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At least 1,387 records · Page 77

Convection-Induced Compositional Patterning at Grain Boundaries in Irradiated Alloys

We consider the stability of precipitates formed at grain boundaries (GBs) by radiation-induced segregation in dilute alloys subjected to irradiation. Here, the effects of grain size and misorientation of symmetric-tilt GBs are quantified using phase field modeling. A novel regime is identified where, at long times, GBs are decorated by precipitate patterns that resist coarsening. Maps of the chemical Péclet number indicate that arrested coarsening takes place when solute advection dominates over thermal diffusion right up to the precipitate/matrix interface, preventing interfacial local equilibrium and overriding capillary effects. This contrasts with liquid-solid mixtures where convection always accelerates coarsening.

36 MATERIALS SCIENCE↗

Fatigue life prediction modeling for turbine hot section materials

A major objective of the fatigue and fracture efforts under the Hot Section Technology (HOST) program was to significantly improve the analytic life prediction tools used by the aeronautical gas turbine engine industry. This was achieved in the areas of high-temperature thermal and mechanical fatigue of bare and coated high-temperature superalloys. The cyclic crack initiation and propagation resistance of nominally isotropic polycrystalline and highly anisotropic single crystal alloys were addressed. Life prediction modeling efforts were devoted to creep-fatigue interaction, oxidation, coatings interactions, multiaxiality of stress-strain states, mean stress effects, cumulative damage, and thermomechanical fatigue. The fatigue crack initiation life models developed to date include the Cyclic Damage Accumulation (CDA) and the Total Strain Version of Strainrange Partitioning (TS-SRP) for nominally isotropic materials, and the Tensile Hysteretic Energy Model for anisotropic superalloys. A fatigue model is being developed based upon the concepts of Path-Independent Integrals (PII) for describing cyclic crack growth under complex nonlinear response at the crack tip due to thermomechanical loading conditions. A micromechanistic oxidation crack extension model was derived. The models are described and discussed.

Halford, G. R.↗

Computational toolkit for predicting thickness of 2D materials using machine learning and autogenerated dataset by large language model

The thickness of 2D materials not only plays a crucial role in determining the performance of nanoelectronic and optoelectronic devices but also introduces complexities in predicting volume-dependent properties, such as energy storage capacity, due to the intrinsic vacuum within these materials. Although a plethora of experimental techniques, including but not limited to optical contrast, Raman spectroscopy, nonlinear optical spectroscopy, near-field optical imaging, and hyperspectral imaging, facilitate the measurement of 2D material thickness, comprehensive data for many materials remain elusive. Over the past decade, the exponential proliferation of 2D materials and their heterostructures has outstripped the capabilities of conventional experimental and computational approaches. In this evolving landscape, machine learning (ML) has emerged as an indispensable tool, offering a scalable approach to augment these traditional methodologies. Addressing the critical gap, we introduce THICK2D—Thickness Hierarchy Inference and Calculation Kit for 2D Materials. This Python-based computational framework harnesses an autogenerated thickness database, developed using large language models, and advanced ML algorithms to facilitate the rapid and scalable estimation of material thickness, relying solely on crystallographic data. To demonstrate the utility and robustness of THICK2D, we successfully used the toolkit to predict the thickness of more than 8000 2D-based materials, sourced from two extensive 2D materials databases. THICK2D is disseminated as an open-source utility, accessible on GitHub at https://github.com/gmp007/THICK2D, and archived on Zenodo at https://10.5281/zenodo.11216648.

Ekuma, Chinedu E. (ORCID:0000000258527556)↗

Fatigue life prediction modeling for turbine hot section materials

A major objective of the fatigue and fracture efforts under the NASA Hot Section Technology (HOST) program was to significantly improve the analytic life prediction tools used by the aeronautical gas turbine engine industry. This was achieved in the areas of high-temperature thermal and mechanical fatigue of bare and coated high-temperature superalloys. The cyclic crack initiation and propagation resistance of nominally isotropic polycrystalline and highly anisotropic single crystal alloys were addressed. Life prediction modeling efforts were devoted to creep-fatigue interaction, oxidation, coatings interactions, multiaxiality of stress-strain states, mean stress effects, cumulative damage, and thermomechanical fatigue. The fatigue crack initiation life models developed to date include the Cyclic Damage Accumulation (CDA) and the Total Strain Version of Strainrange Partitioning (TS-SRP) for nominally isotropic materials, and the Tensile Hysteretic Energy Model for anisotropic superalloys. A fatigue model is being developed based upon the concepts of Path-Independent Integrals (PII) for describing cyclic crack growth under complex nonlinear response at the crack tip due to thermomechanical loading conditions. A micromechanistic oxidation crack extension model was derived. The models are described and discussed.

G R Halford↗

Generalized kinetic model for defect evolution in irradiated materials

A fundamental and open problem in materials science is to determine how the structural properties of irradiated and self-irradiated materials evolve in time. Structural defects generated by irradiation lead to changes in a material’s macroscopic properties, and these macroscopic changes, such as volumetric swelling, can in turn give rise significant alterations of the functionality of a material. Here, we develop a unified analytical model to understand the complex interplay between aggregation, fragmentation, and recombination processes involving mobile clusters of defects such as bubbles, voids, and interstitial atoms in materials subject to radiative sources. Specifically, we employ a mean field approach to derive a system of coupled kinetic equations that describes both the time evolution of the density of each type of defect and how clusters of each defect form and grow as the material ages.

36 MATERIALS SCIENCE↗

A semianalytic radiance model of ocean color

A semianalytical radiance model is developed which predicts the upwelled spectral radiance at the sea surface as a function of the phytoplankton pigment concentration for Morel Case 1 waters. The model is in good agreement with experimental measurements carried out in waters which were not included in the data base used to derive it. It suggests that the observed variability in the radiance is due to variations in the backscattering of plankton and the associated detrital material. The model is extended to include other material in the water, such as dissolved organic material, referred to as yellow substances, and detached coccoliths from coccolithophorids, e.g., Emiliana huxleyi. Potential applications include an improved biooptical algorithm for the retrieval of pigment concentrations from satellite imagery in the presence of interference from detached coccoliths and an improved atmospheric correction for satellite imagery. The model also serves to identify and to interpret deviations from Case 1 waters.

Gordon, Howard R.↗

An Overview of Experiments and Modeling of Polysiloxane-Coated Thermal Protection Systems for Missions to Mars, Titan, and Beyond.

Phenolic Impregnated Carbon Ablator (PICA) gained heritage during the historic Stardust mission, where it successfully returned samples from a comet’s tail and has since been instrumental in delivering payloads to the surface of Mars [1-3]. Most recently, PICA enabled the safe return of samples collected from asteroid Bennu as part of the OSIRIS-REx mission. This rich legacy underscores PICA’s critical role in allowing NASA’s most ambitious exploration missions. However, the friable nature of its phenolic phase presents challenges during handling and pre-launch activities. To mitigate this issue, PICA is coated with a polysiloxane resin system, which serves to suppress particulate dispersion and thereby safeguard spacecraft components. A comprehensive understanding of the polysiloxane resin’s behavior is imperative, as it profoundly shapes the material response of PICA during atmospheric entry by influencing its thermal and oxidative stability. This influence extends to thermocouple plugs embedded within thermal protection systems. These plugs have demonstrated their significance in missions such as Mars Science Laboratory (MSL) and Mars 2020, where the MEDLI and MEDLI2 instrumentation suites delivered in-valuable insights into the performance of thermal protection systems during entry into the Martian atmosphere [4]. Looking ahead, missions such as Dragonfly, set to descend into Titan’s dense atmosphere, aim to leverage advanced sensor technologies to further refine our understanding of thermal protection response [5]. Moreover, thermocouple plugs play an essential role in validating cutting-edge material response models, such as those pioneered under NASA’s Entry Systems Modeling Project (ESM), designed, in-part, to predict the operational integrity of thermal protection systems under the extreme stresses of atmospheric entry. To achieve these modeling goals, ground-based experiments are crucial to provide the foundational data necessary for developing and refining these predictive tools. To this end, an extensive test campaign was conducted at the Hypersonic Materials Environmental Test System (HyMETS) to investigate the high-temperature behavior of the polysiloxane resin in an air environment [6]. These experiments revealed critical phenomena, including the formation of a silicon oxycarbide layer that enhances oxidation resistance, moderates surface temperatures, and alters in-depth thermal response. Building on these findings, subsequent tests were designed to simulate atmospheric entry conditions in reactive gases, such as CO2 and N2, to mimic the environments of Mars and Titan, respectively, as well as non-reactive gases representing the atmospheres of the Ice Giants (Neptune and Uranus). A heating rate dependent decomposition mechanism has been identified for the polysiloxane resin under oxidizing conditions (Fig. 1). In the initial stage, the resin and the underlying thermal protection system undergo pyrolysis, rapidly generating a thin amorphous silicon oxycarbide interwoven with carbonaceous char and residual fibers from PICA. During the second stage, the nascent oxide layer establishes a robust, oxidation-resistant thermal barrier coating, which significantly impedes heat transfer to the underlying carbonaceous char, resulting in a stagnation of the surface temperature. A key factor contributing to this thermal resistance is the low recombination efficiency of atomic oxygen (γ), which further diminishes the heat load on the material’s interior layers [7]. Moreover, as the surface temperature stagnates, the silicon oxycarbide phase separates into distinct regions of silica and free graphite. Ultimately, when the heat flux reaches a critical threshold, a third stage is triggered, leading to the breakdown of the coating through carbothermal reduction, exposing the underlying char layer. This exposure leads to a dramatic surface temperature spike, driven by highly exothermic reactions between atomic oxygen and the char layer, further accelerating material degradation. A detailed mass and heat transfer model of PICA coated with polysiloxane resin was implemented in the Porous material Analysis Toolbox based on OpenFOAM, PATO [8]. The initial stage was considered negligible in this model because the resin decomposition occurs rapidly within a thin surface layer. Instead, the coating was directly considered as an oxygen-resistant thermal barrier coating. For the second stage, the thin amorphous silicon oxycarbide was treated as a pure silica surface to simplify the thermochemical behavior. The model ac-counts for surface equilibrium processes using representative elements of the coating-environment system. For the third stage, specific boundary conditions were developed to estimate the onset and progression of the coating removal. Two-dimensional material response simulations were conducted to compare uncoated and coated PICA using boundary conditions calibrated with HyMETS data. Fig. 2 illustrates that the simulations closely align with experimental data, successfully reproducing measured temperature profiles. This work will include the latest advancements in the coating model, including the calibration of recombination of atomic oxygen at the surface during the second phase. These simulated results will be further validated against additional CO2 data points from HyMETS, reinforcing the models’ predictive capabilities. These mechanisms and their effects on thermal protection systems, including thermochemical behavior and thermocouple probe performance in extreme environments, provide crucial insights for optimizing spacecraft designs that safeguard scientific payload and ensure mission success in future planetary exploration endeavors.

Active Oxidation↗

Using Digital Image Correlation for Material Testing at Cryogenic Temperatures

Recent efforts were made to parametrize an aluminum alloy at cryogenic temperatures to calibrate finite element models simulating material deformation. Digital image correlation (DIC) was used to measure material properties using front/back strains of specimens during tensile tests. Data acquired from DIC was compared to physical extensometer measurements. Two camera pairs (front and back) were mounted via aluminum extrusion to the exterior of an environmental chamber of a hydraulic test stand. Images were taken through single-pane optical glass windows of the environment chamber. Positive pressure bags encased the cameras, attaching to the perimeter of the glass to keep out moisture and prevent windows from frosting. Figure 1 shows the environmental setup and the camera setup during cryogenic testing. Some of the challenges during testing at cryogenic temperatures include the gaseous flow of liquid nitrogen in the optical path of the mounted cameras, frost buildup on the windows as seen in Figure 1b, and frost on the test coupon. The temperature gradient present during the introduction of liquid nitrogen into the chamber can increase the projection error of images captured of the specimen. Figure 2 shows the estimated projection error from DIC as a function of temperature during the cool down process. This presentation addresses some of the concerns and observations when using DIC for testing at cryogenic temperatures using methods of isolated camera system and techniques for maintaining the glass panel clear from frost.

Joseph Cochran↗

Machine learning on neutron and x-ray scattering and spectroscopies

Neutron and x-ray scattering represent two classes of state-of-the-art materials characterization techniques that measure materials structural and dynamical properties with high precision. These techniques play critical roles in understanding a wide variety of materials systems from catalysts to polymers, nanomaterials to macromolecules, and energy materials to quantum materials. In recent years, neutron and x-ray scattering have received a significant boost due to the development and increased application of machine learning to materials problems. This article reviews the recent progress in applying machine learning techniques to augment various neutron and x-ray techniques, including neutron scattering, x-ray absorption, x-ray scattering, and photoemission. We highlight the integration of machine learning methods into the typical workflow of scattering experiments, focusing on problems that challenge traditional analysis approaches but are addressable through machine learning, including leveraging the knowledge of simple materials to model more complicated systems, learning with limited data or incomplete labels, identifying meaningful spectra and materials representations, mitigating spectral noise, and others. We present an outlook on a few emerging roles machine learning may play in broad types of scattering and spectroscopic problems in the foreseeable future.

Chen, Zhantao↗

A fission gas release correlation for uranium nitride fuel pins

A model was developed to predict fission gas releases from UN fuel pins clad with various materials. The model was correlated with total release data obtained by different experimentors, over a range of fuel temperatures primarily between 1250 and 1660 K, and fuel burnups up to 4.6 percent. In the model, fission gas is transported by diffusion mechanisms to the grain boundaries where the volume grows and eventually interconnects with the outside surface of the fuel. The within grain diffusion coefficients are found from fission gas release rate data obtained using a sweep gas facility.

Weinstein, M. B.↗

Blast Loading of Epoxy Panels Using a Shock Tube

The high strain rate mechanical response of thin polymer plates has been studied using a modified shock tube. Diagnostics include the pressure-time history of the incident and reflected pulses and the use of digital image correlation (DIC) techniques to extract the time-history of the out-of-plane displacement distribution. Additionally, finite element models have been developed to understand the plate response and to validate and modify plate material constitutive models that have been proposed.

Pankow, Mark↗

Effects of internal swelling on residual elasticity of a quasi-brittle material through a composite sphere model

This work describes the development of a micromechanical-based constitutive model accounting for the effect of internal expansion on the residual elasticity of a Hashin composite material. This material is made of spherical inclusions that are subjected to gradual swelling within a quasi-brittle matrix. The main focus of this work is to describe and analyze the material mechanical response, with an additional focus on the internal swelling’s effect on the stress–strain response and residual elasticity. Microstructural features and parameters of major importance for the mechanical responses were identified. The innovative characteristics of the proposed approach are summarized as follows: (1) a full determination of the physics of a complete-damage problem throughout the whole process of inclusion swelling with upscaling techniques, which transfers the microcrack-related properties from the lower scale to upper scale; and (2) an evolution of the mechanical fields and the corresponding residual elasticity for various inclusion swelling levels. Concerning the matrix–inclusion composite, it was hypothesized that only the matrix was susceptible to cracking, with varied degrees of damage, whereas the inclusions behave elastically and the elastic modulus of the expanding inclusions remains constant. It is to emphasize that the gradual swelling of inclusions is modeled by an increasing strain in the current micromechanical-based constitutive model, and the microcracks are represented by a set of randomly oriented penny-shaped microcracks with identical radii (namely, closed cracks). The main contribution of the current research is to establish the exact mathematical solutions for the mechanical fields (stress, strain) caused by the swelling of the inclusions (mechanical loading) and derive the effective residual elasticity of a composite (structural response) subject to internal expansion and quasi-brittle damage. Based on the assumption of closed cracks that could be extended to open cracks in the upcoming work, the results proposed by the present paper help to understand the non-linear mechanical behavior of quasi-brittle materials subject to microcracking and provide a theoretical framework to be used as academical benchmark for numerical simulations.

36 MATERIALS SCIENCE↗

Analysis of PICA-NuSil at the Hypersonic Materials Environmental Test System (HyMETS)

Phenolic Impregnated Carbon Ablator (PICA) gained heritage during the stardust mission and is the baseline material for missions to Mars. The phenolic phase of PICA is friable, and therefore the surface is treated with a siloxane resin (NuSil) to mitigate the shedding of particulate matter. Historically, material response models have not accounted for the presence of this coating. Therefore, a test campaign was executed at the Hypersonic Materials Environmental Test System (HyMETS) to investigate the performance of NuSil under multiple heating rates and gas composition. Sphere-cone models were instrumented with thermocouples to measure the in-depth temperature response, and surface temperatures were monitored with a pyrometer. Furthermore, emission spectrometers were used to collect spectra from species emitting at the surface of the test article and the post-shock stagnation region. Post-test analysis suggests that the coating decomposes according to multiple stages. Inspection of silicon emission data reveals a rapid rise and decline in intensity within the first couple of seconds of testing, which is attributed to pyrolysis of NuSil. Pyrolysis is followed by a stagnation in silicon emission and surface temperature which are attributed to the formation of a thin layer of oxidation-resistant silicon oxycarbide. Moreover, the presence of the silicon oxycarbide layer significantly reduces the in-depth thermal response when compared to the baseline material. Eventually, the silicon oxycarbide layer decomposes via high-temperature reactions, which expose the underlying char layer to a highly reactive flow.

PICA-NuSil↗

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

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

97 MATHEMATICS AND COMPUTING↗

Multiscale and Multiphysics Modeling of Additive Manufacturing of Advanced Materials

The objective of this proposed project is to research and develop a prediction tool for advanced additive manufacturing (AAM) processes for advanced materials and develop experimental methods to provide fundamental properties and establish validation data. Aircraft structures and engines demand materials that are stronger, useable at much higher temperatures, provide less acoustic transmission, and enable more aeroelastic tailoring than those currently used. Significant improvements in properties can only be achieved by processing the materials under nonequilibrium conditions, such as AAM processes. AAM processes encompass a class of processes that use a focused heat source to create a melt pool on a substrate. Examples include Electron Beam Freeform Fabrication and Direct Metal Deposition. These types of additive processes enable fabrication of parts directly from CAD drawings. To achieve the desired material properties and geometries of the final structure, assessing the impact of process parameters and predicting optimized conditions with numerical modeling as an effective prediction tool is necessary. The targets for the processing are multiple and at different spatial scales, and the physical phenomena associated occur in multiphysics and multiscale. In this project, the research work has been developed to model AAM processes in a multiscale and multiphysics approach. A macroscale model was developed to investigate the residual stresses and distortion in AAM processes. A sequentially coupled, thermomechanical, finite element model was developed and validated experimentally. The results showed the temperature distribution, residual stress, and deformation within the formed deposits and substrates. A mesoscale model was developed to include heat transfer, phase change with mushy zone, incompressible free surface flow, solute redistribution, and surface tension. Because of excessive computing time needed, a parallel computing approach was also tested. In addition, after investigating various methods, a Smoothed Particle Hydrodynamics Model (SPH Model) was developed to model wire feeding process. Its computational efficiency and simple architecture makes it more robust and flexible than other models. More research on material properties may be needed to realistically model the AAM processes. A microscale model was developed to investigate heterogeneous nucleation, dendritic grain growth, epitaxial growth of columnar grains, columnar-to-equiaxed transition, grain transport in melt, and other properties. The orientations of the columnar grains were almost perpendicular to the laser motion's direction. Compared to the similar studies in the literature, the multiple grain morphology modeling result is in the same order of magnitude as optical morphologies in the experiment. Experimental work was conducted to validate different models. An infrared camera was incorporated as a process monitoring and validating tool to identify the solidus and mushy zones during deposition. The images were successfully processed to identify these regions. This research project has investigated multiscale and multiphysics of the complex AAM processes thus leading to advanced understanding of these processes. The project has also developed several modeling tools and experimental validation tools that will be very critical in the future of AAM process qualification and certification.

Liou, Frank↗

FY25 Theory and Simulation Performance Target: Development of an integrated modeling framework for fusion reactor design and assessment (Final Report)

This report documents the FY25 Theory and Simulation Performance Target (TSPT) of developing an integrated modeling framework for fusion reactor design and assessment (FREDA). Over Q1-Q4, new capabilities were developed across both plasma and engineering domains and demonstrated on an example representation of a Compact Advanced Tokamak with a Dual Cooled Lead Lithium blanket. This represents a first-of-a-kind demonstration of coupled core-to-wall-to-engineering for a reactor. Self-consistent CESOL workflows were applied to provide core, pedestal, and SOL prediction; new modules were developed for energetic particle stability (FAR3D) and transport (TGLF-EP) analysis; and boundary plasma modeling (SOLPS-ITER, BOUT++/Hermes-3) was expanded to evaluate wall and divertor heat fluxes and interface with engineering thermal analysis. A parameterized CAD tool, TRACER, was expanded to generate medium-fidelity divertor, blanket, and coil geometries; OpenFOAM and Diablo workflows were applied for first-wall and divertor thermal analyses with helium cooling; and reduced-order models were created for high-mass-flux divertor cooling. Magnet multiphysics capabilities were verified between Elmer, Diablo, and a new MFEM-based solver, and workflows enable stress, thermal, and neutron-fluence analysis of TF coils with neutronics-driven heating. Nuclear and blanket analysis workflows were demonstrated, including tritium breeding, transport, and CFD-informed thermo-mechanical assessment. Preliminary multi-fidelity uncertainty quantification workflows were applied to boundary modeling codes and shown to achieve variance reductions with fewer high-fidelity boundary simulations. Key findings highlight the challenges of resolving the ITEP gap to find suitable balance between wall and divertor loads, neutron heating, and practical limits of PFC cooling. Next step priorities are to develop automated workflows to check boundary code convergence and detachment, implement tighter physics-engineering CAD provenance tracking, and inclusion of plasma-material interface models for SLAG and tungsten cracking behavior. Collectively, these developments establish sophisticated capabilities for predictive, multi-fidelity, whole-device modeling that integrates plasma physics, materials, magnets, and nuclear engineering to guide pathways to viable Fusion Pilot Plant design points.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dynamic pulse propagation modelling for predictive femtosecond-laser-microbonding of transparent materials

A dynamic pulse propagation modeling for femtosecond laser bonding of Borofloat glass is presented. The temperature evolution and internal modifications are predicted by incorporating the nonlinear electron dynamics along with temperature dependent thermal properties. The modelling predicts the spatial and temporal distribution of absorption coefficient and plasma density that gives quantitative estimations of the heat affected zone and weld geometry. The impact of focusing condition on heat affected zone and weld geometry is investigated, which for the first time to our knowledge allows to numerically determine the desired relative position between the geometrical focus of a femtosecond-laser-pulse and the interface of the two substrates to be welded. The prediction of the modelling on the offset distance is applied to weld Borofloat glass plates having optical contact and can be applied to other dielectric solids.

Sahoo, Pankaj K. (ORCID:0000000209437319)↗

Full-Scale MSL Heatshield Material Response Using DSMC and CFD to Compute the Aerothermal Environments

During Mars atmospheric entry, the Mars Science Laboratory (MSL) was protected by a 4.5 meters diameter ablative heatshield assembled in 113 tiles [1]. The heatshield was made of NASA's flagship ablative material, the Phenolic Impregnated Carbon Ablator (PICA) [2]. Prior work [3] compared the traditional one-dimensional and three-dimensional material response models at different locations in the heatshield. It was observed that the flow was basically one-dimensional in the nose and flank regions, but three-dimensional flow effects were observed in the outer flank. Additionally, the effects of tiled versus monolithic heatshield models were also investigated. It was observed that the 3D tiled and 3D monolithic configurations yielded relative differences for in-depth material temperature up to 18% and 28%, respectively, when compared to the a 1D model.

Aerothermal↗