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Results for “Brittle fracture”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2025

An FFT-based micromechanical model for gradient enhanced brittle fracture

Damage models incorporated within FFT-based micromechanical methods have received much attention recently because of the need to better understand and predict brittle and ductile fracture. An important aspect of a damage model is non-local regularization, which removes the mesh dependence of the predictions that otherwise become physically unacceptable upon grid refinement. In this work, the Helmholtz-type equation for non-local gradient regularization of a damage model on a distorted grid is solved using an FFT-based approach. Further, the resulting system of equations is solved using the Jacobi iterative method. The model is applied to simulate brittle fracture of an intermetallic. The influence of the time and space discretization, the length-scale parameter, and intermetallic crystallographic orientation on crack evolution is studied.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Towards robust surrogate models: Benchmarking machine learning approaches to expediting phase field simulations of brittle fracture

Data-driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning techniques have the potential to provide a much needed speedup that would enable progress in areas such as multi-scale modeling and uncertainty quantification. Currently, phase field modeling (PFM) of fracture is one such approach that offers a convenient variational formulation to model crack nucleation, branching and propagation. To date, machine learning techniques have shown promise in approximating PFM simulations. While standard fracture benchmarks represent realistic scenarios frequently observed in practice, they typically do not provide sufficiently challenging tests for data-driven methods. Here, to address this gap, we introduce a challenging dataset based on PFM simulations designed to benchmark and advance ML methods for fracture modeling. This dataset includes three energy decomposition methods, two boundary conditions, and 1000 random initial crack configurations for a total of 6000 simulations. Each sample contains 100 time steps capturing the temporal evolution of the crack field. Alongside this dataset, we also implement and evaluate Physics Informed Neural Networks (PINN), Fourier Neural Operators (FNO), and UNet models as baselines, and explore the impact of ensembling strategies on prediction accuracy. With this combination of our dataset and baseline models drawn from the literature we aim to provide a standardized and challenging benchmark for evaluating machine learning approaches to solid mechanics. Our results highlight both the promise and limitations of popular current models, and demonstrate the utility of this dataset as a testbed for advancing machine learning in fracture mechanics research.

Benchmark dataset↗

DOE OSTI2026

Predicting fracture behavior in single crystal nickel using a coupled crystal plasticity phase field damage approach

Understanding the fracture behavior of single crystal metals is critical for predicting material performance under mechanical loading. Here, in this study, we investigate the fracture characteristics of single crystal nickel tensile bars using a crystal plasticity coupled phase field damage (CP-PFD) model. Experimental tensile tests were conducted on 15 specimens spanning five crystallographic orientations and three thickness variants per orientation. The results revealed two distinct fracture modes: brittle fractures with 45-degree angled surfaces and ductile fractures characterized by significant necking. The CP-PFD model successfully replicated these fracture behaviors, demonstrating strong agreement with experimental observations. The model effectively predicted the strain at which necking and fracture occurred, as well as the orientation-dependent fracture mechanisms. By comparing experimental and simulated fracture surfaces, we establish the CP-PFD model as a robust tool for predicting single crystal behavior and damage evolution. This work provides insight into the microstructural dependence of fracture behavior and establishes a predictive framework for modeling orientation-dependent damage evolution in single-crystal nickel.

Crystal plasticity↗

DOE OSTI2025

Phase-field modeling and experiments of dynamic fracture in single crystal quartz

Predicting the onset and characteristics of brittle fracture is important for a wide range of engineering and geological material applications. In this paper, we study important aspects of brittle fracture in α-quartz by phase-field modeling and experiments using a top-down approach. In the modeling framework, the work term in the Griffith energy balance is replaced with internal energy contributions that represent surface energy, thermal energy, and elastic strain energy stored in defects. This allows parametrization of individual energy contributions in terms of internal state variables and keeps track of energy partitioning after the onset of fracture. The path and history dependence of fracture is included in evolution laws for internal state variables, e.g., entropy evolution, while the energy remains a true potential. In the experimental part, dynamic compression experiments coupled with X-ray phase contrast imaging are performed on cube-like samples with a hole. In the top-down analysis, dynamic compression and three point bending experiments from the literature are simulated with the developed phase-field damage model. In conclusion, the fitted model highlights the strain rate, size, and stress state dependence of damage nucleation and evolution in single crystal α-quartz.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Investigation of the temperature-dependent failure processes in PVD Cr-coated ZIRLO nuclear fuel cladding using in situ X-ray micro-tomography imaging

In this work, an accident tolerant fuel cladding system with Cr coating deposited using physical vapour deposition (PVD) method onto commercial Optimized ZIRLO™ was studied. The cladding tubes were machined into C-rings and loaded to failure under compression with real-time synchrotron micro-X-ray computed tomography (XCT) imaging at room temperature (RT), 345 °C, 650 °C and 950 °C in argon (Ar) atmosphere. The mechanical behaviour and failure processes were found strongly temperature-dependent where the Cr coating showed brittle fracture at RT and 345 °C, ductile fracture at 650 °C and a reversion to brittle fracture at 950 °C. Nanoindentation measurements and scanning electron microscopy (SEM) imaging were conducted on the materials after high temperature testing. It was found that recrystallisation of the Cr coating occurred at elevated temperatures, which significantly affected its local properties hence the failure behaviour at different temperatures. This work represents the first in situ 3D XCT observation of progressive failure processes in PVD Cr-coated ZIRLO claddings up to 950 °C providing critical insights into its brittle-to-ductile transition (BDTT) behaviour and subsequent ductile-to-brittle reversion with the increase in temperature. Moreover, results are compared with other PVD Cr-coated Zircaloy materials from open literature; the influences of the coating microstructure and local properties on the failure stress/strain and fracture processes are discussed.

Yuan, Guanjie↗

DOE OSTI2025

On the bulk compaction of brittle granular materials, Part III: Brittle‐to‐ductile transition and yield strength

A new and simple method is presented that enables the estimation of the yield strength (σ y ) of brittle materials (e.g., ceramics, glasses). It results from the combination of sufficiently high-stress compaction of their granular form, postmortem analysis of the crushed particles to identify the critical particle size corresponding to their brittle-to-ductile transition, and the use of a developed and simple analytical expression. Here, this method was an outcome from Part I of this three-paper series. To execute it, a granular brittle material is compacted to a sufficiently high stress, whereby the acting comminution produces both a fraction of particles having a sufficiently small size formed by ductile or plastic-like deformation and a remaining fraction of larger particles formed from brittle fracture. Postmortem microscopy is then used to identify the smallest particle size whose morphology indicates it formed from brittle fracture (d B2D ). The brittle material's σ y can then be estimated using a combination of the d B2D , Kendall's and Griffith's theories, a priori knowledge of the material's fracture toughness (K Ic ), and a fracture mechanics shape factor constant (Y) using σ y = √((32 π K Ic 2 )/(3 Y 2 d B2D )). The method's development and its use to estimate σ y for several vitreous silicates, α-quartzes, and NaCl are provided.

Compaction↗

DOE OSTI2025

Impact of position and density of nanoscale voids on fracture initiation in iron from phase field fracture simulation

Understanding the impact of these bubbles on crack propagation, like that of helium bubble-induced cracking in irradiated materials is incredibly complex. A useful first study towards understanding bubble effects on fracture is to examine how voids impact fracture first. In this work, we used phase-field fracture simulations to examine the influence of voids and their distribution on Mode I fracture in Fe. Assuming brittle fracture, two simulation configurations were considered: (1) nanoscale systems with one or two voids, and (2) nanoscale systems with an experimentally relevant distribution of voids, with up to 20% void area. Results from simulations with one and two voids showed that voids within 10 nm of a crack tip reduce the stress required for crack growth, with the magnitude of reduction depending on void-to-crack orientation. Comparisons with linear elastic fracture mechanics and evaluation of one versus two void systems revealed deviations from linear superposition, implying complex interactions between void and crack tip stress fields. In multi-void simulations, as void sizes increase, the nearest void to the crack tip exerts a greater influence on fracture stress than the overall porosity. Furthermore this study provides valuable insights into the relationship between void size and concentration, and the stress necessary for crack growth, marking a step forward towards understanding He bubble-induced fracture in ferrous materials.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Extended Rice–Thomson analysis and atomistic simulations revealing grain boundary effects on fracture in refractory high-entropy alloys

Significance This work serves to extend the fundamental ductile vs. brittle fracture theory, specifically the Rice–Thomson criterion, by introducing a grain boundary ahead of an initiating crack which propagates at an oblique angle to impinge the boundary. Atomistic fracture simulations on two refractory complex concentrated alloys, the brittle NbMoTaW and the ductile Nb 45 Ta 25 Ti 15 Hf 15 , demonstrate qualitative correspondence with the extended Rice–Thomson criterion and experimental observations. Abstract Understanding how grain boundaries mediate fracture remains a critical challenge in designing ductile, high-performance refractory alloys. Here, we extend the Rice–Thomson criterion to account for the angle between cracks and the impinging grain boundaries (GBs), capturing the competition between intergranular fracture and dislocation-mediated plasticity. Using machine learning interatomic potentials, we performed molecular statics simulations to probe fracture mechanisms in nanocrystalline NbMoTaW and Nb 45 Ta 25 Ti 15 Hf 15 , each with two different grain sizes, revealing trends consistent with experimental observations and the extended Rice model. Comparison with averaged R-curves for bulk samples demonstrates that GBs enhance ductility in Nb 45 Ta 25 Ti 15 Hf 15 in both grain sizes investigated. In contrast, GBs only locally improve fracture resistance in NbMoTaW when cracks are temporarily pinned at GBs inclined at high angles from the crack, but generally promote brittle intergranular fracture. These contrasting behaviors are attributed to differences in GB cohesion, reflecting clear alloying trends that align with ab-initio calculations and trends observed experimentally. Our results bridge classical fracture theory, atomistic simulations, and experimental observations, providing a comprehensive understanding of the fracture mechanisms in nanocrystalline refractory complex concentrated alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Assessment of irradiation embrittlement effect on fatigue life of a pressurized-water reactor pressure vessel using the fracture toughness master curve approach

The reactor pressure vessel (RPV) is a critical structural component in pressurized-water reactors, and it is designed to withstand extreme conditions, such as high pressures, elevated temperatures, and prolonged radiation exposure. Ensuring RPV integrity is essential for the safe and reliable long-term operation of nuclear power plants, especially as aging mechanisms such as fatigue and irradiation embrittlement pose increased risks. Fatigue, caused by cyclic thermal and mechanical loading, can lead to crack initiation in localized high-stress regions. Simultaneously, neutron irradiation, particularly in the beltline region, progressively reduces fracture toughness, increasing susceptibility to brittle fracture. These combined effects of fatigue and irradiation embrittlement potentially impact the RPV structural integrity, necessitating fitness-for-service assessments. This study applies the fracture toughness master curve approach to evaluate the impact of irradiation embrittlement on RPV fatigue life. A coupled thermo-mechanical stress analysis identifies critical stress locations under normal service transients, pinpointing regions most vulnerable to fatigue crack initiation and growth. Stress intensity factors for postulated flaws at these locations are calculated, enabling an assessment of fatigue life under irradiated and unirradiated conditions. The results indicate that neutron irradiation embrittlement accelerates the conditions in which a critical crack can form and lead to failure, particularly at lower temperatures. The failure occurs where reduced fracture toughness limits the material’s resistance to crack growth. Axial cracks at nozzle corners are the most life limiting without irradiation, while circumferential cracks demonstrate longer fatigue lives. The findings highlight the importance of incorporating irradiation effects into fatigue life predictions to ensure the long-term structural integrity of RPVs.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

In-Situ Visualization of a Growing Brittle Crack in Aluminum Oxynitride Using Synchrotron X-Rays and the Double-Cleavage Drilled Compression Geometry

Brittle fracture is difficult to study in situ due to the speed of a growing crack and the often-catastrophic nature of failure in brittle materials. As a result, the influence of microstructural considerations, such as orientation, grain boundary locations, and strain field, on the crack path remains poorly understood. Presented in this study is a method addressing this knowledge gap, which utilizes the double-cleavage drilled compression geometry to achieve quasi-stable fracture in aluminum oxynitride (AlON). Synchrotron X-ray micro-computed tomography is used to characterize the crack shape and length, while high-energy diffraction microscopy provides information on the strains, orientations, and shapes of grains in the microstructure surrounding the crack tip. During testing, the crack grew in discrete and irregular jumps while the fracture toughness falls within reported ranges. The crack in AlON is found to have no greater tendency to crack intergranularly as compared to transgranularly, and grains which are cracked transgranularly do not display a trend in orientation or stress when compared to those around which the crack followed a grain boundary. The high resolution of the crack path and microstructural data provides a path forward for modeling and understanding 3D brittle fracture.

Gorske, Sara F.↗

DOE OSTI2025

Inference of phase field fracture models

The phase field approach to modeling fracture uses a diffuse damage field to represent cracks. This representation mollifies singularities that arise in computations with sharp interface models and some of the resultant difficulties in the mathematical and numerical treatment of fracture. Phase field fracture models have proven effective at representing crack propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, lead to an array of possible models. There exists a large body of literature focusing on this class of models and on the impact of model form on the predicted crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here, we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used for the degradation of elastic response due to damage and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). Furthermore, in this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Graph neural networks for mechanical property prediction of 2D fiber composites

This work investigates the ability of graph neural networks (GNNs) to homogenize 2D fiber composite microstructures. We use different inhomogeneity and anisotropy indices to motivate and show that the Volume Elements (VEs) used in ML methods should ideally be far from their Representative Volume Element (RVE) size limit and, consequently, are notably anisotropic. Hence, training only the isotropic limit properties may not be acceptable. Another aspect is the need to normalize elastic stiffness values for ML, especially when high elastic contrast ratios are encountered between composite phases or in the material set. We introduce a normalization technique based on the mean-field method (MFM) to handle such high contrast ratios and train for the entire stiffness tensor. We show that the proposed GNN approaches exhibit high accuracy and efficiency compared to traditional methods and convolutional neural networks, utilizing unstructured graphs constructed from microstructure topology. Our model successfully predicts the stiffness tensor, peak strength under bulk damage, and brittle fracture initiation strength across diverse microstructure configurations while maintaining high accuracy even for extreme material contrasts and volume fractions. We also present a method to improve prediction accuracy for small dataset sizes using Voronoi partitioning.

Brittle strength↗

DOE OSTI2025

High temperature tensile properties of H13 tool steel fabricated via binder jet additive manufacturing

H13 is one of the most used steels for hot work tooling applications like die casting. Binder jet additive manufacturing (BJAM) offers a cost-effective solution to fabricate tools with performance enhancing features like internal cooling channels. While full densification of BJAM H13 has been demonstrated in the literature, the room and high temperature tensile properties of the material, and the effect of post-process treatments like hot isostatic pressing (HIP), and heat treatment (HT) are unknown. Here we use HIP+HT to obtain a combination of ultimate tensile strength (UTS) and elongation to failure that is superior to H13 fabricated via laser powder bed fusion and wire arc additive manufacturing. HIP+HT BJAM H13 has a superior UTS (1836 MPa) compared with conventionally processed (1671 MPa) H13 but has lower plastic elongation. We report that as-sintered samples have an extensive network of continuous grain boundary (GB) carbides that contribute to brittle fracture. HIP+HT results in partial dissolution of GB carbides and formation of a fine martensitic microstructure resulting in superior tensile strength and elongation compared with as-sintered H13. We use thermo-kinetic calculations to rationalize the effects of HIP+HT on microstructure and properties.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Evaluation of corrosion coupons exposed to molten-chloride electrorefiner salts long term

Corrosion mitigation has long been considered a challenge in long-term service of both pyrochemical reprocessing and molten salt reactor applications. Corrosion coupons consisting of 2.25Cr 1Mo ASME SA387 Grade 22 Class 2 steel, were installed in a uranium electrorefiner containing molten chloride salt at 500°C. This electrorefiner went into service at Idaho National Laboratory in 1994. Seven of these coupons were removed in 2019 (i.e., submerged in molten salt for 25 years) for analysis and characterization including neutron imaging, optical microscopy, scanning electron microscopy, and wave/energy dispersive x-ray spectroscopy. The results showed that all seven coupons experienced between 30 to 175 µm of surface degradation without evidence of brittle fracture. Meaning there was no evidence of accelerated corrosion or fractures, and the average steel surface loss was of less than 5 µm per year. All indications were that the environmental conditions inside the electrorefiner were favorable for the steel alloy.

36 - MATERIALS SCIENCE↗

DOE OSTI2026

Validated Reactive Force Field Quantifies MXene Interfacial Properties, Mechanics, and Thermal Transport

MXenes combine rich surface chemistry, mechanical strength, and high conductivity for a multitude of emerging applications. Predictive modeling supports accelerated materials designs and has been limited by the absence of validated and transferable force fields. Here, we introduce an interpretable, reactive INTERFACE force field (IFF and IFF-R) for Ti 3 C 2 T x MXenes that is trained based on chemical knowledge and achieves quantitative agreement with experiments across lattice parameters (<0.5%), density (<0.2%), liquid contact angles, Raman spectra, and the in-plane elastic modulus (∼320 GPa). The models cover surface terminations from hydroxyl (−OH) to fluorine (−F) groups and are extensible to other chemistries. We introduce pH-resolved surface chemistry and identify dopamine adsorption mechanisms at MXene–aqueous interfaces supported by QCM-D and UV–Vis experiments. The data reveal coplanar and perpendicular binding modes and concentration-dependent multilayer assembly. We predict previously inaccessible properties, including termination-dependent cleavage energies, interlayer shear moduli and dynamic shear failure, nanoindentation and brittle fracture, anisotropic in-plane and out-of-plane thermal conductivities, including the role of defects. Agreement with available experimental data is consistently close and exceeds DFT accuracy across the benchmark properties examined. The IFF/IFF-R model is compatible with CHARMM, AMBER, OPLS, and CVFF force fields for simulations of MXenes with diverse surface terminations, electrolyte interfaces, biointerfaces, and polymer composites without additional parameters. Parameter sets, 3D models, and analysis scripts are provided for community use. The validated, reactive, and transferable IFF framework facilitates predictive design of MXene-based films, membranes, sensing interfaces, and composites.

MXene↗

DOE OSTI2025

Design and Analysis of an Integrated Additively Manufactured Test Article for Plasma-Facing Components

Current plasma-facing components (PFCs) used in helium-cooled divertor modules are complex structures with tungsten tile, steel sleeve components, and cartridges, all assembled in a helium-cooled multiple jet (HEMJ) structure. The goal of this project is to simplify the complex PFC design using additive manufacturing techniques to create a single integrated tungsten test article. Apart from the flexibility this opens up in exploring a wide array of geometries for the article, having a single integrated article significantly reduces the number of joints and parts in the article, thus reducing chances of leaks. A process called electron beam melting has shown to produce very high-density samples and unique geometries, enabling HEMJ or similar designs. To validate and optimize this novel design, the model underwent a series of computational fluid dynamics and finite element analysis simulations to replicate steady-state heat flux in the divertors. The simulations presented in this study consider a steady-state base heat flux of 5 MW/m 2 , with water serving as the coolant. Future research will explore the use of helium as a coolant, simulate edge-localized-mode conditions, and include experimental validation. Since 3D-printed tungsten is anisotropic, the build direction versus build plane of the article are taken into consideration for the test article strength. Because of the high operating temperatures and low ductility of tungsten, thermal creep and brittle fracture are important failure mechanisms to consider. In conclusion, the cap is evaluated with various flow velocities and nozzle diameters, and an optimal design choice is made for which this cap will survive the divertor conditions with a conservative safety margin.

Divertor↗

DOE OSTI2025

Coupled momentum balance and phase-field solver with fenicsx module

Code solves momentum balance and phase-field equations simultaneously. The differential equations are solved on a discretized domain with appropriate boundary and initial conditions using finite element method. Primary purpose of the code is to simulate brittle fracture under dynamic loading. Constitutive equations are that of linear elasticity with degradation of stress due to fracture. Small strain formulation is used.

Zecevic, Milovan↗

DOE OSTI2026

Integrated Simulation of Weld Residual Stress Evolution and Crack Propagation Using XFEM

Nuclear power plant components operate in environments that promote multiple degradation mecha- nisms, several of which involve crack initiation and growth. An ongoing effort in the U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program is developing a general capability within the Multiphysics Object Oriented Simulation Environment (MOOSE) framework for simulating three-dimensional crack growth under a range of driving conditions, including fatigue, stress corrosion cracking (SCC), brittle fracture, and stress-relaxation cracking. This report demonstrates an end-to-end workflow that uses this capability to model weld-residual-stress-driven SCC in the J-groove weld of a pressurized-water reactor control rod drive mechanism penetration in the vessel head. The workflow consists of a thermomechanical welding simulation with temperature-dependent plasticity, followed by cooldown to ambient conditions, and a restart of the simulation using the MOOSE extended finite element method (XFEM) module to propagate a three-dimensional crack through the residual stress field. New welding capabilities were developed to properly initialize newly activated elements in the weld region, and robustness improvements were made to the mesh-based algorithm for defining cutting planes in the 3D XFEM algorithm, allowing it to handle complex crack fronts and stress fields. Together these advances allowed the simulated SCC crack to grow from an initial elliptical flaw in the weld, across the weld, through the tube wall, and almost to the triple point (where the weld, tube, and reactor pressure vessel head intersect) over roughly 36 years of simulated service. These results demonstrate a workflow that can be extended to fully three-dimensional welding simulations and more complex crack interaction problems.

42 - ENGINEERING↗