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DOE OSTI2024

Multiobjective Constrained Symbolic Regression for Predictive Modeling of Material Creep Behavior

When creep testing is repeated on samples of the same alloy under the same parametric conditions (i.e., stress and temperature), the resulting strain/time curves can vary from each other considerably as shown in Figure 1 [1]. The time required to creep test a material to rupture can extend to the order of years. Because of this, a numerical model that can quickly analyze the incomplete results of an ongoing experiment to predict 1) the incomplete portion of the strain/time curve leading up to the rupture point and 2) the rupture point itself would be of great utility to the materials community. Such a model has the potential to save 1) the time required to finish running the experiment to rupture 2) the associated monetary cost of finishing said experiment. Furthermore, it would be advantageous if the predictive model could give a parametric function modeling strain/time curves for material scientists to investigate the impact of the temperature and stress parameters on the resulting creep behavior. This work introduces a piecewise symbolic regression algorithm to predict the remainder of the strain/time curve. Preliminary results show good model performance.

36 MATERIALS SCIENCE↗

DOE OSTI2023

High-burnup Experiments in Reactivity Initiated Accidents (HERA)

HERA is a joint experimental program (JEEP) operating within the Nuclear Energy Agency’s (NEA’s) framework for irradiation experiments (FIDES). HERA is dedicated to the understanding of light water reactor (LWR) fuel performance at high burnup under reactivity-initiated accidents (RIA). During RIAs the fuel cladding can be breached by one of two mechanisms; pellet-cladding mechanical interaction or high temperature balloon and rupture. Pellet-cladding mechanical interaction (PCMI) failure occurs in the early phase of an RIA transient where the fuel pellet expands rapidly into the cladding prior to any meaningful heat transfer from the pellet to the cladding. This results in high stresses in the cladding resulting in crack propagation through the base Zircaloy metal and axially along the cladding tube. Failure by PCMI is a brittle failure mode and occurs at low cladding strains, approximately 2% hoop strain. If the cladding survives the PCMI phase of the transient, it may still fail due to ballooning and rupture induced by extended exposure to high temperature. Thermal transport from the fuel pin to the coolant is significantly reduced if a transition to film boiling on the cladding surface occurs. This result in both a rapid increase in fuel temperature, which drives fission gas release, and a spike in cladding temperature, which results in loss of mechanical strength. If the internal pressure of the fuel rod is greater than the system pressure the cladding can inelastically deform and eventually rupture. Failure by swelling and rupture occurs at larger strains, generally greater than 5% hoop strain. While PCMI failures are generally seen as more limiting, the dominance of one failure mode over the other can be affected by both the cladding material conditions, and the transient evolution.

(HERA)↗

DOE OSTI2021

A Stochastic Intracellular Model of Anthrax Infection With Spore Germination Heterogeneity

We present a stochastic mathematical model of the intracellular infection dynamics of Bacillus anthracis in macrophages. Following inhalation of B. anthracis spores, these are ingested by alveolar phagocytes. Ingested spores then begin to germinate and divide intracellularly. This can lead to the eventual death of the host cell and the extracellular release of bacterial progeny. Some macrophages successfully eliminate the intracellular bacteria and will recover. Here, a stochastic birth-and-death process with catastrophe is proposed, which includes the mechanism of spore germination and maturation of B. anthracis . The resulting model is used to explore the potential for heterogeneity in the spore germination rate, with the consideration of two extreme cases for the rate distribution: continuous Gaussian and discrete Bernoulli. We make use of approximate Bayesian computation to calibrate our model using experimental measurements from in vitro infection of murine peritoneal macrophages with spores of the Sterne 34F2 strain of B. anthracis . The calibrated stochastic model allows us to compute the probability of rupture, mean time to rupture, and rupture size distribution, of a macrophage that has been infected with one spore. We also obtain the mean spore and bacterial loads over time for a population of cells, each assumed to be initially infected with a single spore. Our results support the existence of significant heterogeneity in the germination rate, with a subset of spores expected to germinate much later than the majority. Furthermore, in agreement with experimental evidence, our results suggest that most of the spores taken up by macrophages are likely to be eliminated by the host cell, but a few germinated spores may survive phagocytosis and lead to the death of the infected cell. Finally, we discuss how this stochastic modelling approach, together with dose-response data, allows us to quantify and predict individual infection risk following exposure.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

A phase-field model for quasi-dynamic nucleation, growth, and propagation of rate-and-state faults

Despite its critical role in the study of earthquake processes, numerical simulation of the entire stages of fault rupture remains a formidable task. The main challenges in simulating a fault rupture process include the complex evolution of fault geometry, frictional contact, and off-fault damage over a wide range of spatial and temporal scales. Here, in this paper, we develop a phase-field model for quasi-dynamic fault nucleation, growth, and propagation, which features two standout advantages: (i) it does not require any sophisticated algorithms to represent fault geometry and its evolution; and (ii) it allows for modeling fault nucleation, propagation, and off-fault damage processes with a single formulation. Built on a recently developed phase-field framework for shear fractures with frictional contact, the proposed formulation incorporates rate- and state-dependent friction, radiation damping, and their impacts on fault mechanics and off-fault damage. We show that the numerical results of the phase-field model are consistent with those obtained from well-verified approaches that model the fault as a surface of discontinuity, without suffering from the mesh convergence issue in the existing continuous approaches to fault rupture (e.g., the stress glut method). Further, through numerical examples of fault propagation in various settings, we demonstrate that the phase-field approach may open new opportunities for investigating complex earthquake processes that have remained overly challenging for the existing numerical methods.

58 GEOSCIENCES↗

DOE OSTI2022

Deformation and Fracture Behaviors of Cylindrical Battery Shell During Thermal Runaway

Thermal runaway is one of the catastrophic failure modes of lithium-ion cells. During thermal runaway in cylindrical cells, sidewall shell rupture has been identified as a contributing factor for thermal runaway propagation in battery packs. Herein, the deformation and fracture behaviors of the battery shell during thermal runaway are investigated based on in-situ and ex-situ characterization as well as physics-based modeling. The deformation and fracture modes of the battery shell with/without Carbon Fiber Reinforced Polymer (CFRP) sleeves are identified. In the simulation, the strain introduced by thermal expansion of the system is considered, as well as the thermal and strain rate effects on the plastic stage. The final cell shell modeling is validated by cell thermal runaway tests. Results reveal the quantitative relation between shell deformation behaviors and the pressure and temperature distribution. Both the experiment and model demonstrate the effectiveness of adding a tight-fitting CFRP sleeve around the cell in limiting the side-wall rupture of the shell. The use of CFRP tubes introduces a novel phenomenon in the context of uneven temperature distribution. Results shed light on the mechanistic analysis of a cell side-wall rupture during thermal runaway and provide essential guidance for the next-generation safe battery design.

battery casing↗

DOE OSTI2023

Assessment of UTP A 2133 Mn as a Matching Filler Metal for Alloy 800H in Section III, Division 5 Applications

Six alloys are qualified in the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC) for elevated-temperature nuclear components. Due to reactor design alloy restrictions and motivation to improve operational efficiency and plant lifetimes, it is necessary to maximize the usefulness of qualified alloys. One of these alloys is Alloy 800H, which is qualified for a maximum temperature of 760°C and a maximum 300,000-hour service life. However, the welding filler metals qualified to join Alloy 800H have stress rupture factors that reduce the allowable weldment strength by factors as low as 0.59 times the Alloy 800H base metal. In an effort to improve the weldment creep-rupture performance, or to increase the stress reduction factor, non-code qualified filler metals are under investigation by the Department of Energy?s Advanced Reactor Technologies program. For this investigation, UTP A 2133 Mn filler metal (Fe-Cr-Ni-Mn-Nb) was used to join 0.5 in. thick Alloy 800H plate to demonstrate passing an ASME BPVC Section IX weld qualification. The multi-pass, pulsed GTAW process showed successful weld qualification results, and additional property measurements were conducted to compare previous analyses of Alloy 82 and Alloy 617 filler metals. Future work will evaluate the cross-weld creep-rupture performance of the UTP A 2133 Mn in comparison to Alloy 82 and Alloy 617 filler metals.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Directed energy deposition of Haynes 282 nickel superalloy

Laser powder directed energy deposition was employed to fabricate Haynes® 282 Ni-based superalloy for high temperature creep testing. Material was heat treated using a single-step aging heat treatment of 800 °C for 4 h. Microstructural analysis was conducted in the as-deposited, solution-annealed, and age-hardened conditions. γ′ precipitates were absent in the as-deposited and annealed condition but formed during aging with an average size of 48.5 ± 12 nm. γ’ denuded zones ranging in thickness from 73 to 469 nm were observed adjacent to an effectively continuous grain boundary carbide film that covered 72.5% of the measured boundary length. The heat-treated material contained a high-volume fraction of TiC carbides ranging in size from 38 to 457 nm. Electron backscatter diffraction showed partial recrystallization, with 77-83% recrystallized area and a heterogeneous grain-size distribution. Creep testing at 750 °C at 300, 320, and 350 MPa revealed significantly inferior performance compared to wrought material, with higher strain rates, earlier tertiary onset, and shorter rupture lives. Fractography shows that failure was dominated by intergranular rupture. Post rupture microstructural analysis results suggest that the creep behavior was primarily governed by the non-equilibrium interface network rather than the bulk γ/γ’ matrix. In conclusion, the findings indicate that achieving wrought-like creep performance necessitates substantial improvements in the additive process, specifically focusing on enhanced homogenization, full recrystallization, and precise control over the morphology and distribution of carbides.

36 - MATERIALS SCIENCE↗

DOE OSTI2026

Linking microstructure to creep behavior in vertically and horizontally built LPBF Haynes 282 compared with wrought material via θ -projection

Laser Powder Bed Fusion (LPBF) has emerged as a promising route for fabricating intricate geometries in high-performance alloys. Haynes 282 (H282) is a strong candidate for applications such as heat exchangers or engines due to its excellent creep strength and thermal stability; however, the long-term creep behavior of LPBF-processed H282 remains poorly understood. In this study, the θ -projection method is used to analyze and extrapolate the creep behavior of vertically built LPBF, horizontally built LPBF, compared to wrought H282 tested at 816 °C. Vertically built LPBF H282 exhibits the lowest minimum creep rate (MCR), while the horizontally built condition shows a higher MCR comparable to that of wrought H282. Despite these differences, both LPBF conditions exhibit significantly shorter rupture life and reduced rupture strain than the wrought material, with the most severe degradation observed in the horizontal builds, consistent with an earlier onset of tertiary creep and accelerated strain-rate evolution. Microstructural characterization reveals that both LPBF and wrought H282 exhibit abundant twin-related boundary character; however, their grain boundary topologies differ markedly. The wrought alloy contains a higher fraction of low-angle grain boundaries and continuous twin lamellae, whereas the LPBF microstructure is characterized by a suppressed low-angle boundary population and fragmented twin-related boundaries embedded within irregular high-angle grain boundary networks. Fractographic analysis further reveals predominantly intergranular cracking in LPBF H282, accompanied by grain-boundary-decorated carbides, Al 2 O 3 inclusions, and high-aspect-ratio pores. These results demonstrate that grain boundary topology, rather than minimum creep rate alone, plays a critical role in governing creep damage accumulation and rupture behavior in LPBF and wrought H282.

Creep↗

DOE OSTI2020

The Role of Protons and Hydrides in the Catalytic Hydrogenolysis of Guaiacol at the Ruthenium Nanoparticle-water Interface

The mechanistic roles of free hydronium ions, surface hydrides, and interfacial protons during guaiacol hydrodeoxygenation (HDO) on ruthenium nanoparticles are established. As guaiacol adsorbs on Ru, it loses its strong aromaticity and undergoes a rapid H-shift from its hydroxyl to meta carbons (in relation to its hydroxyl group), leading enol and keto surface isomers to exist in chemical equilibrium. HDO occurs via a hydridic H-adatom (H*) attack to the enol, followed by a kinetically relevant C-O bond rupture step, during which water shuttles the hydroxyl proton, enabling its intramolecular attack to the methoxy, evolving a high charged [Ru(s)-(C6H5O-)…(H+)…OCH3]† transition state. The competing HYD begins with a rapid H* attack to the keto, before a second, kinetically relevant H* attack, without proton involvement. Water, despite shifting the thermodynamics towards the more polar surface keto, promotes HDO to a much greater extent than HYD, because of its dual catalytic roles—it mobilizes hydroxyl proton (Brønsted acid) to cleave the strong C-O bond, synchronizing with the Ru metal surface (base) function that stabilizes the resulting [Ru(s)-(C6H5O-)…(H+)…OCH3]† transition state, and the water layers solvate this charged transition state, further reducing its free energy. Free hydronium ions do catalyze a separate homogeneous enol-keto isomerization, but this reaction is kinetically unrelated to HDO catalysis. This mechanistic picture explains the strong effects of polar protic solvent in hydrodeoxygenation, highlighting (i) the requirements of surface hydrides and interfacial protons acting in tandem to complete a HDO turnover and (ii) the cooperative role of protic solvent and metal surface in breaking the aromaticity and stabilizing charged reactive precursors and transition states.

Shangguan, Junnan↗

DOE OSTI2022

Modeling Sequences of Earthquakes and Aseismic Slip (SEAS) in Elasto-Plastic Fault Zones With a Hybrid Finite Element Spectral Boundary Integral Scheme

We present a coupled finite element spectral boundary integral framework for modeling sequences of earthquakes and aseismic slip on a 2-D planar rate-and-state fault with off-fault visco-plastic response in the plane strain approximation. The model resolves both slow aseismic deformation and inertia effects during rapid slip. As an application, we perform two sets of simulations with different choices of cohesion to explore the co-evolution of fault slip, bulk plasticity and local stress fields. The first set implements a relatively large value of the cohesion parameter, which results in limiting inelastic strain accumulation to dynamic rupture phases. The second set implements a smaller cohesion, allowing for plastic strain to accumulate in both seismic and aseismic phases. For the first model, our results indicate that the extent and distribution of plastic strain depend on the angle of maximum compressive principal stress. At larger angles, inelastic strain accumulates on the extensional side of a dynamically propagating rupture. At smaller angles, the extent of plasticity is limited to the compressional side of the domain. At smaller cohesion values, off-fault plasticity may occur during aseismic slip, which alters the nucleation characteristics and earthquake sequence pattern. Furthermore, our results at lower cohesion values indicate that plastic strain accumulation may occur in both the extensional and compressional sides of the off-fault bulk even at higher angles of maximum compression. In conclusion, this produces damage patterns that deviate from the traditional off-fault fan-like distribution observed in dynamic rupture simulations and emphasizes the significance of long-term deformation in interpreting observations.

58 GEOSCIENCES↗

DOE OSTI2023

The Variable Continuous Bimaterial Interface in the San Jacinto Fault Zone Revealed by Dense Seismic Array Analysis of Fault Zone Head Waves

Key factors controlling earthquake ruptures include fault geometry, continuity, and seismic velocity structure around the fault. We present a novel tool that better informs deep bimaterial fault geometry embedded in distributed damage and seismicity, associated velocity contrasts across the fault, and their correlations with surface complexities. The method employs fault zone head and direct body waves and is applied to recordings from five spatiotemporally different seismic arrays along the complex San Jacinto fault zone (SJFZ) in southern California. We detect and distinguish these signals based on instantaneous phase coherence and relative energy in a cascading manner from one scale array to another. The analysis reveals a >70-km long continuous bimaterial interface within the SJFZ with several deep northeast dipping fault segments. The northern SJFZ, for instance, locates ~7 km northeast of its surface expression at 18-km depth. P-wave velocity contrasts range from near 0% to >15%, consistent with other bimaterial faults, and differ by a few % depending on fault-array azimuth, implying directional-dependent velocity contrasts. S-wave head waves and velocity contrasts are also imaged for the first time at the southern SJFZ, averaging to 2.9% in agreement with tomography results. The imaged geometry and continuity suggest the SJFZ initiated along remnant tectonic structures and translates to a rupture potential of M > 7.2, i.e., the sizes of its largest paleo-earthquakes. The P and S contrasts, and their ratios, have important implications for earthquake rupture speed, mode, directivity, and frictional heating along the SJFZ and other major faults globally.

58 GEOSCIENCES↗

DOE OSTI2023

Cascadia Subduction Zone Fault Heterogeneities From Newly Detected Small Magnitude Earthquakes

The Cascadia subduction zone (CSZ) is known to host M9 megathrust ruptures; however, no such event has occurred in historical observation. The distribution and characteristics of small- to moderate-sized earthquakes can be used to determine the behavior of the megathrust fault but are notably absent offshore the CSZ due to the distance from onshore seismometers. We use automated subspace detection coupled with an onshore-offshore seismic deployment to find small-magnitude earthquakes in the offshore seismogenic zone and analyze their locations in the context of interseismic locking and seismogenic zone extent. Here we detected and located 5,282 earthquakes, 4,096 of which had been previously undetected. We find that the downdip extent of the seismogenic zone as defined by interplate seismicity agrees with the 20% locking contour of the Schmalzle et al. (2014, https://doi.org/10.1002/2013GC005172) geodetic model and extends deeper than predicted by previous thermal models. We cannot determine the updip extent of the seismogenic zone; this may be due to a lack of templates for detection in the updip source area, stress shadows updip of asperity loading, and/or strong locking to the trench. We present a map of possible asperities determined by the small earthquakes in this study. Our asperity locations and extents show some, but not complete, agreement with the asperities modeled from the 1700 M9 rupture and geodetic locking models, and good agreement with the paleo-rupture extents determined from offshore turbidites and forearc basin-based asperity estimates. This highlights the need of continued offshore observations over time, and to elucidate fine-scale variation in locking.

58 GEOSCIENCES↗

DOE OSTI2024

Effects of Pollen on Hydrometeors and Precipitation in a Convective System

Anemophilous (wind-driven) pollen is one type of primary biological aerosol particle, which can rupture under high humidity conditions and form smaller sub-pollen particles (SPPs). Both pollen and SPPs can reach the upper troposphere under convective conditions, acting as cloud condensation nuclei (CCN) and ice nucleating particles (INPs), thus influencing cloud formation and precipitation. However, the impacts of these biological aerosols on cold cloud formation and local climate remain unclear as there are large uncertainties on their emission flux and ice nucleating abilities. Here, we incorporate pollen emission and rupture processes in the Weather Research and Forecasting Model with Chemistry (WRF-Chem) simulations and update the Morrison microphysics scheme within WRF-Chem using aerosol-aware INP parameterizations to account for pollen in addition to other anthropogenic and biogenic aerosol. INP parameterizations for pollen and SPP are derived from laboratory experiments. When including pollen rupture rates as observed in a series of chamber studies, SPP concentrations increase, leading to an increase of cloud ice and water by up to 50% and potentially extending the duration of the convective system. Among all simulated hydrometeors, graupel and raindrops exhibit the largest enhancements from the inclusion of SPPs, with intensifying precipitation at the backside of the convective system and a greater spatial extent. Sensitivity simulations indicate that SPPs have a greater effect on cloud microphysical processes than whole pollen grains, and further observational evidence is needed to constrain these processes.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

The Role of Normal Stress and Shear Stress Heterogeneity in the Inferred Depth‐Independence of Stress Drop

Earthquake stress drops are inferred to be independent of source depth, contradicting linear scaling predictions for earthquakes as frictional stick‐slip instabilities that assume increasing fault normal stress due to overburden. Here, we examine the scaling between averaged stress drops and increasing normal stress for simulated earthquake sequences in continuum rate‐and‐state fault models. The models produce a weaker dependence of stress drop on normal stress than the linearity of simple friction, which can be well‐fit by a sublinear power‐law. This result is more prominent when the fault dimension is much larger than nucleation scales. In such cases, the averaged behavior of ruptures is dominated by rupture propagation conditions, reflecting more heterogeneous shear stress conditions. As natural faults can be considerably larger than the smallest earthquakes they host, such a weaker scaling between averaged rupture conditions and normal stress may partially explain the lack of an inferred depth‐dependence of earthquake stress drops.

earthquake source↗

DOE OSTI2020

A new non-diffusional gas bubble production route in used nuclear fuel: Implications for fission gas release, cladding corrosion, and next generation fuel design

The relationship between noble metal phase particles and fission gas bubble production in used nuclear fuel is described. The majority of Te atoms within noble metal phase undergo radioactive decay to form stable Xe within a few hours after particle formation. This results in the production of clusters of Xe atoms contained within the solid metal matrix exhibiting an equivalent gas bubble pressure approaching 1 GPa. These high pressure bubbles are stabilized by the UO2 within the bulk of the fuel. However, when these bubbles form near the fuel / cladding interface, in combination with local and temporal damage caused by fission recoil, they are capable of overcoming the fracture strength of the UO2 and rupturing catastrophically. The force of the resulting bubble rupture is sufficient to eject noble metal phase particles several microns into the cladding. This proposed mechanism explains the observance of noble metal phase in cladding and is consistent with a host of morphological features found near the fuel / cladding interface.

Schwantes, Jon M.↗

DOE OSTI2023

Characteristics and selection of near-fault simulated earthquake ground motions for nonlinear analysis of buildings

Earthquake-induced ground shaking near rupturing faults is highly sensitive to the rupture characteristics, seismic wave propagation patterns and site conditions, and field recordings of near-fault shaking are relatively sparse. These challenges complicate the assessment of the seismic performance of near-fault structures. A common approach to representing near-fault ground motion in engineering analysis is to explicitly consider and select records with strong directivity pulses (pulse records). We use three-dimensional high-resolution physics-based earthquake simulations to test this approach in the context of scenario-based ground motion record selection, and to study the important characteristics of near-fault ground shaking. We highlight the deficiencies associated with classifying near-fault simulated records as “pulse” or “non-pulse,” based on the presence of a single dominating pulse in the velocity time history. We show that this approach is inadequate for characterizing near-fault shaking on soft soils which can be dominated by both forward rupture directivity and basin amplification effects. We conduct ground motion selection experiments for the analysis of near-fault structures with and without explicit classification of the pulse features in the records, and evaluate the bias in the predicted structural demands. We find that the maximum interstory drift demands on building structures imposed by unscaled site-specific simulated ground motion records selected based on relevant spectral shape features are not sensitive to the classification of records as pulse/non-pulse. Therefore, with regard to predicting the maximum interstory drifts in near-fault buildings, we do not find justification for the binary pulse classification of near-fault records.

42 ENGINEERING↗

DOE OSTI2024

Wasatch Fault Structure from Machine Learning Arrival Times and High-Precision Earthquake Locations

Abstract On 18 March 2020, a magnitude 5.7 earthquake hit the Salt Lake valley in the state of Utah, United States. Using a dense geophone deployment and machine learning (ML), an additional several thousand events were detected and located. Currently, both the mainshock and the majority of the aftershocks are suspected to have occurred on or near a deeper portion of the Salt Lake segment of the Wasatch fault—part of a large range-bounding fault system thought to be capable of generating an Mw 7.2 earthquake. However, a small subset of aftershocks may have occurred on a portion of the more steeply, eastward dipping, and poorly understood West Valley fault. Unfortunately, the catalog locations and lack of focal mechanisms for this subset of aftershocks provide only a crude constraint on the true fault structure. To better illuminate fault structure, we relocate the ML-generated catalog with a range of magnitudes from −2 to 4.6, using: (1) NonLinLoc, a nonlinear location algorithm, (2) source-specific station terms, and (3) waveform coherence. We further compute first-motion focal mechanisms for 68 events. Results of the relocation suggest a simpler, minimally listric Wasatch fault geometry, contrary to what has been previously proposed. We also find that analysis of the focal mechanisms and waveform similarity indicates minimal event similarity throughout the Magna sequence, suggesting a highly complex and heterogeneous rupture zone, as opposed to rupture on a single plane. These findings suggest an increased seismic hazard due to the overall shallowness of the earthquake sequence and highly varied rupture mechanisms.

Geochemistry & Geophysics↗

DOE OSTI2020

Identify the influence of microstructure on mesoscale creep and fatigue damage

This report describes the development of a microstructural model that can quantify the uncertainty in the observed rupture life of Grade 91 steel. The model is microstructural, meaning it relates microstructural characteristics of the material to the resulting material response. As such, one of the uses of this model is to identify the key microstructural parameters controlling the development of damage in Grade 91 operating at elevated temperatures. The report describes two veins of work: improvements to the crystal plasticity model required to run the uncertainty quantification analysis and the results of that UQ analysis. For creep, the model identifies the grain boundary diffusivity as the critical parameter controlling the rupture life of the material. The report demonstrates that a reasonable microstructural distribution of grain boundary diffusivity can account for the observed macroscale variation in rupture life at fixed temperature and load.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗