Integrated Monte Carlo Microstructure and Analytical Temperature Simulations of Additive Manufacturing
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Additive manufacturing↗
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A Geometric Approach to Modeling Microstructurally Small Fatigue Crack Formation: Simulation and Prediction of Crack Nucleation in AA 7075-T651 - 2
The objective of this paper is to develop further a framework for computationally modeling microstructurally small fatigue crack growth in AA 7075-T651 [1]. The focus is on the nucleation event, when a crack extends from within a second-phase particle into a surrounding grain, since this has been observed to be an initiating mechanism for fatigue crack growth in this alloy. It is hypothesized that nucleation can be predicted by computing a non-local nucleation metric near the crack front. The hypothesis is tested by employing a combination of experimentation and nite element modeling in which various slip-based and energy-based nucleation metrics are tested for validity, where each metric is derived from a continuum crystal plasticity formulation. To investigate each metric, a non-local procedure is developed for the calculation of nucleation metrics in the neighborhood of a crack front. Initially, an idealized baseline model consisting of a single grain containing a semi-ellipsoidal surface particle is studied to investigate the dependence of each nucleation metric on lattice orientation, number of load cycles, and non-local regularization method. This is followed by a comparison of experimental observations and computational results for microstructural models constructed by replicating the observed microstructural geometry near second-phase particles in fatigue specimens. It is found that orientation strongly influences the direction of slip localization and, as a result, in uences the nucleation mechanism. Also, the baseline models, replication models, and past experimental observation consistently suggest that a set of particular grain orientations is most likely to nucleate fatigue cracks. It is found that a continuum crystal plasticity model and a non-local nucleation metric can be used to predict the nucleation event in AA 7075-T651. However, nucleation metric threshold values that correspond to various nucleation governing mechanisms must be calibrated.
Hochhalter, Jake D.↗
Three-Dimensional In Situ Observations of Polycrystalline Microstructure Evolution During Directional Solidification of Transparent Alloys Aboard the ISS and Quantitative Comparison with Numerical Modeling
Cellular/dendritic microstructures formed during solidification have a crucial influence on the mechanical properties of a wide range of structural alloys. By minimizing the amount of gravity-induced convection in the liquid, directional solidification experiments using transparent organic alloys conducted in the DECLIC-DSI onboard the International Space Station have provided unique 3D in situ observations of the spatiotemporal evolution of the solid-liquid interface during the formation of cellular and dendritic microstructures under purely diffusive growth conditions. Those observations have made it possible to perform benchmark quantitative comparisons with the predictions of state-of-the-art phase-field simulations of microstructure formation in 3D on experimentally relevant length and time scales. This talk will report quantitative comparisons between microgravity experiments and phase-field simulations in succinonitrile-camphor alloys of two different compositions, which shed new light on the selection of dendritic array structures, and on roles of macroscopic curvatures and subgrain boundaries between grains with a small misorientation with respect to the temperature gradient in the spatiotemporal evolution of the primary cellular spacing.
Kaihua Ji↗
Three-dimensional in Situ Observations of Polycrystalline Microstructure Evolution During Directional Solidification of Transparent Alloys Aboard the ISS and Quantitative Comparison with Numerical Modeling
Cellular/dendritic microstructures formed during solidification have a crucial influence on the mechanical properties of a wide range of structural alloys. By minimizing the amount of gravity-induced convection in the liquid, directional solidification experiments using transparent organic alloys conducted in the DECLIC-DSI onboard the International Space Station have provided unique 3D in situ observations of the spatiotemporal evolution of the solid-liquid interface during the formation of cellular and dendritic microstructures under purely diffusive growth conditions in polycrystalline samples containing several grains with a small misorientation with respect to the temperature gradient. Those observations have made it possible to perform benchmark quantitative comparisons with the predictions of state-of-the-art phase-field simulations of microstructure formation in 3D on experimentally relevant length and time scales. This talk will report quantitative comparisons between microgravity experiments and phase-field simulations in succinonitrile-camphor alloys of two different compositions that shed new light on the role of subgrain boundaries in the spatiotemporal evolution of the primary cellular spacing and the selection of dendritic array structures.
Kaihua Ji↗
Physics-Based Modeling and Simulation of Self-Reacting Friction Stir Welding Using Computational Fluid Dynamics
A physics-based model was developed to simulate the behavior of material in a self-reacting friction stir welding (SR-FSW) process for the joining of metals. This steady-state model builds upon fundamental computational fluid dynamic (CFD) principles within Ansys Fluent to solve the discretized equations. The effective viscosity is calculated using a viscoplastic model using a Sheppard-Wright formulation of flow stress. Numerous advancements have been made in the incorporated physics including (1) temperature-dependent material properties; (2) locally adaptable flow and thermal boundary conditions; and (3) adapting material properties in nugget in response to microstructural changes. Simulation strategies to accelerate computation and improve numerical stability include adapting the mesh refinement and solver relaxation factors during simulation. The result is a highly robust and computationally efficient model capable of providing the material flow and temperature history across the domain. As material history determines the local microstructure and ultimately weld strength, an accurate and detailed physics-based model has the potential to accelerate SR-FSW process development. The model is highly adaptable to changes in process parameters, tool design, or alloy.
Process Modeling↗
In Situ Observation of Growth Dynamics in DECLIC Directional Solidification Insert Onboard ISS: DSI-R Flight Campaign
The study of solidification microstructure formation is of utmost importance for materials design and processing, as solid-liquid interface patterns largely govern mechanical and physical properties. Pattern selection occurs under dynamic conditions of growth in which the initial morphological instability evolves nonlinearly and undergoes a reorganization process. The dynamic and nonlinear nature of this instability renders in situ observation of the interface an invaluable tool to gain knowledge on the time-evolution of the interface pattern. Transparent organic analogs, which solidify like metallic alloys, allow direct visualization of interface dynamics. Extensive ground-based studies of both metallic and organic bulk samples have established the presence of significant convection during solidification processes that alters the formation of interfacial microstructures. A reduced-gravity environment is therefore mandatory for fluid flow elimination in bulk samples. In the framework of the CNES project MISOL3D (MIcrostrutures de SOLidification 3D) and the NASA projects DSIP (Dynamical Selection of 3D Interface Patterns), SPADES (SPAtiotemporal Evolution of three-dimensional DEndritic array Structures) and CAMUS (ComputAtional Studies of MicrostrUcture Formation During Alloy Solidification in Microgravity), we participated in the development of the Directional Solidification Insert (DSI) of the DEvice for the study of Critical Liquids and Crystallization (DECLIC). The DECLIC-DSI is dedicated to in situ and real-time characterization of solid-liquid interface patterns during directional solidification of transparent alloys in diffusive transport regime. Between April 2010 and March 2011, the first ISS campaign (DSI) explored the entire range of microstructures resulting in unprecedented observations. A second campaign (DSI-R), performed between October 2017 and December 2018, in which the insert contained an alloy of higher solute concentration, allowed to complete the benchmark database. The increase of solute concentration resulted in well-developed dendritic patterns at lower velocities (lower interface curvature and larger tip radius). The microstructure resulting from dendritic growth is dominant in metallurgy so that it is fundamental to understand the mechanisms of its formation. The main aims of this experimental campaign are to understand: the mechanisms of the cell to dendrite transition, the fundamental mechanisms of sidebranching formation, the dependence of dendrite tip shapes on growth conditions, the interaction of primary array and secondary sidebranches, and the influence of subgrain boundaries on the spatiotemporal organization of the array structure. Preparation, analysis and interpretation of the experiments performed onboard ISS are considerably enhanced by experiments performed on ground using thin-samples (Pr. Trivedi’s group) and phase-field simulations of microstructure formation in a diffuse growth regime (Pr. Karma’s group). In this summary, we will present an initial assessment of the results obtained during the DSI-R campaign. Nomenclature Vp: pulling velocity G: thermal gradient L: solidified length rtip: tip curvature radius Acronyms/Abbreviations CADMOS: Centre d'Aide au Développement des activités en Micro-pesanteur et des Opérations Spatiales CNES: Centre National d’Études Spatiales DECLIC: Device for the study of Critical LIquids and Crystallization DSI: Directional Solidification Insert DSI-R: Directional Solidification Insert - Refurbish ISS: International Space Station NASA: National Aeronautics and Space Administration PF: phase-field SCN: Succinonitrile 3D: three-dimensional
Mota, F.L.↗
Development of a One-Domain Volume-Averaged Navier–Stokes Solver
The interaction between a high-enthalpy flow and a thermal protection material is inherently multiscale and multiphysics. In conventional aerothermal analyses, the external flow and material response are generally modeled using separate computational domains coupled through boundary conditions at the material surface. Although this approach has supported many practical applications, it requires assumptions about the location and behavior of the interface and may become difficult to apply when material decomposition, internal reactions, and surface recession substantially alter the porous structure. This report presents the development of a one-domain formulation in which the free-fluid and porous-material regions are represented within a single computational domain. The formulation is based on the volume-averaged Navier–Stokes (VANS) equations, derived from the governing equations for reacting, compressible flow and condensed material. Volume averaging transfers the influence of the unresolved material microstructure to the macroscale equations through effective transport properties, interfacial source terms, and dispersion fluxes. Particular attention is given to regions in which porosity and permeability vary rapidly, including the diffuse transition between a porous material and the surrounding fluid. The resulting equations are implemented in the Porous-material Analysis Toolbox based on OpenFOAM (PATO). The report describes the pressure–velocity coupling strategy used by the solver, examines spatial filtering techniques for deriving effective properties, and evaluates the influence of a smoothly varying interface permeability. Numerical demonstrations include canonical porous-flow configurations, a flow-tube configuration representative of FiberForm® permeability experiments, and the oxidation of a porous carbon material. The purpose of this work is to establish a mathematical and computational foundation for a unified treatment of flow and thermal protection material response. The present formulation is intended to support the progressive inclusion of additional physical processes, including multicomponent transport, finite-rate gas–surface chemistry, pyrolysis, internal oxidation, and material recession. It also provides a framework for connecting pore-scale simulations and microstructural characterization with macroscale aerothermal-response calculations. This report is intended for researchers and engineers working in computational fluid dynamics, porous-media transport, material response, and thermal protection system modeling. It documents both the theoretical development and the initial numerical assessment of the one-domain approach, while identifying the closure of effective and dispersion terms as an important subject for continued investigation.
Ablation↗
Computational Microstructure Modeling for Powder Bed Fusion Additive Manufacturing
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ICME↗
Computer Simulation of Spatial Arrangement and Connectivity of Particles in Three-Dimensional Microstructure: Application to Model Electrical Conductivity of Polymer Matrix Composite
Computer simulation is a powerful tool for analyzing the geometry of three-dimensional microstructure. A computer simulation model is developed to represent the three-dimensional microstructure of a two-phase particulate composite where particles may be in contact with one another but do not overlap significantly. The model is used to quantify the "connectedness" of the particulate phase of a polymer matrix composite containing hollow carbon particles in a dielectric polymer resin matrix. The simulations are utilized to estimate the morphological percolation volume fraction for electrical conduction, and the effective volume fraction of the particles that actually take part in the electrical conduction. The calculated values of the effective volume fraction are used as an input for a self-consistent physical model for electrical conductivity. The predicted values of electrical conductivity are in very good agreement with the corresponding experimental data on a series of specimens having different particulate volume fraction.
Louis, P.↗
Multiscale Analysis of Structurally-Graded Microstructures Using Molecular Dynamics, Discrete Dislocation Dynamics and Continuum Crystal Plasticity
A multiscale modeling methodology is developed for structurally-graded material microstructures. Molecular dynamic (MD) simulations are performed at the nanoscale to determine fundamental failure mechanisms and quantify material constitutive parameters. These parameters are used to calibrate material processes at the mesoscale using discrete dislocation dynamics (DD). Different grain boundary interactions with dislocations are analyzed using DD to predict grain-size dependent stress-strain behavior. These relationships are mapped into crystal plasticity (CP) parameters to develop a computationally efficient finite element-based DD/CP model for continuum-level simulations and complete the multiscale analysis by predicting the behavior of macroscopic physical specimens. The present analysis is focused on simulating the behavior of a graded microstructure in which grain sizes are on the order of nanometers in the exterior region and transition to larger, multi-micron size in the interior domain. This microstructural configuration has been shown to offer improved mechanical properties over homogeneous coarse-grained materials by increasing yield stress while maintaining ductility. Various mesoscopic polycrystal models of structurally-graded microstructures are generated, analyzed and used as a benchmark for comparison between multiscale DD/CP model and DD predictions. A final series of simulations utilize the DD/CP analysis method exclusively to study macroscopic models that cannot be analyzed by MD or DD methods alone due to the model size.
Saether, Erik↗
Particle-Based Fiber Models of Woven Materials for Earth Entry Thermal Protection
Applications requiring materials with layer-to-layer strength, from basketry to thermal protection systems, use interlaced, three-dimensional woven materials. NASA is developing and deploying woven material heat shields for missions, including Artemis I (3D-MAT for compression pads) and potentially Mars Sample Return - Earth Entry System. These materials are complex, hierarchical and must protect from extreme environments and phenomena, such as deformation, impact and high-enthalpy heating. Woven material performance depends on microstructure, damage and weave geometry. Therefore, fiber-specific models are needed to simulate fiber contacts within the weave hierarchical geometry (fiber to tow to yarn to weave) and the inherent directionality of fibers. Explicit fiber models can simulate how weave microstructure evolution affects thermal and mechanical properties. We parameterize a discrete element bonded particle models (DEM-BPM) of fibers to capture thermal and mechanical behavior within and between fibers, with bonded and contact forces, respectively. We study the proportion of heat transfer and stress via the contact network, fiber bonds and the weave geometry, for example, with respect to yarn warp-weft identity (whether it interlaces weave layers). Our results demonstrate the importance of explicit fiber modeling for connecting microstructure with thermal and mechanical properties.
woven material↗
Particle-Based Fiber Models of Woven Materials for Earth Entry Thermal Protection
Applications requiring materials with layer-to-layer strength, from basketry to thermal protection systems, use interlaced, three-dimensional woven materials. NASA is developing and deploying woven material heat shields for missions, including Artemis I (3D-MAT for compression pads) and potentially Mars Sample Return - Earth Entry System. These materials are complex, hierarchical and must protect from extreme environments and phenomena, such as deformation, impact and high-enthalpy heating. Woven material performance depends on microstructure, damage and weave geometry. Therefore, fiber-specific models are needed to simulate fiber contacts within the weave hierarchical geometry (fiber to tow to yarn to weave) and the inherent directionality of fibers. Explicit fiber models can simulate how weave microstructure evolution affects thermal and mechanical properties. We parameterize a discrete element bonded particle models (DEM-BPM) of fibers to capture thermal and mechanical behavior within and between fibers, with bonded and contact forces, respectively. We study the proportion of heat transfer and stress via the contact network, fiber bonds and the weave geometry, for example, with respect to yarn warp-weft identity (whether it interlaces weave layers). Our results demonstrate the importance of explicit fiber modeling for connecting microstructure with thermal and mechanical properties.
woven material↗
Microstructural Study of Micron-Sized Craters Simulating Stardust Impacts in Aluminum 1100 Targets
Various microscopic techniques were used to characterize experimental micro- craters in aluminium foils to prepare for the comprehensive analysis of the cometary and interstellar particle impacts in aluminium foils to be returned by the Stardust mission. First, SEM (Scanning Electron Microscopy) and EDS (Energy Dispersive X-ray Spectroscopy) were used to study the morphology of the impact craters and the bulk composition of the residues left by soda-lime glass impactors. A more detailed structural and compositional study of impactor remnants was then performed using TEM (Transmission Electron Microscopy), EDS, and electron diffraction methods. The TEM samples were prepared by Focused Ion Beam (FIB) methods. This technique proved to be especially valuable in studying impact crater residues and impact crater morphology. Finally, we also showed that InfraRed microscopy (IR) can be a quick and reliable tool for such investigations. The combination of all of these tools enables a complete microscopic characterization of the craters.
Leroux, Hugues↗
Analytical Simulation of Effects of Local Mechanisms and Microstructure on Creep Response of Unidirectional Ceramic Matrix Composites
A micromechanics-based method has been developed to analyze the creep response of uncoated ceramic matrix minicomposites. Although the global stress level at which the creep response is analyzed is lower than the composite proportional limit, local stresses are assumed to be high enough that localized damage is present in the composite in the form of matrix microcracks. To model the composite creep response, including the effects of matrix cracking, a fiber shear lag-based methodology is employed. In this approach, stresses are assumed to vary in the fiber as a function of time and distance from the crack plane. The varying stresses are then used to compute the overall creep strain for the composite. Various assumptions regarding the level of matrix microcracking in the composite and the level of creep in the fiber and matrix in various portions of the composite unit cell are also examined. The creep response of the fiber is modeled using a linear Burgers model. The model is applied to a SiCf/SiC unidirectional minicomposite system. The computed creep results are compared to experimentally obtained values. The effects of the local fiber volume fraction on the overall creep response of the composite are also studied. This work will allow increased understanding of the key material damage mechanisms and load sharing that take place during creep conditions and can be expanded to provide improved analysis methods for full macrocomposites.
Micromechanics↗
Multiscale Modeling of Damage Processes in Aluminum Alloys: Grain-Scale Mechanisms
This paper has two goals related to the development of a physically-grounded methodology for modeling the initial stages of fatigue crack growth in an aluminum alloy. The aluminum alloy, AA 7075-T651, is susceptible to fatigue cracking that nucleates from cracked second phase iron-bearing particles. Thus, the first goal of the paper is to validate an existing framework for the prediction of the conditions under which the particles crack. The observed statistics of particle cracking (defined as incubation for this alloy) must be accurately predicted to simulate the stochastic nature of microstructurally small fatigue crack (MSFC) formation. Also, only by simulating incubation of damage in a statistically accurate manner can subsequent stages of crack growth be accurately predicted. To maintain fidelity and computational efficiency, a filtering procedure was developed to eliminate particles that were unlikely to crack. The particle filter considers the distributions of particle sizes and shapes, grain texture, and the configuration of the surrounding grains. This filter helps substantially reduce the number of particles that need to be included in the microstructural models and forms the basis of the future work on the subsequent stages of MSFC, crack nucleation and microstructurally small crack propagation. A physics-based approach to simulating fracture should ultimately begin at nanometer length scale, in which atomistic simulation is used to predict the fundamental damage mechanisms of MSFC. These mechanisms include dislocation formation and interaction, interstitial void formation, and atomic diffusion. However, atomistic simulations quickly become computationally intractable as the system size increases, especially when directly linking to the already large microstructural models. Therefore, the second goal of this paper is to propose a method that will incorporate atomistic simulation and small-scale experimental characterization into the existing multiscale framework. At the microscale, the nanoscale mechanics are represented within cohesive zones where appropriate, i.e. where the mechanics observed at the nanoscale can be represented as occurring on a plane such as at grain boundaries or slip planes at a crack front. Important advancements that are yet to be made include: 1. an increased fidelity in cohesive zone modeling; 2. a means to understand how atomistic simulation scales with time; 3. a new experimental methodology for generating empirical models for CZMs and emerging materials; and 4. a validation of simulations of the damage processes at the nano-micro scale. With ever-increasing computer power, the long-term ability to employ atomistic simulation for the prognosis of structural components will not be limited by computation power, but by our lack of knowledge in incorporating atomistic models into simulations of MSFC into a multiscale framework.
Hochhalter, J. D.↗
The importance of properties in modeling
Casting and welding of superalloys, stainless steel and titanium alloys are processes which can be improved through modeling of heat flow, fluid flow, residual stress development, and microstructural evolution. These simulations require inputs of thermophysical data, some of which involves the partially or totally liquid state. In particular, these processes involve melting, flow in the liquid, and solidification. Modeling of such processes can lead to an improved understanding of defects such as shrinkage, inclusions, cracks, incomplete filling (or penetration), macrosegregation, improper grain structure, and deviations from dimensional specifications. Effective modeling can shorten process development time and improve quality. An approach to these problems is to develop efficient models; validate through correlations with thermal, distortion, and microstructural data; run parametric studies; extract knowledge based rules; and apply to adaptive closed loop control systems. With the appropriate pre- and post-processing, such analyses can be made 'user friendly'. This would include graphical user interfaces as well as realistic images and color maps. In such form, these models can be used for sensitivity analyses, which are useful in defining appropriate sensors and in the development of control strategies. Such modeling can be done at several levels, e.g., the MARO level, modeling large scale phenomena such as heat and fluid flow or material deformation; the MICRO level, modeling the development of dendrites, grains or precipitates; or at the NANO level, modeling point defects, dislocations, stacking faults, etc. There are many computational issues associated with these simulations, e.g. computational efficiency and accuracy. In addition, there are many materials issues, not the least of which is the availability of accurate high temperature thermophysical data for complex alloys. This would include latent heat of fusion, temperature dependent heat capacity and thermal conductivity (for liquid and solid), viscosity, surface tension, thermal expansion, mechanical properties, etc. Preliminary data is frequently gathered from the literature; however, this is often not available for modern alloys. If additional data are required, measurements can be used; however, these are costly, time consuming and can be erroneous due to a lack of testing standards or impure materials. Microstructural predictors can be extracted from thermal information, e.g. cooling rate and thermal gradient; the prediction of microstructure is dependent on solidus and liquidus temperature, mushy zone permeability, the solidification curve, volume changes, phase transformations, alloying effects (such as surface tension or viscosity), mold/metal reactions, metal/environment reactions, etc. Defect maps may be needed to predict the onset of shrinkage, hot cracking or 'freckling'. Constants may be needed for stress relaxation, dendrite coarsening, vaporization, etc. Visualization was used as a tool to better comprehend complex data sets associated with the analysis of directional solidification (including crystal growth) and welding. Examples include not only isotherms, but also cooling rate, growth rate and thermal gradient. The latter two are not single valued scalars, but rather time and space dependent vector fields. Efficient models were developed for both casting and welding to predict heat flow and the relationship to dendrite and grain growth. These codes include many of the non-linear effects, e.g. radiation, which dominate these processes. The home-built FDM code(s) were designed to be useful not only to the scientist, but also to the process engineer. Special output can be requested to compare directly to experimental data. Visualization procedures were developed to visualize critical results, e.g. fusion zone width at the surface opposite that where the arc is applied ('penetration'). Both elaborate and simplified distortion analyses were carried out. It is clear that extensive mechanical property data are critical in order to accurately predict residual stress patterns. A scheme is currently being developed to integrate these modeling tools into a set of control algorithms; however, the success of this approach is critically dependent on the availability of accurate high temperature thermophysical data.
Giamei, A. F.↗
Comparison of Commonly-Used Microwave Radiative Transfer Models for Snow Remote Sensing
This paper reviews four commonly-used microwave radiative transfer models that take different electromagnetic approaches to simulate snow brightness temperature (T(sub B)): the Dense Media Radiative Transfer - Multi-Layer model (DMRT-ML), the Dense Media Radiative Transfer - Quasi-Crystalline Approximation Mie scattering of Sticky spheres (DMRT-QMS), the Helsinki University of Technology n-Layers model (HUT-nlayers) and the Microwave Emission Model of Layered Snowpacks (MEMLS). Using the same extensively measured physical snowpack properties, we compared the simulated T(sub B) at 11, 19 and 37 GHz from these four models. The analysis focuses on the impact of using different types of measured snow microstructure metrics in the simulations. In addition to density, snow microstructure is defined for each snow layer by grain optical diameter (Do) and stickiness for DMRT-ML and DMRT-QMS, mean grain geometrical maximum extent (D(sub max)) for HUT n-layers and the exponential correlation length for MEMLS. These metrics were derived from either in-situ measurements of snow specific surface area (SSA) or macrophotos of grain sizes (D(sub max)), assuming non-sticky spheres for the DMRT models. Simulated T(sub B) sensitivity analysis using the same inputs shows relatively consistent T(sub B) behavior as a function of Do and density variations for the vertical polarization (maximum deviation of 18 K and 27 K, respectively), while some divergences appear in simulated variations for the polarization ratio (PR). Comparisons with ground based radiometric measurements show that the simulations based on snow SSA measurements have to be scaled with a model-specific factor of Do in order to minimize the root mean square error (RMSE) between measured and simulated T(sub B). Results using in-situ grain size measurements (SSA or D(sub max), depending on the model) give a mean T(sub B) RMSE (19 and 37 GHz) of the order of 16-26 K, which is similar for all models when the snow microstructure metrics are scaled. However, the MEMLS model converges to better results when driven by the correlation length estimated from in-situ SSA measurements rather than D(sub max) measurements. On a practical level, this paper shows that the SSA parameter, a snow property that is easy to retrieve in-situ, appears to be the most relevant parameter for characterizing snow microstructure, despite the need for a scaling factor.
Snow↗
Characterization and Computational Modeling of Minor Phases in Alloy LSHR
The minor phases of powder metallurgy disk superalloy LSHR were studied. Samples were consistently heat treated at three different temperatures for long times to approach equilibrium. Additional heat treatments were also performed for shorter times, to assess minor phase kinetics in non-equilibrium conditions. Minor phases including MC carbides, M23C6 carbides, M3B2 borides, and sigma were identified. Their average sizes and total area fractions were determined. CALPHAD thermodynamics databases and PrecipiCalc(TradeMark), a computational precipitation modeling tool, were employed with Ni-base thermodynamics and diffusion databases to model and simulate the phase microstructural evolution observed in the experiments with an objective to identify the model limitations and the directions of model enhancement.
Jou, Herng-Jeng↗