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DOE OSTI2026

Minimizing the Electromechanical Stresses in Poloidal Field Coils by Optimizing their Numbers and Locations using FREDA Framework

Poloidal field (PF) and central solenoid (CS) coils play a crucial role in sustaining the equilibrium and preserving the shape of highly confined tokamak plasmas. Ensuring that PF coil current and mechanical stress stay within superconducting and structural limitations is an important check in the design assessment. Minimizing the PF coil currents and mechanical stresses influences reliability, cost, and performance. A free-boundary MHD equilibrium code—FreeGS is employed within the fusion reactor design and assessment (FREDA) whole facility modeling (WFM) framework to construct the plasma equilibrium based on the configuration and currents in the PF coils. Here, we present the capability of the FreeGS code to minimize the currents, forces, and electromagnetic stresses on the PF coils by optimizing their number, sizes, structures, and locations while maintaining an MHD stable plasma configuration with a large confinement factor. The workflow is initialized with a configuration of plasma parameters and coils’ locations from the 0-D tokamak build systems code in the FREDA framework. Then, FreeGS is called to calculate the initial equilibrium at the minimum total current in PF coils. Thereafter, FreeGS’s internal optimizer minimizes the currents and hoop and central forces on the PF coils while maintaining the reference equilibrium. Finally, the input configuration is updated with the optimized parameters for equilibria over the ramp-up phase of a burning-plasma operation. FREDA’s whole facility optimization capability, which includes all magnetic field coil systems, blanket, vacuum vessel (VV), first wall, divertor, etc., is under development and out of the scope for this study.

Hassan, Ehab [ORNL] (ORCID:0000000181060301)↗

NASA NTRS1977

Method for measuring biaxial stress in a body subjected to stress inducing loads

A method is described for measuring stress in test articles including the steps of obtaining for a calibrating specimen a series of transit time differentials between the second wave echo for a longitudinal wave and the first wave echo for each of a pair of shear waves propagated through the specimen as it is subjected to known stress load of a series of stress loads for thus establishing a series of indications of the magnitudes for stress loads induced in the specimen, and thereafter obtaining a transit time differential between the second wave echo for a longitudinal wave and the first wave echo for each of a pair of shear waves propagated in the planes of the stress axes of a test article and comparing the transit time differential thus obtained to the series of transit time differentials obtained for the specimen to determine the magnitude of biaxial stress in the test article.

Clotfelter, W. N.↗

NASA NTRS1988

A re-evaluation of finite-element models and stress-intensity factors for surface cracks emanating from stress concentrations

A re-evaluation of the 3-D finite-element models and methods used to analyze surface crack at stress concentrations is presented. Previous finite-element models used by Raju and Newman for surface and corner cracks at holes were shown to have ill-shaped elements at the intersection of the hole and crack boundaries. These ill-shaped elements tended to make the model too stiff and, hence, gave lower stress-intensity factors near the hole-crack intersection than models without these elements. Improved models, without these ill-shaped elements, were developed for a surface crack at a circular hole and at a semi-circular edge notch. Stress-intensity factors were calculated by both the nodal-force and virtual-crack-closure methods. Both methods and different models gave essentially the same results. Comparisons made between the previously developed stress-intensity factor equations and the results from the improved models agreed well except for configurations with large notch-radii-to-plate-thickness ratios. Stress-intensity factors for a semi-elliptical surface crack located at the center of a semi-circular edge notch in a plate subjected to remote tensile loadings were calculated using the improved models. The ratio of crack depth to crack length ranged form 0.4 to 2; the ratio of crack depth to plate thickness ranged from 0.2 to 0.8; and the ratio of notch radius to the plate thickness ranged from 1 to 3. The models had about 15,000 degrees-of-freedom. Stress-intensity factors were calculated by using the nodal-force method.

Tan, P. W.↗

NASA NTRS1942

The direct-stress fatigue strength of 17S-T aluminum alloy throughout the range from 1/2 to 500,000,000 cycles of stress

Fatigue-test were conducted on six specimens made from 3/4-inch-diameter 17S-T rolled-and-drawn rod for the purpose of obtaining additional data on the fatigue life of the material at stresses up to the static strength. The specimens were tested in direct tension using a stress range from zero to a maximum in tension. A static testing machine was used to apply repeated loads in the case of the first three specimens; the other three specimens were tested in a direct tension-compression fatigue machine. The direct-stress fatigue curve obtained for the material indicates that, in the range of stresses above about two-thirds the tensile strength, the fatigue strength is higher than might be expected by simply extrapolating the ordinary curve of stress plotted against the number of cycles determined at lower stresses.

Hartmann, E C↗

NASA NTRS2002

Slow Crack Growth of Brittle Materials With Exponential Crack-Velocity Formulation: Constant Stress and Cyclic Stress Experiments - Part 3

The previously determined life prediction analysis based on an exponential crack-velocity formulation was examined using a variety of experimental data on advanced structural ceramics tested under constant stress and cyclic stress loading at ambient and elevated temperatures. The data fit to the relation between the time to failure and applied stress (or maximum applied stress in cyclic loading) was very reasonable for most of the materials studied. It was also found that life prediction for cyclic stress loading from data of constant stress loading in the exponential formulation was in good agreement with the experimental data, resulting in a similar degree of accuracy as compared with the power-law formulation. The major limitation in the exponential crack-velocity formulation, however, was that the inert strength of a material must be known a priori to evaluate the important slow-crack-growth (SCG) parameter n, a significant drawback as compared with the conventional power-law crack-velocity formulation.

Choi, Sung R.↗

NASA NTRS1990

Stress Dependence of Ultrasonic Velocity in Unidirectional Graphite/Epoxy Composites for Longitudinal Waves Propagating Along the Direction of Stress

The first measurements of the stress induced velocity changes for propagation directions along the direction of applied stress in gr/ep composites have been presented. For propagation and stress direction perpendicular to the fiber direction, the data demonstrated a linear relation between normalized velocity shift and stress. After corrections for the delay line were made, the slope or SAC was determined and compared favorably with the expected value calculated from the previously determined nonlinear coefficients of this material. The ratio of the SAC to the elastic compliance for this direction of loading was evaluated and found to have a value similar to numerous other materials which have very different linear elastic properties. Measurements with stress and propagation along the fibers yielded unusual behavior. The curves were very nonlinear and even shifted direction at higher loads. The large scatter in the data due to bond variations made separation of material effects from bond induced artifacts impossible. Thus the SAC, R, and the remaining two unknown TOEC's could not be determined for this direction of propagation. These measurements further expand the basis of determining nonlinear elastic properties of composite materials. These properties may be useful in developing much needed NDE techniques to determine such important parameters as residual stress after cure and residual strength after impact damage. Additional study is needed to measure the nonlinear behavior in other composite materials including angle ply laminates. Also, other techniques to measure elastic nonlinearity such as harmonic generation should be applied to composites to improve the understanding of these properties and their importance.

Prosser, William H.↗

NASA NTRS1984

Influence of precracked specimen configuration and starting stress intensity on the stress corrosion cracking of 4340 steel

Experimental results are presented from a study of the effects of precracked specimen configuration and initial starting stress intensity on crack growth rate and threshold stress intensity, for both onset of cracking and crack arrest. Attention is given to AISI 4340 steel in a 3.5-percent NaCl solution, for configurations of a single edge-cracked specimen tested in cantilever bending under constant load, and a modified compact specimen bolt loaded to a constant deflection. The threshold stress intensity value determined was independent of specimen configuration, if the stress intensity value associated with the compact specimen is taken where the discontinuous break occurs in the velocity-stress intensity curve.

Lisagor, W. B.↗

NASA NTRS1987

A hybrid-stress finite element approach for stress and vibration analysis in linear anisotropic elasticity

A hybrid stress finite element method is developed for accurate stress and vibration analysis of problems in linear anisotropic elasticity. A modified form of the Hellinger-Reissner principle is formulated for dynamic analysis and an algorithm for the determination of the anisotropic elastic and compliance constants from experimental data is developed. These schemes were implemented in a finite element program for static and dynamic analysis of linear anisotropic two dimensional elasticity problems. Specific numerical examples are considered to verify the accuracy of the hybrid stress approach and compare it with that of the standard displacement method, especially for highly anisotropic materials. It is that the hybrid stress approach gives much better results than the displacement method. Preliminary work on extensions of this method to three dimensional elasticity is discussed, and the stress shape functions necessary for this extension are included.

Oden, J. Tinsley↗

NASA NTRS1990

Stress dependence of ultrasonic velocity in unidirectional graphite/epoxy composites for longitudinal waves propagating along the direction of stress

Measurements of stress-induced velocity changes for propagation along the direction of applied stress in graphite/epoxy composites are presented. A linear relation between normalized velocity shift and stress is demonstrated for propagation and stress direction perpendicular to the fiber direction. The ratio of the SAC to the elastic compliance for this loading direction was assessed and found to have a value similar to that of numerous other materials which have very different linear elastic properties. Measurements with stress and propagation along the fibers yielded unusual behavior; the curves were very nonlinear and even shifted direction at higher loads.

Prosser, William H.↗

NASA NTRS1999

Thermoelastic Stress Analysis: The Mean Stress Effect in Metallic Alloys

The primary objective of this study involved the utilization of the thermoelastic stress analysis (TSA) method to demonstrate the mean stress dependence of the thermoelastic constant. Titanium and nickel base alloys, commonly employed in aerospace gas turbines, were the materials of interest. The repeatability of the results was studied through a statistical analysis of the data. Although the mean stress dependence was well established, the ability to confidently quantify it was diminished by the experimental variations. If calibration of the thermoelastic response to mean stress can be successfully implemented, it is feasible to use the relationship to determine a structure's residual stress state.

Gyekenyesi, Andrew L.↗

NASA NTRS2012

Stress Free Temperature Testing and Residual Stress Calculations on Out-of-Autoclave Composites

Future launch vehicles will require the incorporation large composite parts that will make up primary and secondary components of the vehicle. NASA has explored the feasibility of manufacturing these large components using Out-of-Autoclave impregnated carbon fiber composite systems through many composites development projects. Most recently, the Composites for Exploration Project has been looking at the development of a 10 meter diameter fairing structure, similar in size to what will be required for a heavy launch vehicle. The development of new material systems requires the investigation of the material properties and the stress in the parts. Residual stress is an important factor to incorporate when modeling the stresses that a part is undergoing. Testing was performed to verify the stress free temperature with two-ply asymmetric panels. A comparison was done between three newly developed out of autoclave IM7 /Bismalieimide (BMI) systems. This paper presents the testing results and the analysis performed to determine the residual stress of the materials.

Cox, Sarah↗

DOE OSTI2025

A Unified Framework to Reconcile Different Approaches of Modeling Transpiration Response to Water Stress: Plant Hydraulics, Supply Demand Balance, and Empirical Soil Water Stress Function

Plant responses to water stress is a major uncertainty to predicting terrestrial ecosystem sensitivity to drought. Different approaches have been developed to represent plant water stress. Empirical approaches (the empirical soil water stress (or Beta) function and the supply-demand balance scheme) have been widely used for many decades; more mechanistic based approaches, that is, plant hydraulic models (PHMs), were increasingly adopted in the past decade. However, the relationships between them—and their underlying connections to physical processes—are not sufficiently understood. This limited understanding hinders informed decisions on the necessary complexities needed for different applications, with empirical approaches being mechanistically insufficient, and PHMs often being too complex to constrain. Here we introduce a unified framework for modeling transpiration responses to water stress, within which we demonstrate that empirical approaches are special cases of the full PHM, when the plant hydraulic parameters satisfy certain conditions. We further evaluate their response differences and identify the associated physical processes. Finally, we propose a methodology for assessing the necessity of added complexities of the PHM under various climatic conditions and ecosystem types, with case studies in three typical ecosystems: a humid Midwestern cropland, a semi-arid evergreen needleleaf forest, and an arid grassland. Notably, Beta function overestimates transpiration when VPD is high due to its lack of constraints from hydraulic transport and is therefore insufficient in high VPD environments. With the unified framework, we envision researchers can better understand the mechanistic bases of and the relationships between different approaches and make more informed choices.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1975

Stress analysis and stress intensity factors for finite geometry solids containing rectangular surface cracks

The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement field in a finite geometry bar containing a variable depth rectangular surface crack under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Using the obtained displacement field, normal stresses and the stress intensity factor variation along the crack periphery are calculated for different crack depth to bar thickness ratios. Crack opening displacements and stress intensity factors are also obtained for a through-thickness, center cracked bar with variable thickness. The reported results show a considerable potential for using this method in calculating stress intensity factors for commonly encountered surface crack geometries in finite solids.

Gyekenyesi, J. P.↗

NASA NTRS1977

Stress analysis and stress-intensity factors for finite geometry solids containing rectangular surface cracks

The line method of analysis is applied to the Navier-Cauchy equations of elastic equilibrium to calculate the displacement field in a finite geometry bar containing a variable depth rectangular surface crack under extensionally applied uniform loading. The application of this method to these equations leads to coupled sets of simultaneous ordinary differential equations whose solutions are obtained along sets of lines in a discretized region. Using the obtained displacement field, normal stresses, and the stress-intensity factor variation along the crack periphery are calculated for different crack depth to bar thickness ratios. Crack opening displacements and stress-intensity factors are also obtained for a through-thickness, center-cracked bar with variable thickness. The reported results show a considerable potential for using this method in calculating stress-intensity factors for commonly encountered surface crack geometries in finite solids

Gyekenyesi, J. P.↗

NASA NTRS1984

Influence of precracked specimen configuration and starting stress intensity on the stress corrosion cracking of 4340 steel

Since the pioneer work of Brown (1966), precracked specimens and related fracture mechanics analyses have been extensively used to study stress corrosion cracking. Certain questions arose in connection with initial attempts to prepare standardized recommended practices by ASTM Committee G-1 on Corrosion of Metals. These questions were related to adequacy of test control as it pertains to acceptable limits of variability, and to validity of expressions for stress intensity and crack-surface displacements for both specimen configurations. An interlaboratory test program, was, therefore, planned with the objective to examine the validity of KIscc testing for selected specimen configurations, materials,and environmental systems. The results reported in the present paper include details of a single laboratory test program. The program was conducted to determine if the threshold value of stress intensity for onset and arrest of stress corrosion cracking was independent for the two specimen configurations examined.

Lisagor, W. B.↗

NASA NTRS1988

Investigation of stress concentration factor - Stress intensity factor interaction for flaws in filleted rods

To predict the fatigue life of machine parts which contain flaws in regions of stress concentration, the engineer needs to treat a series of crack sizes and/or shapes quickly and economically. In this paper the stress intensity factor distributions for circular surface flaws in the roots of fillets in rods loaded by remote tension are presented and examined. The examination reveals insight into the interaction of cracks with other stress concentrating discontinuities, and based on this it is suggested that weight function methods used in conjunction with known crack solutions may provide needed, efficient stress intensity factor prediction methods for such three-dimensional geometries.

Springfield, C. W., Jr.↗

NASA NTRS1990

Evaluation of finite-element models and stress-intensity factors for surface cracks emanating from stress concentrations

Tan, P. W.↗

NASA NTRS1998

Comparative Stress Corrosion Cracking and General Corrosion Resistance of Annealed and Hardened 440 C Stainless Steel - New Techniques in Stress Corrosion Testing

The corrosion and stress corrosion cracking (SCC) characteristics of annealed and hardened 440C stainless steel were evaluated in high humidity and 3.5-percent NaCl solution. Corrosion testing consisted of an evaluation of flat plates, with and without grease, in high humidity, as well as electrochemical testing in 3.5-percent NaCl. Stress corrosion testing consisted of conventional, constant strain, smooth bar testing in high humidity in addition to two relatively new techniques under evaluation at MSFC. These techniques involve either incremental or constant rate increases in the load applied to a precracked SE(B) specimen, monitoring the crack-opening-displacement response for indications of crack growth. The electrochemical corrosion testing demonstrated an order of magnitude greater general corrosion rate in the annealed 440C. All techniques for stress corrosion testing showed substantially better SCC resistance in the annealed material. The efficacy of the new techniques for stress corrosion testing was demonstrated both by the savings in time and the ability to better quantify SCC data.

Mendreck, M. J.↗