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NASA NTRSDate not supplied

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↗

DOE OSTI2026

Microstructural Topology as a Prescriptor for Quantum Coherence: Towards A Unified Framework for Decoherence in Superconducting Qubits

In superconducting quantum circuits, decoherence improvements are frequently obtained through process interventions that simultaneously modify surface chemistry, microstructural topology, and device geometry, leaving mechanistic attribution structurally underdetermined. Predictive materials engineering requires measurable structural statistics to be separated from geometry-dependent coupling coefficients into independently testable factors. We introduce the concept of classical and quantum microstructure. In that context, we formulate a channel-wise separable framework for decoherence in superconducting transmon qubits in which each loss channel is described by a reduced prescriptor. Here, a channel-specific microstructural state variable is determined independently of device geometry, and a geometry-dependent coupling functional is computable from field solutions without reference to surface chemistry. We derive this product form from a spatially resolved kernel representation and establish a perturbative separability criterion that defines the regime where independent variation of the variables is valid. The framework specifies five prescriptor classes for dominant loss pathways in transmon-class devices. Falsifiability is operationalized through a pre-committed 2x2 experimental protocol in which the variables must satisfy independent ratio checks within propagated uncertainty. A Minimum-Dataset Specification standardizes reporting for cross-laboratory inference. Part I establishes the conceptual and mathematical architecture; coordinated experimental validation is reserved for Part II.

Dravid, Vinayak P. [Northwestern U.]↗

DOE OSTI2025

Elasto-viscoplastic fast Fourier transform modeling framework for assessing microstructural effects on stress intensity factors characterizing fracture toughness

A large-strain elasto-viscoplastic fast Fourier transform (LS-EVPFFT) model with non-periodic (NP) velocity-based boundary conditions is adapted to simulate the sensitivity of stress intensity factors on microstructure for 304L stainless steel. The material was characterized via electron backscattered diffraction (EBSD) serial-sectioning to obtain a measured 3-D microstructural cell to perform simulations. The NP-LS-EVPFFT model, including the simulation setup and boundary conditions, was verified using a crystal plasticity finite element (CPFE) model. To this end, the generation of meshes of notched specimens was developed, which involved creating Python scripts for mesh “cutting” in Abaqus, and Sculpt scripts in Cubit for meshing of the measured microstructural cell processed with DREAM.3D. The complexity of the mesh preparation highlighted the advantages of the FFT-based model, which circumvents the mesh generation process. Given the efficiency of the FFT-based model, statistical distribution of stress intensity factors in function of crystal orientation at the crack tip, grain structure, and crystallographic texture surrounding the crack tip were predicted. Further, the distributions reveal about 10% variation of stress intensity factors with microstructure with the most significant sensitivity found to be the crystal orientation at the crack tip. The methodology developed in this work is discussed as a practical simulation tool for predicting the sensitivity of stress intensity factors on microstructural variability in metallic materials.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Advanced Fuels Campaign Execution Plan

The Advanced Fuels Campaign (AFC) Execution Plan outlines the strategy, mission, scope, near-term and long-term goals, structure, and organization associated with nuclear fuels and materials research, development, and demonstration activities within the Department of Energy’s (DOE) Nuclear Fuel Cycle and Supply Chain (NFCSC) program. NFCSC has been given responsibility to identify and mature advanced fuel technologies for the DOE using a science-based approach, focused on developing a fundamental understanding of nuclear fuels and materials to drive development of integrated nuclear fuel and materials technology. This science-based approach combines theory, experiments, and multiscale modeling and simulation to achieve a predictive understanding of relevant behaviors ranging from fuel fabrication processes (and their resulting fuel microstructures) through fuel/cladding performance under irradiation (in contrast to more empirical, observation-based approaches frequently used in fuel performance modeling and fuel qualification). The traditional scope of AFC includes the evaluation and development of multiple fuel forms to support two fuel cycle options: once-through and full recycle. The word “fuel” is used generically to include conventional fuels, transmutation targets, and any associated cladding or duct materials. The once-through fuel cycle addresses advanced light water reactor fuels with enhanced performance, extended burnup, and reduced waste generation. In fiscal year (FY) 2012, AFC’s scope expanded to include research, development, and demonstration (RD&D) for light water reactor (LWR) fuels with enhanced accident tolerance. Fuel fabrication activities include the development of innovative methods to enhance process efficiencies, reduce waste, and improve control over as-fabricated fuel microstructural properties to achieve desired in-reactor performance. Using modern modeling and simulation approaches, the objective is to predict fresh fuel properties given the feedstock characteristics and fabrication process parameters. The performance-related activities include small-scale, in-reactor, and out-of-reactor phenomenological testing (distinct from, but synergistic with, integral prototypic testing) and extensive, quantitative characterization (focusing on characterization of fuel and cladding materials at the scale of microstructure) both before and after testing. Larger-scale, prototypic experiments are conducted in concert with phenomenological testing to drive a Fuel Development and Qualification program, incorporating a fundamental understanding of fuel behavior performance characteristics. Then, using the tools developed under the productive science-based approach, fuels will be optimized to meet specific performance requirements, thereby minimizing the need to repeatedly perform large-scale, integral experiments over a wide parametric range as a means of experimental exploration. Two significant initiatives are underway within AFC. First, a gap analysis completed in early FY 2019 identified critical irradiation testing needs that are lacking within the national light water reactor (LWR) fuels testbed since the shutdown of the Halden Reactor in 2018. The identified gaps are for instrumented, prototypic testing of LWR fuels, especially under boiling water reactor conditions, ramp conditions, and conditions leading to fuel failure; these needs exist for supporting current LWR fuels and their possible extension to higher burnups, but are especially urgent relative to near-term development and qualification of accident-tolerant fuels. Recommendations that resulted from the Halden Gap Analysis focused on enhancements at Advanced Test Reactor (ATR) and Transient Reactor Test Facility (TREAT) to fill gaps in testing capabilities relative to these needs. Second, a concerted effort to develop and demonstrate a systematic approach to accelerating the development, testing, and qualification of new fuel systems has been initiated. This is highlighted by a test strategy that combines the considerable advances in multiscale, mechanistic fuel modeling of recent years with a MiniFuel separate effects test program in the High Flux Isotope Reactor (HFIR) and a Fission Accelerated Steady-state Testing (FAST) semi-integral accelerated test program in ATR. This approach is being tested/demonstrated using the metallic fuel system, but if successful it is expected to be extensible to multiple fuel types and diverse applications. This document includes an overview of the NFCSC program, a definition of science-based development of nuclear fuels, near-term goals for Advanced LWR fuels (ALFs), and longer-term goals for Advanced Reactor Fuels (ARFs) RD&D. This includes the activities that will be conducted to achieve success toward the grand challenge, as well as the goals and milestones to be achieved over the next few decades of research and development. Long-term goals are based on the DOE Office of Nuclear Energ

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1992

Fracture mechanics; Proceedings of the 22nd National Symposium, Atlanta, GA, June 26-28, 1990. Vols. 1 & 2

Current research on fracture mechanics is reviewed, focusing on ductile fracture; high-temperature and time-dependent fracture; 3D problems; interface fracture; microstructural aspects of fatigue and fracture; and fracture predictions and applications. Particular attention is given to the determination and comparison of crack resistance curves from wide plates and fracture mechanics specimens; a relationship between R-curves in contained and uncontained yield; the creep crack growth behavior of titanium alloy Ti-6242; a crack growth response in three heat resistant materials at elevated temperature; a crack-surface-contact model for determining effective-stress-intensity factors; interfacial dislocations in anisotropic bimaterials; an effect of intergranular crack branching on fracture toughness evaluation; the fracture toughness behavior of exservice chromium-molybdenum steels; the application of fracture mechanics to assess the significance of proof loading; and a load ratio method for estimating crack extension.

Ernst, Hugo A.↗

NASA NTRS1993

Thermophysical property sensitivity effects in steel solidification

The simulation of advanced solidification processes via digital computer techniques has gained widespread acceptance during the last decade or so. Models today can predict transient temperature fields, fluid flow fields, important microstructural parameters, and potential defects in castings. However, the lack of accurate thermophysical property data on important industrial alloys threatens to limit the ability of manufacturers to fully capitalize on the technology's benefits. A study of the sensitivity of one such numerical model of a steel plate casting to imposed variations in the data utilized for the thermal conductivity, specific heat, density, and heat of fusion is described. The sensitivity of the data's variability is characterized by its effects on the net solidification time of various points along the centerline of the plate casting. Recommendations for property measurements are given and the implications of data uncertainty for modelers are discussed.

Overfelt, Tony↗

DOE OSTI2026

Controlling homogenization length scales and microstructure in additively manufactured Ti-Ta functionally graded materials

Materials with smooth compositional gradients or functionally grade materials (FGMs) produced via additive manufacturing (AM), enables joining dissimilar materials and optimizing multiple properties in advanced engineering applications. However, as-printed AM microstructures exhibit micro-segregation and solidification defects which, when combined with controlling macroscale gradient properties, complicates necessary post-processing. Here, we use CALPHAD-informed diffusion modelling to design post-processing heat treatments for lightweight to refractory FGMs. Ti-Ta (0 to 85 at. % Ta) FGMs were fabricated using laser-based directed energy deposition AM. Post-processing heat treatments at 1000° C and 1500° C were designed to promote homogenization across specific length scales and experimentally validated. Investigation of chemical segregation and microstructures demonstrated that the length scale of homogenization is controlled as a function of time, temperature, and local composition. Ta-rich regions exhibited incomplete homogenization compared to Ti-rich layers. Unmelted Ta particles were found to completely dissolve at 1500 °C. By controlling cooling rate (200 °C/min), martensitic structures were produced between 14–36 at. % Ta, consistent with martensite-start temperatures calculations, while furnace cooling (2 °C/min) produced α+β morphologies. This work establishes a validated predictive framework for designing post-processing to tailor microstructure and chemical architecture in AM FGMs, facilitating their deployment in demanding environments.

Materials science↗

NASA NTRSDate not supplied

Fast Assessment of Metal Performance through Dislocation Physics and Machine Learning

The microstructure of metals is key to their mechanical properties. The types, density, composition and morphology of crystal defects all have pronounced impact on the properties. Changes to the microstructure occurring during processing and use can be very striking. The emerging technology additive manufacturing (AM) has the potential to improve performance by allowing optimized designs, but the process and environments can lead to unusual microscale features whose properties must be understood and characterized to enable higher technological readiness levels and application. Experimentally, an extensive evaluation of mechanical properties of 3D printed metals is a challenge, and anomalous effects related to the AM process add complexity. We present a new machine learning (ML) model predicting mechanical response based on dislocation mediated plasticity simulations. A large set of 3D discrete dislocation dynamics simulations with wide ranges of loading conditions is transformed to preprocessed data ready for training with the ML model. The trained model can predict the mechanical response of Mo30W for a given microstructure evolution, providing key information essential for optimization of AM processing.

Jaehyun Cho↗

NASA NTRSDate not supplied

Fast Assessment of Metal Performance through Dislocation Physics and Machine Learning

Jaehyun Cho↗

DOE OSTI2024

Virtual texture analysis to understand microstructure effects on deformation twinning and detwinning behavior in BCC metals

Understanding and predicting deformation twinning contributions to plastic deformation in BCC metals has been a long-standing challenge due to the interplay with dislocation slip and non-Schmid effects that render an asymmetry under tension and compression. This paper uses molecular dynamics simulations to understand the effect of unloading and grain orientation on deformation twinning in a nanocrystalline Fe (nc-Fe) system as a model BCC metal. The nc-Fe system is loaded under uniaxial stress tension and compression to understand the effect of grain orientation (Schmid effects) on deformation twinning behavior and the tension/compression asymmetry (non-Schmid effects). A new virtual texture analysis “VirTex” tool is used to understand the role of grain orientation on the nucleation of twins and their contributions to the observed stress–strain response. For certain grain orientations, the twinnability is observed to be different in tension and compression. In addition, the flow stress accommodation from twins in certain grains is observed to be different in tension and compression and different from that for the grains. Subsequent unloading leads to detwinning in the deformed microstructures, where the extent of detwinning depends on the strain from which the system is unloaded and on the morphology of the twin. Lastly, the simulations are carried out to analyze the role of the Schmid factor on the twinnability and asymmetry in tension and compression.

Kannan, Aadhithyan [University of Connecticut, Sto↗

DOE OSTI2024

ExaCA grain structure predictions for laser powder bed fusion processing

This dataset contains simulated cross-sections of laser powder bed fusion grain structures produced using the microstructure model ExaCA, in turn using time-temperature history data produced using the heat transport model AdditiveFOAM. These predictions show the grain structure using various permutations of hatch spacing and nucleation density. Also contained in the dataset are the input files necessary to reproduce the results. AdditiveFOAM (https://github.com/ORNL/AdditiveFOAM) and ExaCA (https://github.com/LLNL/ExaCA), both open source software, are required to reproduce the results in this dataset using the given input files. This DOI was updated 12/09/2025.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Microstructure, Transport, and Mechanics of Compacted Clay Simulated at the 0.1 μm Scale (1400 Smectite Clay Particles) Using a Coarse-Grained Model with Explicit Counterions

Clay-rich geomaterials play a critical role in many subsurface systems. The macroscale properties of these materials (low permeability, high ionic conductivity, high swelling pressure, etc.) are sensitive to molecular-level adsorption and hydration interactions at clay−water interfaces. Efforts to develop multiscale simulation approaches to predict these properties reveal a scale gap between atomistic simulations (typically limited to systems smaller than 10 nm) and continuum-scale models (which use computational grid elements with dimensions ≳ 10 μm). In this study, we present a coarse-grained (CG) framework that partly bridges this gap by simulating compacted smectite clay assemblages with dimensions of 0.1 μm containing 1,400 clay particles across a range of dry densities (1,050 to 1,850 kg·m −3 ) and Na/Ca counterion compositions (Na fraction ranging from 0.2 to 1). The simulated systems, along with their reconstructed binary three-dimensional pore networks, are used to evaluate the microstructure, pore size distribution, tortuosity, ion diffusivity, and swelling pressure of compacted smectite clay. Results show that our approach captures important features of the mesoscale heterogeneity of compacted clays, including tactoid formation, hierarchical porosity, and anisotropic pore networks. Results also reveal how compaction and counterion composition govern emergent behaviors, including dominant pore sizes, directional transport, and electrochemical response. This work highlights the potential of CG simulations to bridge molecular and continuum scales and to advance geotechnical and environmental applications involving clay-rich materials as well as related nanoporous media such as geopolymers and calcium-silicate-hydrate. However, the results also suggest that accurate prediction of certain microstructural and mechanical properties (e.g., swelling pressure) may require even larger-scale systems on the order of 1 μm.

02 PETROLEUM↗

DOE OSTI2025

Microstructure Scale Lithium-Ion Battery Modeling: Part II. On In-Plane Heterogeneities and the Mechanisms that Regulate Them

Li-ion batteries performance and degradation are typically modeled at the macroscopic scale, that is neglecting in-plane heterogeneities that can arise from non-uniform electrode microstructures. Herein, a microstructure scale electrochemical model is used to quantify the impact of microstructure heterogeneity on cell performance during fast charging. The model predicts the electrolyte and solid concentration in-plane standard deviation can reach, respectively, ≈200 mol·m −3 and 6–7 kmol·m −3 locally. Further, the intercalation current density in-plane relative standard deviation can reach extremely high values, around 100% in the cathode and well above 100% in the anode graphite. These denote highly non-uniform lithiation rates and material utilization within each slice of the microstructure along the cell thickness. Non-uniform curvatures, at the particle scale (surface roughness) and between particles (size distribution), were found to initiate these in-plane heterogeneities, while an OCP-induced mechanism subsequently regulates them. The present model provides new insights into small length scale heterogeneity impact on battery performance not available with standard macro-scale/P2D modeling.

25 ENERGY STORAGE↗

NASA NTRS2002

Techniques Optimized for Reducing Instabilities in Advanced Nickel-Base Superalloys for Turbine Blades

The High-Speed Research (HSR) Airfoil Alloy program developed fourth-generation single-crystal superalloys with up to an 85 F increase in creep rupture capability over current production airfoil alloys. Recent results have been generated at the NASA Glenn Research Center on these fourth-generation alloys, but in coated form, for subsonic turbine blade applications under NASA's Ultra-Efficient Engine Technology (UEET) Program. One goal for UEET is to optimize the airfoil alloy/thermal barrier coating system for 3100 F turbine inlet temperatures. The state-of-the art turbine blade airfoil system consists of a superalloy single crystal that provides the basic mechanical performance of the airfoil. A thermal barrier coating is used to reduce the temperature of the base superalloy, and a bondcoat is deposited between the base material and the thermal barrier coating. The bondcoat improves the oxidation and corrosion resistance of the base superalloy and improves the spallation resistance of the thermal barrier coating. A commercial platinum aluminide bondcoat was applied to the HSR-developed alloys, and a diffusion zone developed as a result of interaction between the bondcoat and the superalloy. Optimized strength is obtained for superalloys when the refractory element content is high and the limits of microstructural stability are approached or exceeded slightly. For fourthgeneration alloys, instability leads to the formation of topologically close packed (TCP) phases, which form internally in the superalloy, and a secondary reaction zone (SRZ), which forms under the diffusion zone. There was a concern that excessive quantities of either TCP or SRZ might decrease the mechanical properties of the superalloy, with SRZ thought to be particularly detrimental and its formation unpredictable. Thus, an SRZreduction effort was initiated in the NASA UEET Program so that methods developed during the HSR project could be optimized further to reduce or eliminate the SRZ. An SRZ is a three-phase constituent composed of TCP and stringers of gamma phase in a matrix of gamma prime. An incoherent grain boundary separates the SRZ from the gammagamma prime microstructure of the superalloy. The SRZ is believed to form as a result of local chemistry changes in the superalloy due to the application of the diffusion aluminide bondcoat. Locally high surface stresses also appear to promote the formation of the SRZ. Thus, techniques that change the local alloy chemistry or reduce surface stresses have been examined for their effectiveness in reducing SRZ. These SRZ-reduction steps are performed on the test specimen or the turbine blade before the bondcoat is applied. Stressrelief heat treatments developed at NASA Glenn have been demonstrated to reduce significantly the amount of SRZ that develops during subsequent high-temperature exposures. Stress-relief heat treatments reduce surface stresses by recrystallizing a thin surface layer of the superalloy. However, in alloys with very high propensities to form SRZ, stress relief heat treatments alone do not eliminate SRZ entirely. Thus, techniques that modify the local chemistry under the bondcoat have been emphasized and optimized successfully at Glenn. One such technique is carburization, which changes the local chemistry by forming submicron carbides near the surface of the superalloy. Detailed characterizations have demonstrated that the depth and uniform distribution of these carbides are enhanced when a stress relief treatment and an appropriate surface preparation are employed in advance of the carburization treatment. Even in alloys that have the propensity to develop a continuous SRZ layer beneath the diffusion zone, the SRZ has been completely eliminated or reduced to low, manageable levels when this combination of techniques is utilized. Now that the techniques to mitigate SRZ have been established at Glenn, TCP phase formation is being emphasized in ongoing work under the UEET Program. The limitsf stability of the fourth-generation alloys with respect to TCP phase formation are currently being defined along with high-temperature creep rupture properties. In addition, a regression model is being developed at Glenn for the prediction of the presence of TCP phase in the microstructure and SRZ under the diffusion zone. The model is based on a design-of-experiments methodology with emphasis on the potential synergistic effects of alloying elements.

MacKay, Rebecca A.↗

NASA NTRS1988

Fatigue damage modeling for coated single crystal superalloys

A high temperature, low-cycle fatigue life prediction method for coated single crystal nickel-base superalloys is being developed. The method is being developed for use in predicting crack initiation life of coated single crystal turbine airfoils. Although the models are being developed using coated single crystal PWA 1480, they should be readily adaptable to other coated nickel-base single crystal materials. The coatings choosen for this effort were of two generic types: a low pressure plasma sprayed NiCoCrAlY overlay, designated PWA 286, and an aluminide diffusion, designated PWA 273. In order to predict the useful crack initiation life of airfoils, the constitutive and failure behavior of the coating/substrate combination must be taken into account. Coatings alter the airfoil surface microstructure and are a primary source from which cracks originate. The adopted life prediction approach addresses this complexity by separating the coating and single crystal crack initiation regimes. This provides a flexible means for using different life model formulations for the coating and single crystal materials. At the completion of this program, all constitutive and life model formulations will be available in equation form and as software. The software will use the MARC general purpose finite element code to drive the constitutive models and calculate life parameters.

Nissley, David M.↗

DOE OSTI2026

A User-Friendly GUI Tool for Automated Microstructural Analysis of Fiber-Reinforced Composites and Porous Structures

Understanding and quantifying microstructural features such as fiber orientation and porosity is critical for predicting the mechanical behavior and performance of fiber-reinforced polymer composites. Traditional manual analysis is time-consuming, subjective, and unsuitable for high-throughput datasets. We present a graphical user interface (GUI) application that automates the analysis of microscopy images to extract key microstructural metrics, including fiber orientation tensors, fiber orientation distribution, porosity and pore size distribution. The app integrates multiple image segmentation techniques including global and local thresholding, clustering, and region-based approaches, offering flexibility for different types of image qualities and features. Users can load microstructural images, select regions of interest and segmentation techniques tailored to their image dataset. It also addresses a critical challenge in fiber orientation analysis: the ambiguities caused by touching, overlapping, or partially cut fibers. It supports autorun examples for standardized workflows, enabling reproducible analysis and facilitating training and benchmarking. This tool significantly reduces manual intervention, enhances consistency, and accelerates data generation for structure–property modeling, process optimization, and digital materials research. The tool is intended for use by materials scientists, engineers, and researchers engaged in composite characterization, quality control, and machine learning-based microstructural studies.

Chawla, Komal [ORNL] (ORCID:0000000190327565)↗

NASA NTRSDate not supplied

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↗

DOE OSTI2024

In situ study of microstructure evolution and α → ω phase transition in annealed and pre-deformed Zr under hydrostatic loading

The detailed study of the effect of the initial microstructure on its evolution under hydrostatic compression before, during, and after the irreversible α → ω phase transformation and during pressure release in Zr using in situ x-ray diffraction is presented. Two samples were studied: one is plastically pre-deformed Zr with saturated hardness and the other is annealed. Phase transformation α → ω initiates at lower pressure for a pre-deformed sample but for a volume fraction of ω Zr, c > 0.7, a larger volume fraction is observed for the annealed sample. This implies that the proportionality between the athermal resistance to the transformation and the yield strength in the continuum phase transformation theory is invalid; an advanced version of the theory is outlined. Phenomenological plasticity theory under hydrostatic loading is outlined in terms of microstructural parameters, and plastic strain is estimated. During transformation, the first rule is suggested, i.e., the average domain size, microstrain, and dislocation density in ω Zr for c < 0.8 are functions of the volume fraction, c of ω Zr only, which are independent of the plastic strain tensor prior to transformation and pressure. The microstructure is not inherited during phase transformation. Surprisingly, for the annealed sample, the final dislocation density and the average microstrain after pressure release in the ω phase are larger than for the severely pre-deformed sample. The results suggest that an extended experimental basis is required for the predictive models for the combined pressure-induced phase transformations and microstructure evolutions.

36 MATERIALS SCIENCE↗