Modeling Of Microstructure Formation Research Articles

A Numerical Model of Microstructure Formation Considering Nanoparticle Distribution During Selective Laser Melting Process

Abstract One of the widely used metal additive manufacturing processes, named Selective laser melting (SLM), can facilitate the printing of novel metal matrix nanocomposites through the fusion of metallic powders with nanoparticles. The current study proposes a novel numerical model to simulate microstructure formation considering local nanoparticle distribution during the SLM process. The proposed model formulates a three-dimensional computational fluid dynamics (CFD) model with Lagrangian particle tracking to simulate a single-track, single-layer SLM process of aluminum alloy reinforced with titanium diboride (chemical formula: TiB2) nanoparticles in ANSYS FLUENT. A very low weight fraction (0.0009%) of nanoparticles was considered due to the computational limitations of the software package. The temperature distribution and particle distribution results were first calculated by the 3D CFD model. Then, the results were one-way coupled to a 2D Cellular Automata (CA) model to predict the microstructure evolution using matlab. The coupled CFD-CA model and Lagrangian particle tracking were separately validated in this study. The results showed that the nanoparticles migrate within the recirculation zones formed by both Marangoni and natural convection in the fluid of the molten pool. The microstructure predicted by this model showed that the introduction of the nanoparticles increased bulk nucleation during solidification. The growth of large columnar grains is interrupted by the formation of randomly oriented small equiaxed grains. The average grain diameter decreased by 40% when nanoparticles were present compared to microstructures without nanoparticles.

Phase field model of microstructure formation during cooling slope slurry generation of novel Al-15Mg2Si-4.5Si composite

The present study discusses the development of a two-dimensional phase field model of semi solid microstructure evolution of the novel Al-15Mg2Si-4.5Si composite during cooling slope rheoprocessing. The superheated melt of the said composite undergoes partial solidification during its shear flow over the slope free surface, prior to get collected within the isothermal slurry holding furnace. Seed undercooling based nucleation model is adopted in the present PF model to simulate slurry microstructure of the composite. Experimentally determined cooling rate values are considered to simulate slurry microstructure for different process conditions. Micrographs of melt samples collected during experimentation establishes the developed PF model as an accurate microstructure prediction tool for the composite slurry. Apart from morphological features such as size and degree of sphericity values of the evolving primary Mg2Si and α-Al grains, the model predictions includes melt temperature as well as solid content at any given instant of slurry processing.

Neural Network Modeling of Microstructure Formation in an AlMg6/10% SiC Metal Matrix Composite and Identification of Its Softening Mechanisms under High-Temperature Deformation

The paper investigates the rheological behavior and microstructuring of an AlMg6/10% SiC metal matrix composite (MMC). The rheological behavior and microstructuring of the AlMg6/10% SiC composite is studied for strain rates ranging between 0.1 and 4 s−1 and temperatures ranging from 300 to 500 °C. The microstructure formation is studied using EBSD analysis, as well as finite element simulation and neural network models. The paper proposes a new method of adding data to a training sample, which allows neural networks to correctly predict the behavior of microstructure parameters, such as the average grain diameter, and the fraction and density of low-angle boundaries with scanty initial experimental data. The use of neural networks has made it possible to relate the thermomechanical parameters of deformation to the microstructure parameters formed under these conditions. These dependences allow us to establish that, at strain rates ranging from 0.1 to 4 s−1 and temperatures between 300 to 500 °C, the main softening processes in the AlMg6/10% SiC MMC are dynamic recovery and continuous dynamic recrystallization accompanied, under certain strain and strain rate conditions at 300 and 350 °C, by geometric recrystallization.

Studies on the Microstructure of Epoxy-Cement Mortar

Introduction of polymers into the cement composites improves same of the properties of concretes and mortars. Therefore, the polymer-cement composites are successfully used in construction. The model of microstructure formation in cement composites modified with thermoplastic polymer (pre-mix modifiers) has already been developed and successfully implemented. However, the formation of microstructure in the case of epoxy-cement composites (containing post-mix modifier) demonstrates same peculiarities which should be taken into account when modelling the process. The microstructure of epoxy-cement composites and its formation is discussed in the paper. The model is offered, formulated on the basis of the microscopic observations and results of testing.

Modeling of microstructure formation with gas porosity growth during columnar dendritic solidification of aluminum alloys

In this paper, microstructure formation with gas bubble growth during columnar dendritic solidification has been numerically investigated by using the coupled lattice Boltzmann-cellular automaton-finite difference (LB-CA-FD) model, which combines the physical mechanisms of the redistribution of hydrogen components at the solid–liquid interface and the transportation of hydrogen atoms in liquid. Hydrogen transportation, bubble nucleation and growth are computed by the LB method while the growth of columnar dendrite and the transport of solutes are described by the CA-FD model. Predicted results show that the bubbles begin to nucleate at the roots of primary dendritic trunk and secondary arms, and elongated irregular bubbles are sandwiched between neighboring dendrites after merging and moving during the growth stage. Columnar dendritic change from coarse and ordered to fine and disordered as the cooling rate is increased. Meanwhile, the cooling rate has a significant effect on the incubation time for gas bubbles and the maximum growth rate of porosity. It was found that the misorientation angle has limited effects on the solid fraction and porosity percentage but strongly influences on the morphologies of the columnar dendritic arrays, resulting in the different distributions of bubbles.

Modelling of Microstructure Formation in Metal Additive Manufacturing: Recent Progress, Research Gaps and Perspectives

Microstructures encountered in the various metal additive manufacturing (AM) processes are unique because these form under rapid solidification conditions not frequently experienced elsewhere. Some of these highly nonequilibrium microstructures are subject to self-tempering or even forced to undergo recrystallisation when extra energy is supplied in the form of heat as adjacent layers are deposited. Further complexity arises from the fact that the same microstructure may be attained via more than one route—since many permutations and combinations available in terms of AM process parameters give rise to multiple phase transformation pathways. There are additional difficulties in obtaining insights into the underlying phenomena. For instance, the unstable, rapid and dynamic nature of the powder-based AM processes and the microscopic scale of the melt pool behaviour make it difficult to gather crucial information through in-situ observations of the process. Therefore, it is unsurprising that many of the mechanisms responsible for the final microstructures—including defects—found in AM parts are yet to be fully understood. Fortunately, however, computational modelling provides a means for recreating these processes in the virtual domain for testing theories—thereby discovering and rationalising the potential influences of various process parameters on microstructure formation mechanisms. In what is expected to be fertile ground for research and development for some time to come, modelling and experimental efforts that go hand in glove are likely to provide the fastest route to uncovering the unique and complex physical phenomena that determine metal AM microstructures. In this short Editorial, we summarise the status quo and identify research opportunities for modelling microstructures in AM. The vital role that will be played by machine learning (ML) models is also discussed.

Fast three-dimensional rules-based simulation of thermal-sprayed microstructures

Thermal spray processes involve the repeated impact of millions of discrete particles, whose melting, deformation, and coating-formation dynamics occur at microsecond timescales. The accumulated coating that evolves over minutes is comprised of complex, multiphase microstructures, and the timescale difference between the individual particle solidification and the overall coating formation represents a significant challenge for analysts attempting to simulate microstructure evolution. In order to overcome the computational burden, researchers have created rule-based models (similar to cellular automata methods) that do not directly simulate the physics of the process. Instead, the simulation is governed by a set of predefined rules, which do not capture the fine-details of the evolution, but do provide a useful approximation for the simulation of coating microstructures. Here, we introduce a new rules-based process model for microstructure formation during thermal spray processes. The model is 3D, allows for an arbitrary number of material types, and includes multiple porosity-generation mechanisms. Example results of the model for tantalum coatings are presented along with sensitivity analyses of model parameters and validation against 3D experimental data. The model’s computational efficiency allows for investigations into the stochastic variation of coating microstructures, in addition to the typical process-to-structure relationships.

Multi-phase-field simulation of microstructure evolution in metallic foams

This paper represents a model for microstructure formation in metallic foams based on the multi-phase-field approach. The model allows to naturally account for the effect of additives which prevent two gas bubbles from coalescence. By applying a non-merging criterion to the phase fields and at the same time raising the free energy penalty associated with additives, it is possible to completely prevent coalescence of bubbles in the time window of interest and thus focus on the formation of a closed porous microstructure. On the other hand, using a modification of this criterion along with lower free energy barriers we investigate with this model initiation of coalescence and the evolution of open structures. The method is validated and used to simulate foam structure formation both in two and three dimensions.

Crystallographic model of microstructure formation in Nd2Fe14B type compounds with titanium

The magnetic properties of permanent magnets of the Nd-Fe-B type alloyed with titanium, depending on the chemical composition and heat treatment, are studied. Crystallographic model of formation of a microstructure in compounds of the Nd2Fe14B type with titanium is proposed. Analysis of the experimental data provides an opportunity to suggest that to explain the dependence of the intrinsic coercive force on the parameters of heat treatment for various chemical compositions, it is necessary to take into account the change of state of the main and boundary phases due to diffusion processes and phase transfers.

Revisiting Models for Spheroidal Graphite Growth

Recent experiments resolved nucleation and growth of graphite during solidification of ductile cast iron in 4D using synchrotron X-ray tomography. A numerical model for microstructure formation during solidification is compared with the experiments. Despite very good overall agreement between observations of spheroidal graphite growth and model results, significant deviations exist towards the end of solidification. We use the experimental observations to analyse the relation between graphite growth rate and the state of the particle neighbourhood to pinpoint possible links between growth rate of individual graphite spheres and the overall solidification state. With this insight we revisit existing models for growth of spheroidal graphite and discuss possible modifications in order to correctly describe the critical final stage of solidification.

A multi-fluid model for microstructure formation in polymer membranes.

We develop a multi-fluid model for a ternary polymer solution using the Rayleighian formalism of Doi and Onuki, and give an efficient pseudo-spectral method for solving both the diffusion and momentum equations that result. Subsequently, we find that the numerical simulation is capable of describing systems at the micron length-scale and easily reaches millisecond time-scales. In addition, we characterize the model thermodynamics and kinetics including the (i) phase behavior, (ii) structure of the interfaces, (iii) mutual diffusion coefficients, (iv) bulk spinodal decomposition kinetics with and without hydrodynamics and (v) spinodal decomposition in the presence of an interface with a non-solvent bath. We obtain good qualitative agreement with the expected thermodynamic and kinetic behavior. We also show that a linear stability analysis of the diffusion equation quantitatively predicts the fastest growing mode obtained from simulation and gives insight into the phase separation process relevant for the evolution of microstructure in phase-separating ternary polymer solutions.

Studies on the Microstructure of Epoxy-Cement Composites

Abstract Introduction of polymers into the cement composites improves same of the properties of concretes and mortars. Therefore, the polymer-cement composites are successfully used in construction. The model of microstructure formation in cement composites modified with thermoplastic polymer (pre-mix modifiers) has already been developed and successfully implemented. However, the formation of microstructure in the case of epoxy-cement composites ( containing post-mix modifier) demonstrates same peculiarities which should be taken into account when modelling the process. The microstructure of epoxy-cement composites and its formation is discussed in the paper. The model is offered, formulated on the basis of the microscopic observations and results of testing.

Phase-field modeling of microstructure formation during rapid solidification in Inconel 718 superalloy

The prediction of the equilibrium and metastable phase/grain morphologies during selective laser melting (SLM) of Ni-base superalloys can be accomplished using phase-field modeling (PF). In this paper, a model for binary and multi-component systems is presented and validated via the steady-state growth problem by comparison to theoretical predictions of the Green-function calculations and the Kurz–Fisher model. By means of the PF simulations, a phenomenological dependency of the growth velocity on undercooling during the rapid solidification is evaluated. It is found that the growth velocity does not achieve steady-state values for real process and material parameters. The final microstructure predicted by the PF is in good agreement with the experimental observations. Additionally, the simulations provide concentration profiles, which show a pronounced segregation of solutes to the dendrite core. The simulated microstructures and concentration fields can be used as inputs for the simulation of the precipitation of secondary phases.

Phase Field Modeling of Microstructure Formation, DSC Curves, and Thermal Expansion for AgCu Brazing Fillers Under Reactive Air Brazing Conditions

We discuss phase field simulations of the microstructure evolution in an Ag–Cu brazing filler for conditions close to reactive air brazing (RAB) under air. The simulations show the basic steps of the phase formation in the brazing filler during solidification and provide calculated DSC curves, which allow a direct comparison between simulation and experiment. It is demonstrated that the consideration of transport processes (mainly oxygen) is necessary for a quantitative interpretation of measured differential scanning calorimetry (DSC) curves. Furthermore, simulations demonstrate the effect of different Cu‐contents on the microstructure and the corresponding DSC curves. Finally, the effective temperature‐dependent thermal expansion including the eigenstrain from the phase transformation is calculated for the two‐phase microstructure.

Thermo-Solutal Modelling of Microstructure Formation during Multiphase Alloy Solidification - a New Approach

This paper shows how to move from a specification of free energy for the solidification of a binary alloy to the dynamical equations using the elegance of a dissipative bracket analogous to the Poisson bracket of Hamiltonian mechanics. A key new result is the derivation of the temperature equation for single-phase thermal-solutal models, which contains generalisations and extra terms which challenge standard models. We also present, for the first time, the temperature equation for thermal multi-phase field models. There are two main ingredients: one, the specification of the free energy in terms of the time and space dependent field variables: $n$-phases $\phi_i$, a concentration variable $c$, and temperature $T$; two, the specification of the dissipative bracket in terms of these variables, their gradients and a set of diffusion parameters, which may themselves depend on the field variables. The paper explains the method within this context and demonstrates its thermodynamic admissibility.

Closed Chain Simulations of a Cast Aluminium Component - Incorporating Casting Process Simulation and Local Material Characterization into Stress-strain Simulations

The coupling between simulations of solidification, microstructure and local mechanical behaviour and simulation of stress-strain behaviour is studied by applying a recently developed simulation strategy to a high pressure die cast aluminium component. In the simulation strategy, named a closed chain of simulations for cast components, the mechanical behaviour throughout the component is determined locally by a casting process simulation. The entire casting process, including mould filling and solidification, is simulated to predict the formation of microstructure and residual stresses throughout the component, and material characterization models are applied to relate microstructural features to local elastic and plastic mechanical material behaviour. The local material behaviour is incorporated into a finite element method (FEM) stress-strain simulation of a realistic load case of the component in service.In the current contribution the influences of local variations in mechanical behaviour and residual stresses on the component behaviour are investigated. The simulation results for local microstructure and mechanical behaviour are compared to experimental results, and the predicted local mechanical behaviour is incorporated on an element level into the FEM simulation. The numerical effect of the variations in mechanical behaviour is quantified by comparing the results achieved using local behaviour and homogeneous behaviour. The influence of residual stresses predicted by the casting process simulation on the component behaviour is also studied.The casting process simulation is found to accurately predict the local variations in microstructure throughout the component, and the local variations in mechanical behaviour are well described. The numerical results show that casting process simulation and modelling of microstructure formation, material behaviour and residual stresses are important contributions to correctly predict the behaviour of a cast aluminium component in service. This motivates the use of the proposed simulation strategy, and show the importance of incorporating materials science and casting process simulations into structural analyses of cast components. It is discussed that integration of these areas, e.g. using the closed chain of simulations, is important in order to increase the accuracy of FEM simulations and the product development efficiency in the future.

Multi-Scale Modeling of Microstructure Evolution Induced Anisotropy in Metals

This paper presents two crystal plasticity based computational constitutive models for the intrinsic formation of plastic microstructure during monotonic loading and its altered evolution under strain path changes in metal forming operations. The formation step is modeled via a non-convex strain gradient crystal plasticity framework which could simulate the intrinsic development of the plastic microstructures. The evolution under strain path changes is modeled via phenomenologically based constitutive equations incorporated into crystal plasticity framework. The latter is capable of simulating the transient anisotropy effects (e.g. cross hardening, Bauschinger effect) depending on the change in the strain path. The paper discusses the unification of such models for the continuous modeling of microstructure formation and evolution processes.

Phase-field modelling of microstructure formation during the solidification of continuously cast low carbon and HSLA steels

Cracking in continuous casting of steels has been one of the main problems for decades. Many of the cracks that occur during solidification are hot tears. To better understand the factors leading to this defect, microstructure formation is simulated for a low carbon (LCAK) and two high strength low alloyed (HSLA) steel grades during the initial stage of the process where the first solidified shell is formed inside the mould and where breakouts typically occur. 2D simulation is performed using the multiphase-field software MICRESS [1], which is coupled to the thermodynamic database TCFE6 [2] and the mobility database MOB2 [2], taking into account all elements which may have a relevant effect on the mechanical properties and structure formation during or subsequent to solidification. The use of a moving-frame boundary condition allows travelling through the entire solidification history starting from the slab surface, and tracking the morphology changes during growth of the shell. A heterogeneous nucleation model is included to permit the description of morphological transitions between the initial solidification and the subsequent columnar growth region. Furthermore, a macroscopic one-dimensional temperature solver is integrated to account for the transient and nonlinear temperature field during the initial stage of continuous casting. The external heat flux boundary conditions for this process were derived from thermal process data of the industrial slab caster. The simulation results for the three steel grades have been validated by thickness measurements of breakout shells and microstructure observation of the corresponding grades. Furthermore, the primary dendrite spacing has been measured across the whole thickness of the shell and compared with the simulated microstructures. Significant microstructure differences between the steel grades are discussed and correlated with their hot-cracking behavior.

Prediction of Microstructure and Porosity Formation of Practical Spheroidal Graphite Iron Castings

The mathematical model for microstructure formation and porosity prediction during solidification process of SG iron casting was established and applied to a practical brake housing casting. Quantitative microstructure analysis of specimens machined from the castings was compared with the simulation, and the two results are in acceptable agreement on nodule counts and size, pearlite fractions and hardness. It is indicated that the model can calculate the fraction of ferrite and pearlite more accurately, and specially can reflect the effect of both under-cooling during solidification and the nodules formed in eutectic period on the pearlite content. The present porosity prediction was compared with those of a former method and commercial software, which leads to that the current methods used for porosity prediction should be investigated and improved further.

Simulation of feeding flow and prediction of macro porosity of SGI casting based on microstructure formation

Based on the model of microstructure formation of spheroidal graphite iron (SGI) casting which includes continuous nucleation and growth of graphite nodules, carbides and austenite, a method was proposed to calculate the feeding flow during solidification processes by considering mass conservation and using Darcy's laws. The method takes into account liquid shrinkage as well as shrinkage and expansion caused by different phase formation, and can calculate the flow in liquid and mushy regions. According to calculation of the flow, macro porosity formation could be described through treating free surfaces and boundary of the regions. The proposed method has been applied to an automotive wheel hub SGI casting with two different processing cases. The feeding flow during the casting solidification with two cases, especially in isolated regions, was investigated and discussed. With the flow calculation, expansion or shrinkage of liquid or mushy regions might be judged, which could offer important information for evaluating formation of macro porosity. The results of macro porosity prediction were compared with results of practical castings. It is indicated that two results were in quite good agreement, and the method could predict macro porosity formation more accurately.