Simulated Microstructures Research Articles

Component-based machine learning paradigm for discovering rate-dependent and pressure-sensitive level-set plasticity models

Abstract Conventionally, neural network constitutive laws for path-dependent elasto-plastic solids are trained via supervised learning performed on recurrent neural network, with the time history of strain as input and the stress as input. However, training neural network to replicate path-dependent constitutive responses require significant more amount of data due to the path dependence. This demand on diverse and abundance of accurate data, as well as the lack of interpretability to guide the data generation process, could become major roadblocks for engineering applications. In this work, we attempt to simplify these training processes and improve the interpretability of the trained models by breaking down the training of material models into multiple supervised machine learning programs for elasticity, initial yielding and hardening laws that can be conducted sequentially. To predict pressure-sensitivity and rate dependence of the plastic responses, we reformulate the Hamliton-Jacobi equation such that the yield function is parametrized in the product space spanned by the principle stress, the accumulated plastic strain and time. To test the versatility of the neural network meta-modeling framework, we conduct multiple numerical experiments where neural networks are trained and validated against (1) data generated from known benchmark models, (2) data obtained from physical experiments and (3) data inferred from homogenizing sub-scale direct numerical simulations of microstructures. The neural network model is also incorporated into an offline FFT-FEM model to improve the efficiency of the multiscale calculations.

Deterministic modeling of solidification microstructure formation in directed energy deposition fabricated Ti6Al4V

Metal additive manufacturing (MAM) technology is now widely applied in the manufacturing and remanufacturing industry, among which microstructure simulation gradually shows its importance. Traditional solidification microstructure simulation methods all have their merits as well as drawbacks when applied in MAM cases. In this work, a deterministic solidification microstructure model, named “invasion model”, is established to avoid the essential defects of traditional methods. This model focuses on the interaction between the neighboring bi-crystals instead of simulating the growth kinetics of each columnar grain or deriving the field form of variables. Within a bi-crystal system, the grain boundary tilt from thermal gradient direction is understood as a transient invasion behavior of one grain to another, and the competitive grain growth behavior along the buildup process of MAM is a summary of all the invasions in bi-crystal systems. To fill the gaps in the rapid solidification theory, a database recording the anisotropic growth effect under a rapid directional solidification condition was established with the help of an artificial neural network (ANN). Wire feed directed energy deposition (DED) fabricated Ti6Al4V thin-wall samples with full dendritic columnar grains (prior beta) are used as a benchmark to test the validation of the novel simulation model. The grain geometrical structure of reconstructed prior β grains along the build-up direction has a good agreement with the simulation result. The model can also be applied to other cases of MAM or combine with various models to achieve real-time as-solidified crystallographic feature prediction when it meets the scope of application. • Traditional solidification microstructure simulation methods all have their merits and drawbacks when applied in MAM cases. • Invasion model is established to investigate the transient competitive grain growth behavior within bi-crystal systems. • Wire DED Ti6Al4V thin-wall samples are used as a benchmark to test the validation of the novel simulation model.

Stochastic modeling of the polygonal microstructures of alloys using representative microscopic images

This paper proposes an algorithm to generate a statistically equivalent microstructure of alloys for polygonal mesh-based finite element modeling. Morphological and crystallographic characteristics obtained from scanning electron microscopy images of 2D surface slices are employed to generate the mesh. Titanium alloy microstructures are considered as an example to demonstrate the proposed method. The mean and standard deviation of the grain area distribution obtained from the images are employed as the statistical parameters. The algorithm uses the image data and applies perturbation using a distortion factor and Voronoi tessellation to generate the statistically equivalent polygonal microstructure that captures the randomness of grain shape and size iteratively. The grain area distribution of the simulated microstructure closely matches with the actual distribution. Lower-order elements (quadrilateral) on the domain boundary get introduced that may create artifacts when analyzed with the finite element method. A method to eliminate these artifacts is presented with an analysis of stress concentrations occurring due to grain orientation mismatch. Effective mechanical properties, deformation, and fracture behavior as a function of various microstructural parameters like grain area and crystallographic orientations can be analyzed using the polygonal finite element mesh.

Parameter-free quantitative simulation of high-dose microstructure and hydrogen retention in ion-irradiated tungsten

Hydrogen isotopes are retained in materials for fusion power applications, changing both hydrogen embrittlement and tritium inventory as the microstructure undergoes irradiation damage. But modelling of highly damaged materials - exposed to over 0.1 displacements per atom (dpa) - where asymptotic saturation is observed, for example tungsten facing the plasma in a fusion tokamak reactor, is difficult because a highly damaged microstructure cannot be treated as weakly interacting isolated defect traps. In this paper we develop computational techniques to find the defect content in highly irradiated materials without adjustable parameters. First we show how to generate converged high dose (>1 dpa) microstructures using a combination of the creation-relaxation algorithm and molecular dynamics simulations of collision cascades. Then we make robust estimates of point defects and void regions with simple developments of the Wigner-Seitz decomposition of lattice sites. We use our estimates of the void surface area to predict the deuterium retention capacity of tungsten as a function of dose. This is then compared to 3He nuclear reaction analysis (NRA) measurements of tungsten samples self-irradiated at 290 K to different damage doses and exposed to deuterium plasma at low energy at 370 K. We show that our simulated microstructures give an excellent match to the experimental data, with both model and experiment showing 1.5-2.0 at.% deuterium retained in tungsten in the limit of high dose.

A model for predicting the effects of buoyancy driven convection on solidification of binary alloy with nanoparticles

Convection during the solidification of a binary alloy with nanoparticles governs the nanoparticle, species and temperature distribution in the domain and thus the solidification rate and morphology. Hence, a numerical model to predict the effect of convection on solidification with nanoparticles is essential. In this work, a volume averaged enthalpy method-based model is developed to predict the nanoparticle, solute and temperature distribution during micro-scale solidification of binary alloy with nanoparticles. In addition to nanoparticle transport due to Brownian motion based diffusion, the effects of thermal buoyancy, solutal buoyancy and nanoparticle driven convection are considered in the model. The effect of nanoparticles on the solidification process is also incorporated into the model. From single dendrite simulations, it is observed that convection plays a significant role in dendrite growth and nanoparticle distribution. Also, it is observed that the effect of nanoparticle driven convection is insignificant. Microstructure simulations with large number of dendrites show that the effect of convection on the dendrite growth is diminished due to the reduction in space available for flow in the interdendritic region. It is also found that the presence of convection increases the homogeneity of nanoparticle distribution in the final microstructure.

Integrating phase field and crystal plasticity finite element models for simulations of titanium alloy Ti-5553

The ability to simultaneously predict the microstructure and bulk material properties of 3D printed (additively manufactured or AM) metals is critical to the development of process intelligence that can be used by a digital-twin for forecasting and optimising alloy composition and fabrication parameters. This study proposes a simulation framework for predicting the microstructure and corresponding meso- and macro-scale properties of AM materials. This is achieved by integrating phase-field and crystal plasticity modelling techniques, whereby the phase field model predicts the microstructure and the crystal plasticity constitutive model computes the stress–strain evolution using the microstructure as the input. The simulation of multiple microstructures demonstrates that this integrated approach can be used to test the influence of different microstructures on the mechanical properties of titanium alloy Ti-5553. This includes the influence of grain size and grain orientation on both the meso- and macro-scale behaviour.

A geometrically adapted reduced set of frequencies for a FFT-based microstructure simulation

We present a modified model order reduction (MOR) technique for the FFT-based simulation of composite microstructures. It utilizes the earlier introduced MOR technique (Kochmann et al., 2019), which is based on solving the Lippmann–Schwinger equation in Fourier space by a reduced set of frequencies. Crucial for the accuracy of this MOR technique is on the one hand the amount of used frequencies and on the other hand the choice of frequencies used within the simulation. Kochmann et al. (2019) defined the reduced set of frequencies by using a fixed sampling pattern, which is most general but leads to poor microstructural results when considering only a few frequencies. Consequently, a reconstruction algorithm based on the TV1-algorithm (Candes et al., 2006) was used in a post-processing step to generate highly resolved micromechanical fields. The present work deals with a modified sampling pattern generation for this MOR technique. Based on the idea, that the micromechanical material response strongly depends on the phase-wise material behavior, we propose the usage of sampling patterns adapted to the spatial arrangement of the individual phases. This leads to significantly improved microscopic and overall results. Hence, the time-consuming reconstruction in the post-processing step that was necessary in the earlier work is no longer required. To show the adaptability and robustness of this new choice of sampling patterns, several two dimensional examples are investigated. In addition, also the 3D extension of the algorithm is presented.

Generation of realistic 3D concrete aggregate microstructures using multiscale multifractal evolutionary stochastic manifold and operator-split-genetic algorithm

Concrete aggregates have a random and complex microstructure. This study presents a computational framework and methodology for realistic representation, simulation, and optimization of stochastic 3D aggregate microstructures. Central to the proposed methodology is the representation of aggregate microstructures as multiscale multifractal evolutionary stochastic manifolds that evolve over time in the topological space. In addition to the manifold representation scheme, a coupled-operator-split-genetic algorithm is also developed for the simulation and optimization of aggregate microstructures. The proposed scheme is particularly attractive due to its simplicity and ability to capture the complex morphological, topographical, and evolutionary characteristics of aggregate microstructures. More than a new method, this study introduces a novel concept of multiscale multifractal evolutionary hypersurface for the simulation and optimization of aggregate microstructures. The applicability and capability of the proposed approach may open up new ways to better understand, characterize, simulate, and capture many complex micromechanical behaviors of cementitious materials.

Microstructural simulation of initial particle-matrix interfacial defect in HTPB solid propellants

Impregnation capability at particle-matrix interfacial deteriorates during the preparation of composite solid propellant due to manufacturing and environmental factors, which leads to the initial defects in the HTPB solid propellant. In the present work, the effects of initial particle-matrix interfacial defects on the debonding, nucleation, and crack propagation of the composite solid propellant is investigated experimentally and numerically. A random packing model is developed based on the molecular dynamics method by embedding AP particles in the HTPB propellant. The strength of particle-matrix interface obeys Weibull function. Moreover, a zero-thickness cohesive element is used to simulate the particle-matrix interfacial debonding and matrix rupture. According to the simulation and experiment results, the initial interface defects makes a marked effect on the initial modulus, limit strength and elongation at fracture of the composite solid propellant. The initial modulus, limit strength and elongation at fracture of the composite solid propellant decrease with the increase of the initial interface defects.

Large-deformation crystal plasticity simulation of microstructure and microtexture evolution through adaptive remeshing

The capability of high-resolution modeling of crystals subjected to large plastic strain is essential in predicting many important phenomena occurring in polycrystalline materials, such as microstructure, deformation localization and in-grain texture evolution. However, due to the heterogeneity of the plastic deformation in polycrystals, the simulation mesh gets distorted during the deformation. This mesh distortion deteriorates the accuracy of the results, and after reaching high local strain levels, it is no longer possible to continue the simulation. In this work, two different adaptive remeshing approaches are introduced for simulating large deformation of 3D polycrystals with high resolution under periodic boundary conditions. In the first approach, a new geometry with a new mesh is created, and then the simulation is restarted as a new simulation in which the initial state is set based on the last deformation state that had been reached. In the second approach, the mesh is smoothened by removing the distortion part of the deformation, and then the simulation is continued after finding a new equilibrium state for the smoothed mesh and geometry. The first method is highly efficient for conducting high-resolution large-deformation simulations. On the other hand, the second method’s primary advantage is that it can overcome periodicity issues related to shear loading, and it can be used in conjunction with complex loading conditions. The merits of the methodologies are demonstrated using full-field simulations performed using a dislocation-density-based crystal plasticity model for Interstitial free (IF-) steel. Particular emphasis is put on studying the effect of resolution and adaptive meshing. The algorithms presented have been implemented into the free and open-source software package, DAMASK (Düsseldorf Advanced Material Simulation Kit).

Examining the unloading behavior of dual-phase steels by means of microstructure simulations

Ferritic–martensitic dual-phase (DP) steels exhibit a pronounced nonlinear unloading behavior, which is subjected to strong variations and depends on the complex interaction of parameters of the sheet metal material production process and the resulting heterogeneous microstructure. The knowledge of the unloading behavior in dependence of the governing parameters and their underlying mechanisms play a crucial role in sheet metal forming of high strength dual-phase steels.To analyze the influence of individual parameters on the unloading behavior of dual-phase steels, computational studies on the microstructure level were carried out based on the finite element method. The investigated parameters included microstructural parameters, unloading rate and thermo-mechanical deformation history caused by sheet production. In the course of the simulations, numerous different periodic volume elements were uniaxially loaded and unloaded.The computational results demonstrate that residual stresses of type II in the microstructure cannot fully explain the nonlinear unloading behavior of the steels. The reversible slip of dislocations in ferrite also plays an important role. Of all parameters examined, the martensite volume fraction and the phase strength contrast have the largest impact on the unloading behavior. Furthermore, the distribution of martensite in the microstructure significantly affects the unloading behavior, as well as residual stresses and a plastic pre-deformation both caused by the sheet production.

Interdiffusion and atomic mobilities in bcc V–X (X = Mn, Sn and Ni) alloys: Measurement and modeling

Totally 8 diffusion couples were prepared and the composition-dependent interdiffusion coefficients in bcc V–Mn, V–Sn and V–Ni alloys were measured between 1323 and 1503 K by means of Sauer-Freise method coupled with electronic probe microanalysis (EPMA) technique. The errors of the interdiffusion coefficients were computed by error propagation method. Based on the measured interdiffusivities and thermodynamic parameters from the literature, the atomic mobilities of bcc V–X (X = Mn, Sn and Ni) alloys were obtained by using the CALTPP (CALculation of ThermoPhysical Properties) program with the features of high efficiency and accuracy in the framework of CALPHAD (CALculation of PHAse Diagram) approach. For each system, the presently obtained atomic mobilities were validated by good agreement between the calculated interdiffusivities and the measured ones. The model-predicted concentration profiles in this work are consistent with the experimental ones. This work contributes to the establishment of the atomic mobility database containing V element and the key input for microstructure simulations in V-based alloys.

Investigating the mechanical behavior of multiscale porous ultra-high temperature ceramics using a quasi-static material point method

Ultra-high temperature ceramics (UHTCs) are a class of materials that maintain their structural integrity at high temperatures, e.g. 2000 °C. They have been limited in their aerospace applications because of their relatively high density and the difficulty involved in forming them into complex shapes, like leading edges and inlets. Recent advanced processing techniques have made significant headway in addressing these challenges, where the introduction of multiscale porosity has resulted in lightweight UHTCs and a more tailored thermal conductivity response. The effect of porosity on the properties of UHTCs must be characterized to enable design, but doing so experimentally can be costly, especially when attempting to mimic hypersonic flight conditions. As such, this paper seeks to computationally characterize and understand the effective mechanical properties of porous UHTCs, specifically titanium diboride, and validate those results against experimental results so as to build confidence in the model. An implicit quasi-static variant of the Material Point Method (MPM) is developed, whose capabilities include intrinsic treatment of large deformations and contact which are needed to capture the post-elastic behavior of simulated porous UHTC microstructures. It is found that the MPM can approximately obtain the elastic properties of porous UHTCs without calibration, and that the post-elastic results are found to be qualitatively consistent with experimental results. With calibrated input properties, significantly improved agreement is obtained.

Modelling of Microstructure Evolution during Laser Processing of Intermetallic Containing Ni-Al Alloys

There is a growing interest in laser melting processes, e.g., for metal additive manufacturing. Modelling and numerical simulation can help to understand and control microstructure evolution in these processes. However, standard methods of microstructure simulation are generally not suited to model the kinetic effects associated with rapid solidification in laser processing, especially for material systems that contain intermetallic phases. In this paper, we present and employ a tailored phase-field model to demonstrate unique features of microstructure evolution in such systems. Initially, the problem of anomalous partitioning during rapid solidification of intermetallics is revisited using the tailored phase-field model, and the model predictions are assessed against the existing experimental data for the B2 phase in the Ni-Al binary system. The model is subsequently combined with a Potts model of grain growth to simulate laser processing of polycrystalline alloys containing intermetallic phases. Examples of simulations are presented for laser processing of a nickel-rich Ni-Al alloy, to demonstrate the application of the method in studying the effect of processing conditions on various microstructural features, such as distribution of intermetallic phases in the melt pool and the heat-affected zone. The computational framework used in this study is envisaged to provide additional insight into the evolution of microstructure in laser processing of industrially relevant materials, e.g., in laser welding or additive manufacturing of Ni-based superalloys.

Predicting material microstructure evolution via data-driven machine learning

Predicting microstructure evolution can be a formidable challenge, yet it is essential to building microstructure-processing-property relationships. Yang et al. offer a new solution to traditional partial differential equation-based simulations: a data-driven machine learning approach motivated by the practical needs to accelerate the materials design process and deal with incomplete information in the real world of microstructure simulation.

A mesoscopic digital twin that bridges length and time scales for control of additively manufactured metal microstructures

We present our recent development of an integrated mesoscale digital twin (DT) framework for relating processing conditions, microstructures, and mechanical responses of additively manufactured (AM) metals. In particular, focusing on the laser powder bed fusion technique, we describe how individual modeling and simulation capabilities are coupled to investigate and control AM microstructural features at multiple length and time scales. We review our prior case studies that demonstrate the integrated modeling schemes, in which high-fidelity melt pool dynamics simulations provide accurate local thermal profiles and histories to subsequent AM microstructure simulations. We also report our new mechanical response modeling results for predicted AM microstructures. In addition, we illustrate how our DT framework has been validated through modeling–experiment integration, as well as how it has been practically utilized to guide and analyze AM experiments. Finally, we share our perspectives on future directions of further development of the DT framework for more efficient, accurate predictions and wider ranges of applications.

Pressure drop model for fibrous media in depth filtration: Coupling simulation of microstructure and CFD porous media during dust loading

The micro-scale model of fibrous media was simulated to obtain viscous resistance in clean state, which was provided to the CFD porous media. A macro-scale model for predicting the pressure drop during dust loading was established based on the Euler-Lagrangian method by implementing the UDF in ANSYS-Fluent. The trapping mechanism programs were developed to realize different distribution forms of particles in the porous media. The macro-empirical model was used to calibrate the macro-scale model under different SVFs. The 592*592*292-4 V–F9 filter was simplified to CFD porous media and the numerical simulation was carried out during dust loading. The results show that the pressure drop shows different growth trends under different trapping mechanism programs. Very good agreement was found between the experimental and simulated pressure drop during dust loading. Thus, the macro-scale model broadens the way of studying the pressure drop of fibrous media in depth filtration.

Microstructure simulation and heat transfer optimization for graphene oxide doped anti-/deicing composites

A microstructure simulation model was established to simulate and optimize the heat transfer performance of graphene oxide (GO) doped Glass Fiber/Epoxy (GF/EP) composites. At the microscopic level, the finite element method was employed to simulate the heat transfer characteristics of the GO/GF/EP composites. At the macroscopic level, infrared thermal imaging measurement was performed to obtain the temperature field distribution of the GO/GF/EP composites. In this work, the maximum error of the heat transfer model of the GO/GF/EP composites was 8.81% by comparing the experimental results with numerical results, which verifying the correctness of the proposed microstructure model of the GO/GF/EP composites. Moreover, the response surface method (RSM) was employed to optimize the heat transfer performance of the GO/GF/EP composites. The main influencing factors were determined by Box-Behnken optimization: graphene content is 1.99 wt%, graphene sheet diameter is 4 μm, layer spacing of glass fiber is 50 μm, glass fiber spacing is 1 μm, and glass fiber diameter is 6 μm. Comparing the experimental results with the predicted values of the proposed model, the error between the results is 1.533%, which shows that the model and the experimental data are in good agreement.

Solidification and Microstructure Simulation of A356 Aluminum Alloy Casting

To obtain an A356 aluminum alloy casting with a uniform structure and no internal shrinkage defects, ProCAST software is used to set different filling and solidification process parameters for an A356 aluminum alloy casting with large wall thickness differences, And multiple simulations are conducted to obtain optimized casting process; then, based on the process, the microstructure of the thickest and thinnest part of the casting are simulated. The size, morphology, and distribution of the simulated microstructure of the thinnest part and the thickest part of the casting are very similar. The simulated microstructure is similar to that of the actual casting. This shows that castings with uniform structure and no internal shrinkage defects can be obtained through the optimized casting process .

3D Microstructure Simulation of Reactive Aggregate in Concrete from 2D Images as the Basis for ASR Simulation.

The microstructure of alkali-reactive aggregates, especially the spatial distribution of the pore and reactive silica phase, plays a significant role in the process of the alkali silica reaction (ASR) in concrete, as it determines not only the reaction front of ASR but also the localization of the produced expansive product from where the cracking begins. However, the microstructure of the aggregate was either simplified or neglected in the current ASR simulation models. Due to the various particle sizes and heterogeneous distribution of the reactive silica in the aggregate, it is difficult to obtain a representative microstructure at a desired voxel size by using non-destructive computed tomography (CT) or focused ion beam milling combined with scanning electron microscopy (FIB-SEM). In order to fill this gap, this paper proposed a model that simulates the microstructures of the alkali-reactive aggregate based on 2D images. Five representative 3D microstructures with different pore and quartz fractions were simulated from SEM images. The simulated fraction, scattering density, as well as the autocorrelation function (ACF) of pore and quartz agreed well with the original ones. A mm concrete cube with irregular coarse aggregates was then simulated with the aggregate assembled by the five representative microstructures. The average pore (at microscale m) and quartz fractions of the cube matched well with the X-ray diffraction (XRD) and Mercury intrusion porosimetry (MIP) results. The simulated microstructures can be used as a basis for simulation of the chemical reaction of ASR at a microscale.