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At least 145 records · Page 8

Combined-Accelerated Stress Testing of Photovoltaic Materials

By applying multiple environmental stresses in fieldrepresentative combinations and sequences, combined-accelerated stress testing (CAST) identifies degradation modes and failure mechanisms of photovoltaic (PV) modules and components that are missed by single stress factor accelerated testing.

14 SOLAR ENERGY↗

Cryogenic EM Across Length Scales for Li Metal Anode Batteries

An interfacial understanding is necessary for developing strategies to commercialize high-energy density rechargeable lithium metal anode batteries, as currently, the lithium anode/electrolyte interface is unstable with prolonged cycling. We have used several strategies to improve the cycling performance of lithium metal anodes, including reducing the parasitic reactions between lithium metal and the electrolyte, and improving the electrodeposited lithium metal morphology. These strategies have generated unconclusive electrochemical data, that has required the need for nanoscale interfacial characterization of these solid-liquid interfaces. Our team has used the cryogenic transfer workflow developed by Leica in collaboration with cryo-SEM/FIB tools by Thermo Fisher Scientific to cross-section lithium metal anodes and intact coin cell batteries to observe the interfacial structures, lithium morphology, and failure mechanisms relative to changes in electrode contract pressure and electrolyte chemistry. Cross-sectional SEM images and EDS maps of the lithium metal anodes have provided a better understanding of the electrodeposited lithium morphology, quantity of 'dead' lithium metal, and quantity of solid electrolyte interphase material that has formed alongside the lithium metal. In understanding lithium metal battery failure at the system level, we used a cryogenic stage in a laser plasma FIB to cross-section through the coin cell's cap for imaging/mapping the entire battery stack under cryogenic conditions. The tools, methods, and results of these studies will be detailed in this presentation.

characterization↗

Experimental Considerations for Estimating Degradation in PV Modules

Carefully controlled laboratory experiments and measurements can enable the determination of acceleration factors suitable for extrapolation to durability and performance of a fielded PV module. Ideally, a single mechanism can be identified with appropriate acceleration factors for extrapolation to the field. However, even with a single mechanism, the inherent uncertainty in these factors leads to uncertainty in the extrapolation which is greater the higher the acceleration factor. This course will explain how because of the wide range of acceleration factors for a given degradation mode, utilizing acceleration factors greater than about 10x will typically lead to unacceptable uncertainty in the results. Therefore, if even just a rank ordering of materials is desired, acceleration factors must be minimized which requires a good general understanding of the scale of the different acceleration factors for the degradation mode of interest. In this tutorial we will discuss what the different purposes are for many of the accelerated stress tests used today. E.g., what is a qualification test, a highly accelerated stress test, a rank ordering test, or a service life prediction test. We will discuss how one can understand the relationship between test results and expected field performance. A single accelerated stress test condition cannot duplicate outdoor exposure for all possible degradation pathways; therefore, one must use targeted evaluation of material properties at different stress levels to determine the relevant acceleration factors and fit it to a model. We will also discuss how to interpret the results of experiments understanding what is relevant/not relevant, or not e valuated in a test. There are many common error people make in their test interpretations because they push the stress levels to be too harsh. This creates biases and can mask the relevant failure modes and mechanisms or will erroneously lead one to over design materials against things that aren't relevant. Several case studies will be presented to illustrate appropriate interpretation of accelerated stress testing results.

degradation↗

Identifying multiple synergistic factors on the susceptibility to stress relaxation cracking in variously heat-treated weldments

The 347H austenitic stainless steel has been widely used for pressure vessels and pipeline (PVP) applications due to its excellent creep and corrosion resistance, which fit ideally to the harsh conditions in petrochemical industries, fossil fuel or nuclear power plants, and modern energy storages. However, a failure mode has been commonly observed with cracks emerging at the heat affected zone (HAZ) of weldments during post-weld heat treatment (PWHT) or under intermediate to high temperature service conditions. This phenomenon is termed as Stress Relaxation Cracking (SRC) since the purpose of PWHT is to relieve the welding-induced residual stress fields, or as Stress Age Cracking (SAC) if failure happens during service. A leading literature explanation of this failure suggests that the residual stress relaxation and the precipitation dissolution and/or re-precipitation occur in the same temperature range, which can lead to locally high strains and thus to crack at the grain boundaries. Since in situ spatial measurements of residual stress fields, microstructural evolution, and failure processes are nearly infeasible, this work recourses to a micromechanical finite element framework that models the high temperature failure as the nucleation and growth of grain boundary cavities, whereas various parameters such as thermomechanical loading history and its evolution, the competition of grain-interior dislocation creep and grain-boundary diffusion in failure lifetime, and microstructural heterogeneities (such as the precipitate free zone near grain boundaries) can be quantitatively incorporated. It can be concluded from these microstructure-explicit simulations that an accurate knowledge of residual stress evolution and a carefully calibrated set of material constitutive parameters are the essential prerequisites for lifetime predictions. The understanding of individual governing factors also leads to a mechanistic interpretation of the observed SRC susceptibility C-curves. In conclusion, these results suggest that the criticality of residual stress evolution, but not the precipitation-induced local strains, be the leading factor for SRC.

347H stainless steel weldments↗

Secure Route: Roadway Risk Mapping for Transportation Planners

The secure transport of sensitive materials across U.S. road networks pose unique challenges for local, state, and federal agencies. Threats range from random events (e.g., accidents, medical emergencies, mechanical failures) to opportunistic or organized tactical assaults. Although the probability of such attacks is very low, the consequences of material loss to foreign states or terrorists can be catastrophic, qualifying these scenarios as “grey swan” events—low-probability, high-impact occurrences that are predictable but difficult to quantify. Traditional risk assessments struggle in these contexts, necessitating a shift toward subjective risk perception to inform planning. Risk perception in transport planning is shaped by various factors, including knowledge of adversarial capabilities, vehicle defenses, manifest details, and geographic features along the route. Geographic features such as bridges, tunnels, roadside elevation, and gaps in cellular coverage introduce vulnerabilities, while mitigative features include safe havens, police stations, and medical services. Temporal variables such as congestion, accidents, and weather further complicate route planning. Despite their importance, existing routing tools like Google Maps and commercial software do not explicitly account for geographic risk features, requiring planners to rely on personal familiarity with routes—a time-intensive, non-scalable approach. This work addresses these gaps by: (1) developing datasets that catalog geographic risk features along U.S. roadways, (2) eliciting risk perceptions from experienced transportation security experts, and (3) linking these perceptions to roadway conditions and geographic data. We implement these capabilities within Secure Route a novel mapping tool for classifying route segment risks associated with roadway conditions. This system provides transportation planners with an intuitive interface to assess and contextualize risk along potential routes, improving decision-making for secure transport. We present current progress in this effort and identify next steps.

Stewart, Robert [ORNL] (ORCID:0000000281867559)↗

Surface heterogeneity propagation and homogenization for pouch cell-scale Li metal anodes

Li metal anode is a promising candidate for next-generation energy storage systems and is widely explored in Li-ion and solid-state batteries. Despite its potential, Li metal anodes face instabilities during long-term cycling, especially when paired with NMC or sulfur-based cathodes, where Li is cycled at high capacities of 6-8 mAh/cm2, equivalent to a thickness of 30-40 µm. During such extensive utilization, degradation mechanisms such as excessive solid electrolyte interphase (SEI), dendrites, and dead Li emerge, and ultimately lead to sudden failure and reduced cycle life. The origin of the degradation mechanisms stem from surface heterogeneities introduced during Li foil manufacturing and storage [1, 2]. As cycling progresses, the local heterogeneities propagate, resulting in uneven Li utilization and degradation-prone regions across the electrode [3], which consequently induce performance variations at the cell level. This heterogeneity propagation is particularly pronounced in large-format pouch cells in practical applications, where the surface effects are magnified. Without a clear understanding of the multi-scale heterogeneities and the development of surface homogenization methods, the performance consistency will be compromised, hindering the commercialization of Li metal batteries. In this presentation, we investigate the evolution of surface heterogeneity propagation on commercially available Li foils. We discover that inhomogeneous Li utilization appears as early as the first half-cycle of formation, manifesting as localized clusters and pits. In pouch cell configurations, these features exhibit areal density variations across the electrode on a scale of millimeters. To improve Li utilization homogeneity, a scalable mechanical brushing method is introduced to remove the chemically heterogeneous surface passivation layer. Furtherore, the influence of utilization homogeneity on cell-to-cell consistency is evaluated using 32 Li-NMC811 pouch cells divided into as-received and brushed Li groups. On the brushed Li, clusters and pits are no longer observable, and the cells exhibit significantly improved consistency in discharge capacity trajectories and cycle lifetime. Overall, this study highlights the role of Li surface utilization homogeneity on long-term cycling performance. Our research provides a pathway for improving large-area electrode uniformity and establishing evaluation methods for cell-to-cell consistency, both are key steps toward the commercialization of Li metal batteries and beyond. [1] Otto, Svenja-K., et al. "In-depth characterization of lithium-metal surfaces with XPS and ToF-SIMS: toward better understanding of the passivation layer." Chemistry of Materials 33.3 (2021): 859-867. [2] Hatzell, Kelsey, et al. "Aligning lithium metal battery research and development across academia and industry." Joule (2024). [3] Kim, Sangwook, et al. "Calendar life of lithium metal batteries: Accelerated aging and failure analysis." Energy Storage Materials 65 (2024): 103147.

25 - ENERGY STORAGE↗

Macro-micro multiscale modeling to assist the design of HPDC Al castings microstructure and alloys for EV super-large body structures (Phase 1)

Implementation of High Pressure Die Casting (HPDC) Aluminum (Al) body structures for high volume electrified vehicles (EV) to improve electric efficiency remains a key strategy within many original equipment manufacturer (OEM)s. In addition to high strength for safety requirements, superior Self-Piercing Riveting (SPR) performance is demanded for HPDC Al alloys to be compatible with high volume SPR joining. In this work, it is proposed to extend and validate an existing Contractor finite element multiscale macro-micro modeling approach to quantify the influence of the microstructure of HPDC alloys on the fracture strain/displacement under 3-point bend and clinch testing. The success of this work will allow to replace solution treatment stage with low energy consumption heat treatment (HT) processes, or to design new non heat treatable (NHT) HPDC Al alloys to eliminate HT requirements. Ultimately, this project will facilitate the application of HPDC Al alloys for super-large vehicle structures to significantly reduce vehicle weight, and thus improving energy efficiency. The purpose of this project is to extend and validate an existing finite element code, which is based on the Contractor developed macro-micro multi-scale modeling approach, to numerically simulate the three-point bending and clinch test and study the influences of material microstructural characteristics and phase properties on the rivetability. The macro-micro modeling approach begins with a sample scale model and identify the location, which is mostly prone to failure, the deformation history of the boundaries of that location calculated will be used to drive a microstructure-based sub-models where the material microstructure and microscale properties are considered. Using this approach, the wrap-bending failure for two Al alloys are correctly predicted for the first time. This will start with phase I effort of building a framework of macro-micro three point bending test and clinch test of Al10SiMgMn HPDC alloy in the as-cast and T7 heat treated conditions. Those results will then be validated with experimental test results. The phase II effort will involve the utilization of the knowledge learned in phase I to establish the quantitative correlation between the microstructure characteristics and the riveting performance, which will be further used to guide the optimization of HPDC Al alloy microstructure using heat treatment process to achieve sufficient rivetability to join large thin-wall HPDC alloys.

36 MATERIALS SCIENCE↗

Finite element procedure for thermomechanical and structural integrity analysis of beam intercepting devices subjected to free electron laser

High-energy particles, including photons (x-ray, γ-ray, bremsstrahlung), electrons, and protons, possess the capability to penetrate materials and deposit energy within them. The degree of absorption depends on both the energy and type of particles, as well as the properties of the materials with which they interact. This energy deposition can manifest either at the material's surface or throughout its volume, potentially resulting in various failure modes. The primary aim of this paper is to establish a structured analysis methodology for evaluating the structural integrity of beam-intercepting devices when subjected to high-energy particles. Here, the paper also reviews some of the underlying physics, pertinent to the scope of the thermomechanical analysis, potential failure modes, and introduces verification and validation methodologies. Engineers and researchers can utilize the guidelines presented in this paper to effectively plan the development of beam intercepting devices, thereby ensuring their reliability and performance in the presence of high-energy particle exposure.

Finite element analysis↗

A novel design optimization framework to sustain remanufacturability

The ever-increasing global carbon emissions have urged the need for environmentally conscious/sustainable product design, for which the design for remanufacturing (DfRem) is one potential approach. DfRem targets at designing products that have multiple life cycles, thus significantly reducing raw material usage, energy consumption, and carbon emissions. In this paper, we develop a three-stage framework that consists of (1) systematic design space exploration and a multi-objective optimization formulation to minimize the likelihood of failure causes (such as fatigue and wear) and environmental footprint, (2) topology optimization to further reduce material usage without significantly affecting the load-carrying capability of the product, and (3) post-topology optimization design verification to ensure the proposed design satisfies all design constraints. The environmental impact can be assessed at varying comprehensiveness levels (e.g., design and manufacturing phase, use phase) and in terms of carbon or GHG emission, energy use, and waste generation. Because the novel design framework predominantly adjusted the geometry, we focused on mass-based change and energy savings due to sustained remanufacturability. The multi-objective optimization formulation in the first step results in a Pareto optimal set of possible design solutions that the designer can use for the second step. Finally, we demonstrate the utility of this framework through a case study of an engine cylinder head subjected to thermo-mechanical loads, where we find that about 5% of the product mass can be conserved with only about a 3% increase in surface area that has a fatigue life less than 10,000 cycles.

42 ENGINEERING↗

Mesoscale Modeling Approach for Quantifying Microstructure-Aware Micromechanical Responses in Metal Hydrides

Metal hydrides can undergo significant volume changes upon hydrogen uptake and release, which induce a mechanical response that depends not only on the evolving hydrogen composition but also on the microstructure. We present a comprehensive mesoscale modeling framework based on microelasticity theory to quantify the micromechanical responses of metal hydrides, specifically focusing on a hydrogenating polycrystalline MgH 2x particle within a host material as a model micromechanical system. Utilizing digitally generated realistic microstructures and density-functional-theory-derived parameters, we analyzed highly nonuniform local stress profiles in the polycrystalline hydrides under the clamping force exerted by the host during hydrogenation. Our framework also allows us to predict the corresponding strain energy accumulation and mechanical hot spots formation in the hydrides, highlighting their roles in thermodynamic destabilization and mechanical failure, respectively. Through extensive parametric simulations, we further quantified the influence of interface type, crystallinity, grain size, loading ratio, and host stiffness, providing practical guidance for optimizing microstructural design and host material selection. This proposed approach is broadly applicable to micromechanical systems with complex microstructural features involving chemical reaction- and/or phase-transformation-induced deformation.

36 MATERIALS SCIENCE↗

Survey of baffle plate samples, specimen machining, and hydrogen measurements

This report outlines preliminary results on the survey and characterization of irradiated baffle plate, baffle former, and flux thimble tube specimens as part of the ongoing investigation into irradiation-induced embrittlement in austenitic stainless steels at ambient (room temperature) conditions. The specimens originated from commercial pressurized water reactor (PWR) components, covering displacement damage doses ranging from approximately 0.065 to 75 dpa. Initial scanning electron microscopy (SEM) surveys revealed that specimen surfaces exhibited fine machining marks and in-service-formed oxide layers on the side surfaces of the analyzed specimens. The oxide layers revealed specific features resembling localized "pitting-like" corrosion. An additional set of specimens representing in-service oxidation is being preserved for future microstructure analysis work. As believed, this will provide additional insights into long-term material degradation in PRWs. Specimen machining challenges emerged due to a complex failure of the electric discharge machining (EDM) system located in hot area. Despite partial restoration, issues persist with the EDM’s secondary power supply, necessitating the exploration of alternative EDM or computer numerical control (CNC) machining approaches to facilitate tensile specimen preparation. Currently, low speed saw cutting is in progress to prepare specimens for hydrogen measurements and general microstructure analysis. The near-term goals include completing tensile specimen machining for advanced mechanical testing and characterizing fracture mechanisms, and stress-corrosion cracking testing, ultimately aiming to identify and mitigate the ambient-condition intergranular cracking through targeted post-irradiation annealing strategies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Stress evolution and creep deformation in solid-oxide electrolysis cell systems – Dynamic modeling and multi-objective optimization to maximize stack life and efficiency

Here, this study develops a thermal stress model of solid-oxide electrolysis cells (SOECs) including a model for creep strain and failure probability that is integrated with a dynamic plant-wide model of a hydrogen production process. Uncertainties in key material properties of the cell are quantified to assess their impact on stress profile variability. The oxygen electrode is found to have about 10 times higher failure probability compared to the fuel electrode. The study shows that if the stack operation is not optimized, cycling operation would lead to stress build-up eventually leading to catastrophic failure. A dynamic optimization problem is set up for obtaining the optimal operational profile considering a variable hydrogen production rate. Due to the tradeoff between the efficiency and stress build-up, the dynamic optimization problem is multi-objective. It is observed that the optimizer can considerably reduce the stress build-up (i.e., can increase the stack life) albeit at the cost of a lower efficiency thus exhibiting strong tradeoffs between capital and operating costs. For example, if the stack would be replaced in 0.5 yr, specific energy requirement would be 48.5 kWh/kg H 2 while for a stack replacement time of about 6 yr, the specific energy requirement rises by about 4.2 %.

SOEC↗

Energy absorption of architectured PrintCast interpenetrating composites in tension

Additively manufactured (AM) metal-metal composites consisting of PrintCasted 316 L austenitic stainless-steel lattice structures infiltrated with A356 casting alloy, have recently been developed for use in high energy absorption systems with potential applications ranging from static load bearing to dynamic blast containment structures. This system has a unique mechanical behavior as the volume fraction of lattice increases showing a transition from localized to de-localized failure and dramatic increase in energy absorption capability. In this work, PrintCast A356/316 L composite tensile specimens were produced with lattice volume fractions ranging from 20 % to 50 % to capture the range of this behavior. Finite element simulations support neutron diffraction measurements of stress state. Results illustrate that in tension, the reinforcement material is in tension while the matrix support material is in compression, information offering significant insight into the transition to de-localized failure. Moreover, the simulation results provide further insight into how interfacial bonding (or lack of bonding) affects the energy absorption capabilities of the PrintCast composites.

36 MATERIALS SCIENCE↗

Mitigation of distortion of Al/steel part under simulated paint baking condition: Experiment and numerical model studies

Multi-material joining of lightweight structures is essential to reduce vehicle weight for more energy savings and less greenhouse gas emission. However, mismatch of thermal expansion coefficient for dissimilar materials during the paint baking process can induce part distortion and joint failure for adhesive bonding. Here, in the present work, a thermomechanical model based on contact mechanics and large deformation theory was developed for dissimilar high-strength Al alloy and steel components to study the distortion mechanism and influential factors of the residual gap. The established model was used to optimize joint conditions, such as pitch distance and part geometry. When a weld pitch is shorter than 100 mm, the maximum gap between Al and steel part can be greatly reduced to 0.1 mm, and the local stress and plastic strain around the joint during the oven heating and cooling cycle are also substantially reduced compared with the long pitch case (900 mm). The numerical modeling results revealed that a comparable bending stiffness ratio between the steel and Al cross sections is critical to the minimization of gap and distortion under paint baking condition. Digital image correlation technique was used to measure the overall part distortion and local strain distribution that were used to validate the model prediction. Weld bonding (adhesive bonding with friction bit joining) process was successfully employed to join Al to steel component without gap opening in adhesive after the paint baking and cooling.

36 MATERIALS SCIENCE↗

Destructive PIE and Safety Testing of Six AGR-5/6/7 Capsule 2 Compacts

This study evaluates fission product retention and particle failure mechanisms in AGR-5/6/7 Capsule 2 uranium carbide and uranium oxide (UCO) tristructural isotropic (TRISO) fuel under high-temperature gas reactor accident-relevant conditions using high-temperature safety tests and destructive postirradiation examination. Three Capsule 2 compacts were held isothermally at 1600°C for approximately 300 hours and one compact at 1800°C for approximately 300 hours; two additional compacts were examined in the as-irradiated state. Post-test deconsolidation–leach–burn–leach (DLBL) quantified nuclide inventories in matrix and particles. Individual particles were surveyed for radioisotope inventories, and microanalytical approaches resolved microstructural evolution and fission product distributions within the coating layers. At 1600°C, no krypton was detected above the minimum detectable limit, and cesium releases were far below a single particle equivalent, indicating the absence of full TRISO failure or SiC failures. Silver releases were limited and primarily reflected depleted postirradiation inventories, consistent with prior compact-level exams indicating substantial in-pile 110mAg loss. At 1800°C, cumulative 134Cs release of approximately 2.5 particle equivalents and delayed 85Kr totaling approximately 0.53 particle equivalents were consistent with one full TRISO failure and two SiC failures. Europium and strontium releases were roughly one order of magnitude higher than at 1600°C and comparable to AGR-1/AGR-2 high-temperature tests, with sustained late-hold rates indicating diffusion through intact coatings coupled with matrix depletion. Overall, AGR-5/6/7 Capsule 2 UCO fuel demonstrated fission product retention during safety testing consistent with prior AGR campaigns, while distinctive in-pile 110mAg depletion and measurable 1600°C europium loss motivate targeted follow-on studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

An in-situ view cell system for investigating swelling behavior of elastomers upon high-pressure hydrogen exposure

The transition to hydrogen as a clean and efficient energy carrier is impeded by challenges in the compatibility of hydrogen with materials used within hydrogen infrastructure. Elastomers, crucial in sealing components, often exhibit premature failures in high-pressure hydrogen environments due to excessive swelling. This study employs an innovative in-situ view cell system to assess the swelling behavior of hydrogenated nitrile butadiene rubber (HNBR) under various hydrogen conditions. The system, designed to withstand pressures up to 96.5 MPa, incorporates Digital Image Correlation (DIC) for strain measurements and volume estimation. Results reveal non-linear volume increases during depressurization, challenging conventional assumptions. Furthermore, investigations into peak hydrogen pressures and pressure-holding scenarios during decompression highlight complex swelling trends. The introduction of a novel computer vision (CV) method enhances precision in volume estimation, overcoming DIC limitations. The study provides insights into mitigating elastomer swelling, crucial for developing robust materials to support future hydrogen-driven energy systems.

Elastomer↗

Failure Criteria and Temperature Dependent Elastic Constants in the 3-D Elastic Orthotropic Model

Recent points of emphasis in the Library of Advanced Materials for Engineering (LAMÉ) have been to enable flexibility in formulations via the adoption of a variety of modular frameworks. While more established phenomenologies such as plasticity and viscoelasticity have been considered, elastically orthotropic models (e.g. elastic_3D_orthotropic) have not. For the elasticity component, not much can be modularized. However, a potential feature of interest would be the evaluation of failure criteria to consider the possibility of damage. Many such forms exist in the literature providing a good basis for modularity.

36 MATERIALS SCIENCE↗

Modeling-Based Design and Optimization of a Gradient Composite Transition Joint

An innovative additively manufactured gradient composite transition joint (AM-GCTJ) has been designed to join dissimilar metals, to address the pressing issue of premature failure observed in conventional dissimilar metal welds (DMWs) when subjected to increased cyclic operating conditions of fossil fuel power plants. The transition design, guided by computational modeling, developed a gradient composite material distribution, facilitating a smooth transition in material volume fraction and physical properties between different alloys. This innovative design seeks to alleviate structural challenges arising from distinct material properties, including high thermal stress and potential cracking issues resulting from the thermal expansion mismatch typically observed in conventional DMWs. In this study, we investigated the creep properties of transition joints comprising Grade 91 steel and 304 stainless steel through a combination of simulations and creep testing experiments. The implementation of a gradient composite design in the plate transition joint resulted in a significant enhancement of creep resistance when compared to the baseline conventional DMW. For instance, the creep rupture life of the transition joint was improved by > 400% in a wide range of temperature and stress testing conditions. Meanwhile, the failure location shifted to the base material of Grade 91 steel. Such enhancement can be primarily attributed to the strong mechanical constraint facilitated by the gradient composite design, which effectively reduced the stresses on the less creep-resistant alloy in the transition zone. Beyond examining plate joints, it is crucial to assess the deformation response of tubular transition joints under pressure loading and transient temperature conditions to substantiate and demonstrate the effectiveness of the design. The simulation results affirm that the tubular transition joint demonstrates superior resistance compared to its counterpart DMW when subjected to multiaxial stresses in tubular structures. In addition, optimization of the transition joint’s geometry dimensions has been conducted to diminish the accumulated deformation and enhance the service life. Lastly, the scalability and potential of the innovative transition joints for large-diameter pipe applications are addressed.

Zhang, Wei↗