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At least 271 records · Page 15

Probing multiscale dissolution dynamics in natural rocks through microfluidics and compositional analysis

Mineral dissolution significantly impacts many geological systems. Carbon released by diagenesis, carbon sequestration, and acid injection are examples where geochemical reactions, fluid flow, and solute transport are strongly coupled. The complexity in these systems involves interplay between various mechanisms that operate at timescales ranging from microseconds to years. Current experimental techniques characterize dissolution processes using static images that are acquired with long measurement times and/or low spatial resolution. These limitations prevent direct observation of how dissolution reactions progress within an intact rock with spatially heterogeneous mineralogy and morphology. We utilize microfluidic cells embedded with thin rock samples to visualize dissolution with significant temporal resolution (100 ms) in a large observation window (3 × 3 mm). Here we injected acidic fluid into eight shale samples ranging from 8 to 86 wt % carbonate. The pre- and postreaction microstructures are characterized at the scale of pores (0.1 to 1 µm) and fractures (1 to 1,000 µm). We observe that nonreactive particle exposure, fracture morphology, and loss of rock strength are strongly dependent on both the relative volume of reactive grains and their distribution. Time-resolved images of the rock unveil the spatiotemporal dynamics of dissolution, including two-phase flow effects in real time and illustrate the changes in the fracture interface across the range of compositions. Moreover, the dynamical data provide an approach for characterizing reactivity parameters of natural heterogeneous samples when porous media effects are not negligible. The platform and workflow provide real-time characterization of geochemical reactions and inform various subsurface engineering processes.

58 GEOSCIENCES↗

CROCUS Sodar Measurements of Lower Atmospheric Wind Profiles at Argonne Testbed for Multiscale Observational Science (ATMOS) Site

The Scintec MFAS Sodar (Multiple-Frequency Acoustic Sounder) is an autonomous, ground-based acoustic remote sensing system designed to measure vertical profiles of horizontal wind speed, wind direction, and vertical velocity in the lower atmosphere. The instrument transmits sequences of acoustic pulses and detects the Doppler-shifted sound waves backscattered by small-scale temperature and velocity fluctuations caused by atmospheric turbulence. From these Doppler shifts, the system derives three-dimensional wind vectors by combining radial velocities from multiple beam orientations.The MFAS Sodar operates with a first usable range gate beginning at approximately 30 m above ground level and a configurable vertical resolution of 10 m. Under favorable acoustic conditions, the system provides wind profiles extending up to 600 m above ground level. Measurements are processed into 15-minute averaged profiles containing wind speed, direction, vertical velocity, and diagnostic quantities such as signal-to-noise ratio and echo strength.This dataset was collected at the Argonne Testbed for Multiscale Observational Science (ATMOS) facility in Lemont, Illinois, as part of DOE's CROCUS Urban Integrated Field Laboratory (UIFL) initiative. The purpose of these observations is to characterize the vertical wind structure and boundary-layer evolution across the urban–suburban gradient of the greater Chicago region. In particular, these data are intended to improve understanding of how local meteorology, such as lake-breeze penetration, nocturnal jets, and daytime mixing, varies between the densely built urban core and the suburban periphery. The MFAS observations provide critical context for evaluating high-resolution model simulations and for integrating with complementary lidar, radar, and in-situ meteorological measurements within the broader CROCUS UIFL network.All data are archived in NetCDF (Network Common Data Form) format and include wind and diagnostic parameters. The files can be accessed and analyzed using standard software that supports NetCDF, such as Python (e.g., xarray, netCDF4), MATLAB, R (e.g., ncdf4, raster), or Panoply (NASA’s NetCDF visualization application).

54 ENVIRONMENTAL SCIENCES↗

Earth and Space Science Informatics Perspectives on Integrated, Coordinated, Open, Networked (ICON) Science

Abstract This article is composed of three independent commentaries about the state of Integrated, Coordinated, Open, Networked (ICON) principles (Goldman, et al., 2021b, https://doi.org/10.1029/2021EO153180 ) in Earth and Space Science Informatics (ESSI) and includes discussion on the opportunities and challenges of adopting them. Each commentary focuses on a different topic: (Section 2) Global collaboration, cyberinfrastructure, and data sharing; (Section 3) Machine learning for multiscale modeling; (Section 4) Aerial and satellite remote sensing for advancing Earth system model development by integrating field and ancillary data. ESSI addresses data management practices, computation and analysis, and hardware and software infrastructure. Our role in ICON science therefore involves collaborative work to assess, design, implement, and promote practices and tools that enable effective data management, discovery, integration, and reuse for interdisciplinary work in Earth and space science disciplines. Networks of diverse people with expertise across Earth, space, and data science disciplines are essential for efficient and ethical exchanges of findable, accessible, interoperable, and reusable (FAIR) research products and practices. Our challenge is then to coordinate the development of standards, curation practices, and tools that enable integrating and reusing multiple data types, software, multi‐scale models, and machine learning approaches across disciplines in a way that is as open and/or FAIR as ethically possible. This is a major endeavor that could greatly increase the pace and potential of interdisciplinary scientific discovery.

58 GEOSCIENCES↗

Arrested Phase Separation in Double-Exchange Models: Large-Scale Simulation Enabled by Machine Learning

In this work, we present large-scale dynamical simulations of electronic phase separation in the single-band double-exchange model based on deep-learning neural-network potentials trained from small-size exact diagonalization solutions. We uncover an intriguing correlation-induced freezing behavior as doped holes are segregated from half filled insulating background during equilibration. While the aggregation of holes is stabilized by the formation of ferromagnetic clusters through Hund’s coupling between charge carriers and local magnetic moments, this stabilization also creates confining potentials for holes when antiferromagnetic spin-spin correlation is well developed in the background. The dramatically reduced mobility of the self-trapped holes prematurely disrupts further growth of the ferromagnetic clusters, leading to an arrested phase separation. Implications of our findings for phase separation dynamics in materials that exhibit colossal magnetoresistance effect are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

3D Phase-Field Simulations of Pattern Formation During Freeze Casting

We present the results of a combined experimental and phase-field modeling study of pattern formation during freeze casting. Those studies use unidirectional freezing of simple binary liquid mixtures of water and sugars (sucrose and trehalose) in a temperature gradient, which suffice to produce hierarchical templated structures similar to those observed in more complex multi-component freeze-cast systems including lamellae, undulated ridges, and more exotic “jellyfish-like” substructures. Multiscale 3D phase-field simulations reproduce remarkably well those structures quantitatively and identify key properties of the ice-water interface that control their formation. They further reveal that lamellae form as a result of a novel symmetry-breaking secondary instability of partially faceted cellular structures and pinpoint additional secondary instability mechanisms giving rise to smaller-scale substructures.

Kaihua Ji↗

3D Phase-Field Simulations of Pattern Formation During Freeze Casting

We present the results of a combined experimental and phase-field modeling study of pattern formation during freeze casting. Those studies use unidirectional freezing of simple binary liquid mixtures of water and sugars (sucrose and trehalose) in a temperature gradient, which suffice to produce hierarchical templated structures similar to those observed in more complex multi-component freeze-cast systems including lamellae, undulated ridges, and more exotic “jellyfish-like” substructures. Multiscale 3D phase-field simulations reproduce remarkably well those structures quantitatively and identify key properties of the ice-water interface that control their formation. They further reveal that lamellae form as a result of a novel symmetry-breaking secondary instability of partially faceted cellular structures and pinpoint additional secondary instability mechanisms giving rise to smaller-scale substructures.

Kaihua Ji↗

Assessing Two Approaches for Enhancing the Range of Simulated Scales in the E3SMv1 and the Impact on the Character of Hourly US Precipitation

Abstract Improving the representation of precipitation in Earth system models is essential for understanding and projecting water cycle changes across scales. Progress has been hampered by persistent deficiencies in representing precipitation frequency, intensity, and timing in current models. Here, we analyze simulated US precipitation in the low‐resolution (LR) configuration of the Energy Exascale Earth System Model (E3SMv1) and assess the effect of two approaches to enhance the range of explicitly resolved scales: high‐resolution (HR) and multiscale modeling framework (MMF), which incur similar computational expense. Both E3SMv1‐MMF and E3SMv1‐HR capture more intense and less frequent precipitation on hourly and daily timescales relative to E3SMv1‐LR. E3SMv1‐HR improves the intensity over the Eastern and Northwestern US during winter, while E3SMv1‐MMF improves the intensity over the Eastern US and summer diurnal timing over the Central US. These results indicate that both methods may be needed to improve simulations of different storm types, seasons, and regions.

58 GEOSCIENCES↗

AI-Enhanced Computational Tools for Entry Systems Modeling

To advance the understanding of complex atmospheric entry phenomena, NASA’s Entry Systems Modeling (ESM) team [1] has developed high-fidelity computational tools addressing multiscale challenges, from material microstructures to full-scale heatshield response. This abstract highlights a subset of ESM tools, focusing on AI integration to enhance workflows and predictive modeling. - PuMA [2] computes effective material properties from high-resolution micro-CT scans, supporting TPS analysis for NASA missions. - TomoSAM [3] automates 3D tomography dataset segmentation for PuMA using the Segment Anything Model, reducing manual effort and improving accuracy. - PATO [4] models porous reactive materials under extreme conditions, with advancements such as unified solvers, mechanical erosion, and TPS coatings for NASA missions. - arcjetCV [5] employs deep learning to analyze arc jet test footage, measuring recession rates, shape changes, and shock standoff distances, bridging simulations, and experiments to reveal TPS ablation behavior. - ARCHeS [6] simulates arc heater plasma flows, modeling turbulence, radiation, and electromagnetic interactions to optimize arc heater performance, validate TPS under extreme conditions, and serve as a foundation for developing digital twins of arc heater facilities. - SPARTA [7] simulates rarefied hypersonic flows and gas-surface interactions for planetary entry missions, leveraging GPU architectures for scalable and efficient aerothermal and ablation analyses. AI-driven solutions, such as deep learning segmentation, have streamlined workflows in ESM tools and still hold significant potential to further accelerate processes and enhance automation in entry systems modeling. [1] Haskins, J.B. (2023), [2] Ferguson, J.C. (2018), [3] Meurisse, J.B.E. (2018), [4] Semeraro, F. (2023), [5] Quintart, A. (2024) [6] Meurisse, J.B.E. (2022), [7] Plimpton, S.J. (2019)

Predictive Modeling↗

Modeling Materials: Design for Planetary Entry, Electric Aircraft, and Beyond

NASA missions push the limits of what is possible. The development of high-performance materials must keep pace with the agency's demanding, cutting-edge applications. Researchers at NASA's Ames Research Center are performing multiscale computational modeling to accelerate development times and further the design of next-generation aerospace materials. Multiscale modeling combines several computationally intensive techniques ranging from the atomic level to the macroscale, passing output from one level as input to the next level. These methods are applicable to a wide variety of materials systems. For example: (a) Ultra-high-temperature ceramics for hypersonic aircraft-we utilized the full range of multiscale modeling to characterize thermal protection materials for faster, safer air- and spacecraft, (b) Planetary entry heat shields for space vehicles-we computed thermal and mechanical properties of ablative composites by combining several methods, from atomistic simulations to macroscale computations, (c) Advanced batteries for electric aircraft-we performed large-scale molecular dynamics simulations of advanced electrolytes for ultra-high-energy capacity batteries to enable long-distance electric aircraft service; and (d) Shape-memory alloys for high-efficiency aircraft-we used high-fidelity electronic structure calculations to determine phase diagrams in shape-memory transformations. Advances in high-performance computing have been critical to the development of multiscale materials modeling. We used nearly one million processor hours on NASA's Pleiades supercomputer to characterize electrolytes with a fidelity that would be otherwise impossible. For this and other projects, Pleiades enables us to push the physics and accuracy of our calculations to new levels.

Supercomputing↗

Substitution-Mediated Calcination of Nickel-Based Cathodes: Decoupling Lithiation and Crystallization

Nickel-based layered cathodes such as LiNiO 2 offer high energy density for lithium-ion batteries, yet improvements in cycling performance and safety are required for practical use–often achieved through manganese and cobalt substitution as in LiNi 0.80 Mn 0.10 Co 0.10 O 2 (NMC811). However, how such substitution impacts calcination, the key process that governs lithiation, structural ordering, crystallization, and ultimately the resulting material properties, remains unclear. Here, in this study, we investigate substitution-mediated calcination dynamics in NMC811 compared to LiNiO 2 using multiscale-correlated in situ spectroscopy and atomistic-to-mesoscale modeling. While both systems progress through the same sequence of intermediates toward the thermodynamically favored layered phase, NMC811 exhibits an earlier onset of layering, concurrent with hydroxide decomposition followed by sluggish crystallization. Modeling reveals that Mn and Co lower the energy barrier for lithium incorporation and ordering but increase the penalty for interlayer gliding, thereby slowing crystal growth at elevated temperatures. This substitution-mediated decoupling of lithiation and crystallization explains the fine-grained microstructure observed in NMC811 versus coarsened particles in LiNiO 2 and establishes a mechanistic framework for predictive microstructure engineering of Ni-based cathodes.

Calcination↗

Multiscale simulations for multi-continuum Richards equations

In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation (for pressure head), and these equations are coupled to one another by transfer terms. On its own, Richards equation is already a nonlinear partial differential equation, and it is exceedingly difficult to solve numerically due to the extra nonlinear dependencies involving the soil water. To deal with multiple scales, our strategy is that starting from a microscopic scale, we upscale the coupled system of dual-continuum Richards equations via homogenization by the two-scale asymptotic expansion, to obtain a homogenized system, at an intermediate scale (level). Based on a hierarchical approach, the homogenization’s effective coefficients are computed through solving the arising cell problems. Furthermore, to tackle the nonlinearity, after time discretization, we use Picard iteration procedure for linearization of the homogenized Richards equations. At each Picard iteration, some degree of multiscale still remains from the intermediate level, so we utilize the generalized multiscale finite element method (GMsFEM) combining with a multi-continuum approach, to upscale the homogenized system to a macroscopic (coarse-grid) level. This scheme involves building uncoupled and coupled multiscale basis functions, which are used not only to construct coarse-grid solution approximation with high accuracy but also (with the coupled multiscale basis) to capture the interactions among continua. These prospects and convergence are demonstrated by several numerical results for the proposed method.

97 MATHEMATICS AND COMPUTING↗

Determining Catalytically Relevant Surfaces through Coverage-Dependent Lattice Gas Models: Carbon Adsorption on Fe(100)

Here, we have quantified the C–C lateral interactions on Fe(100) using a density functional theory (DFT)-parameterized lattice gas cluster expansion (LG CE) model trained using 265 unique configurations spanning a C coverage from 0 to 1 monolayer (ML). Our LG CE model shows high predictive accuracy with a leave-multiple-out cross-validation score of 10.2 and 16.6 meV/site for systems with and without the top two layers of Fe atoms fixed, respectively. Electronic ground-state structures identified from the lattice gas model (including the structures at 0 and 1 monolayers) were further used to generate ab initio phase diagrams under a range of temperatures and pressures. At low temperatures (<400 K), we found that the 1.0 monolayer structure is dominant, whereas at higher temperatures (>500 K), the 0.88 ML structure is most likely to form on the Fe surface. Interestingly, our model identified a c (2 × 2) ordered structure at 1/2 ML, which correlates well with previous DFT studies for carbon adsorption on iron surfaces and matches with the experimentally observed low-energy electron diffraction structure. Overall, the DFT-parameterized energies for the C/Fe system including effects of coverage and configurational space can further help in developing multiscale models for various heterogeneous reactions involving C–C and C–Fe interactions.

08 HYDROGEN↗

Multiscale structural analysis of polymorphic phase boundaries in doped antiferroelectric sodium niobate

In the current work, we have performed multiscale structural analysis of a Pb-free sodium niobate-based smart system, i.e., 0.9⁢NaNbO 3 –0.1⁢Ba 0.9 ⁢Ca 0.1 ⁢TiO 3 (NN-10BCT) reported earlier for its high ferroelectric response. We have investigated the temperature-dependent evolution of crystal structure at long, medium, and short ranges using synchrotron x-ray diffraction (SXRD), Raman scattering, and pair distribution function(PDF) techniques in conjunction with dielectric studies. Temperature-dependent synchrotron x-ray diffraction data combined with dielectric analysis suggest two unique polymorphic phase boundaries (PPB) with two coexisting ferroelectric phases stable in the wide temperature ranges. These PPBs are stable in different regions viz. (i) cryogenic temperatures with coexisting R3c and Pmc⁢2 1 phases (ii) vicinity of room temperatures with coexisting Pmc⁢2 1 and Amm2 phases. In contrast to the conclusions drawn from SXRD, PDF reveals structures having lower symmetry (with coexisting Cc+ Pmc2 1 phases at 1.7 ≤r≤ 20 Å) at short ranges for these PPBs. In conclusion, the presence of different long- and short-range symmetries (accommodating tilt-oriented ferroelectric phases) in the unique polymorphic phase boundaries makes them thermally stable and advantageous for technological applications.

36 MATERIALS SCIENCE↗

Exploratory Precipitation Metrics: Spatiotemporal Characteristics, Process-Oriented, and Phenomena-Based

Abstract Precipitation sustains life and supports human activities, making its prediction one of the most societally relevant challenges in weather and climate modeling. Limitations in modeling precipitation underscore the need for diagnostics and metrics to evaluate precipitation in simulations and predictions. While routine use of basic metrics is important for documenting model skill, more sophisticated diagnostics and metrics aimed at connecting model biases to their sources and revealing precipitation characteristics relevant to how model precipitation is used are critical for improving models and their uses. This paper illustrates examples of exploratory diagnostics and metrics including 1) spatiotemporal characteristics metrics such as diurnal variability, probability of extremes, duration of dry spells, spectral characteristics, and spatiotemporal coherence of precipitation; 2) process-oriented metrics based on the rainfall–moisture coupling and temperature–water vapor environments of precipitation; and 3) phenomena-based metrics focusing on precipitation associated with weather phenomena including low pressure systems, mesoscale convective systems, frontal systems, and atmospheric rivers. Together, these diagnostics and metrics delineate the multifaceted and multiscale nature of precipitation, its relations with the environments, and its generation mechanisms. The metrics are applied to historical simulations from phases 5 and 6 of the Coupled Model Intercomparison Project. Models exhibit diverse skill as measured by the suite of metrics, with very few models consistently ranked as top or bottom performers compared to other models in multiple metrics. Analysis of model skill across metrics and models suggests possible relationships among subsets of metrics, motivating the need for more systematic analysis to understand model biases for informing model development.

54 ENVIRONMENTAL SCIENCES↗

Understanding and Strategies for Controlled Interfacial Phenomena in Lithium-Ion Batteries and Beyond

Electrolyte chemistry and properties and electrode structure and chemical properties particularly at the interfaces are crucial for the development of advanced battery components. This project focused on elucidating the roles of the electrolyte and electrode on the formation and evolution of the SEI layer and cell electrochemical performance on silicon and on Li metal anodes. For Si nano/microstructures we evaluated lithiation, volume changes, reactivity, and chemo-mechanical transformations as functions of nanoparticle size, shape, presence of coatings, electrolyte composition, electron leakage to the electrolyte, and cycling. For Li metal anodes we provided detailed analyses of the electrode and electrolyte effects on interfacial reactivity and as a function of microstructural evolution and underlying stochasticity as dendrites nucleate and grow. We thoroughly investigated and simulated how the chemistry of the various components of the electrolyte and the electrode architecture may affect the electrochemical reactions as well as cell degradation. A multiscale modeling approach was utilized, where atomistic simulations informed about the microscopic behavior of the system, and intermediate time and length scales were investigated with mesoscopic models. Results were also tested against selected experiments from our collaborators. The combined theoretical-experimental strategy saves costs by utilizing predictions from computational analyses to guide experimentation.

25 ENERGY STORAGE↗

Multiscale Experiments and Multiphysics Simulation of Multiphase Flow for Transportable Small Modular Reactors

A new type of safe, small, transportable nuclear reactor would address the intense and ever-growing global demand for energy produced via a resilient, carbon-free energy source. In this regard, transportable small modular reactors (SMRs) are being designed and developed for electricity generation within small/micro-grid/off-grid isolated systems, as well as for heat generation in industrial/residential applications. These reactors feature the capability to be fully factory fabricated and then directly transported to utilities’ sites as “plug-and-play” systems. Research and development (R&D) programs are underway at Idaho National Laboratory (INL) to successfully design, develop, and demonstrate such safe-by-design mobile reactor technologies, in collaboration with partner organizations. Multiscale experimental facilities and multiphysics simulation tools are required for reactor design verification and validation (V&V), and licensing. These advanced reactors are intended to feature passive safety systems such as passive containment cooling systems (PCCS), which consist of multiphase flows and multispecies distributions. This seminar talk will focus on designing and analyzing transportable SMR PCCS by using multiscale experiments and multiphysics computational fluid dynamics (CFD) simulations to support reactor licensing and safety. The corresponding research challenges are addressed via supportive verification and validation results generated by the models and simulation tools in combination with selective parametric and uncertainty analysis. This solution approach could blaze the trail for commercial adoption of such technologies. The facilities, simulation capabilities, and research opportunities available at INL in regard to such reactors and the integrated energy systems with which they go hand in hand are also discussed briefly, and may spark interest in deeper research as well as new collaborative projects.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Understanding Solution State Conformation and Aggregate Structure of Conjugated Polymers via Small Angle X-ray Scattering

Donor-acceptor (D-A) conjugated polymers are high-performance organic electronic materials that exhibit complex aggregation behavior. Understanding the solution state conformation and aggregation of conjugated polymers is crucial for controlling morphology during thin-film deposition and the subsequent electronic performance. However, a precise multiscale structure of solution state aggregates is lacking. Here, we present an in-depth small-angle X-ray scattering (SAXS) analysis of the solution state structure of an isoindigo-bithiophene-based D-A polymer (PII-2T) in chlorobenzene and decane as our primary system. Modeling the system as a combination of hierarchical fibrillar aggregates mixed with dispersed polymers, we extract information about conformation and multiscale aggregation and also clarify the physical origin of features often observed but unaddressed or misinterpreted in small-angle scattering patterns of conjugated polymers. The persistence length of the D-A polymer extracted from SAXS agrees well with a theoretical model based on the dihedral potentials. Additionally, we show that the broad high q structure factor peak seen in scattering profiles can be attributed to lamellar stacking occurring within the fibril aggregates and that the low q aggregate scattering is strongly influenced by the polymer molecular weight. Overall, the SAXS profiles of D-A polymers in general exhibit a sensitive dependence on the co-existence of fibrillar aggregate and dispersed polymer chain populations. We corroborate our findings from SAXS with electron microscopy of freeze-dried samples for direct imaging of fibrillar aggregates. Finally, we demonstrate the generality of our approach by fitting the scattering profiles of a variety of D-A polymers based on thieno-isoindigo (PTII-2T), diketopyrrolopyrrole (DPP2T-TT, DPP-BTZ, PDPP2FT-C- 16 ), naphthalenediimide (P(NDI2OD-T2)), and a conjugated block copolymer P3HT-b-DPPT-T. The results presented here establish a picture of the D-A polymer solution state structure and provide a general method of interpreting and analyzing their scattering profiles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Weibull-Based Stochastic Simulation of Mud-Crack Damage Formation in an Environmental Barrier Coating

The integrated Finite Element Analysis Micromechanics Analysis Code/Ceramics Analysis and Reliability Evaluation of Structures (FEAMAC/CARES) program was used to simulate the formation of mudflat-cracks from thermomechanical loading on a multi-layered Environmental Barrier Coating (EBC) system deposited on a ceramic substrate. FEAMAC/CARES combines MAC/GMC (Micromechanics Analysis Code/Generalized Method of Cells) multiscale composite micromechanics code with CARES/Life probabilistic multiaxial failure criteria code and Abaqusfinite element analysis. In this work, step function elastic modulus reduction of randomly damaged finite elements was used to represent discrete cracking events. The use of many small-sized low-aspect-ratio finite elements enabled the depiction of crack boundaries and formation of mudflat patterned damage. Demonstrated examples include finite element models of button-sized disk-shaped 3-D specimen, and a 2-D model of through-the-thickness cross-section. All models were subjected to a progressive cool down from 1300 degrees Centigrade to room temperature. Mudflat crack damage in the coating system resulted from the buildup of residual tensile stresses between the individual material constituents from thermal expansion mismatch. A 2-parameter Weibull distribution characterized the coating layer stochastic strength response and the effect of the Weibull modulus on the formation of damage was studied here.

Residual Tensile Stress↗