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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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At least 109 records · Page 6

Effect of Engineered Cracks in Catalyst Layers on PEMFC Catalyst Layer Durability

Proton exchange membrane fuel cells (PEMFCs) are expected to play a pivotal role in decarbonizing the transportation sector, and particularly heavy-duty vehicles (HDVs). However, improvements in durability are needed for PEMFCs to compete with state-of-the-art power sources for HDVs. Here, we examine how catalyst layer (CL) cracks that are engineered affect the CL durability by using patterned silicon templates to control the CL crack density at the micrometer scale. Electrochemical analyses show that the initial PEMFC performance is relatively unaffected by crack density, but the performance after durability testing was strongly affected. Specifically, CLs with high crack density showed higher performance relative to CLs without cracks after application of a carbon corrosion accelerated stress test. Electrochemical analyses coupled with X-ray computed tomography and scanning transmission electron microscopy with energy dispersive X-ray spectroscopy showed that the cracks provide shorter oxygen diffusion pathways to reaction sites, leading to decreased oxygen transport resistance. Additionally, we observed that the catalyst durability is unaffected by cracks. Our results provide a mechanistic explanation of the role of cracks in CL durability.

30 DIRECT ENERGY CONVERSION↗

Simultaneously improved reversibility and hydrogen production of solid oxide cells through infiltrating air electrode

Among the various fuel cells, solid oxide cells (SOCs) are the unique type that can principally operate reversibly as either fuel cells to produce electricity or as an electrolyser to split water and produce green hydrogen (H 2 ). Nevertheless, the SOCs' reversibility presents enormous challenges that are manifested by the fast degradation through the cycling between fuel cell and electrolysis mode. While the La 0.8 Sr 0.2 MnO 3 /yttria-stabilized zirconia (LSM/YSZ) air electrode possesses significant advantages in terms of high electrical conductivity and high thermal stability under fuel cell mode, the SOCs with the LSM/YSZ air electrode experience rapid performance degradation with catastrophic electrode delamination shortly after switching from fuel cell to electrolysis mode. To prevent such catastrophic delamination and enable the electrolysis H 2 production, a chemical solution with the designed chemistry of SrFe 2 O 4-d was infiltrated into the LSM/YSZ air electrode. The infiltration immediately mitigates the catastrophic delamination, and the infiltrated cells exhibit significantly improved reversibility upon the electrochemical operation. Nanostructure examination reveals nanoscale cracks and second-phase nanograins formed in the air electrode from the baseline cell. By contrast, no delamination was observed at either the micron or the nanoscale for the infiltrated cell, which is attributed to the increased ion conductivity of the Fe-doped LSM mixed conductor induced by the significant interdiffusion between the LSM backbone and infiltrates. Here, this study presents a viable method for preventing electrode delamination while enhancing the durability of H 2 production and power generation for reversible fuel cell/electrolysis cell operation. It further opens new research directions of modifying the electrochemical activity of the electrode of inherently functional cells through the infiltration of the solutions with different chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Caltalyst Layer Crack Detector, or CLCD ("clicked") [SWR-20-60]

The Caltalyst Layer Crack Detector, or CLCD ("clicked") is a program that takes in optical micrographs of catalyst coatings for PEM fuel cells or electrolyzers and calculates the percent area that consist of cracks. It does so using a custom algorithm that searches for dark features larger than the background graininess of the catalyst layer.

Pfeilsticker, Jason↗

Numerical and experimental analysis of mechanically induced failure in electric vehicle battery modules

Mitigating thermal runaway and cell-to-cell propagation is essential for improving the safety of electric and hybrid vehicles. Enhancing digital twin capabilities to predict battery mechanical abuse is particularly critical for automotive and aerospace applications, where crashworthiness is a key concern. Understanding failure conditions and propagation in battery modules during mechanical abuse is complex due to interactions between structural deformation, heat transfer, electrochemical processes, exothermic reactions and mechanical fracture. While prior studies have focused on modeling cell-level behavior, extending these models to module or pack level is necessary for a system level understating of electric vehicle safety. This study develops coupled large deformation finite element models that simultaneously solve for electrochemistry, material failure, internal short circuit and thermal runaway propagation. The models account for mechanical and thermal interactions between lithium-ion cells and other battery components while the contact interfaces are evolving with time. Model-predicted voltage, temperature and force responses are compared with experimental data for validation. The results demonstrate that the approach captures key failure mechanisms, including thermal propagation through heat transfer, electrical propagation from short circuits in parallel-connected cells, and mechanical propagation via penetration and crack formation. These findings show that computational models are valuable tools for understanding battery module failure and providing insight that can reduce the need for extensive experimental testing.

25 ENERGY STORAGE↗

Understanding Chemo-Mechanical Stability of Protonic Ceramic Cells Through Electronic Conduction in the BaCe 0.7 Zr 0.1 Y 0.1 Yb 0.1 O 3-δ Electrolyte

BaCe 0.7 Zr 0.1 Y 0.1 Yb 0.1 O 3-δ (BCZYYb) is a promising ceramic electrolyte for reversible protonic ceramic cells. It is reported that BCZYYb-based cells show excellent long-term durability, particularly in the electrolysis mode, in contrast to the cells based on the conventional electrolyte yttria-stabilized zirconia. In this study, we investigate the chemo-mechanical stability behavior (a low tendency of delamination) of the BCZYYb-based protonic ceramic cells in terms of local electronic conduction in the electrolyte. The local electronic conductivity of the BCZYYb electrolyte is determined using Pt-probe-embedded cells near each electrode interface. The BCZYYb electrolyte exhibits sufficient p-type conductivity (∼10 −3 S cm −1 ) near the oxygen electrode (corresponding p O 2 : 5.27–21 × 10 −2 atm) and n-type conductivity (∼10 −4 S cm −1 ) near the hydrogen electrode (corresponding p O 2 : 0.99–1.30 × 10 −24 atm) at 600 °C. A standard cell is prepared and tested over long-term in the fuel cell (at positive and negative voltages) and electrolysis modes. The cell exhibits stable performance without delamination or cracks in both operating modes, owing to local electronic conduction.

Electrochemistry↗

Mitigating Crack Formation When Using High Oxygen Permeability Ionomer in PEMFC Catalyst Layers

High oxygen permeability ionomers (HOPIs) are being developed as an alternative to conventional perfluorosulfonic (PFSA) ionomers for cathodes in proton exchange membrane fuel cells (PEMFCs). HOPIs aim to reduce local oxygen transport resistance, improving performance and reducing degradation as the catalyst loses surface area. However, HOPIs' more rigid, 3D backbone leads to increased crack density in the cathode, potentially causing accelerated degradation. This study investigates crack formation in HOPI-based and PFSA-bound catalyst layers (CLs). We conducted a comprehensive parametric study to identify conditions and catalyst slurry components that minimize cracking. CLs were fabricated with various ionomer and catalyst types, under different relative humidity (RH) levels, solids weight percentages, solvent ratios, and ionomer-to-carbon ratios (I/C). Results show that HOPI-based CLs exhibit less cracking when fabricated under low RH conditions, with lower solids weight percentage, higher alcohol content, and lower I/C. Additionally, catalysts with low/medium surface area carbon supports show less cracking than those with high surface area carbon supports.

08 HYDROGEN↗

Deconstructing the High Voltage Degradation Mechanisms in Na 2/3 Ni 1/3 Mn 2/3 O 2 with Single Crystals and Advanced Electrolyte

Abstract Sodium layered oxide cathodes can uniquely benefit from the existing lithium‐ion battery industry as sodium‐ion batteries gain traction as a potential low‐cost, drop‐in replacement. However, achieving relevant energy density with a suitable cycle life remains a challenge for sodium layered oxides. At high operating potentials, several competing degradation mechanisms prevent P2‐type Na 2/3 Ni 1/3 Mn 2/3 O 2 (≈550 Wh kg −1 ) from achieving meaningful cycle life—with bulk structural instability and surface reactivity being the primary retractors. Herein, the issue of particle cracking is addressed through detailed synthesis methods of “single‐crystal” materials. By comparison to a polycrystalline baseline, the single‐crystal materials quantify the capacity loss due to isolation of active material caused by intergranular particle cracking. The single crystal materials are then employed in cells with an advanced, “localized saturated electrolyte” (LSE) to demonstrate the magnitude of capacity loss due to electrolyte decomposition at the cathode surface. Mitigation of the surface reactivity through the LSE electrolyte effectively demonstrates the elevated importance of surface reactivity at high voltages despite the onset of egregious particle cracking. This work aims to guide future research into understanding molten‐salt assisted syntheses and advance the debate on surface versus bulk degradation.

Darga, Joe↗

High Throughput In-Line Coating Metrology Development for Solid Oxide Fuel Cell Manufacturing

Coatings play key roles in solid oxide fuel cell (SOFC) stack durability. For example, diffusion barrier coatings on Cr-containing interconnect and balance of plant (BOP) components protect electrodes from Cr poisoning over the long operational lifetimes (>10,000 hours) of the fuel cell stack. Common defects in coatings, such as cracks, pinholes, and porosity, result in a failure to protect the electrodes, resulting in shorter operational lifetime and thus higher cost. It is very unlikely, even in the best coating process, that all these defects can be mitigated, hence identifying critical defects in parts, and removing defective parts from production before they can damage the stack, becomes paramount. Furthermore, these quality control techniques must be operational in the production/assembly line (in-line), i.e., high throughput and non-destructive, and cost effective. Redox Power Systems, LLC (Redox) together with the National Renewable Energy Laboratory (NREL) developed much needed high throughput, in-line metrology techniques for protective coatings. The overall goal of the project is to lower cost while increasing robustness, reliability, and endurance of SOFC stacks. To accomplish this, we had several objectives, including: to identify key coating and substrate defects that lead to coating failure through the use of detailed characterization methods (e.g., microscopy, XRD, EDS, electrochemistry); to assess capabilities of in-line metrology techniques, e.g., optical profilometry (Redox) and thermography (NREL), to probe these defects, or evidence thereof; demonstrate long-term performance of “defect-free” protective coatings, as identified by in-line metrology, in solid oxide fuel cell (SOFC) stack operation. In the first part of this project, the ability to identify key defects expected to lead to coating and SOFC degradation using in-line metrology tools were evaluated. Coated interconnect samples with controlled defect types and populations were tested under conditions similar to SOFC operation, followed by detailed post-test analysis to reveal the defects responsible for observed degradation. In the second part of the project, the optimal in-line metrology techniques and methodologies were used to map the defect distribution in full-size interconnects with critical defects intentionally allowed to exist in some cases. These interconnects underwent SOFC testing for extended periods (up to ~3,000 hours) followed by post-test analysis to evaluate the effectiveness of in-line metrology techniques in mitigating MCO coating related degradation. Key accomplishments in this project included the following: Demonstrated ASR of < 0.05 ohm-cm 2 at 650 °C for 1,000 hours with low defect (determined by in-line metrology) interconnect samples (average ASR=37 milliohms-cm 2 after over 1,000 hours). Demonstrated that low defect coatings on interconnects (as screened using in-line metrology) have low volatilization of chromium at ~650 °C for 1,000 hours as detected using Cr-getter material (< 5 at% increase above baseline); 1022 hour duration tests under humidified, elevated temperature (750 °C rather than 650 °C) compared a base case against different coating thicknesses. Demonstrated capability to identify initial key defects of interest with in-line metrology techniques using up to 8 cm by 10 cm having coatings with and without intentional defects of interest using thermal imaging and optical profilometry. Correlated key defects identified using metrology techniques with observed coating performance (e.g., ASR and Cr volatility). Conducted several 4 cm by 4 cm cell tests using MCO-interconnects that were pre-screened using some of the metrology techniques developed in the project (e.g., optical profilometry). An analysis of ASR measurements were able to show that defect-free coatings resulted in the anticipated performance in the cell tests.

01 COAL, LIGNITE, AND PEAT↗

Theoretical understanding of stability of the oxygen electrode in a proton-conductor based solid oxide electrolysis cell

The oxygen electrode in a proton-conductor based solid oxide cells is often a triple-conducting material that enables the transport and exchange of electrons (e - ), oxygen ions (O 2- ), and protons (H + ), thus expanding active areas to enhance the oxygen electrode activity. In this work, a theoretical model was developed to understand stability of tri-conducting oxygen electrode by studying chemical potentials of neutral species (i.e., μ o 2 , μ H 2 , and μ H 2 O ) as functions of transport properties, operating parameters, and cell geometry. Our theoretical understanding shows that (1): In a conventional oxygen-ion based solid oxide cell, a high μ o 2 (thus high oxygen partial pressure) exists in the oxygen electrode during the electrolysis mode, which may lead to the formation of cracks at the electrode/electrolyte interface. Further, while in a proton-conductor based solid oxide cell, the μ o 2 is reduced significantly, suppressing the crack formation, and resulting in improved performance stability (2). In a typical proton-conductor based solid oxide electrolyzer, the dependence of μ o 2 on the Faradaic efficiency is negligible. Hence, approaches to block the electronic current can improve the electrolysis efficiency while achieving stability (3). The difference of the μ o 2 (thus p o 2 ) between the oxygen electrode and gas phase can be reduced by using higher ionic conducting components and improving electrode kinetics, which lead to further improvement of electrode stability.

08 HYDROGEN↗

SPUTTERED THIN FILMS FOR VERY HIGH POWER, EFFICIENT, AND LOW-COST COMMERCIAL SOFCS

The aim of this project was to leverage the low area specific resistance (ASR) of Redox’s GDC electrolyte-based cell architecture and increase solid oxide fuel cell (SOFC) efficiency (i.e., open circuit voltage, or OCV) without significantly increasing cell resistance. The key to achieving the increased SOFC efficiency is the introduction of a thin sputtered yttria stabilized zirconia (YSZ) electron-blocking layer and a thin sputtered gadolinia doped ceria (GDC) barrier layer on top of the half-cell substrate (i.e., anode and GDC electrolyte). A key initial effort of the project was to improve the quality of the half-cell substrate surface so that any remaining defects were significantly smaller than the desired film thickness. During lab-scale trials, we had to overcome challenges with film cracking during post-sputtering treatments (e.g., thermal anneals) as well as damage to the sputtering targets. After the initial lab-scale trials, the focus shifted toward the use of commercial scale sputtering equipment with a sputtering equipment manufacturer in the microelectronics industry. Using the commercial sputtering equipment, we deposited films with different variations of power, PO2, sputtering time, platen speed, etc. We then determined the combinations of sputtering conditions and post-sputtering treatments that yielded high-quality films without cracks or other significant defects. While thin films were deposited on cells as large as 10 cm by 10 cm, the processing was optimized using 4 cm by 4 cm cells. Cell performance was evaluated in stainless-steel test fixtures between 500 °C and 700 °C with hydrogen fuel fed to the anode and air fed to the cathode. Extensive studies allowed us to determine that modified cathode and cathode contact firing processes were required to achieve theoretical OCV. Moreover, use of the new firing processes resulted in the need for a modified cathode contact to achieve a low ASR. In summary, the project demonstrated the performance of high OCV (1.13 V at 650 °C) from sputtered layers and a low ASR (~0.25 Ohms-cm2 at 650 °C) resulting from a modification of cathode/contact processing and the introduction of alternative contact layers that are sufficient to yield a Gen-1 cell with a maximum power density of approximately 1.2 W/cm2. At an operating voltage of 0.74 V, this would yield a cell power density of ~1.1 W/cm2. While not utilized in this project, a Redox Gen-2 cell has a catalyst-infiltrated porous anode that reduces the ASR by more than 50% from that of the Gen-1 cells used in this project. Therefore, if the sputtered YSZ electron-blocking layer and GDC barrier layer are added to a Gen-2 half cell with a similar increase in OCV to the theoretical value of ~1.13 V at 650 °C, and if the same improvement in ASR (from that demonstrated in this project) is achieved when using the Gen-2 half-cell architecture as a sputtered cell substrate, then the power density at 0.74 Vop could be as high as ~2.6 W/cm2. The impact of such power density gains, while still maintaining high cell efficiency, and thus high system efficiency, is a dramatic decrease in system cost because the stack represents ~30-40% of the SOFC system cost.

01 COAL, LIGNITE, AND PEAT↗

Analysis of electrically conductive adhesives in shingled solar modules by X-ray imaging techniques

The failure mechanisms of electrically conductive adhesives (ECAs) in solar modules are difficult to study since the ECA layer is not easily accessible within the module package. In this work, we present two complementary imaging modalities—X-ray radiography and X-ray microcomputed tomography (XCT)—that reveal important morphological features of the ECA within a shingled module. X-ray radiography uses single X-ray projections to provide fast and non-destructive imaging of the shingled interconnection, illuminating the alignment of the ECA relative to the busbars, the size and shape of the ECA, and the presence of voids within it. Through X-ray radiography, we observed, for example, that the average void coverage area of ECA segments reduced from 36.7% to 4.4% when an ECA was cured for 60 s prior to module lamination. XCT is a three-dimensional imaging technique that can identify regions in which the ECA makes electrical contact to busbars on cells and regions in which the ECA has cracked, among other features. XCT can also be used to image the individual metal particles within ECA, from which the metal volume fraction of an ECA was found here to be 70.4%. This is a quantity that is not often reported by ECA manufacturers but is important to ensure isotropic conduction. As X-ray projections can be performed non-destructively on full modules, the technique may be used to pinpoint ECA failures in accelerated degradation testing. XCT is complementary and is suited to forensic analysis of failing modules.

14 SOLAR ENERGY↗

Designing carbon wetting layers with inorganic salts as additives for enhanced adhesion and molten sodium wettability in electrochemical application

ß” alumina solid-state electrolyte (BASE) is considered one of the most promising materials for sodium batteries due to its high ionic conductivity and exceptional stability with molten sodium. However, at lower operating temperatures, the poor physical contact at the liquid-solid interface between molten sodium and BASE results in high interfacial resistance. In this study, we explore the optimization of carbon wetting layers with various salt additives to enhance adhesion and improve molten sodium wettability. Using a spray-coating method, carbon layers incorporating sodium hexametaphosphate (Na6(PO3)6, SHMP) as an additive demonstrate superior adhesion, mechanical stability, and enhanced wettability with molten sodium. Scanning Electron Microscopy (SEM) analysis reveals that SHMP preserves the porous carbon network required for efficient sodium transport while minimizing structural defects such as cracks and voids. Electrochemical testing using Na symmetric cells confirms that SHMP-modified layers significantly reduce interfacial resistance and overpotential, outperforming No salts counterparts. These findings highlight that the strategic incorporation of suitable additives, such as SHMP, in the design of microscale carbon layers could significantly enhance the performance of molten sodium batteries at lower operating temperatures.

Han, Henry H.↗

Crack nucleation at forging flaws studied by non-local peridynamics simulations

We present a computational study and framework that allows us to study and understand the crack nucleation process from forging flaws. Forging flaws may be present in large steel rotor components commonly used for rotating power generation equipment including gas turbines, electrical generators, and steam turbines. The service life of these components is often limited by crack nucleation and subsequent growth from such forging flaws, which frequently exhibit themselves as non-metallic oxide inclusions. The fatigue crack growth process can be described by established engineering fracture mechanics methods. However, the initial crack nucleation process from a forging flaw is challenging for traditional engineering methods to quantify as it depends on the details of the flaw, including flaw morphology. We adopt the peridynamics method to describe and study this crack nucleation process. For a specific industrial gas turbine rotor steel, we present how we integrate and fit commonly known base material property data such as elastic properties, yield strength, and S-N curves, as well as fatigue crack growth data into a peridynamic model. The obtained model is then utilized in a series of high-performance two-dimensional peridynamic simulations to study the crack nucleation process from forging flaws for ambient and elevated temperatures in a rectangular simulation cell specimen. The simulations reveal an initial local nucleation at multiple small oxide inclusions followed by micro-crack propagation, arrest, coalescence, and eventual emergence of a dominant micro-crack that governs the crack nucleation process. The dependence on temperature and density of oxide inclusions of both the details of the microscopic processes and cycles to crack nucleation is also observed. The results are compared with fatigue experiments performed with specimens containing forging flaws of the same rotor steel.

97 MATHEMATICS AND COMPUTING↗

Insight into the deformation features and capacity loss mechanisms of lithium-ion pouch cells under spherical indentation conditions

Mechanical deformation under extreme conditions is one of the important reasons for the failure of lithium-ion batteries in automotive application. However, the deformation features and component failure of lithium-ion cells to external loading has never been a design consideration. Here, in this study, we conduct spherical indentation tests on a dozen of lithium-ion cells with different capacities under different control mode conditions to investigate their deformation features and capacity loss mechanisms. The experimental results show that, under mechanical deformation conditions, internal faults of cells occur in stages, and energy accumulation and sudden release are two key processes of cell's mechanical failure. The cells' state of charge is the main factor affecting their thermal runaway behaviors. In addition, a finite element model is developed to simulate the deformation features and the failure mechanism of key components of lithium-ion pouch cells; the 3D x-ray computed tomography is employed to demonstrate its internal configuration. With this model, the force-strain response, the deformation features as well as the size of the failure area of lithium-ion cells under spherical indentation conditions are accurately predicted. In 3D x-ray computed tomography images, unique mud cracks in cooper current collector are observed, and the influence mechanisms of the isolated fragments on the cell capacities are revealed. These results may provide useful information for the mechanical structure design of the components of lithium-ion pouch cells.

25 ENERGY STORAGE↗

Electrochemically Engineered, Highly Energy-Efficient Conversion of Ethane to Ethylene and Hydrogen below 550 °C in a Protonic Ceramic Electrochemical Cell

Ethylene is one of the largest building blocks in the petrochemical industry, mainly produced by steam cracking of ethane derived from naphtha or shale gas at high temperatures (>800 °C). Despite its technical maturity and economic competitiveness, the thermal steam cracking of ethane is highly energy-intensive. In this work, an electrochemically engineered direct conversion process of ethane to produce hydrogen and ethylene using a planar protonic ceramic membrane reactor with a bi-functional three-dimensional catalytic electrode is reported, with a single-pass ethane conversion of 40% and ethylene yield of 26.7% at 550 °C. Compared with the industrial ethane steam cracking, this method saves process energy input by 45.1% and improves process energy efficiency by 50.6%, based on comprehensive process simulation using Aspen Plus software. Further, steam electrolysis treatment under the solid oxide electrolysis cell mode can regenerate the system’s catalytic performance and significantly alleviate catalytic degradation by 74%, demonstrating high techno-economic viability.

bi-functional electrode↗

Computational Model for Microballistic Perforation of Multilayer Graphene

The peridynamic theory of solid mechanics is applied to the continuum modeling of the impact of small, high-velocity silica spheres on multilayer graphene targets. The model treats the laminate as a brittle elastic membrane. The material model includes separate failure criteria for the initial rupture of the membrane and for propagating cracks. Material variability is incorporated by assigning random variations in elastic properties within Voronoi cells. The computational model is shown to reproduce the primary aspects of the response observed in experiments, including the growth of a family of radial cracks from the point of impact.

36 MATERIALS SCIENCE↗

High-Energy Solid-State Lithium Batteries with Organic Cathode Materials (Final Report)

Organic materials made from abundant elements via low-energy processes are emerging as sustainable and low-cost alternatives to transition metal oxides as the electrode materials for high- energy batteries in the wake of supply chain and environmental issues associated with critical materials during the transition to clean energy. Organic insertion materials (OIMs) offer material- level energy comparable to transition metal oxides, but they have durability difficulties owing to dissolving in common liquid electrolytes. Combining ceramic-based solid electrolytes with organic electrode materials is one intriguing solution. The goal of this project is to design and synthesize high-energy OIMs, to understand the chemical dynamics and mechanical properties at the OIM-sulfide interface during electrochemical cycling, and to develop methods for constructing the optimum cathode microstructure, which will lead to improved electrochemical performance. The project team has accomplished the following over the last four years: (a) demonstrating that the mechanical softness of organic electrode materials is uniquely beneficial in suppressing crack formation at the electrode-electrolyte interface during cell operation; (b) understanding the interaction between cathode microstructure and the mechanical properties of individual components; and (c) establishing predictive control of cathode microstructure by tuning the mechanical properties of solid electrolytes and OIMs; (d) determining the chemical combability of sulfide electrolyte with high-energy OIMs and finally (f) laying out a road map toward a specific energy of 500 Wh kg -1 for solid-state lithium batteries. 14 publications resulted from this project.

25 ENERGY STORAGE↗

Peridynamic Model for Microballistic Perforation of Multilayer Graphene

The peridynamic theory of solid mechanics is applied to the continuum modeling of the impact of small, high-velocity silica spheres on multilayer graphene targets. The model treats the laminate as a brittle elastic membrane. The material model includes separate failure criteria for the initial rupture of the membrane and for propagating cracks. Material variability is incorporated by assigning random variations in elastic properties within Voronoi cells. Here, the computational model is shown to reproduce the primary aspects of the response observed in experiments, including the growth of a family of radial cracks from the point of impact.

42 ENGINEERING↗