Simulated Microstructures Research Articles

Revealing the mechanism of superimposing ultrasonic vibration on microstructure evolution in friction stir welding by multi-physical multi-scale simulation

Ultrasonic vibration-enhanced friction stir welding (UVeFSW) is a promising joining method for aluminum‑lithium (Al-Li) alloy. However, directly observing the microstructural evolution in UVeFSW only by experimental methods is still a challenge. The mechanism of ultrasonic vibration (UV) on the microstructure evolution during FSW of Al-Li alloy remains unrevealed. In this study, a multi-physical multi-scale model was developed by coupling the finite element (FE) method and the Monte Carlo (MC) method to quantitatively study the impact of superimposing UV on the microstructure evolution in FSW. The preheating effect, acoustoplastic effect and residual hardening effect of UV were all considered in the model. Welding thermal processes, microstructure evolution of the material on the advancing side (AS) and in the center of the weld were quantitatively analyzed. And dislocation density and grain size in UVeFSW and FSW of Al-Li alloy were compared. Temperature field simulation results show that superimposing UV on FSW has a certain preheating effect in front of the tool. Microstructure simulation results show that the main effect of UV on microstructure evolution is the dynamic recrystallisation (DRX) process, where the maximum dislocation density in the weld nugget zone (WNZ) increases from 2.49 × 1013 m−2 to 3.49 × 1013 m−2 after superimposing UV, leading to an increase in the plastic deformation stored energy. Thereby, the driving force for nucleation and DRX increases, resulting in more nuclei in the WNZ, together with an increase in the width of the WNZ. Superimposing ultrasonic vibration in FSW can significantly refine the grain size by enhancing the activity and multiplication of dislocation in the UVeFSW of Al-Li alloy. The model is validated by the experimental results.

In situ conductometry for studying the homogenization of Al-Mg-Si alloys and predicting extrudate grain structure through machine learning

In industrial practice, no sensors capable of obtaining microstructural information in situ during thermo-mechanical processing of Al alloys are commonly employed. Inductive electrical conductivity measurement is safe, inexpensive, and capable of acquiring valuable information about precipitation and dissolution processes. However, commercial eddy current sensors work only at low temperatures near room temperature and are thus not suitable for in situ conductometry during heat treatments of Al alloys. We designed a high-temperature eddy current sensor and performed in situ conductometry during the homogenization of six Al-Mg-Si wrought alloys, three of which are experimental recycling-friendly alloys with increased Fe content. The results are interpreted with regard to microstructural investigations, and the advantages and limitations of our approach are discussed. As a proof-of-concept, we show how the conductivity curves and extrusion process parameters can be combined to predict final extrudate grain structures using machine learning. To achieve this, we employed finite element simulation of extrusion coupled with microstructural simulation over a wide parameter range, validated by extrusion experiments and metallography, and trained a feedforward neural network. We believe our interdisciplinary approach can lead to improvements in the industrial processing of Al wrought alloys.

Thermo-mechanical effects and microstructural evolution-coupled numerical simulation on the hot forming processes of superalloy turbine disk

Abstract Macroscopic deformation and microstructural evolution simultaneously exist in the hot forming processes of superalloy. In order to effectively and accurately study the hot forming processes of superalloy turbine disk with the numerical simulation method, a multi-scale finite element model of GH4065 superalloy turbine disk involving macroscopic and microscopic aspects was established by defining macro- and micromaterial model of superalloy, hot forming processing parameters, and boundary conditions. Via the numerical simulations of superalloy turbine disk, the macroscopic material flow and microstructural evolution behaviors in the hot forming processes of superalloy turbine disk were studied. Besides, the macroscopic deformation and microstructure distribution states after the hot forming processes were revealed and analyzed. A corresponding hot forming physical test of superalloy turbine disk was conducted to verify the results of the numerical simulation. Via the qualitative and quantitative analyses, it was concluded that the macroscopic deformation and microstructural evolution in the hot forming processes of superalloy turbine disk can be accurately predicted by the numerical simulation method.

Study of the Dynamic Recrystallization Behavior of Mg-Gd-Y-Zn-Zr Alloy Based on Experiments and Cellular Automaton Simulation

The exploration of the relationship between process parameters and grain evolution during the thermal deformation of rare-earth magnesium alloys using simulation software has significant implications for enhancing research and development efficiency and advancing the large-scale engineering application of high-performance rare-earth magnesium alloys. Through single-pass hot compression experiments, this study obtained high-temperature flow stress curves for rare-earth magnesium alloys, analyzing the variation patterns of these curves and the softening mechanism of the materials. Drawing on physical metallurgical theories, such as the evolution of dislocation density during dynamic recrystallization, recrystallization nucleation, and grain growth, the authors of this paper establish a cellular automaton model to simulate the dynamic recrystallization process by tracking the sole internal variable—the evolution of dislocation density within cells. This model was developed through the secondary development of the DEFORM-3D finite element software. The results indicate that the model established in this study accurately simulates the evolution process of grain growth during heat treatment and the dynamic recrystallization microstructure during the thermal deformation of rare-earth magnesium alloys. The simulated results align well with relevant theories and metallographic experimental results, enabling the simulation of the dynamic recrystallization microstructure and grain size prediction during the deformation process of rare-earth magnesium alloys.

Interface Microstructure and Numerical Simulation Investigations of Ni/TC18 Composite Tube Fabricated by Explosive Welding

Interface Microstructure and Numerical Simulation Investigations of Ni/TC18 Composite Tube Fabricated by Explosive Welding

GrainGNN: A dynamic graph neural network for predicting 3D grain microstructure

We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically performed using multicomponent partial differential equations (PDEs) with moving interfaces. The inherent randomness of the PDE initial conditions (grain seeds) necessitates ensemble simulations to predict microstructure statistics, e.g., grain size, aspect ratio, and crystallographic orientation. Currently such ensemble simulations are prohibitively expensive and surrogates are necessary.In GrainGNN, we use a dynamic graph to represent interface motion and topological changes due to grain coarsening. We use a reduced representation of the microstructure using hand-crafted features; we combine pattern finding and altering graph algorithms with two neural networks, a classifier (for topological changes) and a regressor (for interface motion). Both networks have an encoder-decoder architecture; the encoder has a multi-layer transformer long-short-term-memory architecture; the decoder is a single layer perceptron.We evaluate GrainGNN by comparing it to high-fidelity phase field simulations for in-distribution and out-of-distribution grain configurations for solidification under laser power bed fusion conditions. GrainGNN results in 80%–90% pointwise accuracy; and nearly identical distributions of scalar quantities of interest (QoI) between phase field and GrainGNN simulations compared using Kolmogorov-Smirnov test. GrainGNN's inference speedup (PyTorch on single x86 CPU) over a high-fidelity phase field simulation (CUDA on a single NVIDIA A100 GPU) is 150×–2000× for 100-initial grain problem. Further, using GrainGNN, we model the formation of 11,600 grains in 220 seconds on a single CPU core.

Accelerate microstructure evolution simulation using graph neural networks with adaptive spatiotemporal resolution

Surrogate models driven by sizeable datasets and scientific machine-learning methods have emerged as an attractive microstructure simulation tool with the potential to deliver predictive microstructure evolution dynamics with huge savings in computational costs. Taking 2D and 3D grain growth simulations as an example, we present a completely overhauled computational framework based on graph neural networks with not only excellent agreement to both the ground truth phase-field methods and theoretical predictions, but enhanced accuracy and efficiency compared to previous works based on convolutional neural networks. These improvements can be attributed to the graph representation, both improved predictive power and a more flexible data structure amenable to adaptive mesh refinement. As the simulated microstructures coarsen, our method can adaptively adopt remeshed grids and larger timesteps to achieve further speedup. The data-to-model pipeline with training procedures together with the source codes are provided.

Simulation of gas porosity formation and interaction with dendrite and eutectic structures during solidification of Al-Si alloys

A two-dimensional (2-D) multi-phase cellular automaton (CA)-finite difference (FD)-lattice Boltzmann (LB) coupled model is developed to simulate the hydrogen pore formation during dendritic and eutectic solidification of hypoeutectic Al-Si alloys. In this model, the dendrite and eutectic structures are simulated using a CA technique. The solute diffusion is solved by the FD method. The nucleation, growth, and motion behavior of gas pore, and hydrogen transport are simulated by a LB Shen-Chen scheme. It is found that the pores can grow fully but compete in the primary dendrite growth stage. Conversely, pores newly nucleated in residual inter-dendrite liquid during the eutectic solidification stage grow restrictedly and independently. Pore shape severely deformed by the compression of the surrounding solid structures. Moreover, the effects of the initial Si composition, initial hydrogen concentration and cooling rate on the pore formation are qualitatively and quantitatively studied. It is found that the initial Si composition significantly impacts on the pore size and distribution, but little effect on the porosity percentage which decreases markedly with the decreasing initial hydrogen concentration and increasing cooling rate. Comparison reveals that the simulated microstructure morphological characteristics and the predicted porosity percentage agree well with the experimental observation reported in the literature.

Simulation of Solidification Structure in the Vacuum Arc Remelting Process of Titanium Alloy TC4 Based on 3D CAFE Method

Vacuum arc remelting is the main production method of titanium alloy ingots at present. In order to obtain good quality ingots, it is of great significance to study the formation of the solidification structure of ingots via vacuum arc remelting. In order to select and optimize the nucleation parameters for the solidification microstructure simulation of an ingot, a 3D CAFE model for microstructure evolution during vacuum arc remelting was established, taking into account heat transfer, flow, and solute diffusion. The Gaussian distribution continuous nucleation model and extended KGT model were used to describe the grain nucleation and dendrite tip growth rates, respectively. The multi-point mass source and moving boundary method were used to simulate the ingot growth. The results show that there are three typical crystal regions in the solidification structure of vacuum arc remelting titanium alloy ingots, namely the surface fine crystal region, columnar crystal region, and central equiaxed crystal region. The proportion of the columnar crystal region in the solidification structure of an ingot increases gradually with the increase in the undercooling of the maximum bulk nucleation. With an increase in the maximum bulk nucleation density, the equiaxed grain zone gradually increases, and the grain size gradually decreases. The proportion of the columnar crystal region in the solidification structure of an ingot increases gradually with an increase in the undercooling of the maximum bulk nucleation. The maximum volume nucleation variance has no obvious effect on the change in the solidification structure. When the maximum volume nucleation undercooling is 5.5 K, the maximum volume nucleation standard deviation is 4 K, and the maximum volume nucleation density is 5 × 108. The solidification structure simulation results are in good agreement with the experimental results.

Flash sintering can induce an anisotropic microstructure in ceramics. A phase field modeling insight

Field-assisted sintering techniques are at the forefront of advanced energy-saving procedures to create fully dense ceramic materials. At present, there is an extraordinary interest in understanding the sintering process and effectively controlling the final specimen's microstructure. This latter aspect is critical, but unfortunately, the short sintering times and intense electric fields under non-equilibrium conditions prevent a rigorous prediction in most cases. This paper is a theoretical contribution to gain insight into an outstanding effect of applying intense electric fields: the formation of non-spherical grain structures. A phase field simulation approach has been carried out to reproduce and determine the origin of this effect. The final simulated microstructures are proved to be textured. These results are explained in the framework of a recent model and compared with experimental evidence reported in the literature.

Numerical simulation of friction extrusion: process characteristics and material deformation due to friction

This study employs a finite element thermo-mechanical model, using a Lagrangian incremental setting to investigate friction extrusion (FE) under varying process conditions. The incorporation of rotation in FE generates substantial frictional heat, leading to significantly reduced process forces in comparison to conventional extrusion (CE). The model reveals the interplay between temperature, strain, and strain rate across different microstructural zones of the resulting wire. Specifically, the sticking friction condition in FE enhances initial shear deformation, aligning with a homogeneous spatial strain distribution and predicting complete grain refinement in the extruded wire, as per Zener-Hollomon calculations. On the other hand, under the sliding friction condition in FE, the shear deformation is reduced which results in an inhomogeneous microstructure in the extruded wire. The analysis of material flow in the workpiece reveals distinct transitions from the base material to the thermo-mechanically affected zones. The simulated process force, thermal history, and microstructure during sliding friction conditions align well with the findings from performed friction extrusion experiments.

Microstructure and finite element simulation (tensile test) of stainless steel wall produced by wire and arc additive manufacturing

This investigation aims to provide functional insight into simulating the tensile behavior of additively fabricated stainless steel 316L plate using finite element simulation and the Johnson-Cook model of ductile damage. The stainless steel 316L plate is fabricated through wire arc additive manufacturing using ideal process variables selected through numerous trial and error experiments. There is a significant increase in the strength of additively fabricated specimens (517.9 MPa) than wrought alloy samples (491.3 MPa). Finite element simulation was used successfully to simulate the tensile test, and the outcomes were predicted with an error percentage of less than 1. The significant enhancement in the strength is due to variations in the microstructure such as dendritic growth, phase changes influenced by complex thermal cycle, and residual δ-ferrite in wire arc additive manufacturing plate. The presence of residual δ-ferrite is also clear through the evaluation of ferrite number as it varied from bottom to top in the range of 5.2–4.9.

Modeling of rapid solidification in Laser Powder Bed Fusion processes

This paper addresses a numerical framework for modeling site-specific microstructure evolution in Laser Powder Bed Fusion (LPBF), where rapid solidification significantly influences the microstructure and properties of manufactured components. The fine microstructure and rapid solidification can enhance mechanical properties in final parts, yet pose challenges in controlling microstructure and addressing potential defects. In this study, an in-house developed free surface thermo-fluidic Computational Fluid Dynamics (CFD) model is coupled with a binary alloy phase-field model characterized by rapid solidification kinetics. The CFD model considers complex fluid flows related to Marangoni and recoil pressure, laser-material interactions, and rapid melting and solidification of the melt pool. A convergence study for the phase-field model is conducted, comparing simulated partition coefficients with the Continuous Growth Model (CGM) theory. The study investigates the individual effects of temperature gradients and solidification rates on simulated microstructure. Results indicate that, for the same order of magnitude change, the solidification rate has a more pronounced effect on microstructure than temperature gradients. The paper concludes with the simulation of site-specific microstructure evolution within the melt pool, comparing the results with experiments conducted at varied scanning speeds. The predicted microstructure aligns well with experimental measurements, suggesting the potential utility of the developed phase-field model in quantitative microstructural modeling. Overall, this work contributes to understanding microstructure evolution under rapid solidification conditions, providing a fundamental basis for optimizing the LPBF process.

Review on Cellular Automata for Microstructure Simulation of Metallic Materials.

The cellular automata (CA) method has played an important role in the research and development of metallic materials. CA can interpret the microstructure changes of materials and obtain more abundant, accurate and intuitive information of microstructure evolution than conventional methods. CA can visually represent the process of grain formation, growth, development and change to us in a graphical way, which can assist us in analysis, thinking and solving problems. In the last five years, the application of CA in materials research has been rapidly developed, and CA has begun to occupy an increasingly important position in the simulation research of metallic materials. After introducing the advantages and limitations of CA compared to other widely used simulation methods, the purpose of this paper is to review the recent application progress on the microstructure simulation of metallic materials using CA, such as solidification, recrystallization, phase transformation and carbide precipitation occurring during forming and heat treatment. Specifically, recent research advances on microstructure simulation by CA in the fields of additive manufacturing, welding, asymmetrical rolling, corrosion prevention, etc., are also elaborated in this paper. Furthermore, this paper points out the future work direction of CA simulation in the research of metallic materials, especially in the simulation of the crystal structure, the prediction of mechanical properties, CA simulation software and rule systems, etc. These are expected to attract wide attention of researchers in the field of metallic materials and promote the development of CA in materials research.

Advancement of Analytical Model for Hydrophobic Rectangular Pillared Array on Al-Surface and Its Experimental Validation

AbstractOver the past few decades, self-cleaning surfaces have been significantly investigated due to their commercial applications in various fields. However, the researchers are still lagging in developing better mathematical models and fabricating hydrophobic surfaces for direct espousal in industry. In this study, a force-balanced system-based mathematical model is modified for a rectangular pillared array-based micro-structure and MATLAB simulations were used to validate it theoretically. The same pattern was developed on Al-surface using a single-point diamond turning (SPDT) machine experimentally. The experimental results were validated using coherence correlation interferometry (CCI), optical microscopy, drop shape analyser (DSA), and field emission scanning electron microscopy (FESEM). The experimentally estimated and theoretically predicted contact angles of the rectangular pillared array are found in close agreement. Further, the advancement in mathematical models and models-based surface manufacturing strategies can boost the research in this domain to develop robust self-cleaning hydrophobic surfaces.

An effective anisotropic visco-plastic model dedicated to high contrast ductile laminated microstructures: Application to lath martensite substructure

In particular types of layer- or lamellar-like microstructures such as pearlite and lath martensite, plastic slip occurs favorably in directions parallel to inter-lamellar boundaries. This may be due to the interplay between morphology and crystallographic orientation or, more generally, due to constraints imposed on the plastic slip due to the lamellar microstructural geometry. This paper proposes a micromechanics based, computationally efficient, scale independent model for a particular type of lamellar microstructures containing softer lamellae which are sufficiently thin to be considered as discrete slip planes embedded in a matrix representing the harder lamellae. Accordingly, the model is constructed as an isotropic visco-plastic model which is enriched with an additional orientation-dependent planar plastic deformation mechanism. This additional mode is activated when the applied load, projected on the direction of the soft films, induces a significant amount of shear stress. Otherwise, the plastic deformation is governed solely by the isotropic part of the model. The response of the proposed model is assessed via a comparison to an infinite periodic two-phase laminate. It is shown that the yielding of the model follows the same behavior as the reference model. The proposed model is highly anisotropic, and the degree of anisotropy depends on the contrast between the slip resistance of the planar mode versus that of the isotropic part. The framework is applied to the substructure of lath martensite with thin films of inter-lath retained austenite, and exploited in a mesoscale simulation of a dual-phase steel microstructure. The results are compared with those of a standard isotropic model and a full crystal plasticity model which does not have the additional planar plastic mechanism. Predictions made with the proposed model show distinct differences compared with the crystal plasticity results, while keeping the computational cost comparable to that of the isotropic model — and significantly lower than that of the crystal plasticity simulation.

Thermomechanical and microstructural simulation of rotary friction welding process of Inconel718 alloy using the finite element method

Thermomechanical and microstructural simulation of rotary friction welding process of Inconel718 alloy using the finite element method

Quantifying phase mixing and separation behaviors across length and time scales

Phase mixing and separation phenomena abound in the formation of natural and synthetic material systems, including alloys, composites, granular media, geological media, complex fluids, and biological media. While characterizing phase mixing is critical to understanding material microstructure formation and physical properties, previous metrics that measure the degree of mixing in condensed phases often rely on empirical observation, are applicable only to certain microstructures, and/or fail to detect nontrivial changes in mixing with respect to length scale. To overcome these shortcomings, we introduce and study a mixing metric that is applicable to a broad spectrum of complex microstructures and leverages the hyperuniformity concept to provide a unifying framework to rank and classify mixing in materials across both length and time scales. Specifically, we employ the local phase volume-fraction/field-intensity variance σV/F2(R,t) associated with a spherical sampling window of radius R at time t as our metric. We demonstrate that σV/F2(R,t) provides a sensitive measure of mixing across both length and time scales of a structurally diverse set of real and simulated material microstructures: exotic disordered multihyperuniform avian retina photoreceptor cell patterns, time-evolving spinodal decomposition patterns, and a model material mixed via the baker’s transformation. We also describe how this metric can be used to guide future work on fabricating materials whose bulk properties can be controlled by tuning their mixing characteristics across length and time scales.

Thermal-Mechanical and Microstructural Simulation of Rotary Friction Welding Processes by Using Finite Element Method.

Rotary friction welding is one of the most crucial techniques for joining different parts in advanced industries. Experimentally measuring the history of thermomechanical and microstructural parameters of this process can be a significant challenge and incurs high costs. To address these challenges, the finite element method was used to simulate thermomechanical and microstructural aspects of the welding of identical superalloy Inconel 718 tubes. Numerical simulation results were used to compute essential mechanical and metallurgical parameters such as temperature, strain, strain rate, volume fraction of dynamic recrystallization, and grain size distribution. These parameters were subsequently verified using experimental test results. The Johnson-Avrami model was utilized in the microstructural simulation to convert thermomechanical parameters into metallurgical factors, employing a FORTRAN subroutine. The calculated thickness of the recrystallization zone in the wall was 480 and 850 μm at the tube wall's center and edge, respectively. These values were reported from experimental measurements as 500 and 800 μm, respectively. The predicted grain size changes from the center to the edge of the wall thickness, near the weld interface, ranged from 2.07 to 2.15 μm, comparable to the experimental measurements ranging from 1.9 to 2.2 μm. Various curves are also presented to explore the correlation between thermomechanical and microstructural parameters, with the experimental results revealing predictable microstructure evolutions correlated with thermomechanical changes.

Comparative analysis on corrosion behavior of lightweight and dense mullite–corundum refractories: Role of Si‐rich phase

AbstractThe corrosion resistance of lightweight and dense mullite–corundum refractories to cement materials was examined. The specimens following static crucible treatment were investigated using phase analysis, microstructure, and thermodynamic simulation. The results reveal that diffusion of the silica‐rich phase enhances alumina saturation solubility in the slag, reducing the corrosion resistance of the mullite–corundum refractories. The large proportion of closed pores and the continuous net‐like structure of anorthite created by the corrosion reaction in the matrix, on the other hand, prevent further slag penetration into the lightweight mullite–corundum refractories. As a result, the presence of the silica‐rich phase assures better slag penetration resistance of lightweight mullite–corundum refractories.