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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

Elastic-plastic models for multi-site damage

This paper presents recent developments in advanced analysis methods for the computation of stress site damage. The method of solution is based on the p-version of the finite element method. Its implementation was designed to permit extraction of linear stress intensity factors using a superconvergent extraction method (known as the contour integral method) and evaluation of the J-integral following an elastic-plastic analysis. Coarse meshes are adequate for obtaining accurate results supported by p-convergence data. The elastic-plastic analysis is based on the deformation theory of plasticity and the von Mises yield criterion. The model problem consists of an aluminum plate with six equally spaced holes and a crack emanating from each hole. The cracks are of different sizes. The panel is subjected to a remote tensile load. Experimental results are available for the panel. The plasticity analysis provided the same limit load as the experimentally determined load. The results of elastic-plastic analysis were compared with the results of linear elastic analysis in an effort to evaluate how plastic zone sizes influence the crack growth rates. The onset of net-section yielding was determined also. The results show that crack growth rate is accelerated by the presence of adjacent damage, and the critical crack size is shorter when the effects of plasticity are taken into consideration. This work also addresses the effects of alternative stress-strain laws: The elastic-ideally-plastic material model is compared against the Ramberg-Osgood model.

Actis, Ricardo L.

Thermal Cycling and Isothermal Deformation Response of Polycrystalline NiTi: Simulations vs. Experiment

A recent microstructure-based FEM model that couples crystal-based plasticity, the B2<-> MB190 phase transformation and anisotropic elasticity at the grain scale is calibrated to recent data for polycrystalline NiTi (49.9 at.% Ni). Inputs include anisotropic elastic properties, texture and differential scanning calorimetry data, as well as a subset of recent isothermal deformation and load-biased thermal cycling data. The model is assessed against additional experimental data. Several experimental trends are captured - in particular, the transformation strain during thermal cycling monotonically increases and reaches a peak with increasing bias stress. This is achieved, in part, by modifying the martensite hardening matrix proposed by Patoor et al. [Patoor E, Eberhardt A, Berveiller M. J Phys IV 1996;6:277]. Some experimental trends are underestimated - in particular, the ratcheting of macrostrain during thermal cycling. This may reflect a model limitation that transformation-plasticity coupling is captured on a coarse (grain) scale but not on a fine (martensitic plate) scale.

Phase Transformations

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

Summary of Research Report

Ten papers, published in various publications, on buckling, and the effects of imperfections on various structures are presented. These papers are: (1) Buckling mode localization in elastic plates due to misplacement in the stiffner location; (2) On vibrational imperfection sensitivity on Augusti's model structure in the vicinity of a non-linear static state; (3) Imperfection sensitivity due to elastic moduli in the Roorda Koiter frame; (4) Buckling mode localization in a multi-span periodic structure with a disorder in a single span; (5) Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling; (6) Derivation of multi-dimensional ellipsoidal convex model for experimental data; (7) Passive control of buckling deformation via Anderson localization phenomenon; (8)Effect of the thickness and initial im perfection on buckling on composite cylindrical shells: asymptotic analysis and numerical results by BOSOR4 and PANDA2; (9) Worst case estimation of homology design by convex analysis; (10) Buckling of structures with uncertain imperfections - Personal perspective.

Isaac Elishakoff

Influence of Processing Parameters on the Mechanical Properties of 3D Printed Borosilicate Particulate Reinforced Polymer Composites

Emerging composite materials are expanding the potential of additive manufacturing and enabling applications previously restricted by traditional manufacturing methods. The multi-phase nature of these composite materials combined with the complex in-ternal geometry of additively manufactured parts have enabled unique behavior, and potentially new applications. Additionally, these materials can be pyrolyzed to create dense metal, ceramic, and glass parts with geometries typically not achievable by tra-ditional processes. Additive manufacturing of borosilicate glass-based systems can open new applications in nuclear engineering, astronomy, and bone regrowth therapy. To elucidate the process-parameter relationship of borosilicate-polylactic acid (PLA) composites, mechanical testing was conducted and compared with a pure polylactic acid polymer baseline. Test specimens were fabricated by fused-filament fabrication with minimal post-processing. Yield strength, ultimate strength, and elastic modulus were calculated from stress-strain curves. Optical and scanning electron microscopy were conducted to observe the specimen microstructure before and after testing. The highest compressive yield strength for the composite was 28.22 MPa, and the highest compressive yield strength for PLA was 49.30 MPa. Print orientation was found to benefit the composite material but have a detrimental effect on the pure matrix material. An elastic modulus of 2.66 GPa was recorded for the borosilicate-PLA composite at 100% infill, 1 shell wall, and layer lines parallel to compression axis. Microscopy revealed that lower modulus composite specimens had the particulates re-distributed within the matrix. Tensile testing was done according to a polymer testing standard, which caused difficulties obtaining consistent fracture within the gauge length.

mechanical testing

Force-Strain Characteristics and Rupture-Load Capability of Viking-Type Suspension-Line Material Under Dynamic Loading Conditions

A series of tests has been conducted to investigate the elastic behavior of Viking-type suspension-line material under dynamic loading conditions. Results indicate that there is a decrease in both rupture-load capability and elongation at rupture as the test strain rate is increased. Preliminary examination of force-strain characteristics indicates that, on the average, the material exhibits some type of viscous effect which results in a greater force being produced, for a particular value of strain, under dynamic loading conditions than that produced under quasi-static loading conditions.

Langley Working Papers

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

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

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.

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

Radiation-Resistant Ti/BN Coatings: Insights From 171 Days Exposure to Space Radiation and Atomic Oxygen in Low Orbit

Atmospheric Plasma Spray (APS) and Vacuum Plasma Spray (VPS) techniques were used to develop Ti/2 vol.% hBN coatings, for extreme space environments and tested aboard the International Space Station as part of the MISSE-17 (Materials International Space Station Experiments) program. The coatings were exposed to atomic oxygen, space radiation, and low-orbit thermal cycling. VPS coatings showed a 56% increase in microhardness, a 26% rise in elastic modulus, minimal porosity and crack density changes compared to APS coatings. The change in mechanical properties is attributed to the formation of TiO, TiO₂ and TiN from nitrogen retention, alongside radiation-induced dislocations, which enhanced surface hardening. The oxidation of titanium led to the formation of TiO and TiO₂, while boron nitride was retained and underwent transmutation in VPS coatings. XPS and EDS analyses confirmed the enhanced space-environment resistance of VPS coatings, making them ideal for long-term spacecraft protection in lunar and Martian conditions.

Abhijith Kunneparambil Sukumaran

A SIMULINK Environment for Flight Dynamics and Control Analysis - Application to the DHC-2 'Beaver', Part 1. Implementation of a Model Library in SIMULINK

The design of advanced Automatic Aircraft Control Systems (AACS's) can be improved upon considerably if the designer can access all models and tools required for control system design and analysis through a graphical user-interface, from within one software environment. This MSc-thesis presents the first step in the development of such an environment, which is currently being done at the Section for Stability and Control of Delft University of Technology, Faculty of Aerospace Engineering. The environment is implemented within the commercially available software package MATLAB/SIMULINK. The report consists of two parts. Part I gives a detailed description of the AACS design environment. The heart of this environment is formed by the SIMULINK implementation of a nonlinear aircraft model in block-diagram format. The model has been worked out for the old laboratory aircraft of the Faculty, the De Havilland DHC-2 'Beaver', but due to its modular structure, it can easily be adapted for other aircraft. Part I also describes MATLAB programs which can be applied for finding steady-state trimmed-flight conditions and for linearization of the aircraft model, and it shows how the built-in simulation routines of SIMULINK have been used for open-loop analysis of the aircraft dynamics. Apart from the implementation of the models and tools, a thorough treatment of the theoretical backgrounds is presented. Part II of this report presents a part of an autopilot design process for the 'Beaver' aircraft, which clearly demonstrates the power and flexibility of the AACS design environment from part I. Evaluations of all longitudinal and lateral control laws by means of nonlinear simulations are treated in detail. The AACS design environment from part I proved to be a very useful tool for designing the control laws of the 'Beaver' autopilot within a very tight time-schedule. The autopilot design process itself will be used as a guideline for future AACS research at the Faculty of Aerospace Engineering. Flight tests of the 'Beaver' autopilot, done after evaluating the control laws in the SIMULINK package, proved to be quite successful. In the future, the AACS design package will evolve into a standardized, integrated design environment which can be applied to virtually any type of aircraft. The AACS design cycle will be shortened further by developing tools for automatically porting control laws from the MATLAB/SIMULINK environment to a piloted real-time flight simulator and the Flight Control Computers of the aircraft.

Aircraft Modelling

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

Development and Experimental Validation of a Path-Dependent Spin Forming Finite Element Model

Spin forming is an advanced manufacturing process widely used in the aerospace and defense sectors to produce lightweight, high-strength cylindrical components with tight dimensional tolerances. This study explores the applicability of the path-dependent Mechanical Threshold Stress (MTS) constitutive model by simulating the evolution of geometry, machining forces, and plastic deformation during the spin forming of a 10-mm thick 6061-O aluminum cylinder. While numerical modeling of spin forming has advanced substantially over the past decade, systematic verification and experimental validation of material models remain limited, particularly in predicting through-thickness process evolution. The MTS model, incorporating a Voce hardening rule, is employed for its ability to represent cyclic loading, rapidly varying temperature fields, and strain rates characteristic of spin forming. Numerical convergence analysis indicates discretization uncertainties between 0.3% and 9.2% for key quantities of interest. Experimental validation demonstrates that the MTS model, when implemented with a verified mesh, accurately reproduces both elastic and plastic behavior of 6061-O aluminum, predicting peak roller loads within 11–18% of measurements, geometric tolerances within 3%, and plastic strain distributions within 10% of experimental values. Collectively, these results establish a validated computational framework for predictive spin-forming simulations with quantified confidence, providing a foundation for extension to other alloys, geometries, and forming conditions.

Spin forming

Aerothermodynamic Analysis of a Flexible Thermal Protection System under Reentry Loads

The Carryall Block 1 reentry vehicle being developed by Outpost Space utilizes a strut supported semirigid deployable heatshield. This consists of a flexible thermal protection system, a heat-resistant fabric stack, stretched over actuated spars. The advantages of a deployable heatshield include reduced heat loading and earlier deceleration in the trajectory. However, the nature of the flexible thermal protection system necessitates considering the loaded shape of the heat shield. The flexible thermal protection system will deflect under reentry loads leading to areas of higher heating rates as well as a reduced axial coefficient as compared to the nominal shape. The Carryall Block 1 is analyzed using NASA’s FUN3D and DPLR CFD solvers with a deflected shape based on the catenary equations. The aerodynamic results are found to be within a percent for both solvers and both structured and unstructured mesh types. Fluid Structure Interaction (FSI) analysis is currently a work in progress, using file I/O to communicate between FUN3D and LS-DYNA, a commercial nonlinear structural solver. Challenges in deforming the geometry, mesh, and initial results are presented here.

thermal protection system

Nitrile/Buna N Material Failure Assessment for an O-Ring used on the Gaseous Hydrogen Flow Control Valve (FCV) of the Space Shuttle Main Engine

After the rollout of Space Shuttle Discovery in April 2005 in preparation for return-to-flight, there was a failure of the Orbiter (OV-103) helium signature leak test in the gaseous hydrogen (GH2) system. Leakage was attributed to the Flow Control Valve (FCV) in Main Engine 3. The FCV determined to be the source of the leak for OV-103 is designated as LV-58. The nitrile/Buna N rubber O-ring seal was removed from LV-58, and failure analysis indicated radial cracks providing leak paths in one quadrant. Cracks were eventually found in 6 of 9 FCV O-rings among the three Shuttle Orbiters, though none were as severe as those for LV-58, OV-103. Testing by EM10 at MSFC on all 9 FCV O- rings included: laser dimensional, Shore A hardness and properties from a dynamic mechanical analyzer (DMA) and an Instron tensile machine. The following test data was obtained on the cracked quadrant of the LV-58, OV-103 O-ring: (1) the estimated compression set was only 9.5%, compared to none for the rest of the O-ring; (2) Shore A hardness for the O.D. was higher by almost 4 durometer points than for the rest of the O-ring; and (3) DMA data showed that the storage/elastic modulus E was almost 25% lower than for the rest of the O-ring. Of the 8 FCV O-rings tested on an Instron, 4 yielded tensile strengths that were below the MIL spec requirement of 1350 psi-a likely influence of rubber cracking. Comparisons were made between values of modulus determined by DNA (elastic) and Instron (Young s). Each nitrile/Buna N O-ring used in the FCV conforms to the MIL-P-25732C specification. A number of such O-rings taken from shelf storage at MSFC and Kennedy Space Center (KSC) were used to generate a reference curve of DMA glass transition temperature (Tg) vs. shelf storage time ranging from 8 to 26 years. A similar reference curve of TGA onset temperature (of rubber weight loss) vs. shelf storage time was also generated. The DMA and TGA data for the used FCV O-rings were compared to the reference curves. Correlations were also made between the DMA modulus (at 22 C) and Shore A hardness for all 9 of the FCV O-rings used among the three Shuttle Orbiters. The radial cracking in the FCV O-rings was determined to be due to ozone attack, as nitrile/Buna N rubber is susceptible to such attack. Nitrile/Buna N material under MIL-P25732C should be used in a hydraulic fluid environment to help protect it from cracking. However, the FCV O-rings were used in an air only environment. The FCV design has as much as a 9-mil gap that allows the O.D. of the O-ring to be directly exposed to ozone, pressurized air and some elevated temperatures, accelerating the weathering process that leads to O-ring cracking. Space Shuttle flights will likely not continue past 2010. Therefore, Shuttle management decided to continue using the nitrile/Buna N material for the FCVs, but have each O-ring replaced after 3 years to minimize any chances for crack initiation.

Doug Wingard

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