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DOE OSTI2020

NDX: Neutron Dose Rate Meters with Extended Capabilities

Particle accelerators, irradiation facilities, and nuclear power plants would benefit from using neutron dose rate meters featuring improved energy response covering full range of expected neutron energies, improved dynamic range of measured dose rates while providing the real-time data, and improved ability to operate in harsh radiation environments including heavy photon backgrounds and pulsed beams. The novel design of the neutron moderator for the NDX dose rate meter implements a layer of a Beryllium-loaded medium Z material which, similar to the earlier known WENDI detectors, allows the device to detect higher energy neutron flux and convert it to dose. Using Beryllium helps to fill the known dip in the response functions around 5-50 MeV. Optimized design parameter set, obtained using FLUKA Monte Carlo simulations, features the NDX moderator made of polyethylene embedding a layer of BeCu alloy inside, with the dose rate response constant within ±10% in the neutron energy range from about 100 keV to 500 MeV, and ±25% essentially in the full energy range above thermal. A new sensor technique implemented in the NDX is based on using the Ionization Chamber (IC) filled with 3He gas to capture the moderated neutron fluence, and includes a symmetric IC filled with regular 4He to evaluate the contributions due to the non-neutron ionizing radiation. Advantages of the method include large accessible dynamic range, relative insensitivity of the IC probes to photon radiation fields, and the ability to subtract their contribution. Two prototype NDX detectors were built, calibrated, and operated in various conditions at the CEBAF 12 GeV electron accelerator at JLab. The first results showed reliable neutron dose rate measurements in the presence of overwhelming photon radiation fields, and at practical high dose rate levels of up to approximately 10 Sv/h. Detector design, operation, first results, and further development plans are presented.

Degtiarenko, Pavel V.↗

DOE OSTI2018

In situ dynamic compression wave behavior in additively manufactured lattice materials

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Lind, Jonathan (ORCID:0000000164060617)↗

DOE OSTI2014

A non-linear elastic constitutive framework for replicating plastic deformation in solids.

Ductile metals and other materials typically deform plastically under large applied loads; a behavior most often modeled using plastic deformation constitutive models. However, it is possible to capture some of the key behaviors of plastic deformation using only the framework for nonlinear elastic mechanics. In this paper, we develop a phenomenological, hysteretic, nonlinear elastic constitutive model that captures many of the features expected of a plastic deformation model. This model is based on calculating a secant modulus directly from a material s stress-strain curve. Scalar stress and strain values are obtained in three dimensions by using the von Mises invariants. Hysteresis is incorporated by tracking an additional history variable and assuming an elastic unloading response. This model is demonstrated in both single- and multi-element simulations under varying strain conditions.

Roberts, Scott Alan↗

NASA NTRS2003

Application of Probability Methods to Assess Crash Modeling Uncertainty

Full-scale aircraft crash simulations performed with nonlinear, transient dynamic, finite element codes can incorporate structural complexities such as: geometrically accurate models; human occupant models; and advanced material models to include nonlinear stress-strain behaviors, and material failure. Validation of these crash simulations is difficult due to a lack of sufficient information to adequately determine the uncertainty in the experimental data and the appropriateness of modeling assumptions. This paper evaluates probabilistic approaches to quantify the effects of finite element modeling assumptions on the predicted responses. The vertical drop test of a Fokker F28 fuselage section will be the focus of this paper. The results of a probabilistic analysis using finite element simulations will be compared with experimental data.

Lyle, Karen H.↗

NASA NTRS2007

Application of Probability Methods to Assess Crash Modeling Uncertainty

Lyle, Karen H.↗

NASA NTRS2010

Modification of a Macromechanical Finite-Element Based Model for Impact Analysis of Triaxially-Braided Composites

A macro level finite element-based model has been developed to simulate the mechanical and impact response of triaxially-braided polymer matrix composites. In the analytical model, the triaxial braid architecture is simulated by using four parallel shell elements, each of which is modeled as a laminated composite. For the current analytical approach, each shell element is considered to be a smeared homogeneous material. The commercial transient dynamic finite element code LS-DYNA is used to conduct the simulations, and a continuum damage mechanics model internal to LS-DYNA is used as the material constitutive model. The constitutive model requires stiffness and strength properties of an equivalent unidirectional composite. Simplified micromechanics methods are used to determine the equivalent stiffness properties, and results from coupon level tests on the braided composite are utilized to back out the required strength properties. Simulations of quasi-static coupon tests of several representative braided composites are conducted to demonstrate the correlation of the model. Impact simulations of a represented braided composites are conducted to demonstrate the capability of the model to predict the penetration velocity and damage patterns obtained experimentally.

Goldberg, Robert K.↗

NASA NTRS2019

JSC-Rocknest: a Large-Scale Mojave Mars Simulant (MMS) Based Soil Simulant for In-Situ Resource Utilization Water-Extraction Studies

The Johnson Space Center Rocknest (JSC-RN) simulant was developed in response to a need by NASA's Advanced Exploration Systems (AES) In Situ Resource Utilization (ISRU) project for a simulant to be used in component and system testing for water extraction from Mars regolith. JSC-RN was de-signed to be chemically and mineralogically similar to material from the aeolian sand shadow named Rocknest in Gale Crater, particularly the 1-3 weight percentage water release as measured by the Sample Analysis at Mars (SAM) instrument. Rocknest material is a proxy for average martian soils, which are unconsolidated and could be easily scooped by rovers or landers in order to extract water. One way in which water can be extracted from aeolian material is through heating, where adsorbed and structural water is thermally removed from minerals. The water can then be condensed and used as drinking water or split and used as propellant for spacecraft or as a source of breathable O2. As such, it was essential that JSC-RN contained evolved gas profiles, especially low temperature water (less than 400 degrees Centigrade), that mimicked what is observed in martian soils. Because many of these ISRU tests require hundreds of kilograms of Mars soil simulant, it was essential that JSC-RN be cost-effective and based on com-ponents that could be purchased commercially (i.e., not synthesized in the lab). Here, we describe the JSC-RN martian soil simulant, which is ideal for large-scale production and use in ISRU water extraction studies.

Hogancamp, J. V.↗

NASA NTRS2019

Challenges in Qualification of Thermal Protection Systems for Extreme Entry Environments

Planetary entry vehicles employ ablative TPS materials to shield the aeroshell from entry aeroheating environments. To ensure mission success, it must be demonstrated that the heatshield system, including local features such as seams, does not fail at conditions that are suitably margined beyond those expected in flight. Furthermore, its thermal response must be predictable, with acceptable fidelity, by computational tools used in heatshield design. Mission assurance is accomplished through a combination of ground testing and material response modelling. A material's robustness to failure is verified through arcjet testing while its thermal response is predicted by analytical tools that are verified against experimental data. Due to limitations in flight-like ground testing capability and lack of validated high-fidelity computational models, qualification of heatshield materials is often achieved by piecing together evidence from multiple ground tests and analytical simulations, none of which fully bound the flight conditions and vehicle configuration. Extreme heating environments (>2000 W/cm2 heat flux and >2 atm pressure), experienced during entries at Venus, Saturn and Ice Giants, further stretch the current testing and modelling capabilities for applicable TPS materials. Fully-dense Carbon Phenolic was the material of choice for these applications; however, since heritage raw materials are no longer available, future uses of re-created Carbon Phenolic will require re-qualification. To address this sustainability challenge, NASA is developing a new dual-layer material based on 3D weaving technology called Heatshield for Extreme Entry Environments (HEEET) [1]. Regardless of TPS material, extreme environments pose additional certification challenges beyond what has been typical in recent NASA missions.Scope of this presentation: This presentation will give an overview of challenges faced in verifying TPS performance at extreme heating conditions.

Mahzari, Milad↗

DOE OSTI2014

“Elegant Tool” Delivers Genome-Level Science for Electrolytes

Now, a ‘disruptive, virtual scientific simulation tool’ delivers a new, genome-level investigation for electrolytes to develop better, more efficient batteries. Dr. Kevin Gering, an Idaho National Laboratory researcher, has developed the Advanced Electrolyte Model (AEM), a copyrighted molecular-based simulation tool that has been scientifically proven and validated using at least a dozen ‘real-world’ physical metrics. Nominated for the 2014 international R&D 100 Award, AEM revolutionizes electrolyte materials selection, optimizing combinations and key design elements to make battery design and experimentation quick, accurate and responsive to specific needs.

25 ENERGY STORAGE↗

DOE OSTI2020

Elastic Properties of Plasma-Exposed Tungsten Predicted by Molecular-Dynamics Simulations

We report results of systematic molecular-dynamics computations of the elastic properties of single-crystalline tungsten containing structural defects, voids and overpressurized He nanobubbles, related to plasma exposure of tungsten serving as a plasma- facing component (PFC) in nuclear fusion devices. Our computations reveal that the empty voids are centers of dilatation resulting in development of tensile stress in the tungsten matrix, whereas He-filled voids (nanobubbles) introduce compressive stress in the plasma-exposed tungsten. We find that the dependence of the elastic moduli of plasma-exposed tungsten, namely, the bulk, Young, and shear modulus, on its void fraction follows a universal exponential scaling relation. We also find that the elastic moduli of plasma-exposed tungsten soften substantially as a function of He content in the tungsten matrix, following an exponential scaling relation; this He-induced exponential softening is in addition to the softening caused in the matrix with increasing temperature. A systematic characterization of the dependence of the elastic moduli on the He bubble size reveals that He bubble growth affects significantly both the bulk modulus and the Poisson ratio of plasma-exposed tungsten, while its effect on the Young and shear moduli of the plasma-exposed material is weak. Our findings contribute directly to the development of a structure-properties database that is required for the predictive modeling of the dynamical response of PFCs in nuclear fusion devices.

36 MATERIALS SCIENCE↗

NASA NTRS1980

A three-dimensional spacecraft-charging computer code

A computer code is described which simulates the interaction of the space environment with a satellite at geosynchronous altitude. Employing finite elements, a three-dimensional satellite model has been constructed with more than 1000 surface cells and 15 different surface materials. Free space around the satellite is modeled by nesting grids within grids. Applications of this NASA Spacecraft Charging Analyzer Program (NASCAP) code to the study of a satellite photosheath and the differential charging of the SCATHA (satellite charging at high altitudes) satellite in eclipse and in sunlight are discussed. In order to understand detector response when the satellite is charged, the code is used to trace the trajectories of particles reaching the SCATHA detectors. Particle trajectories from positive and negative emitters on SCATHA also are traced to determine the location of returning particles, to estimate the escaping flux, and to simulate active control of satellite potentials.

Rubin, A. G.↗

DOE OSTI2022

Mesoscale simulations of pressure-shear loading of granular tungsten carbide

Numerical simulations of pressure-shear loading of a granular material are performed using the shock physics code CTH. A simple mesoscale model for the granular material is used that consists of a randomly packed arrangement of solid circular or spherical grains of uniform size separated by vacuum. The grain material is described by a simple shock equation of state, elastic perfectly plastic strength model, and fracture model with baseline parameters for WC taken from previous mesoscale modeling work. Simulations using the baseline material parameters are performed at the same initial conditions of pressure-shear experiments on dry WC powders. Except for some localized flow regions appearing in simulations with an approximate treatment of sliding interfaces among grains, the samples respond elastically during shear, which is in contrast to experimental observations. By extending the simulations to higher shear wave amplitudes, macroscopic shear failure of the simulated samples is observed with the shear strength increasing with increasing stress confinement. The shear strength is also found to be strongly dependent on the grain interface treatment and on the fracture stress of the grains, though the variation in shear strength due to fracture stress decreases with increasing stress confinement. At partial compactions, the transverse velocity histories show strain-hardening behavior followed by formation of a shear interface that extends through the transverse dimensions of the sample. Near full compaction, no strain hardening is observed and, instead, the sample transitions sharply from an elastic response to formation of an internal shear interface. Agreement with experiment is shown to worsen with increasing confinement stress with simulations overpredicting the shear strengths measured in experiment. The source of the disagreement can be ultimately attributed to the Eulerian nature of the simulations, which do not treat contact and fracture realistically.

36 MATERIALS SCIENCE↗

DOE OSTI2016

A molecular dynamics study of the effect of thermal boundary conductance on thermal transport of ideal crystal of n-alkanes with different number of carbon atoms

Phase change materials such as n-alkanes that exhibit desirable characteristics such as high latent heat, chemical stability, and negligible supercooling are widely used in thermal energy storage applications. However, n-alkanes have the drawback of low thermal conductivity values. The low thermal conductivity of n-alkanes is linked to formation of randomly oriented nano-domains of molecules in their solid structure that is responsible for excessive phonon scattering at the grain boundaries. Thus, understanding the thermal boundary conductance at the grain boundaries can be crucial for improving the effectiveness of thermal storage systems. The concept of the ideal crystal is proposed in this paper, which describes a simplified model such that all the nano-domains of long-chain n-alkanes are artificially aligned perfectly in one direction. In order to study thermal transport of the ideal crystal of long-chain n-alkanes, four (4) systems (C{sub 20}H{sub 42}, C{sub 24}H{sub 50}, C{sub 26}H{sub 54}, and C{sub 30}H{sub 62}) are investigated by the molecular dynamics simulations. Thermal boundary conductance between the layers of ideal crystals is determined using both non-equilibrium molecular dynamics (NEMD) and equilibrium molecular dynamics (EMD) simulations. Both NEMD and EMD simulations exhibit no significant change in thermal conductance with the molecular length. However, the values obtained from the EMD simulations are less than the values from NEMD simulations with the ratio being nearly three (3) in most cases. This difference is due to the nature of EMD simulations where all the phonons are assumed to be in equilibrium at the interface. Thermal conductivity of the n-alkanes in three structures including liquid, solid, and ideal crystal is investigated utilizing NEMD simulations. Our results exhibit a very slight rise in thermal conductivity values as the number of carbon atoms of the chain increases. The key understanding is that thermal transport can be significantly altered by how the molecules and the nano-domains are oriented in the structure rather than by the length of the n-alkane molecules.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Technical Note: Influence of the phantom material on the absorbed-dose energy dependence of the EBT3 radiochromic film for photons in the energy range 3 keV–18 MeV

Purpose: Water is the reference medium for radiation therapy dosimetry, but for film dosimetry it is more practical to use a solid phantom. As the composition of solid phantoms differs from that of water, the energy dependence of film exposed within solid phantoms may also differ. The energy dependence of a radiochromic film for a given beam quality Q (energy for monoenergetic beams) has two components: the intrinsic energy dependence and the absorbed-dose energy dependence f(Q), the latter of which can be calculated through a Monte Carlo simulation of radiation transport. The authors used Monte Carlo simulations to study the influence of the phantom material on the f(Q) of the EBT3 radiochromic film (Ashland Specialty Ingredients, Wayne, NJ) for photon beams with energies between 3 keV and 18 MeV. Methods: All simulations were carried out with the general-purpose Monte Carlo code PENELOPE 2011. The geometrical model consisted of a cylindrical phantom, with the film positioned at different depths depending on the initial photon energy. The authors simulated monoenergetic parallel photon beams and x-ray beams from a superficial therapy system. To validate their choice of simulation parameters, they also calculated f(Q) for older film models, EBT and EBT2, comparing with published results. In addition to water, they calculated f(Q) of the EBT3 film for solid phantom materials commonly used for film dosimetry: RW1 and RW3 (PTW-Freiburg, Freiburg, Germany), Solid Water (Gammex-RMI, Madison, WI), and PMMA. Finally, they combined their calculated f(Q) with published overall energy response data to obtain the intrinsic energy dependence of the EBT3 film in water. Results: The calculated f(Q) for EBT and EBT2 films was statistically compatible with previously published data. Between 10 keV and 18 MeV, the variation found in f(Q) of the EBT3 film for water was within 2.3%, with a standard statistical uncertainty less than 1%. If the quantity dose-to-water in the phantom is considered, which is the common practice in radiation dosimetry, the maximum difference of energy dependence for the solid phantoms with respect to water is about 6%, at an energy of 50 keV. Conclusions: The EBT3 film shows a reasonably constant absorbed-dose energy dependence when irradiated in water. If the dose-to-water in the phantom is considered, the maximum difference of EBT3 film energy dependence with the solid phantoms studied with respect to water is about 6% (at an energy of 50 keV). The reported overall energy dependence of the EBT3 film in water at energies below 100 keV is mainly due to the intrinsic energy dependence.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2022

Continued Verification of MOOSE Structural Mechanics Tools for Modeling Core Bowing Phenomena in Fast Reactors

Under the U.S. Department of Energy Office of Nuclear Energy’s Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism whereby increased power (which leads to temperature and flux gradients) influences the core to bow into less reactive configurations when the restraint system is properly designed. The phenomenon includes a complex interplay of radiation transport, duct temperature calculations involving fluid flow and heat transfer, and thermo-mechanical responses to the induced temperature and flux gradients. Structural material properties are also important to determining inelastic response to longer term flux gradients which cause irradiation creep and swelling. While core bowing provides a strong negative reactivity feedback when the restraint system is designed properly, it also results in additional forces between assemblies which increase the loads required to extricate them during refueling or control rod movement. Therefore, the restraint system must be designed with these tradeoffs in mind. The first stage of the work, which commenced in FY21 and continues through FY22, assesses thermo-mechanical modeling tools for producing core bowing predictions consistent with conventional tools. The Multiphysics Object Oriented Simulation Environment (MOOSE) Tensor Mechanics and Contact Modules are employed. This status report describes work on additional thermo-mechanical benchmark verification problems with increased complexity from the examples demonstrated in FY21. Several benchmark verification examples were selected from the IAEA verification and validation report. These examples involve clusters of ducts representative of a sector of a hexagonal reactor core which bow into each other and cause contact and load pad elevations, as well as single ducts subjected to irradiation fields undergoing swelling and subsequent bowing. The MOOSE-based results were compared to both IAEA benchmark participants’ results, analytic equations as available, and NUBOW-3D, a beam model code developed by Argonne National Laboratory. In every case, the MOOSE results agreed with other simulations results, providing additional verification basis of the tools for this particular physics application.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

FY23 Status Report on MOOSE-Based Approaches to Modeling Core Bowing in Fast Reactors

Under the U.S. Department of Energy Office of Nuclear Energy’s Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism whereby increased power (which leads to temperature and flux gradients) influences the core to bow into less reactive configurations when the restraint system is properly designed. The phenomenon includes a complex interplay of radiation transport, duct temperature calculations involving fluid flow and heat transfer, and thermo-mechanical responses to the induced temperature and flux gradients. Structural material properties are also important to determining inelastic response to longer term flux gradients which cause irradiation creep and swelling. While core bowing provides a strong negative reactivity feedback when the restraint system is designed properly, it also results in additional forces between assemblies which increase the loads required to extricate them during refueling or control rod movement. Therefore, the restraint system must be designed with these tradeoffs in mind. The first stage of the work, which commenced in FY21 and continues through FY23, assesses thermo-mechanical modeling tools for producing core bowing predictions consistent with conventional tools. The Multiphysics Object Oriented Simulation Environment (MOOSE) Tensor Mechanics and Contact Modules are employed. This status report describes work on additional thermo-mechanical benchmark verification problems with increased complexity from the examples demonstrated in FY21 and FY22. Several benchmark verification examples were selected from the IAEA verification and validation report with increased number of ducts and more complex contact interaction behavior. These examples involve a full symmetric sector with restraint rings at multiple load pad locations to simulate a limited free-bow restraint system concept, as well as irradiation induced swelling and creep effects in a sector. In addition, improvements to the contact module sideset assignment were assessed and compared with previous MOOSE results to verify the contact behavior. The MOOSE-based results were compared to IAEA benchmark participants’ results. In every case, the MOOSE results agreed with other simulations results for estimating bowing behavior, providing additional verification basis of the tools for this particular physics application. Estimation of contact forces were mostly in agreement, with a few outlier results. A plan was suggested for dealing with the discrepancies with estimating contact force values. In addition, a 1-way coupling demonstration was performed using subchannel analysis code Pronghorn-SC and MOOSE on an ABR-1000-design sodium-cooled fast reactor assembly to evaluate coolant and duct wall temperatures.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2018

Analyzing the microstructural evolution and hardening response of an Al-Si-Mg casting alloy with Cr addition

Highlights: • The formation of β-Al{sub 5}FeSi intermetallics was suppressed since impurity Fe has been consumed by Al{sub 13}Cr{sub 4}Si{sub 4} intermetallics; • A large number of Al{sub 13}Cr{sub 4}Si{sub 4} dispersoids were observed in Al dendrites in the as-quenched and aged alloy; • The precipitation of Cr-bearing dispersoids harden the as-quenched alloy by over 10HV; • The current thermodynamic database underestimate the solubility of Fe in Al{sub 13}Cr{sub 4}Si{sub 4} intermetallics during solidification simulation. - Abstract: Chromium is added to Al-Si based casting alloys for the mitigation of die soldering. In the present work, EBSD, EDS and TEM characterizations are combined with thermodynamic simulations to study the microstructural evolution and hardening response of an Al-Si-Mg-Cr casting alloy during heat treatments. It is shown that the Fe-containing intermetallic compounds formed in the inter-dendritic region were acicular π-Al{sub 8}(Fe, Cr)Mg{sub 3}Si{sub 6} phase and polyhedral Al-(Cr, Fe)-Si phase which is structurally similar to face-centered cubic Al{sub 13}Cr{sub 4}Si{sub 4}. The polyhedral Al-(Cr, Fe)-Si intermetallics that crystallized prior to β-Al{sub 5}FeSi consumed impurity Fe, suppressing the formation of β phase during gravity die casting process. Also, Cr-addition enables the precipitation of nano-scale Cr-bearing dispersoids in Al dendrite during solution treatment at 813 K. Hardness increment of over 10 HV can be induced by the Cr-bearing dispersoids for as-quenched alloy. Though the dispersoids have a moderate hardening effect on the as-quenched alloy, they may impair the ageing hardening response by acting as heterogeneous nucleation sites for coarse Mg-Si rods and Si particles when quenching into water at 338 K.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Deformed Materials: Towards a Theory of Materials Morphology Dynamics

This grant supported work on the response of crystals to external stress. Our primary work described how disordered structural materials break in two (statistical models of fracture in disordered materials), studied models of deformation bursts (avalanches) that mediate deformation on the microscale, and developed continuum dislocation dynamics models for plastic deformation (as when scooping ice cream bends a spoon, Fig. 9). Glass is brittle -- it breaks with almost atomically smooth fracture surfaces. Many metals are ductile -- when they break, the fracture surface is locally sheared and stretched, and it is this damage that makes them hard to break. Bone and seashells are made of brittle material, but they are strong because they are disordered -- lots of little cracks form as they are sheared and near the fracture surface, diluting the external force. We have studied materials like bone and seashells using simulations, mathematical tools, and statistical mechanics models from physics. In particular, we studied the extreme values of fracture strengths (how likely will a beam in a bridge break far below its design strength), and found that the traditional engineering tools could be improved greatly. We also studied fascinating crackling-noise precursors -- systems which formed microcracks of a broad range of sizes before they broke. Ductile metals under stress undergo irreversible plastic deformation -- the planes of atoms must slide across one another (through the motion of dislocations) to change the overall shape in response to the external force. Microscopically, the dislocations in crystals move in bursts of a broad range of sizes (termed 'avalanches' in the statistical mechanics community, whose motion is deemed 'crackling noise'). In this grant period, we resolved a longstanding mystery about the average shape of avalanches of fixed duration (using tools related to an emergent scale invariance), we developed the fundamental theory describing the shapes of avalanches and how they are affected by the edges of the microscope viewing window, we found that slow creep of dislocations can trigger an oscillating response explaining recent experiments, we explained avalanches under external voltage, and we have studied how avalanches in experiments on the microscale relate to deformation of large samples. Inside the crystals forming the metal, the dislocations arrange into mysterious cellular structures, usually ignored in theories of plasticity. Writing a natural continuum theory for dislocation dynamics, we found that it spontaneously formed walls -- much like models of traffic jams and sonic booms. These walls formed rather realistic cellular structures, which we examined in great detail -- our walls formed fractal structures with fascinating scaling properties, related to those found in turbulent fluids. We found, however, that the numerical and mathematical tools available to solve our equations were not flexible enough to incorporate materials-specific information, and our models did not show the dislocation avalanches seen experimentally. In the last year of this grant, we wrote an invited review article, explaining how plastic flow in metals shares features with other stressed materials, and how tools of statistical physics used in these other systems might be crucial for understanding plasticity.

36 MATERIALS SCIENCE↗