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A Data-Driven Method for Modeling Creep-Fatigue Stress- Strain Behavior Using Neural ODEs

In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.

creep-fatigue

Draft ASME Code Case to qualify L-PBF 316H material for Section III, Division 5 applications

This report documents the AMMT program’s development and submission of a draft ASME Code Case to qualify Laser Powder Bed Fusion (L PBF) Type 316H stainless steel for Section III, Divi-sion 5 Class A and SM high temperature nuclear applications. It summarizes the technical basis, the comprehensive high temperature mechanical test database assembled between 2023–2026, and the proposed code language and qualification framework submitted to ASME. The work was co-ordinated across multiple national laboratories and leverages prior ASME efforts to integrate additive manufacturing into the Boiler & Pressure Vessel Code. The body of the report describes the experimental database and analysis supporting the Code Case: tensile, creep, fatigue, creep fatigue, and thermal aging tests collected from multiple additive manufacturing sites, machine types, and powder lots, with material processed by a solution anneal heat treatment. The dataset — including both full size and subsized specimens and tests oriented parallel and perpendicular to build direction — shows limited tensile anisotropy, tensile properties comparable to wrought 316H, creep strength within the scatter of wrought material, but markedly reduced creep ductility above about 650 °C associated with rapid σ phase formation in L PBF microstructures. The draft Code Case itself prescribes a staged qualification model (manufacturing process qualification, component qualification, and per build witness testing), treats L PBF components as equivalent to Type 316 weld metal for design and inspection, and requires mechanical, chemical, and metallographic controls tied to ASTM/ISO 52946. Key acceptance criteria include tensile tests within a 90% prediction interval of the AMMT dataset, a creep fatigue screening test adapted from ASME Section III, Division 5, Subsection HB, HBB 2800 but with the cycle acceptance reduced to 100 for L PBF material, and double volumetric inspection of production components. The report concludes that the present data support treating L PBF 316H as analogous to conventional fusion weld metal for Division 5 design and inspection, while highlighting important caveats: the σ phase driven loss of creep ductility above ~650 °C, preliminary indications of enhanced creep fatigue sensitivity in some lots, and remaining gaps in long term aging and additional cyclic testing. Recommended next actions include completing outstanding cyclic and long duration creep/aging tests on the solution annealed condition, supporting inclusion of the 316H chemistry and heat treatment in ASTM/ISO 52946, and continuing engagement with ASME and NRC during balloting and review to enable industry adoption.

Messner, Mark C. (ORCID:0000000200404385)

Development of a Framework and Methodology for an Advanced Reactor Materials Environmental Effects Design Guide

Advanced non-light-water reactor components may operate at elevated temperature while experiencing cyclic loading, significant neutron irradiation, and exposure to reactor coolant. ASME Boiler and Pressure Vessel Code, Section III, Division 5, provides design rules for elevated-temperature service but does not include specific procedures to account for environmental effects on material properties. This report develops an initial framework and methodology for an Environmental Effects Design Guide (EEDG) focused on neutron irradiation; coolant-environment effects are reserved for future work. The proposed approach treats irradiation as a property-based overlay on the existing Division 5 design process, with two routes: a sparse-data route applying two reduction factors — FCR on creep-rupture strength and FF on fatigue life — for the creep-fatigue evaluations that typically control the design of advanced high-temperature reactor components, and a fuller framework developing the property-to-rule chain across the four Division 5 checks (primary load, strain limits and ratcheting, creep-fatigue, and buckling), together with swelling and weldments as scope items. Both routes are scoped by an in-pile qualification that restricts the use of post-irradiation-examination-derived properties in regimes where an in-pile mechanism could control the design outcome. Illustrative outputs derived on a compiled annealed Type 316 database — FCR ≈ 0.78–0.86 and FF ≈ 0.4 — demonstrate the calculation method within that specific dataset. The framework is an initial, testable design-rule concept; it identifies a practical path for preliminary design evaluations under sparse data and the material data and testing needed to develop the framework further.

Barua, Bipul (ORCID:0000000247184113)

Improving creep resistance of Al-0.27Zr-0.08Sn (wt%) via cold swaging while maintaining high electrical conductivity

This study investigates the effect of mechanical cold work (0, 50, and 90% cross-sectional area reduction via swaging) on the creep properties of cast aluminum alloys with high electrical conductivity including high-purity Al (HP-Al), Al-0.15Zr (Al-Zr), and Al-0.27Zr-0.08Sn (Al-Zr-Sn, wt%). The Al-Zr alloy is strengthened by Zr in solid solution while the Al-Zr-Sn alloy is additionally strengthened by Al3Zr nanoprecipitates (8 nm diameter). After 90% cold swaging, the alloys exhibit grains elongated along the swaging direction with their widths ranging between 8 and 152 μm perpendicular to the swaging direction. Creep testing at 200 °C shows that the minimum creep rate of all 90% swaged alloys shows high sensitivity to stress, which can be modeled via a threshold stress σth. Increasing swaging magnitude from 0 to 50 to 90% in Al-Zr-Sn improves the creep resistance without reducing electrical conductivity. The formation of subgrains, increased dislocation density, and columnar grain structure in swaged alloys all enhance creep resistance. HP-Al swaged to 90% exhibits much lower creep resistance (σth = 18 MPa) due to subgrain coarsening and the absence of precipitates compared to Al-Zr (σth = 40 MPa) and Al-Zr-Sn (σth = 40 MPa), which maintain stable subgrain structures and benefit from solid solution strengthening and Al3Zr nanoprecipitates, respectively. Although Al3Zr precipitates are known to stabilize the deformed microstructure by pinning grain-boundaries, this work demonstrates that Zr in solid solution alone can effectively stabilize the deformed microstructure resulting in enhanced creep resistance. This effect of Zr solute on stabilizing grain boundaries for creep performance was not previously well-defined in the literature. Despite similar creep performances of Al-Zr and Al-Zr-Sn, the latter shows 70% higher room-temperature microhardness and slightly improved electrical conductivity (56%IACS (International Annealed Copper Standard) vs. 57%IACS, respectively). This work provides new insights into creep mechanisms of cold-worked Al–Zr alloys that will guide the design of heat-resistant Al conductors for high-demand applications.

Coello ramirez, Ismael [Northwestern University,]

Softening the Gap between Wöhler and Paris – New Approaches for Fatigue Analysis –

Fatigue analysis tools can vary across industries. For example, automotive engineers often use the Wöhler (S-N) approach to design for safe-life, while aerospace engineers prioritize damage tolerance and inspection intervals, relying instead on crack growth models such as Paris’ law. Although both approaches may deal with the control of cracks in similar materials, their analysis tools and material characterizations are fundamentally distinct. This divide mirrors the classic split between stress-based strength analysis and linear elastic fracture mechanics. However, modern nonlinear models that incorporate material softening, such as cohesive laws, blur this boundary and capture fracture behaviors across scales. This presentation describes the CF23 fatigue model, which uses cohesive softening to link S-N crack initiation with crack propagation rates. CF23 spans the full fatigue spectrum, from initial propagation transients to steady-state growth and threshold conditions, offering a unified framework that bridges Wöhler and Paris-based methodologies. Example applications include fatigue crack propagation transients in adhesive interfaces and skin/stiffener separation.

cohesive elements

Fatigue Behavior of Laser Powder Bed Fused HAYNES 214: Effects of Different Surface Treatments

In this study, under NASA’s Rapid and Analysis Manufacturing Propulsion Technology (RAMPT) project, effects of different surface post-treatments on surface texture and fatigue behavior of L-PBF Alloy 214 were investigated. Various subtractive SPTs including abrasive flow machining (AFM), machining (M), shot peening (SP), vapormatt (VM), dry electropolishing (DE), chemical milling (CM), chemical-mechanical polishing (CMP), electro chemical (ECP) were applied to study the variations of the surface texture, microstructure and uniaxial fatigue behavior under fully reversed strain-controlled condition at four different strain amplitudes of 0.005, 0.004, 0.003, and 0.0025 mm/mm. The insights gained regarding the relationship between structural and mechanical properties for different SPTs can help establish guidelines for selecting the most effective process to enhance the performance of Laser Powder Bed Fusion (L-PBF) Alloy 214, especially for critical aerospace applications.

Post-Processing

Probing the fatigue enhancement in a thermally aged cast duplex stainless steel by in situ neutron diffraction

After long-term thermal aging at 400 °C for 3000 h and 10,000 h, a cast duplex stainless steel exhibits promoted fatigue performance, including enhanced three-stage cyclic hardening and prolonged fatigue life. Utilizing in situ neutron diffraction, the phase-specific stresses are resolved, and their evolutions over entire fatigue cycling reveal the underlying mechanisms of the fatigue enhancement. It is found that the ferrite phase bears a much higher stress than the austenite matrix under both as-received and aged conditions. The enhanced cyclic hardening in Stage I is attributed to the strengthening of both phases due to thermal aging, while the enhancement in Stage III results from the martensitic transformation induced strengthening. The fatigue life is prolonged thanks to the cyclic hardening and the delay of martensitic transformation in the austenite phase after thermal aging.

Yu, Dunji [ORNL] (ORCID:0000000189467851)

Predicting microstructurally sensitive fatigue‐crack path in WE43 magnesium using high‐fidelity numerical modeling and three‐dimensional experimental characterization

Abstract Microstructurally small fatigue‐crack growth in polycrystalline materials is highly three‐dimensional due to sensitivity to local microstructural features (e.g., grains). One requirement for modeling microstructurally sensitive crack propagation is establishing the criteria that govern crack evolution, including crack deflection. Here, a high‐fidelity finite‐element modeling framework is used to assess the performance and validity of various crack‐growth criteria, including slip‐based metrics (e.g., fatigue‐indicator parameters), as potential criteria for predicting three‐dimensional crack paths in polycrystalline materials. The modeling framework represents cracks as geometrically explicit discontinuities and involves voxel‐based remeshing, mesh‐gradation control, and a crystal‐plasticity constitutive model. The predictions are compared to experimental measurements of WE43 magnesium samples subject to fatigue loading, for which three‐dimensional grain structures and fatigue‐crack surfaces were measured post‐mortem using near‐field high‐energy x‐ray diffraction microscopy and x‐ray computed tomography. Findings from this work are expected to improve the predictive capabilities of simulations involving microstructurally small fatigue‐crack growth in polycrystalline materials.

Engineering

Influence of Powder Characteristics and Processing Methods on Creep Performance of Powder Metallurgy Hot Isostatic Pressed SS316

The U.S. nuclear energy expansion goals are driving the demand for manufacturing routes that can rapidly produce large, complex, near net shape components. Powder metallurgy hot isostatic pressing (PM HIP) is an advanced manufacturing technique that can be economically scaled-up, while alleviating the supply chain challenges that forging and casting face in terms of cost and lead time constraints. This makes PM-HIP a viable technology to aid and accelerate large-scale part manufacturing for nuclear applications. However, large-scale qualification and deployment of this technology require a thorough understanding of the influence of powder feedstock quality, powder handling history, hot isostatic pressing (HIP) parameters, and subsequent heat treatment on microstructural evolution and elevated temperature mechanical performance. The present work focusses on 316 austenitic stainless steel (SS316) which is most commonly used in high temperature environments for nuclear applications Results from this study show that PM HIPed SS316 meets ASME tensile requirements at room temperature and at elevated temperature. However, creep performance of PM-HIPed SS316 remains inferior to its wrought counterpart, demonstrating that tensile performance alone is not a reliable metric for long duration high temperature integrity. Further, this report delineates powder derived microstructural features that govern creep damage, with key evidences pointing to “microstructural inheritance” from gas atomized powder feedstocks. Commercial SS316 powders of varying chemical compositions and recycling histories were studies, and the results showed large differences in elemental segregation, oxide surface layers and secondary phase distributions. Multi-scale characterization revealed segregation of chromium, molybdenum, manganese and silicon at the boundaries and the precipitation of manganese-, silicon-, and molybdenum-oxides. During HIP consolidation, these surface oxides transform into decorated prior particle boundaries (PPBs) and grain boundary inclusions that persist through conventional post-HIP solution annealing treatment. The retained oxides in post-HIP microstructures were found to influence grain growth, precipitation behavior, and ultimately creep cavitation and fracture. Such post-HIP heat treatments are therefore limited by a complex trade-off between grain growth, and oxide coarsening which aggravate creep damage by acting as nucleation sites for cavities. The objective of this work is to establish an integrated processing–structure–property framework for PM-HIP 316 stainless steel by investigating the influence of powder feedstock characteristics in pre- and post-HIP processing as well as to understand the significance of post-HIP heat treatment on microstructural evolution and creep properties. The results from this report emphasize the significance of powder feedstock integrity in improving creep performance of PM-HIPed SS316, by highlight the effect of rapid solidification, elemental segregation, oxide formation and powder recycling on microstructural defect inheritance following HIP consolidation. Rather than considering HIP processing, solution annealing, and mechanical performance independently, this report treats powder production, HIP consolidation, post-HIP thermal processing, and creep deformation as interconnected stages within a continuous metallurgical process. The resulting framework will provide a scientific basis for developing feedstock engineering strategies capable of improving long-term reliability of PM-HIP stainless steels and accelerating their qualification for advanced nuclear applications.

Ajjarapu, Pavan [Oak Ridge National Laboratory (OR

Evaluation of Fatigue Damage Accumulation Functions for Delamination Initiation and Propagation

The present report follows on the cohesive fatigue damage model methodology proposed in NASA-TP-2018-219838. In that report, an empirical function describing the incremental damage due to cyclic loading was used to calculate fatigue damage within a cohesive formulation. The form of the function was developed such that, when integrated at a constant stress amplitude from no damage to failure, it produces a life versus load response that is consistent with an S-N diagram. Therefore, the parameters of the damage model could be obtained by fitting the model predictions to an S-N diagram. The finite element analyses performed demonstrate that the cohesive fatigue accumulation function provides a link between the S-N diagram that describes crack initiation, and the Paris law that characterizes the rate of crack propagation. However, when the model was proposed, it was not known whether the form of the damage accumulation function associated with a desired S-N diagram is unique and, if not, if the link between S-N and the Paris law is unique and independent of the fatigue function selected. In the effort described herein, several alternative forms of the damage function that reproduce the desired features of S-N diagrams were found and evaluated. The effects of each of these functions on the predicted parameters of the Paris law and the propagation threshold are discussed. The results indicate that the predicted exponent m of the Paris law is indeed independent of the damage accumulation function. However, different functions predict different values for the pre-factor C of the Paris law. Therefore, the proper damage accumulation function must be selected by comparison with experiments. One of the new damage accumulation functions proposed herein was found to be particularly useful for analysis because of the ease with which the model parameters can be determined with a minimal amount of experimental information. The effectiveness of the proposed methodology and damage function was demonstrated by conducting analyses of a double cantilever beam test, a mixed-mode bending test, and a three-point bending test of a skin/doubler specimen. The results indicate that the same set of model parameters can provide accurate predictions of the rate of fatigue crack propagation for a variety of material interfaces, mode mixities, load levels, and stress ratios.

DKIN/Stiffener Debonding

Fatigue Life of Flow-Formed Aluminum 2195 and 6061 Alloys

The successful design and fabrication of metallic cryotanks for commercial aviation applications require lightweight, durable materials capable of withstanding high pressures and cryogenic temperatures through tens of thousands of thermomechanical refueling cycles. Flow forming is an advanced manufacturing technique that offers high-rate production and scalability for fabricating integrally stiffened cylinders suitable for cryotank applications. This work establishes the durability of flow-formed aluminum alloys by characterizing their fatigue life performance under conditions that mimic cryotank refueling cycles. Residual stresses in flow-formed aluminum-lithium (Al-Li) 2195-T6 cylinders were assessed using the contour method and found to be minimal. Fatigue life testing was conducted on flow-formed Al-Li 2195-T6 at room temperature and cryogenic temperatures (-321°F [-196°C]), with wrought Al-Li 2195-T6 serving as a baseline for comparison. Results showed that flow-formed materials exhibited fatigue performance comparable to or better than wrought materials, with no statistically significant differences observed between different specimen orientations relative to processing directions. Fractography revealed reduced delaminations in the flow-formed Al-Li 2195 samples as compared to wrought, indicating potential improvement to the microstructure that could result in improved service properties. Texture analysis using electron backscattered diffraction (EBSD) indicated recrystallization during heat treatment, potentially contributing to reduced delamination susceptibility. These findings demonstrating flow-formed material durability coupled with the high manufacturing efficiency of flow forming, makes flow forming an attractive process to produce aircraft cryotanks.

EBF3

Influences of Introduced Yttrium Oxide Particles on Superalloy 718

Additive manufacturing has proven useful for introducing oxide particles into superalloys, to provide oxide dispersion strengthening (ODS) at high temperatures. This study screened how such an approach can influence microstructure and failure modes for superalloy 718. The objective of this study was to compare tensile and creep failure modes for additively manufactured superalloy 718 having introduced oxide particles. Fine yttrium-oxide (yttria) particles were introduced into 718 powder using two different powder mixing methods. Additive manufacturing by laser powder bed fusion was then used to prepare specimen blanks for each case, oriented parallel and transverse to the building direction. These were subsequently given consistent stress relief, hot isostatic pressurization, and final heat treatments, then subjected to tensile and creep tests at varied temperatures. Additively manufactured 718 without ODS (“no-ODS”) had nearly equiaxed grains at 50 μm in width. Roll-mixed ODS material had a bimodal grain size distribution, with fine grains at 9 μm and coarse grains at 66 μm in average width. The fine grains were elongated about 5x in the building direction. Acoustic-mixed ODS materials had grains at 10 μm in width that were elongated about 10x in the build direction. Compared to no-ODS, roll-mixed and acoustic mixed ODS materials did not show improved tensile strengths at room temperature, 760 °C, and 1093 °C. The tensile failure strains parallel to the building direction of roll-mixed ODS material were lowest in these tests. Flattened clumps of yttria had formed transverse to the building direction in roll-mixed material, which were easily cracked. Creep rupture response at 760 °C in the building direction was highest for acoustic-mixed material test. Creep tests at 1093 °C showed varied results, with low rupture lives associated with enhanced cavitation at grain boundaries and surface oxidation. Transverse to the building direction, all three materials had low failure strains in tests at 760 °C. The elongated grain boundaries failed readily in all transverse specimens tested at 760 °C and 1093 °C.

oxide dispersion strengthening

Preliminary Plan to Inform Testing of a Heat Exchanger Test Article

This report presents a preliminary plan to guide the qualification testing of advanced heat exchanger (HX) components for nuclear-to-industrial heat transfer applications. The objective is to establish a defensible, physics-based methodology that integrates computational modeling, targeted experimentation, and in-service inspection considerations to demonstrate component performance and reliability under representative reactor conditions. The analysis identifies Sodium-cooled Fast Reactor (SFR) and High-Temperature Gas-cooled Reactor (HTGR) systems as reference configurations in terms of temperature, pressure, and chemical environment. Within these operating envelopes, dominant degradation mechanisms— including creep–fatigue interaction, flow-induced vibration, corrosion, and diffusion-bond deterioration—were evaluated to define test requirements. A comprehensive computationalexperimental framework is proposed to support life prediction and qualification activities. The framework couples high-fidelity structural-mechanics, thermal-hydraulic, and fluid-structure interaction models with accelerated degradation testing to produce a traceable linkage between microstructural evolution, mechanical performance, and remaining useful life (RUL). The approach adheres to established Verification, Validation, and Uncertainty Quantification (VVUQ) standards (ASME V&V 10/20; NUREG-2152) and incorporates a digital-twin architecture for continuous model refinement through data assimilation. The plan further outlines testing methodologies, including pre-test analyses, test-loop design parameters, and sensor placement strategies that maximize information yield while maintaining mechanistic fidelity. Complementary sections describe in-service inspection (ISI), on-line monitoring (OLM), and structural-health-monitoring (SHM) techniques applicable to compact HX geometries typical of advanced reactors. Collectively, these activities establish the technical foundation for demonstrating 40-60-year equivalent service life of advanced heat exchangers in support of the U.S. Department of Energy’s Advanced Reactor and Integrated Energy Systems programs. The forthcoming phase will execute the defined pre-test analyses, initiate hardware fabrication, and implement the integrated testing campaign to validate the proposed qualification methodology.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Validation Data for Benchmarking Wire Arc Additive Manufacturing Process Simulations

Residual stresses cause geometric distortion and affect mechanical performance of additively manufactured structures, yet they are notoriously difficult to assess and predict. Distortion (warpage) can drive parts outside dimensional tolerance limits, leading to part rejection or rework. For parts that meet tolerance, locked-in residual stress fields can affect structural integrity during operation, particularly subcritical cracking by fatigue, creep, or corrosion. This work develops benchmark data for a common additive manufacturing process (Wire Arc Additive Manufacturing) that can be applied for calibration and validation of physical process models that predict residual stress fields. The work includes design of two different samples of differing geometry, detailed manufacturing records for a set of physical samples, and an extensive set of residual stress measurement data developed using two diverse techniques (the contour method and neutron diffraction). An initial application of the work is also reported, where a modeling challenge was issued to secure residual stress model predictions from two independent laboratories that were blind to residual stress measurement data. These initial blind residual stress predictions show significant discrepancies relative to the measurement data, illustrating the potential value of the underlying validation data. An open repository for this work, including the sample designs, manufacturing process records, and the residual stress data, is also provided for future application in non-blind validation efforts.

36 MATERIALS SCIENCE