructure heterogeneity increases with decreasing standoff height, and is higher for hourglass-shaped solder joints. The average von Mises stress was found to be positively related to the microstructure index. The strong correlation between microstructure index and average von Mises stress was confirmed by nonlinear regression analysis using an artificial neural network. This indicates that the mechanical behavior of ultrafine interconnects can be predicted more accurately on the basis of the microstructure index. [ABSTRACT FROM AUTHOR]

Highlights: [•] The real microstructural dimensions of magnesium alloy were calculated by PFM. [•] The columnar dendrites were obtained by directional solidification process. [•] FEM analysis results were coupled into the microstructural calculation. [•] Microstructural evolution of crystal growth was showed by numerical simulation. [ABSTRACT FROM AUTHOR]

Abstract: Selection mechanisms of primary dendritic spacing in directional solidification are investigated by the phase field method. Results show that the lower and upper limits of primary spacing are determined by the interdendritic solutal interactions and the interdendritic undercooling respectively. The upper limit of primary spacing resulting from overgrowth of the tertiary arm could be about four times as large as the lower limit. The microstructural evolution from the onset of planar instability during directional solidification with a constant pulling velocity can be divided into three stages: an initial competition stage, a submerging stage and a lateral adjustment stage. Simulation results also demonstrate that the final primary spacing with a constant pulling velocity is very close to the lower limit due to the dendrite submerging mechanism. [Copyright &y& Elsevier]

High-temperature oxidation is an important property to evaluate thermal protection materials. However, since oxidation is a complex process involving microstructure evolution, its quantitative analysis has always been a challenge. In this work, a phase field method (PFM) based on the thermodynamics theory is developed to simulate the oxidation behavior and oxidation induced growth stress. It involves microstructure evolution and solves the problem of quantitatively computational analysis for the oxidation behavior and growth stress. Employing this method, the diffusion process, oxidation performance, and stress evolution are predicted for Fe-Cr-Al-Y alloys. The numerical results agree well with the experimental data. The linear relationship between the maximum growth stress and the environment oxygen concentration is found. PFM provides a powerful tool to investigate high-temperature oxidation in complex environments. [ABSTRACT FROM AUTHOR]

Abstract: Structural and functional materials inherit their macroscopic properties from the complex microstructures they develop at mesoscale. We discuss here the ability of the phase field method to capture the physical mechanisms at the origin of these complex morphologies in two different situations. First, we analyze the polytwinned microstructures observed in martensitic alloys, and show that, due to the large rotations involved in the accommodation mechanism, a correct modeling of the microstructures requires the use of a geometrically nonlinear model. Second, we present an elasto-viscoplastic phase field model and show its application to the understanding of the rafting phenomena observed in superalloys under creep. [ABSTRACT FROM AUTHOR]

In the macroscopic composition gradient (MCG) method, it is important to ensure that the MCG itself does not influence the phase transformation and microstructure behavior of the MCG alloy. The following two points should be theoretically and experimentally assessed to (1) ensure that the macroscopic composition profile is unchanged during aging at the lower temperature and (2) clarify the influence of the MCG on phase transformation, as it may influence microstructure formation even if the MCG profile does not change during aging. On the basis of experimental and theoretical investigations, 10 at. %/µm is considered the maximum composition gradient which does not influence microstructure formation. [ABSTRACT FROM AUTHOR]

A phase field model for anisotropic, elastoplastic fracture model in layered structures obtained by 3D printing processes is proposed. An extension of anisotropic phase field to elastoplasticity model is developed. The model is able to describe a transition from quasi-brittle to elastoplastic fracture behaviors depending on the angle of layers in the microstructure with respect to the external loading. Such feature is of special interest to describe the anisotropic fracture behavior in layered 3D printed materials. The present model introduces two phase field variables, one bulk fracture damage and one micro interfacial damage variables, describing two different micro damage mechanisms. Finally, we have proposed an original methodology to identify the macroscopic strain density as a function of the micro interfacial damage variable using numerical homogenization on Representative Volume Elements. Numerical investigations show that the present model is convergent with respect to mesh refinement, and allows to describe complex crack initiation and propagation in layered elastoplastic structures. An experimental comparison is provided to validate the use of such model for 3D printed polymer materials. [ABSTRACT FROM AUTHOR]

It is well known that nickel coarsening plays an important role in influencing the performance degradation of solid oxide fuel cell nickel-yttria-stabilized zirconia composite anode during long-term operation. Different anode microstructures fabricated by identical nickel oxide-yttria-stabilized zirconia powder mixture are reconstructed using dual-beam focused ion beam-scanning electron microscopy technique in this work. The nickel coarsening processes in nine anode microstructures are simulated using phase field method in order to quantitatively investigate the influences of nickel coarsening on the stability of a specific composite anode during long-term operation. Based on the simulation results, time-dependent evolutions of triple-phase-boundary density, specific nickel surface are and nickel-yttria-stabilized zirconia interfacial area, isolated nickel volume fraction, and tortuosity factors of different phases are quantified and compared. The simulation results show the possibility that the sintering scheme and reduction process of the anode can be optimized to enhance the anode performance and stability during long-term operation. Image 1 • Different composite anode microstructures are reconstructed in three-dimension. • Microstructure evolutions during operation are simulated using phase field method. • Factors determining anode stability during long-term operation are analyzed. • Ultra-fast microwave sintered anode shows the highest performance and stability. [ABSTRACT FROM AUTHOR]

• Quasi-static and dynamic fracture in a simplified wood microstructure is studied. • Wood microstructural features are shown to affect crack path and crack dynamics. • At increased loading velocity damage evolves in a large area ahead of the tip. As a simplified model, wood can be considered as consisting of hollow cells held together by a weaker middle lamella. We use a high-resolution finite element model, endowed with a phase field model for brittle fracture to model such a structure. The micro-structured discretised materials, with and without middle lamella, differ significantly from a homogenous continuum reference in terms of damage patterns. There is also significant difference between the models with and without middle lamella, since damage localises in the weaker middle lamella, which underlines the importance to include the middle lamella in mechanical analyses. At increased loading velocity, the damage becomes scattered over a larger region ahead of the crack tip, indicating that dynamic effects affect the crack behaviour and that dynamics need to be taken into consideration when loading rates are high or when crack propagation is unstable. [ABSTRACT FROM AUTHOR]

Mechanical properties of polymers highly depend on microstructure and the thermal and/or mechanical histories during the forming process have an important influence on the final microstructure. For example, crystallized polyethylene terephthalate (PET) highlights different mechanical properties than amorphous PET and to be able to predict the microstructure of polymers is a scientific goal. In this article, we propose to model the crystallization of PET at the mesocopic scale of spherulite by using the phase field method coupled to finite element method. We first present a simulation of the PET crystallization under thermal conditions where spherulite growth is modeled by the phase field method. The phase variable governing equation describes the state (amorphous and crystallized) in the material as a function of space and time. Coupled to the thermal equations, the problem can be solved without tracking the interface. Parameters of the phase field model are adjusted from the experimental results in order to reproduce accurately the growth of one spherulite, and the crystallization kinetic of PET at different temperature. Second, a multiphase field version is implemented and the influence of the germs positions and initial radius is discussed using a stochastic approach. [ABSTRACT FROM AUTHOR]