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↗
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↗
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↗
Nonleaking battery terminals.
Three different terminals were designed for usage in a 40 ampere/hour silver zinc battery which has a 45% KOH by weight electrolyte in a plastic battery case. Life tests, including thermal cycling, electrical charge and discharge for up to three years duration, were conducted on these three different terminal designs. Tests for creep rate and tensile strength were conducted on the polyphenylene oxide plastic battery cases. Some cases were unused and others containing KOH electrolyte were placed on life tests. The design and testing of nonleaking battery terminals for use with a KOH electrolyte in a plastic case are considered.
Snider, W. E.↗
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↗
Nonleaking battery terminals
Three different terminals were designed for usage in a 40 ampere/hour silver zinc battery which has a 45 percent KOH by weight electrolyte in a plastic battery case. Life tests, including thermal cycling, electrical charge and discharge for up to three years duration, were conducted on these three different terminal designs. Tests for creep rate and tensile strength were conducted on the polyphenylene oxide (PPO) plastic battery cases. Some cases were unused and others containing KOH electrolyte were placed on life tests. The design and testing of nonleaking battery terminals for use with a potassium hydroxide (KOH) electrolyte in a plastic case are discussed.
Snider, W. E.↗
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↗
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↗