Modeling Fatigue Crack Growth Using Symbolic Regression
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Keven Carlson↗
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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↗
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↗
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↗
Microgravity Effects on Standardized Cognitive Performance Measures
The purpose of this experiment, selected to fly on the International Microgravity Laboratory (IML-2) Spacelab mission, is to determine the effects of microgravity upon the cognitive skills which are critical to successful performance of many tasks on board the Space Shuttle. Six tests from the Unified Tri-service Cognitive Performance Assessment Battery (UTC-PAB) will be administered to the Mission Specialists to fulfill the goals of this experiment. These tests are based upon current theoretical models of human performance and the hypothesized effects of microgravity. The principle objective is the identification of the effects of microgravity upon specific information processing skills affecting performance from those of fatigue and shifts in work/rest cycles. Multiple measures of both short and long term fatigue will be obtained and used as a major independent variable for the analysis of these performance data. Scientific supporting studies will determine optimum practice and performance testing schedules for the astronauts. The same tests will be used post-flight to collect data on the recovery of any cognitive performance impairment compared with pre-flight, baseline levels.
Samuel G Schiflett↗
Medical Aspects of Gemini Extravehicular Activities
The medical aspects of Gemini extravehicular activities are principally concerned with the physiological responses to high workloads, high thermal stresses, and low fatigue tolerance. Analysis of physiological instrumentation data. from extravehicular flights and training operations contributed significantly to the understanding of extra-vehicular workloads and the means of controlling these workloads.
G Fred Kelly↗
Polymer Composite Material Screening for a Cryotank Application
Composite cryotanks will play a key role in enabling the next generation of efficient aircraft. Carbon fiber reinforced polymer (CFRP) composites have the benefits of reduced weight and potentially higher structural strength compared to traditional metallic fuel tanks. A material screening study was conducted to inform material selection for liquid hydrogen (LH2) fuel storage. Three composite materials were considered because of their aerospace grade toughness, strength, and existing data to compare against. These materials were a thermoplastic low-melt polyaryletherketone (LM-PAEK)/carbon fiber (CF), thermoset/CF, and hybrid thermoset/thermoplastic polyurethane (TPU) veil/CF composite. Mechanical screening tests included tension, compression, in-plane shear (IPS), and tensile-tensile fatigue (TTF). Each material was tested at both a baseline (no liquid nitrogen/LN2 cycling) and 100 LN2-cycled conditions to determine the knockdown factor, if any, of each material when exposed to environmental loading effects in a cryotank. Results show minimal effects of the LN2-cycling compared against baseline values. The three materials behaved similarly in tension; however, the thermoplastic/CF had the highest IPS toughness. The hybrid thermoset/TPU/CF composite had the lowest IPS strength, compressive strength, and toughness. LN2-cycling had minimal effects on tensile-tensile fatigue performance of the thermoplastic/CF material. Mechanical data was captured to guide material down selection for future commercially viable hydrogen aircraft design.
Composites↗
Polymer Composite Material Testing for a Cryotank Application
Composite cryotanks will play a key role in enabling the next generation of efficient aircraft. Carbon fiber reinforced polymer (CFRP) composites have the benefits of reduced weight and potentially higher structural strength compared to traditional metallic fuel tanks. A material screening study was conducted to inform material selection for liquid hydrogen (LH2) fuel storage. Three composite materials were considered because of their aerospace grade toughness, strength, and existing data to compare against. These materials were a thermoplastic low-melt polyaryletherketone (LM-PAEK)/carbon fiber (CF), thermoset/CF, and hybrid thermoset/thermoplastic polyurethane (TPU) veil/CF composite. Mechanical screening tests included tension, compression, in-plane shear (IPS), and tensile-tensile fatigue (TTF). Each material was tested at both a baseline (no liquid nitrogen/LN2 cycling) and 100 LN2-cycled conditions to determine the knockdown factor, if any, of each material when exposed to environmental loading effects in a cryotank. Results show minimal effects of the LN2-cycling compared against baseline values. The three materials behaved similarly in tension; however, the thermoplastic/CF had the highest IPS toughness. The hybrid thermoset/TPU/CF composite had the lowest IPS strength, compressive strength, and toughness. LN2-cycling had minimal effects on tensile-tensile fatigue performance of the thermoplastic/CF material. Mechanical data was captured to guide material down selection for future commercially viable hydrogen aircraft design. In its current state, there does not exist a consolidated, publicly available database for CFRP composite material performance data at cryogenic temperatures. The next step in this work is to test the thermoplastic and thermoset CFRP composites, as well as the neat resins, at LH2 relevant temperature (20 K) to capture this crucial material property data. These results are essential to inform cryotank design and modeling efforts. The process to start this next round of testing has begun. Planned mechanical tests include toughness (single-edge notched beam), tension (unidirectional and quasi-isotropic), thermal expansion, and thermal conductivity. Some tests will also be conducted at an intermediate temperature of 111 K relevant to liquid natural gas (LNG), another attractive fuel choice. The ultimate goal is to manufacture a sub-scale cryotank part that can pass relevant burst, fatigue, permeation, and thermal cycling tests. This work is a part of NASA’s Commercially viable Hydrogen Aircraft for Robust Growth in Efficiency (CHARGE) Project under the larger NASA Subsonic Vehicle Technologies and Tools (SVTT) Project.
composites↗
Structural Integrity and Durability of Reusable Space Propulsion Systems
A two-day conference on the structural integrity and durability of reusable space propulsion systems was held on June 4 and 5, 1985, at the NASA Lewis Research Center. Presentations were made by industry, university, and government researchers organized into four sessions: aerothermodynamic loads; structural dynamics, fatigue, fracture, and constitutive modeling; and instrumentation. The principal objectives of the conference were to disseminate research results to date and future plans in each of the four areas. This publication contains the extended abstracts and the visual material presented during the conference.
Stanley J Marsik↗
Thrust Chamber Thermal Barrier Coating Techniques
Methods for applying thermal barrier coatings to the hot-gas side wall of rocket thrust chambers in order to significantly reduce the heat transfer in high heat flux regions has been the focus of technology efforts for many years. A successful technique developed by NASA-Lewis that starts with the coating on a mandrel and then builds the thrust chamber around it by electroforming appropriate materials is described. This results in a smooth coating with exceptional adherence, as was demonstrated in hot fire rig tests. The low cycle fatigue life of chambers with coatings applied in this manner was increased dramatically compared to uncoated chambers.
Richard J Quentmeyer↗
New Trends in Coatings Developments for Turbine Blades: Materials Processing and Repair
Turbine engines for aeronautic applications now have to face strenuous requirements concerning not only operating performances but also reliability and repairability. This evolution of the specifications induces important consequences regarding the choice and the design of turbine blade protective coatings. This paper presents several key features concerning the deposition techniques and the real-life behavior of such coatings: (1) complex aluminides well suited to the protection against high temperature oxidation and hot corrosion of directionally solidified nickel-base superalloy turbine blades; (2) ceramic coatings used as thermal barriers - they have to exhibit both high resistance to thermomechanical fatigue and adequate smoothness; (3) processing techniques for thermal barriers, including plasma spraying, electron beam physical vapor deposition and plasma enhanced chemical vapor deposition; and (4) blades and coatings repair techniques.
S Alpérine↗
Mechanical Design and Operation of a Novel Lunar Environment Structural Test Rig (LESTR)
The Lunar Environment Structural Test Rig (LESTR) was developed to address a critical gap in mechanical property data for metal alloy wire materials under lunar-relevant conditions down to 40 K. Conventional aerospace material databases provide thermophysical properties for bulk metals over a wide temperature range, but validated mechanical and physical property data below 77 K, particularly for small-diameter wires, remain limited and are generally the exception rather than the rule. These conditions are essential for Artemis mission hardware such as shape memory alloy (SMA) rover tires. LESTR’s design requirements were to combine a high-stiffness electrodynamic load frame with closed- cycle cryogenic cooling, high-vacuum capability (10–6 torr), and noncontact optical strain measurement to enable tensile, four-point bend, and fatigue testing of wires or other materials and geometries at temperatures from 40 to 125 K. These considerable requirements were merged with the need to lower the barrier of testing for the end user as measured in terms of cost-per-test cycle, safety improvement, and reduction in upkeep costs associated with state-of-the-art solutions associated with cryomechanical material characterization. The system incorporates modular gripping and alignment fixtures; precision thermal management using cryocoolers and embedded heaters; and integrated instrumentation for displacement, load, temperature, and vacuum control. Calibration procedures establish correlations between tooling and specimen temperature, ensuring accurate thermal conditions across the design envelope unbound by cryofluid conditions in heritage immersion-based test systems. Initial validation tests using Inconel (Special Metals Corp.) wire demonstrated accurate ultimate strength and post-yield behavior. The load frame operation was also verified under representative service conditions, including thermal cycling and prolonged fatigue loading. By generating mechanical property data at ultralow temperatures, LESTR fills a critical gap in existing materials databases and provides a scalable platform for iterative alloy development and durability assessment for planetary hardware. This capability supports NASA’s long-term objectives for surface exploration by enabling design confidence for components operating in extreme cryogenic environments.
LESTR↗
Thermal Testing of High Performance: Thermal Barrier Coatings for Turbine Blades
A 350 micron thick 7 wt.% Y 2 O 3 -ZrO 2 (7YSZ) ceramic Thermal Barrier Coating (TBC) was manufactured in an argon atmosphere and with a strictly controlled substrate temperature on flat IN 600 samples and on IN 100 aircraft turbine blades. This new atmosphere and temperature controlled spraying (ATCS) allows the reduction of the residual stresses and an improvement in the microstructure and in the mechanical properties of the coating. The good performance of these new TBC's was assessed in thermal fatigue and in thermal shock tests carried out in air at 1100°C and at 1280°C respectively. The oxidation rate of the metal-ceramic interface was measured at 1100°C. Failure of the TBC's was induced only by the deterioration (like oxidation, cracking, ...) of the uncoated parts of the samples, as testing temperature was too severe for the base metals. Spalling was thereafter driven by compressive stresses near the aluminum oxide layer at the metal-ceramic interface. The results of these tests underline the good quality of the ceramic coating manufactured by the new ATCS technology.
L Bertamini↗
The Role of Tribology in the Development of an Oil-Free Turbocharger
Gas-turbine-based aeropropulsion engines are technologically mature. Thus, as with any mature technology, revolutionary approaches will be needed to achieve the significant performance gains that will keep the U.S. propulsion manufacturers well ahead of foreign competition. One such approach is the development of oil-free turbomachinery utilizing advanced foil air bearings, seals, and solid lubricants. By eliminating oil-lubricated bearings and seals and supporting an engine rotor on an air film, significant improvements can be realized. For example, the entire oil system including pipes, lines, filters, cooler, and tanks could be removed, thereby saving considerable weight. Since air has no thermal decomposition temperature, engine systems could operate without excessive cooling. Also, since air bearings have no diameter-rpm fatigue limits (D-N limits), engines could be designed to operate at much higher speeds and higher density, which would result in a smaller aeropropulsion package. Because of recent advances in compliant foil air bearings and high temperature solid lubricants, these technologies can be applied to oil-free turbomachinery. In an effort to develop these technologies and to demonstrate a project along the path to an oil-free gas turbine engine, NASA has undertaken the development of an oil-free turbocharger for a heavy duty diesel engine. This turbomachine can reach 120000 rpm at a bearing temperature of 540 C (1000 F) and, in comparison to oil-lubricated bearings, can increase efficiency by 10 to 15 percent because of reduced friction. In addition, because there are no oil lubricants, there are no seal-leakage-induced emissions.
Christopher Dellacorte↗
Microstructural Evolution and Mechanical Properties of LP-DED NASA HR-1 – A Hydrogen Resistant AM Superalloy for Space Propulsion Applications
The National Aeronautics and Space Administration (NASA) has actively pursued metal additive manufacturing (AM) technologies for spaceflight applications since the late 2000s. AM offers transformative advantages in cost, schedule, part consolidation, and design flexibility. Among the various AM techniques, laser powder directed energy deposition (LP-DED) is particularly well suited for fabricating complex geometries with fine feature resolution. In propulsion systems that utilize high-pressure gaseous hydrogen—such as liquid hydrogen rocket engines—hydrogen environment embrittlement (HEE) presents a serious threat to material performance 1,2 . Mechanical property degradation under these conditions can compromise component reliability, especially under cyclic loading. To address this challenge, NASA developed NASA HR-1 (Hydrogen Resistant-1) as a solution for liquid rocket engine components operating in hydrogen-rich environments, using the LP-DED technique 3-9 . A key component in a liquid rocket engine is the exhaust nozzle, which is typically regeneratively cooled (regen) due to the high heat flux. NASA HR-1 was specifically developed for regen nozzle applications using hydrogen as a propellant, providing resistance to HEE, a critical issue for many materials. The AM version of NASA HR-1 was also formulated to achieve high ultimate tensile strength, along with high yield strength and ductility in this environment 5,6 . Low-cycle fatigue (LCF) is another important consideration in nozzle design, as components are expected to endure multiple starts and missions. Additionally, the LP-DED version of the alloy exhibits improved thermal conductivity compared to its wrought counterpart, which benefits nozzle cooling. Overall, NASA HR-1 offers an excellent balance of high strength, HEE resistance, LCF performance, thermal conductivity, and ductility to meet the demanding requirements of channel-cooled nozzles and other components used with hydrogen and other propellants. The LP-DED–processed NASA HR-1 requires several post-processing heat treatment steps to achieve the material properties desirable for its intended application 6 . These steps include stress relief, homogenization, solution annealing, and aging for precipitation hardening. The stress relief treatment mitigates residual stresses accumulated during the LP-DED process and minimizes the potential for distortion. Homogenization, a common step for AM materials, reduces elemental segregation and promotes recrystallization to develop a more equiaxed grain structure. The subsequent solution annealing treatment heats the part to a solid solution temperature to dissolve the undesirable η-phase that forms during cooling from homogenization, followed by rapid cooling to retain an η-phase–free microstructure. Finally, aging promotes precipitation of the strengthening γ′ phase in the alloy. The integration of compositional design and optimized thermal processing enables high-quality LP-DED NASA HR-1 components with excellent microstructural and mechanical stability. Improved chemical and microstructure homogeneity enhances ductility and fatigue resistance—both critical for safe and reliable operation in high-pressure hydrogen environments. NASA has successfully fabricated and hot-fire tested multiple subscale and full-scale channel wall nozzles using LP-DED NASA HR-1 5,6, 9-14 . These efforts included process refinements to support thin-wall construction and various channel geometries. Throughout development, several key observations emerged. After homogenization, the as-built columnar grain structure transforms into a fully equiaxed microstructure. However, subsequent treatments—such as solution annealing and aging—result in changes that are more difficult to track. The grain structure remains largely unchanged, and the γ′ precipitates, typically 5–10 nm in diameter, are beyond the resolution of scanning electron microscopy (SEM). While transmission electron microscopy (TEM) can resolve these fine precipitates, TEM sample preparation is time-consuming and difficult for LP-DED material. As an alternative, differential scanning calorimetry (DSC) offers a useful, qualitative approach to monitor precipitate evolution throughout different stages of heat treatment. The overall goal is to improve the understanding of how heat treatment affects the microstructure and mechanical performance of LP-DED NASA HR-1. This paper presents heat treatment design considerations, microstructural characterization, mechanical testing – including tensile and LCF testing in both air and hydrogen environments.
Superalloy↗
In-Situ Scanning Electron Microscope Experiments for Microscale Mechanical Testing and Validated Modeling of Fiber Reinforced Thermoplastics
A novel, in-situ, scanning electron microscope (SEM) mechanical testing capability for materials at the microscale which provides experimental validation to a machine learning (ML) toolset for full-field validation of physics-based micromechanics models is being developed by researchers at NASA Glenn Research Center. These are enabling technologies for the integration of multiscale digital twins for materials into system level models which will result in the improved performance, material discovery, reduced production cost and time, rapid characterization, and prognostic structural health monitoring (SHM) for materials and structures for extreme environments in support of NASA space exploration missions. In order to bridge the material structure-to-system gap for digital twins, physics-based models must be experimentally validated at multiple length scales. Seminal microscale experiments, conducted at the Air Force Research Laboratory (AFRL), were limited to transverse compression of single-layer, unidirectional thermoset polymer matrix composite (PMC) micropillar specimens [1]. The early phases of the current project followed those initial results and setup to reproduce the compression testing of PMC material on the custom-built piezoelectric actuated micromechanical testing rig built by MicroTesting Solutions LLC. In this work, samples of thermoplastic PMC material were first machined into 3 mm cubes, and then further machining and final milling was done using a Focused Ion Beam (FIB). The initial experiment was done on a pillar roughly 20 µm x 20 µm x 40 µm tall. Additional pillars were milled with final sizes ranging from 20 µm x 20 µm x 40 µm tall to 40 µm x 40 µm x 65 µm tall. A speckle pattern for in-situ full-field measurements using Digital Image Correlation (DIC) was applied with platinum, which was coated on the surface, and then the FIB was used to mill away some of the coating to produce an irregular pattern of Pt on the pillar surface. The samples were loaded into the custom testing rig and placed into the SEM and loaded under compression until failure. Images were collected in the SEM during testing. Post-processing of the images was conducted using DIC to obtain full-field displacement and strain measurements elucidating the role of the matrix as well as fiber-fiber interaction at the microscale within the composite subjected to compression loading well into the non-linear regime of the material. Moreover, the evolution of fiber-matrix debonding and matrix cracking is observed in-situ at the microscale. This data, along with images segmented with a newly developed ML toolset [2], was used to create and validate physics-based micromechanics models. An image of the failed micropillar is shown in Figure 1. The techniques developed in the initial compression experiment was tailored to the validation needs of the models and expanded to include different sized samples as well as possibly tension and fatigue.
Laura Wilson↗