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DOE OSTI2025

A chain stretch-based gradient-enhanced model for damage and fracture in elastomers

Similar to quasi-brittle materials, it has been recently shown that elastomers can exhibit a macroscopically diffuse damage zone that accompanies the fracture process. In this study, we introduce a stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm of the phase field method for fracture, where a sharp crack is numerically approximated in a diffuse manner. Capturing fracture localization and diffuse damage in our approach is achieved by considering nonlocal effects that encompass network topology, heterogeneity, and imperfections. These considerations motivate the use of a statistical damage function dependent upon the nonlocal deformation state. From this model, fracture toughness is realized as an output. While GED models have been classically utilized for damage modeling of structural engineering materials (e.g., concrete), they face challenges when trying to capture the cascade from damage to fracture, often leading to damage zone broadening (de Borst and Verhoosel, 2016). This deficiency contributed to the popularity of the phase-field method over the GED model for elastomers and other quasi-brittle materials. Other groups have proceeded with damage-based GED formulations that prove identical to the phase-field method (Lorentz et al., 2012), but these inherit the aforementioned limitations. To address this issue in a thermodynamically consistent framework, we implement two modeling features (a nonlocal driving force bound and a simple relaxation function) specifically designed to capture the evolution of a physically meaningful damage field and the simultaneous localization of fracture, thereby overcoming a longstanding obstacle in the development of these nonlocal strain- or stretch-based approaches. Here, we discuss several numerical examples to understand the features of the approach at the limit of incompressibility, and compare them to the phase-field method as a benchmark for the macroscopic response and fracture energy predictions.

Elastomers↗

DOE OSTI2022

Experimentally validated multiphysics modeling of fracture induced by thermal shocks in sintered UO 2 pellets

Uranium Dioxide (UO 2 ) fuel powers almost all commercial Nuclear Power Plants (NPPs) worldwide, generating carbon-free energy and contributing to the fight against climate change. UO 2 fuel incurs damage and fractures due to large thermal gradients that develop across the fuel pellet during normal and transient operating conditions. A comprehensive understanding of the underlying mechanisms by which these processes take place is still lacking. A combined experimental and computational approach is utilized here to quantify the behavior of UO 2 fuel fracture induced by thermal shock. Here, this work introduces both (1) an experimental study to understand the fuel fracturing behavior of sintered UO 2 pellets when exposed to thermal shock, and (2) a Multiphysics phase-field fracture model capable of simulating this process. Parametric studies were conducted to evaluate the effects of uncertainties in fracture properties on the fracture behavior of UO 2 due to thermal shocking. A set of energy release rate (or equivalently fracture toughness) and contract area (the part of the fuel pellet in direct contact with the cold bath) were able to capture the overall fracture trends of the corresponding experimental data. Our combined approach presents a new method for accounting for the effects of microstructure and sample size on the energy release rate/fracture toughness. The experimental data were collected from multiple experiments that exposed UO 2 pellets to high-temperature conditions (589–676 °C) followed by a quench in sub-zero water. This work demonstrates that joint experimental and computational efforts are able to advance the understanding of thermal fracture in the primary fuel source for existing and future NPPs.

36 MATERIALS SCIENCE↗

DOE OSTI2020

The Complicated Link Between Material Properties and Microfracture Density for an Underground Explosion in Granite

Geophysical techniques are often implemented as quick and inexpensive ways to locate and characterize fractures in the subsurface, which is important for a number of geoscience fields. Seismic velocities are the most widely used proxies for identification of fractures, but the correlation is not always well-defined. In this study we present material property data: unconfined compressive strength (UCS), bulk density (ρ), Young's modulus (E), Poisson's ratio (ν), P wave velocity (V p ), and S wave velocity (V s ), in conjunction with microfracture densities measured on samples of granite collected before and after underground chemical explosions. Results indicate the relationship between fractures and material properties is complex, even in this single-lithology environment. We interpret that this complexity arises from varying fracture mechanisms (e.g. dilation-inducing fractures vs compression-inducing fractures) in different parts of the core, due to differences in stress conditions. Additional complexity may result from chemical interactions between the fresh fractures and the fluids in the area. Water content appears to have a significant, if not dominant, role in the unconfined compressive strength (UCS) of the samples. We suggest caution when using elastic property measurements as a proxy for fracturing in areas of explosion-induced damage, or in other areas where a variety of mechanisms induce fracturing.

58 GEOSCIENCES↗

DOE OSTI2022

Plasma surface modification coupled with thermal and step-over distance effects on significant fracture improvement of adhesively-bonded metal-$\mathrm{CFRTP}$ dissimilar materials

Here, this work proposes an approach to improve the interfacial bonding between carbon-fiber-reinforced thermoplastic polymers (CFRTP) and thermoset adhesive by using the surface modification with the combination of air plasma, thermal, and step-over effects. Thanks to the proper heating which causes the exposure of carbon fibers on the CFRTP surface, both polymer matrix and these exposed carbon fibers can have improved bonding with adhesive due to air plasma treatment. By conducting the Double Cantilever Beam (DCB) tests performed on adhesively-bonded AA5052/CFRP-PA66 dissimilar joints, it was shown in this work that the average Mode I specific fracture energy can be improved up to about 180% compared to non-treated counterparts. The foregoing improvement can be further increased by considering the step-over distance of the surface treatment, which triggers the tortuous damage path in the failure process of adhesively-bonded structures. By manipulating this treatment parameter, often overlooked in the literature, and other parameters (i.e., treatment speed, nozzle tip-to-surface distance, etc.) investigated in this study, the average Mode I specific fracture energy of adhesively-bonded AA5052/CFRP-PA66 dissimilar joints can be improved reaching up to about 410% compared to non-treatment counterparts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Mapping of fracture and ionic conductivity changes in ion implanted solid electrolytes: Insights from molecular dynamics

Ion implantation emerges as a promising technique to address the persistent challenge of lithium (Li) filament growth in solid-state electrolytes as it can induce compressive stresses inhibiting crack growth and deflect dendrites, de facto mitigating early electrolyte failure. In this study, we examine the potential paradox of ion implantation: while aiming to enhance electrolyte performance, the radiation damage associated with implantation might inadvertently compromise both the ionic conductivity and the intrinsic fracture toughness of the material, rendering the material unsuitable for battery applications. Specifically, we employed molecular dynamics simulations to examine the scope of the downsides of ion implantation, specifically: (i) reduced ionic conductivity (due to radiation-induced amorphization) and (ii) mechanical stability (due to radiation-induced embrittlement) in ion-implanted Li 7 La 3 Zr 2 O 12 (LLZO) solid-state electrolytes. We explore how radiation damage impacts LLZO’s crystalline structure, Li-ion diffusion, and fracture properties at various temperatures and radiation damage levels. The study aims to provide insights into the competing effects of ion implantation and suggest potential engineering strategies for developing more robust solid-state electrolytes with improved conductivity and dendrite resistance.

Conductivity↗

DOE OSTI2022

A Novel Rotating Flexure-Test Technique for Brittle Materials with Circular Geometries

The four-point bend test is one of the simplest and often the preferred flexural strength evaluation method for brittle materials. In this loading mode, fracture often initiates from a critical surface (or subsurface) flaw when subjected to a tensile stress state. However, if the critical flaw exists on the compression side of the test specimen, it may not activate to grow a crack and hence the resulting flexural strength will be higher than the true value. The goal of this study is to measure the true flexural strength of a solid or hollow cylindrical brittle specimen by ensuring that failure occurs at its weakest point by rotating along its longitudinal axis, thereby exposing and activating its critical surface flaw during a four-point bend test. A novel test fixture has been designed and fabricated, and the true flexural strengths of cylindrical brittle and quasi-brittle tubular specimens have been measured and compared to existing experimental data obtained through traditional four-point bend tests. In this work, experimental results showcase the orientation dependance on flexural strength for various materials. Additionally, similarities between experimental findings and those available in literature, including observations of fracture surfaces and relationships between surface roughness and material strength, are discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Stress Relaxation Cracking in 347H Stainless Steel Arc Welds: Susceptibility Evaluation of Heat-Affected Zone

Stress relaxation cracking (SRC) is considered one of the major failure mechanisms for 347H stainless steel welds at elevated service temperatures or during post weld heat treatment (PWHT), especially within the heat-affected zone (HAZ). This work focuses on the characterization of SRC susceptibility within 347H physically simulated arc welded HAZ at elevated temperatures. A four-step SRC thermomechanical test in combination with finite element modeling (FEM) of the welding and testing processes is developed to establish a susceptibility map for HAZ. The test first runs a thermal cycle with three different peak temperatures (1335, 1275, and 1150 °C) to duplicate representative HAZ subzone microstructures, followed by time-to-failure examination under a variety of pre-stress (260–600 MPa) and pre-strain conditions (0.03–0.19) as a function of reheat temperatures between 750 and 1050 °C. With the aid of FEM, SRC susceptibility maps are generated to identify the threshold stress, plastic strain, and creep strain as a function of test temperature. It was found out that HAZ subzone with a lower peak temperature (1150 °C) appears to be slightly less susceptible to SRC than the other two subzones that experienced higher peak temperatures. Generally, time-to-fracture reduces with increasing initially applied stress and strain for all test temperatures. The pre-stress thresholds decrease from about 500 to 330 MPa as the testing temperature increases from 800 to 1050 °C, while the corresponding initial plastic strain thresholds reduces from 0.15 to 0.06. The SRC susceptibility was also evaluated through the Larson–Miller Parameter (LMP) analysis as a function of plastic strain, initial stress and starting stress upon reaching the testing temperature, respectively. The 1050 °C test with a high pre-applied strain (0.1) exhibits an extremely short time to failure (t = 3 s) that lies outside the general trend in LMP analysis. Additionally, it was identified that a plastic strain above 0.07 is identified to significantly reduce the bulk creep strain tolerance to fracture and therefore increases SRC susceptibility. Hardness measurement and fractography analysis indicated that the strain aging of niobium carbonitrides and other potential phases in conjunction with intergranular precipitates contributes to an increase in microhardness and increased intergranular cracking susceptibility.

14 SOLAR ENERGY↗

DOE OSTI2022

Dynamic aspects of graphene deformation and fracture from approximate density functional theory

Graphene is one of the most intriguing two-dimensional carbon materials. Its mechanical strength and failure are key concerns for materials engineering and applications. Despite the success of fracture mechanics, the mechanism of how pristine materials fail remains an elusive problem. While many theoretical studies based on molecular dynamics using empirical forcefields have tried to address this question, atomic-scale mechanics are not clearly understood. Especially, a widely employed bond-breaking approach based on the critical bond length has not been rigorously tested. Here, utilizing molecular dynamics simulations with density functional based tight binding, we investigate how the failure of the pristine material initiates. The Wiberg bond order (W BO ) to estimate the change of chemical bonds shows a transition from sp 2 (W BO ~ 1.33) to sp 3 (WBO < 1.0) during the deformation. However, it reveals that a single threshold value for either the WBO or bond length is insufficient to decide failure of pristine material without free edges or defects. Instead, collective behaviors of the local atomic group govern the fracture initiation of pristine graphene. Overall, our study provides dynamic mechanical responses based on quantum mechanics, which have not been captured by empirical forcefields, opening opportunities to design properties by precisely coupling the mechanics and quantum mechanics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Microstructure and water absorption of ancient concrete from Pompeii: An integrated synchrotron microtomography and neutron radiography characterization

There is renewed interest in using advanced techniques to characterize ancient Roman concrete due to its exceptional durability and low-carbon footprint. In the present work, samples were drilled from the “Hospitium” in Pompeii and were analyzed by synchrotron microtomography (μCT) and neutron radiography to study how the microstructure, including the presence of induced cracks, affects their water adsorption. The water distribution and absorptivity were quantified by neutron radiography. The 3D crack propagation, pore size distribution and orientation, tortuosity, and connectivity were analyzed from μCT results using advanced imaging methods. Porosity was also measured by mercury intrusion porosimetry (MIP) as a reference. Ductile fracture patterns were observed once cracks were introduced. Compared to Portland cement mortar/concrete, the Pompeii samples had relatively high porosity, low connectivity, and a similar coefficient of capillary penetration. In addition, permeability was predicted from models based on percolation theory and pore structure data to evaluate the fluid transport properties. Understanding the microstructure of ancient Pompeii concrete is important because it could inspire the development of modern concrete with high durability.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Recent advances in the mechanical characterization of shales at nano-to micro-scales: A review

Understanding geomechanical properties of shales, such as stiffness properties and fracture toughness, is important in different areas of petroleum industry-related activities. Nanoscale to microscale experiments on shale samples require a much smaller sample compared to macroscale experiments. This is a major advantage because irregularly-shaped drill cuttings from shales can be used for experimental analyses, such as nanoindentation or atomic force microscopy (AFM). However, characterization of mechanical properties at the nano- to micro-scale is a relatively new addition to classical geomechanical experiments on shales, and there is still a lack of both fundamental knowledge and standard procedures for conducting experiments at this scale. The theoretical principles of nanoindentation-based (Gridded Nanoindentation and Modulus Mapping) and AFM-based experimental methods (PeakForce QNMTM and AFM-IR), a review of the literature results and the major findings are explained in Sections 2 and 3, respectively. These experimental techniques are compared in Section 4. Overall, nanoindentation experiments reveal the anisotropy of organic matter (OM)-rich shales at the nanoscale, and it is shown that gridded nanoindentation is capable of characterizing different minerals with respect to their stiffness properties. The capability of AFM (PeakForce QNMTM) to differentiate between different minerals within OM-rich shales with distinct mechanical properties, in particular stiffness, is also demonstrated. It is shown that AFM-based methods are more straightforward than gridded-nanoindentation to characterize OM-rich shales based on the stiffness of different constituent minerals of OM-rich shales, but nanoindentation can apply higher loads than AFM-based methods. Therefore, they can measure creep properties and fracture toughness of OM-rich shales. Here, it is shown that the OM is the most compliant part of the OM-rich shales, but it is still unclear if thermal maturation has an impact on the stiffness of OM. It is necessary to investigate if there is a relationship between the OM type (kerogen, bitumen, etc.) and mechanical properties such as Young’s modulus and Creep rate.

36 MATERIALS SCIENCE↗

DOE OSTI2024

DNA Strand Displacement Driven Molecular Additive Manufacturing (DSD-MAM)

The goal of this project was to validate two-dimensional molecular printers, initially selfassembled from DNA and then actuated by externally driven cycles of DNA strand displacement, as prototype integrated nanosystems for molecular additive manufacturing. Novel functionalities of these nanomachines were explored during this project, including the following: nanometer-precision positioning mechanisms based on DNA strand displacement with multivalent interactions for discrete stepping or else diffusive capture; integration of independently moving layers of DNA origami to achieve 2D controllable motion; integration of spatial positioning with deposition functionality. The principal importance of this project was to provide an essential step in the development of a new technology for atomically precise manufacturing. Our first generation molecular 2D printer offers several advantages over conventional DNA-origami patterning, such as faster prototyping, faster dynamic rearrangement of patterns, and the ability to respond with feedback. We anticipate that our first-generation molecular printers may inspire future generations of molecular printers with iterative improvements in robustness and throughput. Potential applications of atomically precise manufacturing include the following: photovoltaics; photosynthetic and fuel cells; thermoelectrics and anisotropic heat spreaders; solid-state lighting; molecular electronic and plasmonic circuits; selectively preamble membranes; self-repairing materials with high strength-to-weight and fracture resistance.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Critical Scaling of Solid Fragmentation at Quasistatic and Finite Strain Rates

Here, using two-dimensional simulations of sheared, brittle solids, we characterize the resulting fragmentation and explore its underlying critical nature. Under quasistatic loading, a power-law distribution of fragment masses emerges after fracture which grows with increasing strain. With increasing strain rate, the maximum size of a grain decreases and a shallower distribution is produced. We propose a scaling theory for distributions based on a fractal scaling of the largest mass with system size in the quasistatic limit or with a correlation length that diverges as a power of rate in the finite-rate limit. Critical exponents are measured using finite-size scaling techniques.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Challenges and Prospects of All-Solid-State Electrodes for Solid-State Lithium Batteries

In the development of all-solid-state lithium batteries (ASSLB), progress is made with solid-state electrolytes; however, challenges regarding compatibility and stability still exist with solid electrodes. These issues result in a low battery capacity and short cycle life, which limit the commercial application of ASSLBs. Here, this review summarizes the recent research progress on solid-state electrodes in ASSLBs including the solid–solid interface phenomena such as the interface between electrode materials and electrolytes. The mechanical stability problems in solid electrodes, including fracture, brittleness, and deformation of electrode materials, are also discussed, and corresponding methods to measure the solid electrode stress are provided. In addition, strategies for mitigating stress-related issues are examined. Finally, the fabrication process of solid electrodes is introduced and their future developments, including the exploration of new electrode materials and the design of more intelligent electrode structures, are proposed.

25 ENERGY STORAGE↗

DOE OSTI2021

Inelastic peridynamic model for molecular crystal particles

The peridynamic theory of solid mechanics is applied to modeling the deformation and fracture of micrometer-sized particles made of organic crystalline material. A new peridynamic material model is proposed to reproduce the elastic–plastic response, creep, and fracture that are observed in experiments. The model is implemented in a three-dimensional, meshless Lagrangian simulation code. In the small deformation, elastic regime, the model agrees well with classical Hertzian contact analysis for a sphere compressed between rigid plates. Under higher load, material and geometrical nonlinearity is predicted, leading to fracture. Finally, the material parameters for the energetic material CL-20 are evaluated from nanoindentation test data on the cyclic compression and failure of micrometer-sized grains.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

A guide to the design of the virtual element methods for second- and fourth-order partial differential equations

Here we discuss the design and implementation details of two conforming virtual element methods for the numerical approximation of two partial differential equations that emerge in phase-field modeling of fracture propagation in elastic material. The two partial differential equations are: (i) a linear hyperbolic equation describing the momentum balance and (ii) a fourth-order elliptic equation modeling the damage of the material. Inspired by, we develop a new conforming VEM for the discretization of the two equations, which is implementation-friendly, i.e., different terms can be implemented by exploiting a single projection operator. We use C 0 and C 1 virtual elements for the second-and fourth-order partial differential equation, respectively. For both equations, we review the formulation of the virtual element approximation and discuss the details pertaining the implementation.

42 ENGINEERING↗

DOE OSTI2022

Microbial colonization and persistence in deep fractured shales is guided by metabolic exchanges and viral predation

Background: Microbial colonization of subsurface shales following hydraulic fracturing offers the opportunity to study coupled biotic and abiotic factors that impact microbial persistence in engineered deep subsurface ecosystems. Shale formations underly much of the continental USA and display geographically distinct gradients in temperature and salinity. Complementing studies performed in eastern USA shales that contain brine-like fluids, here we coupled metagenomic and metabolomic approaches to develop the first genome-level insights into ecosystem colonization and microbial community interactions in a lower-salinity, but high-temperature western USA shale formation. Results: We collected materials used during the hydraulic fracturing process (i.e., chemicals, drill muds) paired with temporal sampling of water produced from three different hydraulically fractured wells in the STACK (Sooner Trend Anadarko Basin, Canadian and Kingfisher) shale play in OK, USA. Relative to other shale formations, our metagenomic and metabolomic analyses revealed an expanded taxonomic and metabolic diversity of microorganisms that colonize and persist in fractured shales. Importantly, temporal sampling across all three hydraulic fracturing wells traced the degradation of complex polymers from the hydraulic fracturing process to the production and consumption of organic acids that support sulfate- and thiosulfate-reducing bacteria. Furthermore, we identified 5587 viral genomes and linked many of these to the dominant, colonizing microorganisms, demonstrating the key role that viral predation plays in community dynamics within this closed, engineered system. Lastly, top-side audit sampling of different source materials enabled genome-resolved source tracking, revealing the likely sources of many key colonizing and persisting taxa in these ecosystems. Conclusions: These findings highlight the importance of resource utilization and resistance to viral predation as key traits that enable specific microbial taxa to persist across fractured shale ecosystems. We also demonstrate the importance of materials used in the hydraulic fracturing process as both a source of persisting shale microorganisms and organic substrates that likely aid in sustaining the microbial community. Moreover, we showed that different physicochemical conditions (i.e., salinity, temperature) can influence the composition and functional potential of persisting microbial communities in shale ecosystems. Together, these results expand our knowledge of microbial life in deep subsurface shales and have important ramifications for management and treatment of microbial biomass in hydraulically fractured wells.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Fracture behavior of irradiation induced nanocrystalline UO 2 studied by in-situ mechanical testing in transmission electron microscopy

Uranium Dioxide (UO 2 ) is widely used as a fuel in current light water reactors (LWRs). Upon accumulation of radiation damage, LWR UO 2 fuel pellets start to develop a different microstructure at the pellet periphery when fuel burnup exceeds 45–50 GWd/tHM. The resulting porous, nanocrystalline microstructure is one of the most prominent microstructural changes occurring in such fuel. Its fracture mechanisms, which causes fuel fine fragmentation, could impact safety limits when the cladding breaches. Direct measurements of these properties are challenging, therefore a surrogate obtained via ion irradiation can be used. In this study, multiple microcantilevers were fabricated by focused ion beam from both fresh UO 2 and UO 2 irradiated with 84 MeV Xe 26+ ions to a peak dose of 1357 displacements per atom (dpa). Further, the irradiation produced a pseudo high burnup structure approximately 2 µm below the surface. In-situ nano-mechanical bending tests were conducted to investigate the fracture behavior and the effect of the surrogate UO 2 high burnup structure on local fracture properties. Fresh UO 2 fuel was observed to fracture in transgranular mode without nucleation or movement of dislocations. However, the Xe-irradiated nanocrystalline microcantilevers fractured along the grain boundaries, with no influence from the pre-existing micro-cracks in the microcantilever. Fracture toughness for this type of surrogate high burnup UO 2 structure is reported for the first time in literature. Both the fracture stress and toughness show degradation for UO 2 as a result of Xe-irradiation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Synergistic Effects of Molten Salt Corrosion and Proton Irradiation on Grain Boundary Strength in Ni-20Cr

Nickel-based alloys are leading contenders for use as structural materials in molten salt reactors. While there have been extensive studies on the impact of fluoride/chloride-based molten salt corrosion on the microstructural evolution of various nickel-based alloys, the effects of simultaneous molten salt corrosion and radiation on the mechanical integrity of grain boundaries (GBs) remain underexplored. In this study, we use a Ni-20Cr model alloy to investigate this issue, subjecting it to simultaneous molten fluoride salt corrosion and proton irradiation. We performed cross-sectional and chemically-sensitive electron microscopy characterization of the microstructures of these materials, identifying the characteristic corrosion-induced microstructure and local chemical heterogeneity near GBs. After developing a sample preparation method for reliable characterization of GB strength, we assess the mechanical degradation of GBs using in situ push-to-pull micro tensile tests. Our findings reveal that voids induced by corrosion are the primary influence on the failure mode of GBs, regardless of whether proton irradiation is present. For materials that exhibit ductile fracture, those subjected to simultaneous corrosion and radiation exhibit lower yield strengths than those exposed to corrosion alone, which may be linked to the previously observed phenomenon of proton irradiation-decelerated intergranular corrosion in molten salt.

36 - MATERIALS SCIENCE↗