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Development, Characterization, and Validation of Elevated-Temperature Constitutive Models: Deformation and Damage

This report provides a brief review of experimentally observed hereditary and nonhereditary material behavior along with background information on standard as well as advanced internal state variable constitutive modeling at elevated temperature. A description of exploratory, characterization, and validation testing is presented along with a detailed outline of what constitutes “sufficient” data content (i.e., quality and quantity) for developing or enhancing, characterizing, and validating a particular sophisticated nonlinear time- and history-dependent (hereditary) class of constitutive models known as GVIPS (generalized viscoplasticity with potential structure). The tests described are necessary to reveal a material’s behavior in the reversible (or viscoelastic) and irreversible (or viscoplastic) regimes, for the identification of both deformation and damage model parameters. Results presented are primarily for metallic materials. In all cases, both uniaxial and multiaxial tests are described, and the linkage between the specific tests and the parameters within the model that can be characterized from the results of these tests are also discussed. Discussion is also provided relative to the role information management must play relative to material data collection, analysis, maintenance, and dissemination. The need for such an information system is particularly important as both analyst and designer move toward utilizations of sophisticated, nonlinear time- and history dependent (hereditary) constitutive models. Lastly, the concept of state space and its utility in understanding and establishing constitutive models is addressed throughout. The intent behind this document is to help both the modeler and experimentalist understand each other’s specific points of view and provide guidance for both model development and characterization. Emphasis has been placed on providing the mechanician with information regarding how tests are performed and what issues to be aware of when interpreting results. It is hoped that experimentalists will take away a new perspective on the types of information that modelers and analysts are looking for from them.

Constitutive Modeling

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry

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

Optimal Battery Charging for Damage Mitigation

Our control philosophy is to charge the NiH2 cell in such a way that the damage incurred during the charging period is minimized, thus extending its cycle life. This requires nonlinear dynamic model of NiH2 cell and a damage rate model. We must do this first. This control philosophy is generally considered damage mitigating control or life-extending control. This presentation covers how NiH2 cells function, electrode behavior, an essentialized model, damage mechanisms for NiH2 batteries, battery continuum damage modeling, and battery life models. The presentation includes graphs and a chart illustrating how charging a NiH2 battery with different voltages and currents affects damages the battery and affects its life. The presentation concludes with diagrams of control system architectures for tracking battery recharging.

Hartley, Tom T.

Development of a Digital Twin for Electrified Aircraft Powertrain Health Management

The augmentation of aircraft powertrains with electrical power systems is a promising path to reducing aircraft fuel consumption, emissions, and noise. Like conventional propulsion systems, electrified aircraft propulsion (EAP) systems will be subject to wear and tear throughout their lifecycles. System health management for EAP will enable efficient flight and maintenance scheduling, realizing economic, safety, and reliability benefits. A digital twin is, broadly, a dynamically updated virtual representation of an individual physical asset. This paper presents a Kalman filter-based approach for the development of a digital twin for an electrified powertrain and applies the approach to an EAP controls testbed. Measurements from nominal testbed operations are used to update a nonlinear model of the testbed. A Kalman filter is then created and used to identify and isolate anomalous testbed behavior based on measurements from off- nominal operations. Results show that the Kalman filter-based digital twin can monitor individual powertrain components’ health for degradation or other changes in performance. The applicability of the presented digital twin approach to any hybrid- or fully-electrified powertrain is emphasized.

Electrified Aircraft Propulsion

Satellite Material Contaminant Optical Properties

The Air Force Wright Research and Development Center and the Arnold Engineering Development Center are continuing a program for measuring optical effects of satellite material outgassing products on cryo-optic surfaces. Presented here are infrared (4000 to 700 cm -1 ) transmittance data for contaminant films condensed on a 77 K geranium window. From the transmittance data, the contaminant film refractive and absorptive indices (n, k) were derived using an analytical thin-film interference model with a nonlinear least-squares algorithm. To date 19 materials have been studied with the optical contents determined for 13 of those. The materials include adhesives, paints, composites, films, and lubricants. This program is continuing and properties for other materials will be available in the future.

B E Wood

Behavior of HfB2-SiC Materials in Simulated Re-Entry Environments

The objectives of this research are to: 1) Investigate the oxidation/ablation behavior of HfB2/SiC materials in simulated re-entry environments; 2) Use the arc jet test results to define appropriate use environments for these materials for use in vehicle design. The parameters to be investigated include: surface temperature, stagnation pressure, duration, number of cycles, and thermal stresses.

Don Ellerby

Effect of Thermomechanical Processing on the Microstructure, Properties, and Work Behavior of a Ti50.5 Ni29.5 Pt20 High-Temperature Shape Memory Alloy

TiNiPt shape memory alloys are particularly promising for use as solid state actuators in environments up to 300 °C, due to a reasonable balance of proper ties, including acceptable work output. However, one of the challenges to commercializing a viable high-temperature shape memory alloy (HTSMA) is to establish the appropriate primary and secondary processing techniques for fabrication of the material in a required product form such as rod and wire. Consequently, a Ti 50.5 Ni 29.5 Pt 20 alloy was processed using several techniques including single- pass high-temperature extrusion, multiple-pass high-temperature extrusion, and cold drawing to produce bar stock, thin rod, and fine wire, respectively. The effects of heat treatment on the hardness, grain size, room temperature tensile properties, and transformation temperatures of hot- and cold-worked material were examined. Basic tensile properties as a function of temperature and the strain-temperature response of the alloy under constant load, for the determination of work output, were also investigated for various forms of the Ti 50.5 Ni 29.5 Pt 20 alloy, including fine wire.

Grain Size

GVIPS Prediction of Cyclic Ratchetting Behavior and Cycles with Interrupted Relaxation Periods of TIMETAL 21S at 650 °C

The predictive performance of a multimechanism GVIPS model with saturating hardening function is assessed against a set of high temperature cyclic experiments under both strain-control and stress-control at varying rates of loading as well as several complex interrupted cyclic responses. The material specimens were composed of the titanium alloy, TIMETAL 21S, and tested at 650 °C, see Lissenden et al., 2007. The model did a very good job of predicting the variety of tests, particularly given the fact that only monotonic loading tests (tensile, creep, relaxation) and a single fully reversed cycle was used for characterization. It was particularly interesting that the model was capable of reasonably capturing the rate of accumulated strain during ratchetting under tensile mean stress. Given complex interrupted cyclic response, the model was able to both qualitatively and even quantitatively predict reasonably well both the cyclic and associated relaxation periods (in all quadrants of the stress-strain space) thus confirming the validity of the chosen functional forms for both hardening and thermal recovery. The quantitative inaccuracy is associated with the fact that the material specimens tested by Lissenden et al., 2007 was significantly “softer” than those tested by Castelli in Saleeb et al., 1994 which were used for characterization of the GVIPS model parameters.

Viscoplaticity

Erosion Behavior of Ti-hBN Multifunctional Coatings in A Custom-Made Planetary Test Rig at Extreme Lunar Temperatures

Spacecraft landings and takeoffs on the lunar surface, along with extreme temperature variations between day and night (-196 to 150° C), cause high-velocity dust impacts and erosion, resulting in the premature failure of structures. Ti/2 vol% hBN coatings were deposited using atmospheric (APS) and vacuum plasma spray (VPS) using cryo-milled powder feedstock to protect the structural components. The erosion performance of coatings at extreme lunar temperature regimes (-150 to 150° C) was evaluated in a custom-made planetary erosion test rig (PETR) at low (50 mph) and high impact velocities (250 mph). The mass loss of VPS coatings was reduced by 50% compared to the APS coatings and 40% compared to the Ti6Al4V substrate. The cryogenic temperature induces brittleness in the material, rendering it susceptible to extreme conditions of material loss. The particle impact-deformation behavior was captured using a high-speed camera to study the erosion mechanism. This analysis revealed chipping in substrates and brittle APS coatings, while particles rebounding and embedding were observed in VPS coatings. Energy calculations, aided by particle trajectory tracking from the high-speed camera, have conclusively shown that VPS coatings absorb 5–10% more energy than APS coatings during erosion tests. A modified erosion index was developed incorporating the fracture toughness and temperatures. New erosion models for brittle and ductile target materials are proposed for developing erosion-resistant material systems.

Abhijith Kunneparambil Sukumaran

Behaviors of Lunar Regolith Simulant Under Varying Gravitational Conditions

Understanding the behavior of regolith in varying gravity conditions is critical for space exploration and future missions. In this work, the gravity-driven hopper flow of lunar regolith simulant in different gravitational accelerations (terrestrial, lunar) is first observed experimentally. Numerical simulations (DEM) are then developed to understand the role which cohesive inter-particle forces play in such gravity-driven flow, using the theoretical framework of granular Bond number. Qualitative comparison between a terrestrial experiment and numerical simulation validated this framework. Following that, we numerically studied the dynamic behavior under varying gravitational conditions (from terrestrial to lunar to asteroid gravitational accelerations). We find that this behavior is extremely sensitive to the interplay of the gravity conditions and the attractive/cohesive forces among particles. The numerical and experimental results show that the complex interaction of these forces can drastically change the dynamics of the material producing effects relevant for variable gravity applications.

Soft Matter

Computation of Optimal Interplanetary Low-Thrust Trajectories With Bounded Thrust Magnitude By Means of the Generalized Newton-Raphson Method

The generalized Newton-Raphson method, an iterative procedure for solving nonlinear operator equations, has been extended in application to variational problems with bounded control variables. A minimum fuel interplanetary low thrust orbital transfer problem is worked out in detail to demonstrate the practical aspects of the algorithm as well as its computational effectiveness. The control variables are the thrust magnitude, limited from zero to some prescribed maximum value, and the thrust steering angle.

Computation

Lyotropic Liquid Crystalline Phase Behavior of Boron Nitride Nanotube Aqueous Dispersions

Boron nitride nanotubes (BNNTs) are gaining significant interest due to their outstanding mechanical and thermal properties, as well as their potential to serve as a model nanorod system. Processing BNNT liquid crystalline (LC) dispersions enables precise control over BNNT orientation in macroscopic assemblies, while their low absorption in the visible spectrum facilitates studying LCs at exceptionally high concentrations. Here, we investigate the behavior of BNNTs in aqueous solutions stabilized by the surfactant sodium deoxycholate (SDC), examining the effect of BNNT purity and BNNT−SDC concentrations on lyotropic LC formation. We disperse up to 15wt% BNNT in SDC solutions and use polarized light microscopy to detail the transition from an isotropic state to a biphasic regime, where isotropic and nematic domains coexist due to phase separation, to a single fully nematic phase. Cryogenic electron microscopy provides direct evidence of BNNT alignment within nematic domains. Our results show that enhanced depletion-induced attractions, driven by increased surfactant concentration, lower the threshold concentration of BNNT required to form nematic domains. In contrast, low surfactant concentrations relative to BNNT result in insufficiently coated nanotube surfaces, leading to poor dispersions and BNNT aggregation. Additionally, we fabricate well-aligned BNNT films from aqueous LC dispersions. Our findings advance the understanding of BNNT LCs, offering insight into controlling their orientation and highlighting their potential for high-performance materials.

Joe Khoury

Properties and Potential of Two (Ni,Pt)Ti Alloys for Use as High-Temperature Actuator Materials

The microstructure, transformation temperatures, basic tensile properties, shape memory behavior, and work output for two (Ni,Ti)Pt high-temperature shape memory alloys have been characterized. One was a Ni 30 Pt 20 Ti 50 alloy (referred to as 20Pt) with transformation temperatures above 230 °C and the other was a Ni 20 Pt 30 Ti 50 alloy (30Pt) with transformation temperatures above 530 °C. Both materials displayed shape memory behavior and were capable of 100% (no-load) strain recovery for strain levels up to their fracture limit (3-4%) when deformed at room temperature. For the 20Pt alloy, the tensile strength, modulus, and ductility dramatically increased when the material was tested just above the austenite finish (A f ) temperature. For the 30Pt alloy, a similar change in yield behavior at temperatures above the A f was not observed. In this case the strength of the austenite phase was at best comparable and generally much weaker than the martensite phase. A ductility minimum was also observed just below the A s temperature in this alloy. As a result of these differences in tensile behavior, the two alloys performed completely different when thermally cycled under constant load. The 20Pt alloy behaved similar to conventional binary NiTi alloys with work output due to the martensite-to-austenite transformation initially increasing with applied stress. The maximum work output measured in the 20Pt alloy was nearly 9 J/cm 3 and was limited by the tensile ductility of the material. In contrast, the martensite-to-austenite transformation in the 30Pt alloy was not capable of performing work against any bias load. The reason for this behavior was traced back to its basic mechanical properties, where the yield strength of the austenite phase was similar to or lower than that of the martensite phase, depending on temperature. Hence, the recovery or transformation strain for the 30Pt alloy under load was essentially zero, resulting in zero work output.

High-Temperature Shape Memory Alloy

Properties of a Ni19.5Pd30Ti50.5 High-Temperature Shape Memory Alloy in Tension and Compression

Potential applications involving high-temperature shape memory alloys have been growing in recent years. Even in those cases where promising new alloys have been identified, the knowledge base for such materials contains gaps crucial to their maturation and implementation in actuator and other applications. We begin to address this issue by characterizing the mechanical behavior of a Ni 19.5 Pd 30 Ti 50.5 high-temperature shape memory alloy in both uniaxial tension and compression at various temperatures. Differences in the isothermal uniaxial deformation behavior were most notable at test temperatures below the martensite finish temperature. The elastic modulus of the material was very dependent on strain level; therefore, dynamic Young’s Modulus was determined as a function of temperature by an impulse excitation technique. More importantly, the performance of a thermally activated actuator material is dependent on the work output of the alloy. Consequently, the strain-temperature response of the Ni 19.5 Pd 30 Ti 50.5 alloy under various loads was determined in both tension and compression and the specific work output calculated and compared in both loading conditions. It was found that the transformation strain and thus, the specific work output were similar regardless of the loading condition. Also, in both tension and compression, the strain-temperature loops determined under constant load conditions did not close due to the fact that the transformation strain during cooling was always larger than the transformation strain during heating. This was apparently the result of permanent plastic deformation of the martensite phase with each cycle. Consequently, before this alloy can be used under cyclic actuation conditions, modification of the microstructure or composition would be required to increase the resistance of the alloy to plastic deformation by slip.

High-Temperature Shape Memory Alloy

Thermal expansion behavior of LDEF metal matrix composites

The effects of the space environment on the thermal expansion stability of metal matrix composites (graphite/Al and graphite/Mg) will be presented. A sample from each category of metal matrix composites mounted on the leading and trailing edge was chosen for analysis of the temperature-time-thermal strain histories. Typical thermal expansion curves over the same range of temperature were selected at the beginning, mid, and end of the recording duration. The thermal expansion of selected post-flight LDEF samples were measured over the same range of temperature in the laboratory using a Michelson laser interferometer. The thermal strains were monitored concurrently with a laser interferometer and a mounted strain gage.

T. D. Le

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

Analysis of Surface and Bulk Behavior in Ni-Pd Alloys

The most salient features of the surface structure and bulk behavior of Ni-Pd alloys have been studied using the BFS method for alloys. Large-scale atomistic simulations were performed to investigate surface segregation profiles as a function of temperature, crystal face, and composition. Pd enrichment of the first layer was observed in (111) and (100) surfaces, and enrichment of the top two layers occurred for (110) surfaces. In all cases, the segregation profile shows alternate planes enriched and depleted in Pd. In addition, the phase structure of bulk Ni-Pd alloys as a function of temperature and composition was studied. A weak ordering tendency was observed at low temperatures, which helps explain the compositional oscillations in the segregation profiles. Finally, based on atom-by-atom static energy calculations, a comprehensive explanation for the observed surface and bulk features will be presented in terms of competing chemical and strain energy effects.

Ordering