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At least 343 records · Page 19

Strategies for simultaneous strengthening and toughening via nanoscopic intracrystalline defects in a biogenic ceramic

While many organisms synthesize robust skeletal composites consisting of spatially discrete organic and mineral (ceramic) phases, the intrinsic mechanical properties of the mineral phases are poorly understood. Using the shell of the marine bivalve Atrina rigida as a model system, and through a combination of multiscale structural and mechanical characterization in conjunction with theoretical and computational modeling, we uncover the underlying mechanical roles of a ubiquitous structural motif in biogenic calcite, their nanoscopic intracrystalline defects. These nanoscopic defects not only suppress the soft yielding of pure calcite through the classical precipitation strengthening mechanism, but also enhance energy dissipation through controlled nano- and micro-fracture, where the defects’ size, geometry, orientation, and distribution facilitate and guide crack initialization and propagation. These nano- and micro-scale cracks are further confined by larger scale intercrystalline organic interfaces, enabling further improved damage tolerance.

36 MATERIALS SCIENCE↗

Sub-pilot-scale Production of High-Value Products from U.S. Coals

Investigators from the University of Utah, University of Wyoming and Marshall University pursued a program to study the conversion of raw coal to high-value products of carbon fiber and silicon carbide. Team members also developed an initial framework for a data portal that can incorporate laboratory data on coal processing and product quality, and also work with tools for machine learning for data analysis, data visualization and economic assessment. Experimental R&D efforts focused on the conversion of raw coal to coal tar and other byproducts, and the resulting tar intermediates were upgraded to form anisotropic and isotropic pitch materials. These pitch materials were produced from coal using both thermal (pyrolysis) and chemical (mild solvolysis liquefaction) decomposition of raw coal. Four different coals were studied: Utah bituminous coal (Sufco), Wyoming PRB coal (Black Thunder), Illinois bituminous coal (Illinois #6), and West Virginia bituminous coal (Flying Eagle). Both metallurgical-grade coking coals and lower-grade steam coals were investigated, and controlled secondary gas-phase reactions were used during a two-stage pyrolysis process to induce cracking and condensation reactions among the pyrolytic tar species. This approach successfully improved the performance of the lower grade coals for yielding pitch materials, with properties more consistent with a commercial-grade pitch that had previously demonstrated success for quality carbon fiber production. The use of waste plastic materials was also studied, to help improve physical and chemical characteristics of the intermediate tars and final pitch product; in particular, for lowering the pitch softening point to an acceptable level for melt spinning carbon fiber. Mild solvolysis liquefaction was also used as a method for producing pitch for carbon fiber production. As expected, significantly higher pitch yields were obtained using this approach, and waste plastic materials were also successfully used to reduce pitch softening point to an acceptable level. The plastic materials were also utilized to create a solvent for the mild solvolysis process, and this plastic-derived solvent was shown to provide results consistent with more expensive commercial chemical solvents, and could thus avoid the need for costly recovery and recycle of a liquefaction solvent. Additional experimental R&D focused on the production of silicon carbide (β-SiC) from the residual char byproduct from pitch production, and also on the production of carbon fiber from the anisotropic pitch. SiC was successfully synthesized using a mixture of residual char and sandstone at a ratio of 1:1. Reaction temperature and residence time were optimized and yielded a product purity of 81%. For carbon fiber production, the most successful pitch samples were obtained from the mild solvolysis liquefaction approach, combined with the use of a plastic (HDPE)-derived solvent. Fiber properties improved over time as laboratory fiber production methodologies improved, and final yields of carbon fiber were obtained with a diameter of 12.14 ± 1.10 um, Modulus of 173.73 ± 15.25 GPa, and Tensile Strength of 1.04 ± 0.10 GPa. A proof-of-concept Modern Community Research Data Portal (MCRDP) was developed and deployed for coal and coal-derived pitch characterization, with the full support of (i) remote web-based access, (ii) distributed analysis, (iii) interactive visualization and exploration, (iv) shared and long-term data access, (v) advanced query capabilities and (vi) real-time collaboration. The Coal to Products Data Portal “coaltoproducts.org” provides researchers with space to store and share data within a project, tools for analyzing and understanding data for scientific investigation, and the ability to publish data to the broader community for reproducibility. The portal leverages the Material Commons 2.0 (MC) platform developed by the Center for PRedictive Integrated Structural Materials Science (PRISMS) of the University of Michigan, to achieve long-term longevity of data collections and, more importantly, collaborative science. A number of data visualization tools were also assessed and implemented for interrogating the experimental and modeling data. The machine learning portion of this project analyzed datasets from two different coal conversion processes performed on a diverse set of coal samples from both the coal pyrolysis experiments and the solvent liquefaction experiments. The work was initiated by exploring standard regression models on the pyrolysis data, aiming to understand the impact of sample characteristics and processing conditions on key product metrics. Over the course of the project, the focus expanded to include a variety of machine learning tools, delving into both supervised and unsupervised learning methods. Models tested on the pyrolysis data included linear, ridge, lasso, elastic-net, Gaussian process, random forest regression, and AutoSklearn, and the approach was continually refined to enhance predictive accuracy and model interpretability. Similar techniques were applied to the liquefaction data with an additional focus on feature engineering. Along with mesophase content, additional outputs of interest were the pitch yield, softening point, and QI content. Insights derived from these analyses are crucial in determining the factors influencing the quality and yield of coal-derived products. As the work progressed, the research evolved from foundational model comparisons to analyses of random forests, decision paths, and feature importance scores. A thorough market analysis was performed to examine the prospects of coal-based carbon fibers. The best opportunities for coal come from its lower and more stable price relative to petroleum, particularly for subbituminous coals, which is the primary advantage that a coal refinery may have over a petroleum refinery. Before a commercial CTP production facility can be modeled, however, several things need to be understood regarding the nature of the would-be coal refinery. These include the technology to be deployed, the size of facility, the volume(s) of co-product(s), and the waste and emissions profile of the plant. The volume of co-products and waste may be substantial and will require separate market analysis to ensure viability. In the near-term, the importance of coal tar pitch, in the form of carbon pitch, to the aluminum and steel industries is likely to overshadow the alternative use of this material as an input for carbon fiber. The importance of steel and aluminum in building materials, and the need for carbon materials in their manufacturing, will ensure that demand for these products remains for the long run. In addition, carbon fiber may also be the best substitute for steel and aluminum well into the future. While society will eventually be able to shift production of much of its electricity needs to renewables, it will not be able to shift away from fossil fuels for production of high-strength construction and vehicular materials. Demand for carbon fiber is expected to increase quickly, but the volume of carbon fiber and the amount of coal that would be needed to produce even a sizeable share of this market may still be relatively small compared to current coal production. Thus, other coal-based products like graphene, graphite, carbon foams, resins, and carbon-based building products will play important roles in sustaining coal production as coal-fired power generation continues to decline.

01 COAL, LIGNITE, AND PEAT↗

Investigation of some problems in developing standards for precracked Charpy slow bend tests

The reported investigation was undertaken in connection with an attempt to develop procedures which would be useful in standardizing a test method for the precracked Charpy slow bend specimen. A number of alloys was studied for which valid plane-strain fracture toughness values have been established. The investigation shows that useful relations between precracked Charpy slow bend results and crack size factors can be obtained under some circumstances. However, it is not yet known what factors control these circumstances.

Succop, G.↗

Quantitative Assessment of Fatigue Damage Accumulation in Wavy Slip Metals from Acoustic Harmonic Generation

A comprehensive, analytical treatment is presented of the microelastic-plastic nonlinearities resulting from the interaction of a stress perturbation with dislocation substructures (veins and persistent slip bands) and cracks that evolve during high-cycle fatigue of wavy slip metals. The nonlinear interaction is quantified by a material (acoustic) nonlinearity parameter beta extracted from acoustic harmonic generation measurements. The contribution to beta from the substructures is obtained from the analysis of Cantrell [Cantrell, J. H., 2004, Proc. R. Soc. London A, 460, 757]. The contribution to beta from cracks is obtained by applying the Paris law for crack propagation to the Nazarov-Sutin crack nonlinearity equation [Nazarov, V. E., and Sutin, A. M., 1997, J. Acoust. Soc. Am. 102, 3349]. The nonlinearity parameter resulting from the two contributions is predicted to increase monotonically by hundreds of percent during fatigue from the virgin state to fracture. The increase in beta during the first 80-90 percent of fatigue life is dominated by the evolution of dislocation substructures, while the last 10-20 percent is dominated by crack growth. The model is applied to the fatigue of aluminium alloy 2024-T4 in stress-controlled loading at 276MPa for which experimental data are reported. The agreement between theory and experiment is excellent.

Cantrell, John H.↗

Fracture behavior of large-scale thin-sheet aluminum alloy

A series of fracture tests on large-scale, pre-cracked, aluminum alloy panels is being carried out to examine and to characterize the process by which cracks propagate and link up in this material. Extended grips and test fixtures were specially designed to enable the panel specimens to be loaded in tension, in a 1780-kN-capacity universal testing machine. Twelve panel specimens, each consisting of a single sheet of bare 2024-T3 aluminum alloy, 3988 mm high, 2286 mm wide, and 1.016 mm thick are being fabricated with simulated through-cracks oriented horizontally at mid-height. Using existing information, a test matrix has been set up that explores regions of failure that are controlled by fracture mechanics, with additional tests near the boundary between plastic collapse and fracture. In addition, a variety of multiple site damage (MSD) configurations have been included to distinguish between various proposed linkage mechanisms. All tests but one use anti-buckling guides. At this writing seven specimens have been tested. Three were fabricated with a single central crack, three others had multiple cracks on each side of the central crack, and one had a single crack but no anti-buckling guides. Each fracture event was recorded on film, video, computer, magnetic tape, and occasionally optical microscopy. The visual showed the crack tip with a load meter in the field of view, using motion picture film for one tip and SVHS video tape for the other. The computer recorded the output of the testing machine load cell, the stroke, and twelve strain gages at 1.5 second intervals. A wideband FM magnetic tape recorder was used to record data from the same sources. The data were analyzed by two different procedures: (1) the plastic zone model based on the residual strength diagram; and (2) the R-curve. The first three tests were used to determine the basic material properties, and these results were then used in the analysis of the two subsequent tests with MSD cracks. There is good agreement between measured values and results obtained from the model.

Dewit, Roland↗

Fracture Control for Additively Manufactured Spacecraft Structures

This paper describes how the intent of current NASA fracture control requirements may be applied to “fracture critical” additively manufactured spacecraft hardware. Fracture control is a multi-discipline design and certification methodology that is applied in order to mitigate catastrophic failure of structures resulting from growth of an undetected crack-like defect. The methodology is defined in existing NASA standards and is required on all human-rated space structures. As legacy spacecraft structures have been built using primarily metallic and composite materials manufactured using well established methods, guidance for application of fracture control to parts composed of these material types has been established and is documented in several NASA requirements. Additive manufactured structures offer advantages in design flexibility and manufacturing efficiency and as a result are expected to continue to be used more and more in the future. Recently, relevant guidance has been published by NASA to define materials and processes requirements for certain additive manufactured hardware, but procedures for fracture control are not addressed yet in any requirements or guidance document. While use of additive manufactured parts in non-critical scenarios may be of relatively low concern in current structural certification processes, there is a need for new fracture control guidance in order to use and certify additively manufacture hardware that is “fracture critical” where failure of the part may result in loss of life or loss of vehicle. Assurance of damage tolerance, i.e., that as-built flaws in a given part either do not exist or will not grow to become catastrophic, is of particular interest to the fracture control community. This poses a challenge due to the fact that damage tolerance behavior is not well understood in additive manufactured parts compared to legacy material types and manufacturing techniques. The discussion contained herein is necessary at this time as new guidance in this area should be founded collaboratively by the technical community at large. Different hardware types (e.g., pressure vessel, structural member) are described to highlight specific challenges and solutions for each. The discussion concludes with considering specific disciplines within fracture control (non-destructive evaluation, materials & processes, fracture mechanics, and structural certification) in a proposed extension of existing fracture control requirements to additive manufactured parts.

McElroy, Mark↗

Fracture Control for Additive Manufactured Spacecraft Structures

This paper describes how the intent of current NASA fracture control requirements may be applied to “fracture critical” additively manufactured spacecraft hardware. Fracture control is a multi-discipline design and certification methodology that is applied in order to mitigate catastrophic failure of structures resulting from growth of an undetected crack-like defect. The methodology is defined in existing NASA standards and is required on all human-rated space structures. As legacy spacecraft structures have been built using primarily metallic and composite materials manufactured using well established methods, guidance for application of fracture control to parts composed of these material types has been established and is documented in several NASA requirements. Additive manufactured structures offer advantages in design flexibility and manufacturing efficiency and as a result are expected to continue to be used more and more in the future. Recently, relevant guidance has been published by NASA to define materials and processes requirements for certain additive manufactured hardware, but procedures for fracture control are not addressed yet in any requirements or guidance document. While use of additive manufactured parts in non-critical scenarios may be of relatively low concern in current structural certification processes, there is a need for new fracture control guidance in order to use and certify additively manufacture hardware that is “fracture critical” where failure of the part may result in loss of life or loss of vehicle. Assurance of damage tolerance, i.e., that as-built flaws in a given part either do not exist or will not grow to become catastrophic, is of particular interest to the fracture control community. This poses a challenge due to the fact that damage tolerance behavior is not well understood in additive manufactured parts compared to legacy material types and manufacturing techniques. The discussion contained herein is necessary at this time as new guidance in this area should be founded collaboratively by the technical community at large. Different hardware types (e.g., pressure vessel, structural member) are described to highlight specific challenges and solutions for each. The discussion concludes with considering specific disciplines within fracture control (non-destructive evaluation, materials & processes, fracture mechanics, and structural certification) in a proposed extension of existing fracture control requirements to additive manufactured parts.

McElroy, Mark↗

Crack Instability Predictions Using a Multi-Term Approach

Present crack instability analysis for fracture critical flight hardware is normally performed using a single parameter, K(sub C), fracture toughness value obtained from standard ASTM 2D geometry test specimens made from the appropriate material. These specimens do not sufficiently match the boundary conditions and the elastic‐plastic constraint characteristics of the hardware component, and also, the crack instability of most commonly used aircraft and aerospace structural materials have some amount of stable crack growth before fracture which makes the normal use of a K(sub C) single parameter toughness value highly approximate. In the past, extensive studies have been conducted to improve the single parameter (K or J controlled) approaches by introducing parameters accounting for the geometry or in‐plane constraint effects. Using 'J‐integral' and 'A' parameter as a measure of constraint is one of the most accurate elastic‐plastic crack solutions currently available. In this work the feasibility of the J‐A approach for prediction of the crack instability was investigated first by ignoring the effects of stable crack growth i.e. using a critical J and A and second by considering the effects of stable crack growth using the corrected J‐delta a using the 'A' parameter. A broad range of initial crack lengths and a wide range of specimen geometries including C(T), M(T), ESE(T), SE(T), Double Edge Crack (DEC), Three‐Hole‐Tension (THT) and NC (crack from a notch) manufactured from Al7075 were studied. Improvements in crack instability predictions were observed compared to the other methods available in the literature.

Zanganeh, Mohammad↗

Fracture Control for Additive Manufactured Spacecraft Structures

Final Paper is attached. This paper discusses how the intent of current NASA fracture control requirements may be applied to "fracture critical" additive manufactured spacecraft hardware. Fracture control is a multi-discipline design and certification methodology that is applied in order to mitigate catastrophic failure of structures resulting from growth of an undetected crack-like defect. The methodology is defined in existing spacecraft standards and is required by NASA on all human-rated space structures. Recently, standards have been published by NASA to define materials and processes requirements for certain metallic additive manufactured hardware, but procedures for fracture control implementation on additive manufactured parts are not yet addressed in detail in any standard or guidance document.The discussion contained herein is necessary at this time as new guidance in this area should be founded collaboratively by the technical community at large including industry, academia, and government. Three Fracture Control Certification Methods are proposed for discussion. Additionally, a concept for "Design for AM fracture control" is introduced. The goals of this paper are to further expose the need for maturing additive manufacturing fracture control guidance in the spacecraft industry and to generate discussion on what this guidance should consist of.

McElroy, Mark↗

Implementation on a nonlinear concrete cracking algorithm in NASTRAN

A computer code for the analysis of reinforced concrete structures was developed using NASTRAN as a basis. Nonlinear iteration procedures were developed for obtaining solutions with a wide variety of loading sequences. A direct access file system was used to save results at each load step to restart within the solution module for further analysis. A multi-nested looping capability was implemented to control the iterations and change the loads. The basis for the analysis is a set of mutli-layer plate elements which allow local definition of materials and cracking properties.

Herting, D. N.↗

Gearbox bearing crack growth prognostics and uncertainty quantification with physics-informed machine learning

This paper introduces the extreme theory of functional connections (X-TFC), a physics-informed machine learning algorithm, and tailors it to estimate the remaining useful life (RUL) of wind turbine gearbox bearings experiencing fatigue crack growth. Unlike purely data-driven methods, X-TFC embeds a physics model, based on Head's theory in this work, into its training objective. The core of X-TFC is a random-projection single-layer neural network trained via an extreme learning machine, which requires only limited damage progression data and solves for output weights with a least-squares optimization algorithm. A composite loss function balances the network's fit to observed degradation data against the residuals of the governing crack growth differential equation, ensuring the learned damage trajectory remains physically plausible. When applied to a vibration-based health-index (HI) dataset measured during the growth of a crack on the inner ring of a high-speed bearing in a wind turbine gearbox (Bechhoefer and Dubé, 2020), X-TFC achieves near-zero prediction bias. Even when trained on only the first 10 %–20 % of the damage progression data, with sufficient physics weighting its predictions remain monotonic and smooth, delivering high prognosability and trendability. To quantify the epistemic uncertainty, we employ a Monte Carlo ensemble of independently initialized X-TFC models trained on noise-perturbed data, which yields confidence intervals around each RUL estimate and captures both model-parameter and epistemic uncertainty. In addition to a vibration-based HI, we demonstrate that the proposed framework can be directly applied to a supervisory control and data acquisition (SCADA) data-based HI (Eftekhari Milani et al., 2026) measured during similar wind turbine gearbox bearing crack faults, preserving its accuracy and interpretability. This extension shows the versatility of our approach, which is applicable to bearings of multiple gearbox manufacturers, models, and ratings using only SCADA data. By integrating domain knowledge with machine learning, X-TFC offers a rapid, reliable tool for crack prognostics. Its adaptability to other bearing failure modes, such as pitch bearing ring cracks, positions X-TFC as a powerful enabler of data-driven, physics-informed asset management in the wind energy sector and beyond.

17 WIND ENERGY↗

RuKY Catalyst‐Packed Permeation Membrane for Quantitative Ammonia and d3‐Ammonia Dehydrogenation to Ultrapure Hydrogen

Ammonia is a promising carbon-free hydrogen carrier, but incomplete ammonia dehydrogenation (cracking) generates atmospheric emissions of NO x , a potent greenhouse gas. Additionally, incomplete cracking of ammonia leads to regulatory challenges in nuclear and fusion power, where tritiated ammonia (NT 3 ) emissions are strictly controlled. Therefore, we report the use of low-temperature ammonia dehydrogenation catalysts (3%Ru/1%Y/12%K/Al 2 O 3 ) in a palladium alloy H 2 permeation membrane for quantitative conversion of ammonia into hydrogen and nitrogen at industry-relevant conditions. This catalytic membrane reactor system achieved an astonishing effluent concentration of <1 ppm at 450°C under a 100% NH 3 stream, which is far beyond the 99.6% conversion target required for the adoption of ammonia as a vehicle fuel. The low-temperature ammonia dehydrogenation catalyst was tested in a packed bed reactor with NH 3 and ND 3 to both elucidate the reaction mechanism and to quantify the kinetic isotope effect of the membrane reactor. The rate-limiting step at temperatures relevant to the palladium membrane are isotope independent, indicating that the isotopologue content will not modify the desired reaction kinetics. By reducing emissions to below-trace levels with no additional separation, this work provides a path to greatly simplified and miniaturized ammonia cracking processes.

ammonia decomposition↗

Development of the space shuttle body flap actuation subsystem

Development of the Body Flap Actuation Subsystem for Space Shuttles included alterations from the original design to mechanical stops, planet gears, control valves, and solenoid valves. The mechanical stops were redesigned to absorb stall load and rotating inertia of the hydraulic motors instead of only stall load. The institution of a quill shaft (torsion spring) was a successful solution. The planet gears in the geared rotary actuators developed cracks during testing. This failure was alleviated via modification to the gears. A motor pressurization - brake release timing technique was developed thru analysis and testing. This resulted in a control valve configuration which would not permit freewheeling of the body flap surface. Finally, several solenoid valve configurations were tested to obtain the desired performance. Conceptual redesigns and modifications were weighted against each other to optimize a solution. Tradeoffs were usually made between life, performance, failure tolerance, and reliability versus weight, envelope, and maintainability.

Boggs, C. R.↗

Operando neutron diffraction reveals mechanisms for controlled strain evolution in 3D printing

Abstract Residual stresses affect the performance and reliability of most manufactured goods and are prevalent in casting, welding, and additive manufacturing (AM, 3D printing). Residual stresses are associated with plastic strain gradients accrued due to transient thermal stress. Complex thermal conditions in AM produce similarly complex residual stress patterns. However, measuring real-time effects of processing on stress evolution is not possible with conventional techniques. Here we use operando neutron diffraction to characterize transient phase transformations and lattice strain evolution during AM of a low-temperature transformation steel. Combining diffraction, infrared and simulation data reveals that elastic and plastic strain distributions are controlled by motion of the face-centered cubic and body-centered cubic phase boundary. Our results provide a new pathway to design residual stress states and property distributions within additively manufactured components. These findings will enable control of residual stress distributions for advantages such as improved fatigue life or resistance to stress-corrosion cracking.

36 MATERIALS SCIENCE↗

Materials and processes for Shuttle engine, external tank, and Solid Rocket Booster

The paper deals with the materials and processes for three Space Shuttle elements: Space Shuttle Main Engines (SSME), the External Tank (ET), and the Solid Rocket Boosters (SRB), beginning with an overview of the materials selection, tracking and control system. SSME materials and processes are considered with emphasis on hydrogen environment embrittlement, LOX/GOX compatibility, stress corrosion cracking, and hydraulic fluid testing and qualification. The ET is examined with attention given to welding and fracture mechanics, and the thermal protection system. The SRB is discussed with emphasis on corrosion prevention, stress corrosion and fracture toughness, the integrated test bed for in situ corrosion protection verification, aluminum processing, and the thermal protection system.

Schwinghamer, R. J.↗

The role of peel stresses in cyclic debonding

When an adhesively bonded joint is undergoing cyclic loading, one of the possible damage modes that occurs is called cyclic debonding - progressive separation of the adherends by failure of the adhesive bond under cyclic loading. In most practical structures, both peel and shear stresses exist in the adhesive bonding during cyclic loading. The results of an experimental and analytical study to determine the role of peel stresses on cyclic debonding in a mixed mode specimen are presented. Experimentally, this was done by controlling the forces that create the peel stresses by applying a clamping force to oppose the peel stresses. Cracked lap shear joints were chosen for this study. A finite element analysis was developed to assess the effect of the clamping force on the strain energy release rates due to shear and peel stresses. The results imply that the peel stress is the principal stress causing cyclic debonding.

Everett, R. A., Jr.↗

Bithermal Low-Cycle Fatigue Behavior of a NiCoCrAlY-Coated Single Crystal Superalloy

Specimens of a single crystal superalloy, PWA 1480, both bare and coated with a NiCoCrAlY alloy, PWA 276, were tested in low-cycle fatigue at 650 and 1050 C, and in bithermal thermomechanical fatigue tests. In the two bithermal test types, tensile strain was imposed at one of the two temperatures and reversed in compression at the other. In the high-strain regime, lives for both bithermal test types approached that for the 650 C isothermal test on an inelastic strain basis, all being controlled by the low ductility of the superalloy at 650 C. In the low-strain regime, coating cracking reduced life in the 650 C isothermal test. The bithermal test imposing tension at 650 C, termed out-of-phase, also produced rapid surface cracking, but in both coated and bare specimens. Increased crack growth rates also occurred for the out-of-phase test. Increased lives in vacuum suggested that there is a large environmental contribution to damage in the out-of-phase test due to the 1050 C exposure followed by tensile straining at the low temperature.

Gayda, J.↗

Cyclic fatigue damage characteristics observed for simple loadings extended to multiaxial life prediction

Fully reversed uniaxial strain controlled fatigue tests were performed on smooth cylindrical specimens made of 304 stainless steel. Fatigue life data and cracking observations for uniaxial tests were compared with life data and cracking behavior observed in fully reversed torsional tests. It was determined that the product of maximum principle strain amplitude and maximum principle stress provided the best correlation of fatigue lives for these two loading conditions. Implementation of this parameter is in agreement with observed physical damage and it accounts for the variation of stress-strain response, which is unique to specific loading conditions. Biaxial fatigue tests were conducted on tubular specimens employing both in-phase and out-of-phase tension torsion cyclic strain paths. Cracking observations indicated that the physical damage which occurred in the biaxial tests was similar to the damage observed in uniaxial and torsional tests. The Smith, Watson, and Topper parameter was then extended to predict the fatigue lives resulting from the more complex loading conditions.

Jones, David J.↗