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DOE OSTI2025

Ductility mechanisms in complex concentrated refractory alloys from atomistic fracture simulations

The striking variation in damage tolerance among refractory complex concentrated alloys is examined through the analysis of atomistic fracture simulations, contrasting behavior in elemental Nb with that in brittle NbMoTaW and ductile Nb45Ta25Ti15Hf15. We employ machine-learning interatomic potentials (MLIPs), including a new MLIP developed for NbTaTiHf, in atomistic simulations of crack tip extension mechanisms based on analyses of atomistic fracture resistance curves. While the initial behavior of sharp cracks shows good correspondence with the Rice theory, fracture resistance curves reveal marked changes in fracture modes for the complex alloys as crack extension proceeds. In NbMoTaW, compositional complexity appears to promote dislocation nucleation relative to pure Nb, despite theoretical predictions that the alloy should be relatively more brittle. In Nb45Ta25Ti15Hf15, alloying alters the fracture mode compared to elemental Nb, promoting crack tip blunting and enhancing resistance to crack propagation.

Computational methods↗

DOE OSTI2019

Cascading parallel fractures on Enceladus

Active eruptions from the south polar region of Saturn’s ~500-km-diameter moon Enceladus are concentrated along a series of lineaments known as the ‘tiger stripes’, thought to be partially open fissures that connect to the liquid water ocean beneath the ice shell. To date, no study simultaneously explains why the tiger stripes should be located only at the south pole, why there are multiple approximately parallel and regularly spaced fractures, what accounts for their spacing of about 35 km, and why similarly active fissures have not been observed on other icy bodies. Here in this paper, we propose that secular cooling, which leads to a thickening of the ice shell and building of global tensile stresses, causes the first fracture to form at one of the poles, where the ice shell is thinnest owing to tidal heating. The tensile stresses are thereby relieved, preventing a similar failure at the opposite pole. The steadily erupting water ice loads the flanks of the open fissure, causing bending in the surrounding elastic plate and further tensile failure in bands parallel to the first fracture—a process that may be unique to Enceladus, where the gravity is too weak for compressive stresses to prevent fracture propagation through the thin ice shell. The sequence of fissures then cascades outwards until the loading becomes too weak or the background shell thickness becomes too great to permit through-going fractures.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

A primer on selecting grain boundary sets for comparison of interfacial fracture properties in molecular dynamics simulations

In this study, all grain boundaries are not equal in their predisposition for fracture due to the complex coupling between lattice geometry, interfacial structure, and mechanical properties. The ability to understand these relationships is crucial to engineer materials resilient to grain boundary fracture. Here, a methodology is presented to isolate the role of grain boundary structure on interfacial fracture properties, such as the tensile strength and work of separation, using atomistic simulations. Instead of constructing sets of grain boundary models within the misorientation/structure space by simply varying the misorientation angle around a fixed misorientation axis, the proposed method creates sets of grain boundary models by means of isocurves associated with important fracture-related properties of the adjoining lattices. Such properties may include anisotropic elastic moduli, the Schmid factor for primary slip, and the propensity for simultaneous slip on multiple slip systems. This approach eliminates the effect of lattice properties from the comparative analysis of interfacial fracture properties and thus enables the identification of structure-property relationships for grain boundaries. As an example, this methodology is implemented to study crack propagation along Ni grain boundaries. Segregated H is used as a means to emphasize differences in the selected grain boundary structures while keeping lattice properties fixed.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Phase instability-coupled fracture behavior in garnet LLZO solid electrolytes: a machine learning-enabled atomistic study

Fracture in the garnet-type solid electrolyte Li 7 La 3 Zr 2 O 12 (LLZO) poses a critical threat to both the performance and safety of solid-state batteries. To unravel the coupled chemomechanical processes that govern fracture in LLZO under external loading, we carry out large-scale molecular-dynamics simulations with a validated machine-learning force field. Our results demonstrate that triaxial stresses at crack flanks trigger a localized cubic-to-tetragonal phase transformation, which is accompanied by Li-ion rearrangement. The emergent tetragonal domains feature lattice contraction normal to the fracture plane, imposing coherent misfit strains that provide an additional driving force for further crack propagation. Crucially, introducing Li deficiencies stabilizes the cubic phase, postponing the phase transition and thereby delaying fracture initiation. These findings highlight the role of intrinsic phase instability in dictating LLZO's fracture resistance and its critical connection to local Li concentration. This chemomechanical coupling points toward targeted strategies to enhance the mechanical robustness of garnet electrolytes, including tuning Li content, ensuring dopant homogeneity, and refining processing protocols.

Materials science↗

DOE OSTI2024

Sprain energy consequences for damage localization and fracture mechanics

The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the “sprain,” as the localization limiter. The key idea was that, in the finite element implementation, the displacement vector and its gradient should be treated as independent fields with the lowest ( C 0 ) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as microplane model M7, the known limitations of the classical Crack Band Model were eliminated. Here, we show that the slCBM closely reproduces the size effect revealed by the gap test at various crack-parallel stresses. To describe it, we present an approximate corrective formula, although a strong loading-path dependence limits its applicability. Except for the rare case of zero crack-parallel stresses, the fracture predictions of the line crack models (linear elastic fracture mechanics, phase-field, extended finite element method (XFEM), cohesive crack models) can be as much as 100% in error. We argue that the localization limiter concept must be extended by including the resistance to material rotation gradients. We also show that, without this resistance, the existing strain-gradient damage theories may predict a wrong fracture pattern and have, for Mode II and III fractures, a load capacity error as much as 55%. Finally, we argue that the crack-parallel stress effect must occur in all materials, ranging from concrete to atomistically sharp cracks in crystals.

Science & Technology - Other Topics↗

DOE OSTI2021

Toughening materials: enhancing resistance to fracture

It has been said that ‘God invented plasticity, but the Devil invented fracture!’ Both mechanisms represent the two prime modes of structural failure, respectively, plastic collapse and the rupture/breaking of a component, but the concept of developing materials with enhanced resistance to fracture can be difficult. This is because fracture resistance invariably involves a compromise—between strength and ductility, between strength and toughness—fundamentally leading to a ‘conflict’ between nano-/micro-structural damage and the mechanisms of toughening. Here, we examine the two major classes of such toughening: (i) intrinsic toughening, which occurs ahead of a crack tip and is motivated by plasticity—this is the principal mode of fracture resistance in ductile materials, and (ii) extrinsic toughening, which occurs at, or in the wake of, a crack tip and is associated with crack-tip shielding—this is generally the sole mode of fracture resistance in brittle materials. We briefly examine how these distinct mechanistic processes have been used to toughen synthetic materials—intrinsically in gradient materials and in multiple principal-element metallic alloys with the example of metallic glasses and high-entropy alloys, and extrinsically in ceramics with the example of ceramic-matrix composites—in comparison to Nature which has been especially adept in creating biological/natural materials which are toughened by one or both mechanistic classes, despite often consisting of constituents with meagre mechanical properties. The success of Nature has been driven by its ability to cultivate the development of materials with multiple length-scale hierarchical structures that display ingenious gradients and structural adaptability, a philosophy which we need to emulate and more importantly learn to synthesize to make structural materials of the future with unprecedented combinations of mechanical properties.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Master Curve Fracture Toughness Characterization of Eurofer97 Steel Variants Using Miniature Multi-Notch Bend Bar Specimens for Fusion Applications

In this study, we performed fracture toughness testing of ten Eurofer97 steel variants using precracked miniature multi-notch bend bar (M4CVN) specimens based on the Master Curve method in the ASTM E1921 standard. Additional Vickers microhardness and room temperature tensile testing complemented the fracture toughness testing. Compared with standard Eurofer97, the ten variants didn’t show a comprehensive improvement of mechanical properties. The Master Curve method was found to yield a reasonable prediction of fracture toughness results obtained from M4CVN specimens with most valid fracture toughness data within the 2% and 98% tolerance boundaries of the Master Curve. The three-parameter Weibull distribution with Weibull exponent b = 4 also yielded excellent prediction of the relationship between fracture toughness results KJc and the cumulative probability for failure pf for one steel variant.

Chen, Xiang↗

DOE OSTI2021

Wide-blocky veins explained by dependency of crystal growth rate on fracture surface type: Insights from phase-field modeling

Vein microstructures contain a wealth of information on coupled chemical and mechanical processes of fracturing, fluid transport, and crystal growth. Numerical simulations have been used for exploring the factors controlling the development of vein microstructures; however, they have not been quantitatively validated against natural veins. Here we combined phase-field modeling with microtextural analysis of previously unexplained wide-blocky calcite veins in natural limestone and of the fresh fracture surface in this limestone. Results show that the wide-blocky vein textures can only be reproduced if ~10%–20% of crystals grow faster than the rest. This fraction corresponds to the amount of transgranularly broken grains that were observed on the experimental fracture surfaces, which are dominantly intergranular. We hypothesize that transgranular fractures allow faster growth of vein minerals due to the lack of clay coatings and other nucleation discontinuities that are common along intergranular cracks. Our simulation results show remarkable similarity to the natural veins and reproduce the nonlinear relationship between vein crystal width and vein aperture. This allows accurate simulations of crystal growth processes and related permeability evolution in fractured rocks.

Geology↗

DOE OSTI2026

Demonstration of thermal fracture limits of gas-cooled Nd:APG-1 and Tm:YLF slabs

High-energy short-pulse laser systems demonstrated to date have been limited to low repetition rates due to significant thermal management challenges associated with scaling these systems to high average power, including the need to understand the thermal fracture limits of laser gain media. In this paper, we demonstrate the thermal fracture limits of two high-average-power gain media in a realistic diode-pumped amplifier geometry: a 5 mm thick Nd:APG-1 slab and a 2 mm thick Tm:YLF slab, both cooled by room-temperature helium gas. Finite element analysis revealed maximum tensile stress at fracture of 25 ± 3 MPa for Nd:APG-1 and 30 ± 3 MPa for Tm:YLF. These stress levels correspond to average volumetric heat loads of 13 ± 1 W/cm 3 in Nd:APG-1 and 247 ± 12 W/cm 3 in Tm:YLF. Additional simulations show geometric scaling: thinner slabs tolerate higher heat loads before fracture, while larger pump spots reach the fracture stress at lower heat loads.

Lasers↗

DOE OSTI2019

Stress and Fracture of Crystalline Silicon Cells in Solar Photovoltaic Modules – A Synchrotron X-ray Microdiffraction based Investigation

Fracture of crystalline silicon (c-Si) solar cells in photovoltaic modules is a big concern to the photovoltaics (PV) industry. Cell cracks cause performance degradation and warranty issues to the manufacturers. The roots of cell fractures lie in the manufacturing and integration process of the cells and modules as they go through a series of elevated temperature and pressure processes, involving bonding of dissimilar materials, causing residual stresses. Evaluation of the exact physical mechanisms leading to these thermomechanical stresses is highly essential to quantify them and optimize the PV modules to address them. Here we present a novel synchrotron X-ray microdiffraction based techniques to characterize the stress and fracture in the crystalline silicon PV modules. We show the detailed stress state after soldering and lamination process, using the synchrotron X-ray microdiffraction experiments. We also calculate the maximum tolerable microcrack size in the c-Si cells to sustain the residual stress after lamination. We further demonstrate the effect of these residual stresses on the cell fractures using the widely accepted fracture (4-point bending) tests. These test results show that the soldering and lamination induced localized residual stresses indeed reduce the load-carrying capacity of the c-Si cells.

14 SOLAR ENERGY↗

DOE OSTI2022

Assessment of Lost Circulation Material Particle-Size Distribution on Fracture Sealing: A Numerical Study

Summary Lost circulation materials (LCMs) are essential to combat fluid loss while drilling and may put the whole operation at risk if a proper LCM design is not used. The focus of this research is understanding the function of LCMs in sealing fractures to reduce fluid loss. One important consideration in the success of fracture sealing is the particle-size distribution (PSD) of LCMs. Various studies have suggested different guidelines for obtaining the best size distribution of LCMs for effective fracture sealing based on limited laboratory experiments or field observations. Hence, there is a need for sophisticated numerical methods to improve the LCM design by providing some predictive capabilities. In this study, computational fluid dynamics (CFD) and discrete element methods (DEM) numerical simulations are coupled to investigate the influence of PSD of granular LCMs on fracture sealing. Dimensionless variables were introduced to compare cases with different PSDs. We validated the CFD-DEM model in reproducing specific laboratory observations of fracture-sealing experiments within the model boundary parameters. Our simulations suggested that a bimodally distributed blend would be the most effective design in comparison to other PSDs tested here.

Engineering↗

DOE OSTI2023

Nanoparticle-Surfactant Stabilized Strong Foam for Enhanced Oil Recovery in High-Salinity Fractured Carbonate Reservoirs

Summary Foam flooding can minimize bypassing in gasfloods in fractured reservoirs. Finding a foam formulation effective in high-salinity brine is challenging, especially with divalent cations, e.g., American Petroleum Institute (API) brine (8% NaCl with 2% CaCl2). When formulating with nanoparticles, the colloidal dispersion stability is difficult due to the dramatic reduction in zeta potential and the Debye length at high salinity. The aim of this work was to develop a strong foam in API brine at the ambient temperature, using a nonionic surfactant and ethyl cellulose nanoparticles (ECNP), for gasflooding in fractured carbonate reservoirs. ECNPs was synthesized and dispersed in API brine using a nonionic surfactant (also denoted as SF). SF and SF/ECNP foams were generated, and their stability was studied at atmospheric pressure and 950 psi. Foam mobility was measured in a sandpack at high pressure. Foam flood experiments were conducted in oil-saturated fractured carbonate cores. The nonionic surfactant proved to be a good dispersion agent for ECNP in API brine. The SF/ECNP mixture stabilized foam in API brine, even in the presence of oil. Injecting a partially miscible gas (below its minimum miscibility pressure) as an SF foam into a fractured core more than doubles the oil recovery over injection of the gas alone. The injection of the strong foam (SF/ECNP) further improves the oil recovery over that of the SF foam, indicating the synergy between ECNP and surfactant. ECNP accumulates in the foam lamella and induces larger pressure gradients in the fracture to divert more gas into the matrix for oil displacement.

Engineering↗

DOE OSTI2023

Autonomous Fracture Conductivity Using Expandable Proppants in Enhanced Geothermal Systems

Summary Early thermal breakthrough in enhanced geothermal systems (EGS) due to the presence of preferential flow channels is a major challenge that endangers efficient and economic heat extraction in such systems. Previous studies mainly focused on adjusting circulation rates of the working fluid, which still leaves significant amounts of untapped heat behind. Currently, there is a lack of technologies for altering flow distribution within the fracture network to achieve uniform heat sweeping in the reservoir. This work presents a novel concept for making proppants to autonomously control fracture conductivity based on the surrounding temperature. Here, proppants with negative thermal expansion coefficients have demonstrated the capability for appropriate fracture conductivity adjustment as a function of temperature to achieve uniform flow across the fracture network. Particle-particle interactions governing such functions are explicitly modeled, and then the Lattice Boltzmann methods (LBM) is used to determine the potential impact of closure stress and temperature changes on the permeability of the proposed proppant packs. Microscale analyses are further used to determine the required material properties to achieve a certain improvement in the permeability of the proppant pack. Our analyses show an enhancement in permeability and the associated fracture conductivity by half of their initial values. Field-scale analysis further confirms the effectiveness of the proposed concept as 31.4% more heat can be extracted from EGS over 50 years of production when the proposed proppants are used. Such novel proppants may effectively delay thermal breakthrough, sweep heat from larger rock volumes, and elongate the life span of the EGS project.

Engineering↗

DOE OSTI2016

The Assessment and Validation of Mini-Compact Tension Test Specimen Geometry and Progress in Establishing Technique for Fracture Toughness Master Curves for Reactor Pressure Vessel Steels

Small specimens are playing the key role in evaluating properties of irradiated materials. The use of small specimens provides several advantages. Typically, only a small volume of material can be irradiated in a reactor at desirable conditions in terms of temperature, neutron flux, and neutron dose. A small volume of irradiated material may also allow for easier handling of specimens. Smaller specimens reduce the amount of radioactive material, minimizing personnel exposures and waste disposal. However, use of small specimens imposes a variety of challenges as well. These challenges are associated with proper accounting for size effects and transferability of small specimen data to the real structures of interest. Any fracture toughness specimen that can be made out of the broken halves of standard Charpy specimens may have exceptional utility for evaluation of reactor pressure vessels (RPVs) since it would allow one to determine and monitor directly actual fracture toughness instead of requiring indirect predictions using correlations established with impact data. The Charpy V-notch specimen is the most commonly used specimen geometry in surveillance programs. Assessment and validation of mini-CT specimen geometry has been performed on previously well characterized HSST Plate 13B, an A533B class 1 steel. It was shown that the fracture toughness transition temperature measured by these Mini-CT specimens is within the range of To values that were derived from various large fracture toughness specimens. Moreover, the scatter of the fracture toughness values measured by Mini-CT specimens perfectly follows the Weibull distribution function providing additional proof for validation of this geometry for the Master Curve evaluation of rector pressure vessel steels. Moreover, the International collaborative program has been developed to extend the assessment and validation efforts to irradiated weld metal. The program is underway and involves ORNL, CRIEPI, and EPRI.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Transition Fracture Toughness Characterization of Eurofer 97 Steel using Pre-Cracked Miniature Multi-notch Bend Bar Specimens

In this report, we present the feasibility study of using pre-cracked miniature multi-notch bend bar specimens (M4CVN) with a dimension of 45mm (length) x 3.3mm (width) x 1.65mm (thickness) to characterize the transition fracture toughness of Eurofer97 based on the ASTM E1921 Master Curve method. From literature survey results, we did not find any obvious specimen size effects on the measured fracture toughness of unirradiated Eurofer97. Nonetheless, in order to exclude the specimen size effect on the measured fracture toughness of neutron irradiated Eurofer97, comparison of results obtained from larger size specimens with those from smaller size specimens after neutron irradiation is necessary, which is not practical and can be formidably expensive. However, limited literature results indicate that the transition fracture toughness of Eurofer97 obtained from different specimen sizes and geometries followed the similar irradiation embrittlement trend. We then described the newly designed experimental setup to be used for testing neutron irradiated Eurofer97 pre-cracked M4CVN bend bars in the hot cell. We recently used the same setup for testing neutron irradiated F82H pre-cracked miniature multi-notch bend bars with great success. Considering the similarity in materials, specimen types, and the nature of tests between Eurofer97 and F82H, we believe the newly designed experimental setup can be used successfully in fracture toughness testing of Eurofer97 pre-cracked M4CVN specimens.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Multiscale Modeling of Deformation, Fracture and Failure of Fusion Materials and Structures Final Report

The main objective of the research performed at UCLA under grant number DE-FG02-03ER54708 was to develop a physical understanding of the underlying mechanisms that control high-temperature deformation and fracture of fusion structural materials. The key aspect is the synergistic interaction between thermo-mechanical damage phenomena (e.g. creep, fatigue, and fracture), and irradiation damage phenomena (helium and hydrogen bubbles, and irradiation-induced defects). Another thrust area of the research was on the development of constitutive equations for the mechanical behavior of irradiated structures in fusion components (mainly the First Wall and Plasma-Facing components), and in utilizing them in descriptions in large-scale Finite Element Modeling of fusion structures. A parallel experimental effort on thermo-mechanical and plasma-induced damage is designed to validate and confront the developed theoretical and computational predictions. The models have been experimentally validated through experimental tests in simulated plasma transients on specially-designed W samples. This grant started at UCLA on November 14, 2003 and has had successive continuations till November 14, 2017. Research performed under the grant was to develop a range of hierarchical models for the post-elastic deformation, fracture and failure of fusion structural materials. The developed multiscale modeling approach has been based on rigorous mathematical, physical, and computational methods at the forefront of computational materials science. At the fundamental and smallest length scale (nm-μm), we developed advanced rate theory and Monte Carlo approaches to model microstructure evolution, non-equilibrium phase transformations, and dislocation-defect interactions. Microscopic and mesoscopic models of radiation hardening, ductile-to-brittle-transition, post-elastic deformation, plastic instabilities, and fracture processes are based on Dislocation Dynamics (DD) and Grain Growth Dynamics (GGD). At the continuum level, we focused on modeling fracture and failure mechanisms for Virtual Integrated Testing (VISTA), and for understanding the limits of both materials-by-design versus structural component design through advancing the new approach of multiscale-multiphysics. The overall research has been strongly coupled with the U.S. national experimental program to ascertain and verify the range of investigated phenomena. In the following, we give a summary of research progress supported by this grant since its inception till November 14, 2017. Detailed research results are available in our publications, listed in the publications section of this report.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Chemical-Mechanical Modeling of Subcritical-to-Critical Fracture in Geomaterials

Predicting chemical-mechanical fracture initiation and propagation in materials is a critical problem, with broad relevance to a host of geoscience applications including subsurface storage and waste disposal, geothermal energy development, and oil and gas extraction. In this project, we have developed molecular simulation and coarse- graining techniques to obtain an atomistic-level understanding of the chemical- mechanical mechanisms that control subcritical crack propagation in materials under tension and impact the fracture toughness. We have applied these techniques to the fracture of fused quartz in vacuum, in distilled water, and in two salt solutions - 1M NaC1, 1M NaOH - that form relatively acidic and basic solutions respectively. We have also established the capability to conduct double-compression double-cleavage experiments in an environmental chamber to observe material fracture in aqueous solution. Both simulations and experiments indicate that fractures propagate fastest in NaC1 solutions, slower in distilled water, and even slower in air.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Hydrogen-Assisted Fracture of Stainless Steel

Symmetric four-point bending (S4PB) and anti-symmetric four-point bending (AS4PB) were applied to assess the effect of hydrogen on crack initiation and propagation in a stable, nitrogen-strengthened austenitic stainless steel (21Cr-6Ni-9Mn). Specimens of a high strength aluminum alloy (AA2219-T851), which has also been identified as hydrogen-compatible, were used for test method development prior to completing the stainless steel test matrix. Single edge notched bend (SEN(B)) specimens were extracted from forged 21Cr-6Ni-9Mn bar and AA2219 plate. The 21Cr-6Ni-9Mn specimens were then hydrogen charged with ~200 wt. ppm hydrogen; AA2219 specimens were not charged. Aluminum specimens were tested in S4PB to induced mode I (pure bending), and AS4PB to attain varying levels of mode I/II mixity and mode II (pure shear), where the ratio of mode I to mode II varies with the position of the crack plane relative to the load line. After test method troubleshooting and validation, hydrogen charged stainless steel specimens were then subjected to mode I and two ratios of mixed mode I/II. Mode II loading was not achieved due to high load limitations. Analyses of fracture profiles for both materials reveal a marked effect of loading mode mixity on initial crack propagation orientation, however a specific contribution of hydrogen was not readily identifiable. Fracture initiation toughness in the presence of hydrogen, J IH , was calculated following the J-integral approach; the mode I J IH calculated for stainless steel samples fractured in S4PB were consistent with published values determined from compact tension specimens. The peak loads required to initiate fracture during AS4PB far exceeded those required during S4PB. This is attributed to the increasing shear force applied to the specimens as the degree of mode mixity increases. Ultimately, understanding the fracture response of hydrogen exposed stainless steels subjected to mixed mode I/II loading is critical for designing hydrogen containment vessels or gas transfer systems (GTS).

36 MATERIALS SCIENCE↗