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DOE OSTI2022

Integrated simulation, machine learning, and experimental approach to characterizing fracture instability in indentation pillar-splitting of materials

Measuring fracture toughness of materials at small scales remains challenging due to limited experimental testing configurations. A recently developed indentation pillar-splitting method has shown promise of improved flexibility in fracture toughness measurements at the microscale, partly due to the occurrence of an unusual fracture instability, i.e., a transition from stable to unstable crack propagation. In spite of growing interest in this method, the underlying mechanism of this phenomenon is yet to be elucidated. Furthermore, we provide a comprehensive description of fracture instability in indentation pillar-splitting by combining in situ experiments with high-fidelity simulations based on cohesive zone and J-integral methods. In addition, a machine-learning-based solution for predicting the critical indentation load of fracture instability is established through Gaussian processes regression for broad use of this method by the community.

36 MATERIALS SCIENCE↗

DOE OSTI2022

A thermodynamically consistent finite strain phase field approach to ductile fracture considering multi-axial stress states

Phase field models for ductile fracture have gained significant attention in the last two decades due to their ability in implicitly tracking the nucleation and propagation of cracks. However, most crack phase field formulations for elastoplastic solids focus only on the effects of plastic deformation, and do not consider the different multi-axial stress states that may arise in practical designs. In this work, a thermodynamically consistent phase field approach coupled with finite strain plasticity, considering multi-axial stress states is presented. In order to account for the coupling between plasticity and stress states, the Stress-Weighted Ductile Fracture Model (SWDFM) is utilized. The SWDFM represents a criterion for predicting ductile crack initiation under both monotonic and cyclic loadings based on histories of an internal plastic variable, stress triaxiality, and the Lode angle parameter. The excellent performance of the SWDFM for predicting ductile crack initiation motivates for its incorporation into a phase field approach for predicting both crack initiation and propagation through degradation of the fracture toughness. Moreover, based on the second law of thermodynamics, exact requirements are imposed on the rate at which the fracture toughness can evolve. Here, a novel function for degrading the plastic yield surface during the evolution of damage is introduced. This function, in line with experimental observations, leads to an accumulation of plastic deformation in damaged regions of a solid, and avoids numerical instabilities arising from concentrations of large plastic deformations in severely damaged regions. For validating the proposed model, results of computational simulations are compared to data from selected tests considering different multi-axial stress states. Comparisons of the numerical results with data from laboratory experiments demonstrate the capabilities of the proposed framework.

42 ENGINEERING↗

DOE OSTI2021

Prediction of Probabilistic Shock Initiation Thresholds of Energetic Materials Through Evolution of Thermal-Mechanical Dissipation and Reactive Heating

The ignition threshold of an energetic material (EM) quantifies the macroscopic conditions for the onset of self-sustaining chemical reactions. The threshold is an important theoretical and practical measure of material attributes that relate to safety and reliability. Historically, the thresholds are measured experimentally. In this work, we present a new Lagrangian computational framework for establishing the probabilistic ignition thresholds of heterogeneous EM out of the evolutions of coupled mechanical-thermal-chemical processes using mesoscale simulations. Furthermore, the simulations explicitly account for microstructural heterogeneities, constituent properties, and interfacial processes and capture processes responsible for the development of material damage and the formation of hotspots in which chemical reactions initiate. The specific mechanisms tracked include viscoelasticity, viscoplasticity, fracture, post-fracture contact, frictional heating, heat conduction, reactive chemical heating, gaseous product generation, and convective heat transfer. To determine the ignition threshold, the minimum macroscopic loading required to achieve self-sustaining chemical reactions with a rate of reactive heat generation exceeding the rate of heat loss due to conduction and other dissipative mechanisms is determined. Probabilistic quantification of the processes and the thresholds are obtained via the use of statistically equivalent microstructure sample sets (SEMSS). The predictions are in agreement with available experimental data.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Interpretation of HFTS 2 Microseismic Data Using Bedding-Plane-Slip Mechanism

Summary The objective of this study is to understand how microseismic events are generated during hydraulic fracturing, as well as the role of geomechanical conditions (i.e., stress and mechanical stratigraphy) in this process. In the industry, microseismic event clouds have been generally used as an “outer boundary” of the “stimulated reservoir volume” (SRV). However, by comparing with other surveillance data (low-frequency distributed acoustic sensing, or LF-DAS, strain) in the Hydraulic Fracturing Test Site (HFTS) 2 experiment, we show that this assumption is fundamentally flawed. The HFTS 2 data have three unique observations that have not been commonly observed in other datasets: (1) Due to the influence of offset pad depletion, microseismic data show that hydraulic fractures from the child well can propagate over 3,000 ft into the depleted low-stress zone. (2) By comparing microseismic and horizontal fiber LF-DAS strain data, we observe that the microseismic event cloud does not necessarily reflect the created hydraulic fracture volume. Particularly, the extent of microseismic event clouds near heel stages is much shorter than what is shown with LF-DAS strain data. (3) Microseismic event magnitudes are larger in the depleted regions. Through geomechanical analysis, we demonstrate that the “bedding-plane-slip” model is likely the mechanism for microseismic generation during hydraulic fracturing. This model successfully explains the above field observations from the HFTS 2 experiment. We also provide a quantitative relationship connecting the microseismic event magnitude with fracture width increment and layer mechanical property contrast.

Engineering↗

DOE OSTI2026

Evaluating Fracture Behavior of Bioinspired Alumina-YSZ Composites through Static and Dynamic Mechanical Testing

Ceramic materials are known for their high hardness and strength but are limited by low toughness and sudden failure. Inspired by the microstructure of dental enamel, which features undulating rods that promote crack deflection and energy absorption, architected specimens were designed and manufactured. A bespoke ball-on-ring (BoR) testing apparatus measured the static biaxial rupture strength of these bioinspired materials. Additionally, impact testing with spherical steel projectiles assessed their behavior under dynamic conditions. Monolithic alumina specimens were compared to architected alumina reinforced with yttria-stabilized zirconia (YSZ) rods produced via direct ink write 3D printing. BoR tests revealed that monolithic alumina had a Weibull modulus of 10.53 and a characteristic strength of 372.3 MPa, while the composite specimens showed a Weibull modulus of 5.46 and a characteristic strength of 213.3 MPa. Although the composite failed at lower stresses and projectile velocities, it exhibited notable crack deflection and fracture resistance, with cracks being effectively interrupted by the rod inclusions. The composite specimens also resulted in fewer and larger fragments upon impact. Finite element simulations confirmed the effectiveness of the rod structures in enhancing fracture resistance.

Bioinspired materials↗

DOE OSTI2023

A multiscale phase field fracture approach based on the non-affine microsphere model for rubber-like materials

Rubber-like materials have a broad scope of applications due to their unique properties like high stretchability and increased toughness. Hence, computational models for simulating their fracture behavior are paramount for designing them against failures. In this study, the phase field fracture approach is integrated with a multiscale polymer model for predicting the fracture behavior in elastomers. At the microscale, damaged polymer chains are modeled to be made up of a number of elastic chain segments pinned together. Using the phase field approach, the damage in the chains is represented using a continuous variable. Both the bond stretch internal energy and the entropic free energy of the chain are assumed to drive the damage, and the advantages of this assumption are expounded. A framework for utilizing the non-affine microsphere model for damaged systems is proposed here by considering the minimization of a hypothetical undamaged free energy, ultimately connecting the chain stretch to the macroscale deformation gradient. At the macroscale, a thermodynamically consistent formulation is derived in which the total dissipation is assumed to be mainly due to the rupture of molecular bonds. Using a monolithic scheme, the proposed model is numerically implemented and the resulting three-dimensional simulation predictions are compared with existing experimental data. The capability of the model to qualitatively predict the propagation of complex crack paths and quantitatively estimate the overall fracture behavior is verified. Additionally, the effect of the length scale parameter on the predicted fracture behavior is studied for an inhomogeneous system.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Atomistic measurement and modeling of intrinsic fracture toughness of two-dimensional materials

Quantifying the intrinsic mechanical properties of two-dimensional (2D) materials is essential to predict the long-term reliability of materials and systems in emerging applications ranging from energy to health to next-generation sensors and electronics. Currently, measurements of fracture toughness and identification of associated atomistic mechanisms remain challenging. Herein, we report an integrated experimental–computational framework in which in-situ high-resolution transmission electron microscopy (HRTEM) measurements of the intrinsic fracture energy of monolayer MoS 2 and MoSe 2 are in good agreement with atomistic model predictions based on an accurately parameterized interatomic potential. Changes in crystalline structures at the crack tip and crack edges, as observed in in-situ HRTEM crack extension tests, are properly predicted. Such a good agreement is the result of including large deformation pathways and phase transitions in the parameterization of the inter-atomic potential. The established framework emerges as a robust approach to determine the predictive capabilities of molecular dynamics models employed in the screening of 2D materials, in the spirit of the materials genome initiative. Moreover, it enables device-level predictions with superior accuracy (e.g., fatigue lifetime predictions of electro- and opto-electronic nanodevices).

Zhang, Xu↗

DOE OSTI2020

Coupled Thermo–Hydro–Mechanical Modeling of Hydro-Shearing Stimulation in an Enhanced Geothermal System in the Raft River Geothermal Field, USA

The Raft River Enhanced Geothermal System (EGS) demonstration project aims to improve the geothermal production by enhancing the reservoir permeability via shear stimulation in well RRG-9. In this paper, we performed a series of 3D thermo– hydro–mechanical (THM) simulations to investigate the influence of hydraulic and thermal effects on the development of this EGS. The model includes synthetic fracture populations based on borehole televiewer images and in-situ stress measurements from well RRG-9. Fracture permeability evolution is determined using an empirical permeability law developed from laboratory experiments. The model was calibrated by comparing the hydraulic response to field observations, including wellhead pressure, injection rate, and well injectivity. Particularly, we analyzed the enhancement of reservoir permeability and the spatial extent of the stimulation zone for the given injection schedule. Our results indicate that the permeability enhancement of fractured geothermal reservoir is caused by the combined effects of injection-induced cooling and fluid pressure increase. The decrease of temperature plays a dominant role in reactivation of natural fractures under the hydro-shearing mechanism, while the higher injection pressure promotes shear failure and enlarges the stimulation zone. Finally, for the specified extensional stress state, the model favors greatest permeability enhancement along the maximum horizontal principal stress, a moderate vertical enhancement, and a smaller gain along the minimum horizontal principal stress.

58 GEOSCIENCES↗

DOE OSTI2024

Microscale mechanical property variations of Al-substituted LLZO: insights from compression testing and molecular dynamics simulations

Ceramic solid electrolytes based on LLZO (Li 7 La 3 Zr 2 O 12 ) are promising candidates for all-solid-state batteries due to their high ionic conductivity and good apparent stability vs. lithium metal, however they are prone to mechanical failure. Lithium metal intrusions, alongside cell stack pressure, transition polycrystalline solid electrolyte grains into a compressed state that promotes crack propagation and fracture. Here this work examines the mechanical response of Al-substituted LLZO to compressive forces by measuring ultimate strength under pillar compression with a flat punch tip. Failure modes characterized by in situ scanning electron microscopy show diverse splitting patterns arising from internal porosity, grain boundaries, and slip planes. Large correlated variations in compressive strength (0.93–2.63 GPa) and Young's modulus (72.1–150.97 GPa) are observed across microscale regions of the solid electrolyte. Molecular dynamics simulations of LLZO with different porosities describe the variation of compressive strength and Young's modulus, and enable a microscale porosity model to be fit accounting for Young's modulus reduction across the solid electrolyte. Overall, the results indicate the importance of microscale mechanical testing of ceramic solid electrolytes to identify preferential sites for mechanical degradation and Li intrusion, and ensure the robust design of all-solid-state lithium metal batteries.

25 ENERGY STORAGE↗

DOE OSTI2024

Complex Fluid‐Driven Fractures Caused by Crack‐Parallel Stress

Abstract Managing fluid‐driven fracture networks is crucial for subsurface resource utilization, yet the current understanding of the key controlling factors remains insufficient. While geologic discontinuities have been shown to significantly influence fracture network complexity, this study identifies another major contributor. We conducted a new set of experiments using a transparent true triaxial cell, which enabled video recording of the temporal evolution of fluid‐driven fracture paths. Using pseudo‐2D samples without macroscale structural discontinuities, we observed multiple occurrences of hydraulic fracture curving and branching under anisotropic boundary stresses. We proposed a theoretical model demonstrating that the stress parallel to the crack line in the solid matrix near the crack tip (i.e., the T ‐stress) accounts for the observed fracture curving behavior. This finding suggests that T ‐stress is an additional mechanism contributing to the complexity of fluid‐driven fracture networks in the subsurface, besides the geologic discontinuities.

58 GEOSCIENCES↗

DOE OSTI2024

Leveraging a Neural Network-Enhanced Reproducing Kernel Particle Method for Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and resulting in reduced performance and service life. A coupled electro-chemo-mechanical reproducing kernel particle method (RKPM) formulation has been developed to analyze this system. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based model construction by RKPM is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. Here, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1, 2] is introduced to effectively model damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RKPM is additionally used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022. [2] Baek, J., Chen, J. S., "A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture", Computer Methods in Applied Mechanics and Engineering Vol. 410, 116590, 2024.

degradation↗

DOE OSTI2024

Multiphysics Degradation Modeling of Energy Storage Materials via RKPM with a Neural Network-Enhancement

In energy storage materials, strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking during charge/discharge cycling, resulting in reduced performance and service life. A coupled electro-chemo-mechanical reproducing kernel particle method (RKPM) formulation is developed, and a patch-test is formulated to certify optimal convergence of the proposed RKPM method for the coupled physics system. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based model construction by RKPM is then used to represent the complex material microstructures for modeling the coupled physics of these systems. Further, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1, 2] is introduced to effectively model damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022. [2] Baek, J., Chen, J. S., "A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture", Computer Methods in Applied Mechanics and Engineering Vol. 410, 116590, 2024.

electro-chemo-mechanical coupling↗

DOE OSTI2026

Sequential Fracture Activation and Stress Evolution During EGS Stimulation at Utah FORGE Revealed by Waveform Cross‐Correlation

Mapping fracture networks in Enhanced Geothermal Systems (EGS) is essential for optimizing reservoir performance, yet complex fracture evolution during stimulation remains difficult to resolve. This study examines the evolution of microseismicity and fracture networks during stage 3 of the 2022 EGS stimulation at the Utah Frontier Observatory for Research in Geothermal Energy site. We map the fracture network represented by 20 clusters of seismic events identified by waveform similarities with cross-correlation. We characterize their geometric properties such as strike, dip, length, and width, and analyze the time evolution of activated fractures. The results reveal a systematic fracture evolution: early activation of pre-existing natural fractures, complex network development during peak injection, and continued activation of less favorably oriented fractures post-injection. Magnitude calibration using the Principal Component Analysis of cross-correlated waveforms improves relative amplitude measurements, refining estimations of the Gutenberg-Richter b-values with spatial variations in b-values suggesting stress re-distribution across the stimulated area. Analysis of the stress state of selected fractures further shows that fractures requiring higher excess pore pressure primarily activate at the end of injection and post-injection, highlighting stress transfer due to pore pressure as a dominant triggering mechanism. These findings provide insights into fracture propagation, stress evolution, and seismic hazard assessment in EGS reservoirs.

Asirifi, Richard [Texas A & M Univ., College Stati↗

DOE OSTI2026

DEMO-FTES: Development, Monitoring, and Control of Fracture Thermal Energy Storage in Crystalline Rock Formations (CRADA Final Report)

The DEMO-FTES project investigated the feasibility of Fracture Thermal Energy Storage (FTES) as a seasonal energy storage solution in crystalline rock formations. FTES leverages hydraulically induced fractures to exchange heat between circulating fluids and the surrounding rock mass, enabling long-term thermal energy retention due to the high specific heat and low thermal conductivity of rock. This approach has the potential to reduce heating and cooling energy demands and enhance building energy resilience. The project combined dimensional analysis, numerical modeling, laboratory experiments, and meso-scale field tests to evaluate FTES performance and advance its technology readiness level from 3 to 5. Scaling analysis identified key dimensionless parameters governing heat transfer and fluid flow, ensuring laboratory and field tests were representative of larger-scale systems. Numerical simulations using TOUGH and iTOUGH2 frameworks supported experiment design and interpretation, modeling fracture geometry, thermal-hydraulic behavior, and thermo-mechanical coupling. Laboratory tests at EPFL involved creating single and multiple fractures in 25 cm cubic samples of Gabbro and Granite under true triaxial stress.

25 ENERGY STORAGE↗

DOE OSTI2022

Compatibility of Medium Density Polyethylene (MDPE) for Distribution of Gaseous Hydrogen

Hydrogen has emerged as a convenient energy storage medium and is being considered as an alternative for reducing the use of carbon-based fuels. Numerous projects are looking into distributing blends of natural gas and different amounts of gaseous hydrogen through the existing natural gas distribution system, which is widely composed of medium density polyethylene (MDPE) line pipes. The mechanical behavior of MDPE with hydrogen is not well understood; therefore, the effect of gaseous hydrogen on the mechanical properties of MDPE needs to be examined. In the current study, we investigate the effects of gaseous hydrogen on fatigue crack growth rate, fracture resistance, and fatigue life of MDPE in the presence of 3.4 MPa gaseous hydrogen. Fatigue crack growth behavior and fracture resistance are measured using compact tension specimens, while the fatigue life tests are carried out using circumferential notched tensile specimens. In addition, fatigue and fracture tests were conducted in air to determine the baseline properties of MDPE, which was then compared with the ones observed in gaseous hydrogen environment. After the completion of mechanical testing, fracture surfaces are also analyzed using optical and scanning electron microscopes to understand salient fracture features of MDPE with and without the presence of gaseous hydrogen.

Shrestha, Rakish↗

DOE OSTI2022

Detection of voids in hydrogen embrittled iron using transmission X-ray microscopy

Hydrogen embrittlement remains a barrier to widespread adoption of hydrogen as a carbon-neutral energy source. Here, hydrogen embrittlement mechanisms are investigated across length scales in iron using transmission X-ray microscopy (TXM), digital image correlation (DIC), and notched tensile testing during in-situ electrochemical hydrogen charging. TXM reveals void size and spatial distribution ahead of a propagating crack. We find hydrogen charging leads to voids within ~10 μm of the crack tip and suppression of voids beyond this distance. Near the crack tip, voids are elongated in the direction of the crack and are smaller than voids in an uncharged sample. In the presence of hydrogen, these voids lead to quasi-cleavage fracture and a sharper crack tip. DIC shows localization and reduction of plastic strain with hydrogen charging, and tensile testing reveals a reduction in fracture energy and elongation at failure. Finally, these results are discussed in the context of hydrogen embrittlement mechanisms.

08 HYDROGEN↗

DOE OSTI2021

Determining failure properties of as-received and hydrided unirradiated Zircaloy-4 from ring compression tests

An integrated experimental and computational approach was developed to determine the plastic strain at fracture and to investigate the fracture energy of as-received and hydrided unirradiated Zircaloy-4 nuclear cladding tubes in the hoop direction at room temperature from ring compression testing (RCT). This work builds on previous methods in the literature that were developed to obtain the mechanical properties of nuclear cladding before fracture (Young’s modulus, yield stress, and strain-hardening parameters) from experimental RCT results and extends the characterization of this material class to include material failure properties. Furthermore, a ductile damage approach was developed and implemented in a validated finite element model to predict material failure, evaluate fracture energy, and quantify the plastic strain at fracture initiation. The hydrogen content of the Zircaloy-4 specimens was varied up to 610 wppm when the failure became brittle. As expected, increasing hydrogen content caused embrittlement of the Zircaloy-4 samples tested and the plastic strain at fracture and fracture energy to decrease.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Aqueous-Based Polyimine Functionalization of Cellulose Nanofibrils for Effective Drying and Polymer Composite Reinforcement

Here a simple strategy was developed to synthesize polyimine-coated cellulose nanofibrils (CNF) for effective CNF drying and composite reinforcement. The polyimine was synthesized in an aqueous medium using a selective hydrophilic and hydrophobic component that forces the polyimine to precipitate, which prevents the reverse imine reaction. The polyimine coating allowed the CNF to be easily oven-dried while maintaining a fibrillar morphology to provide mechanical reinforcement in poly(ethylene terephthalate glycol) (PETG) composites. In comparison, poor mechanical performance and a heterogeneous fracture surface were observed when the coated CNF were incorporated into poly(l-lactide) (PLA) composites. It is hypothesized that intermolecular aromatic–aromatic interactions are formed at the interface between fibers and the polymer matrix in the PETG system, while no such phenomena occur in the PLA system. Overall, this facile strategy to produce modified, easily dried CNF can be adapted to produce polyimine-coated CNF with unique functionalities that are useful in a range of applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗