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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Measurement of single-diffractive dijet production in proton-proton collisions at $\sqrt{s} =$ 8 TeV with the CMS and TOTEM experiments

Measurements are presented of the single-diffractive dijet cross section and the diffractive cross section as a function of the proton fractional momentum loss $\xi $ and the four-momentum transfer squared t. Both processes ${\text{ p }{}{}} {\text{ p }{}{}} \rightarrow {\text{ p }{}{}} {\text{ X }} $ and ${\text{ p }{}{}} {\text{ p }{}{}} \rightarrow {\text{ X }} {\text{ p }{}{}} $, i.e. with the proton scattering to either side of the interaction point, are measured, where ${\text{ X }} $ includes at least two jets; the results of the two processes are averaged. The analyses are based on data collected simultaneously with the CMS and TOTEM detectors at the LHC in proton–proton collisions at $\sqrt{s} = 8\,\text {Te}\text {V} $ during a dedicated run with $\beta ^{*} = 90\,\text {m} $ at low instantaneous luminosity and correspond to an integrated luminosity of $37.5{\,\text {nb}^{-1}} $. The single-diffractive dijet cross section $\sigma ^{{\text{ p }{}{}} {\text{ X }}}_{\mathrm {jj}}$, in the kinematic region $\xi < 0.1$, $0.03< |t | < 1\,\text {Ge}\text {V} ^2$, with at least two jets with transverse momentum $p_{\mathrm {T}} > 40\,\text {Ge}\text {V} $, and pseudorapidity $|\eta | < 4.4$, is $21.7 \pm 0.9\,\text {(stat)} \,^{+3.0}_{-3.3}\,\text {(syst)} \pm 0.9\,\text {(lumi)} \,\text {nb} $. The ratio of the single-diffractive to inclusive dijet yields, normalised per unit of $\xi $, is presented as a function of x, the longitudinal momentum fraction of the proton carried by the struck parton. The ratio in the kinematic region defined above, for x values in the range $-2.9 \le \log _{10} x \le -1.6$, is $R = (\sigma ^{{\text{ p }{}{}} {\text{ X }}}_{\mathrm {jj}}/\Delta \xi )/\sigma _{\mathrm {jj}} = 0.025 \pm 0.001\,\text {(stat)} \pm 0.003\,\text {(syst)} $, where $\sigma ^{{\text{ p }{}{}} {\text{ X }}}_{\mathrm {jj}}$ and $\sigma _{\mathrm {jj}}$ are the single-diffractive and inclusive dijet cross sections, respectively. The results are compared with predictions from models of diffractive and nondiffractive interactions. Monte Carlo predictions based on the HERA diffractive parton distribution functions agree well with the data when corrected for the effect of soft rescattering between the spectator partons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Solute effects upon dislocation motion and recovery in Mg alloys (Final Report)

The objective the research was to develop a firmer understanding of the interactions between substitutional solute atoms and dislocations within Mg alloys. These interactions govern the absolute and relative mobilities of various types of dislocations in Mg (e.g., basal < a>, non-basal < a>, and pyramidal < c+a>). Furthermore, they have an impact on dislocation recovery processes (e.g., cross-glide, climb, rearrangement, and annihilation). Ultimately, solute-dislocation interactions strongly impact a) strain hardening, b) strain rate sensitivity, c) plastic anisotropy of textured polycrystals, d) texture evolution, e) dislocation substructures evolution, and even f) recrystallization behavior. It is broadly known that Mg alloys exhibit poor low temperature formability. Since formability is largely governed by properties (a) – (c) in this list, it is critical to develop a better understanding of solute-dislocation interactions, if one hopes to improve the situation. While the theory of static solute strengthening is well developed, especially for alloys with face centered cubic (FCC) crystal structures, there are outstanding questions related to applications to hexagonal close packed (HCP) crystal structures and dynamic strain aging (DSA) in materials of various structures. DSA has far-reaching implications for metal formability and, in the case of Mg alloys, appears to correlate with the so-called rare-earth (RE) texture which has been shown to benefit formability. The Portevin-Le Chatelier (PLC) effect, and associated negative strain rate sensitivity, occur at higher temperatures (>100℃) in Mg alloys as compared with similar Al alloys, even though they have similar melting points and solute diffusivities. Our preliminary research has shown that modern, physics-based models of DSA can be tuned to describe the behavior of Mg alloys if a rather higher activation enthalpy is assumed for cross-core diffusivity. While this partially explains the delay in DSA to higher temperatures, it is also hypothesized that this delay is due in part to the intrinsically more thermally activated (rate sensitive) nature of non-basal < a> dislocation motion which is required for macroscopic flow of Mg alloys, whereas octahedral slip in many FCC metals like aluminum is essentially athermal at room temperature. It was originally proposed to employ a combination of in-situ diffraction-based experimental characterization to validate existing theory. It was envisioned to perform in-situ transmission electron microscopy (TEM) to assess individual dislocation behavior and in-situ high-energy X-ray diffraction (HEXRD) techniques which were showing great promise for elucidating collective dislocation behavior, 2 including recovery, especially if the contributions to various forms of diffraction peak broadening (𝜂𝜂,𝜔𝜔,and 2𝜃𝜃) can be effectively integrated. Finally, it was envisioned to perform discrete dislocation dynamics (DDD) modeling approaches to aide in the interpretation of both TEM and HEXRD experiments. In the end, mechanical tests were performed on more complex Mg alloys which exhibited evidence of dynamic strain aging, and this led to the establishment of another project. Mechanical test data obtained at McMaster University served as the basis of an assessment of the applicability of Bazinski’s “stress equivalence” theory of solute strengthening to polycrystalline alloys of Mg. Although we did not succeed in applying the approach to Mg alloys, we did develop expertise with the HEXRD approach using a BCC, β-Ti alloy and demonstrated numerous new capabilities that may be applied to any polycrystalline material in collaboration with researchers at CHESS and around the world: (1) assessment of details of the elastoplastic transition (yielding) using a combination of HEXRD and full-field polycrystal plasticity modeling, (2) the first-ever experimental observation of strong stress rotation within the individual grains of a polycrystalline material, and (3) a comprehensive analysis of the grain-level dislocation density evolution based upon diffraction peak broadening along 𝜂𝜂,𝜔𝜔,and 2𝜃𝜃 directions. This final aspect allowed us to confirm that dislocations were gliding on multiple plane types and not restricted to {110} type planes, and it also provided clues as to why some grains were unloading during straining, with surprising implications for our understanding of the effects of geometrically necessary dislocations (GNDs). Finally, graduate student, Mohammed Shabana, developed a MATLAB code which confirmed the conclusions of Prof. Catalin Picu (Rensallear Polytechnic Institute, RPI) regarding the effect of solute-trapped, forest dislocations on the breaking stress of Lomer lock junctions in FCC metal alloys. He applied the same anisotropic line-tension model to a variety of dislocation junction configurations and found an inconsistency in the widely cited results of Dupuy and Fivel regarding the Hirth Lock, and he outlined an approach to extend these finding to HCP Mg alloys that we are still pursuing with discretionary fundings at UVA.

36 MATERIALS SCIENCE↗
NASA NTRS2009

Device for Measuring Low Flow Speed in a Duct

A multiple-throat venturi system has been invented for measuring laminar flow of air or other gas at low speed (1 to 30 cm/s) in a duct while preserving the laminar nature of the flow and keeping the velocity profile across the duct as nearly flat as possible. While means for measuring flows at higher speeds are well established, heretofore, there have been no reliable means for making consistent, accurate measurements in this speed range. In the original application for which this system was invented, the duct leads into the test section of a low-speed wind tunnel wherein uniform, low-speed, laminar flow is required for scientific experiments. The system could also be used to monitor a slow flow of gas in an industrial process like chemical vapor deposition. In the original application, the multiple- throat venturi system is mounted at the inlet end of the duct having a rectangular cross section of 19 by 14 cm, just upstream of an assembly of inlet screens and flow straighteners that help to suppress undesired flow fluctuations (see Figure 1). The basic venturi measurement principle is well established: One measures the difference in pressure between (1) a point just outside the inlet, where the pressure is highest and the kinetic energy lowest; and (2) the narrowest part (the throat) of the venturi passage, where the kinetic energy is highest and the pressure is lowest. Then by use of Bernoulli s equation for the relationship between pressure and kinetic energy, the volumetric flow speed in the duct can be calculated from the pressure difference and the inlet and throat widths. The design of this system represents a compromise among length, pressure recovery, uniformity of flow, and complexity of assembly. Traditionally, venturis are used to measure faster flows in narrower cross sections, with longer upstream and downstream passages to maintain accuracy. The dimensions of the passages of the present venturi system are sized to provide a readily measurable pressure drop. Multiple throats are used to minimize the length needed to recover internal energy and enable the velocity profile to recover to near flatness.

Quinn, Frank↗
NASA NTRS2009

Measuring Thermal Conductivity of a Small Insulation Sample

A multiple-throat venturi system has been invented for measuring laminar flow of air or other gas at low speed (1 to 30 cm/s) in a duct while preserving the laminar nature of the flow and keeping the velocity profile across the duct as nearly flat as possible. While means for measuring flows at higher speeds are well established, heretofore, there have been no reliable means for making consistent, accurate measurements in this speed range. In the original application for which this system was invented, the duct leads into the test section of a low-speed wind tunnel wherein uniform, low-speed, laminar flow is required for scientific experiments. The system could also be used to monitor a slow flow of gas in an industrial process like chemical vapor deposition. In the original application, the multiple- throat venturi system is mounted at the inlet end of the duct having a rectangular cross section of 19 by 14 cm, just upstream of an assembly of inlet screens and flow straighteners that help to suppress undesired flow fluctuations (see Figure 1). The basic venturi measurement principle is well established: One measures the difference in pressure between (1) a point just outside the inlet, where the pressure is highest and the kinetic energy lowest; and (2) the narrowest part (the throat) of the venturi passage, where the kinetic energy is highest and the pressure is lowest. Then by use of Bernoulli s equation for the relationship between pressure and kinetic energy, the volumetric flow speed in the duct can be calculated from the pressure difference and the inlet and throat widths. The design of this system represents a compromise among length, pressure recovery, uniformity of flow, and complexity of assembly. Traditionally, venturis are used to measure faster flows in narrower cross sections, with longer upstream and downstream passages to maintain accuracy. The dimensions of the passages of the present venturi system are sized to provide a readily measurable pressure drop. Multiple throats are used to minimize the length needed to recover internal energy and enable the velocity profile to recover to near flatness.

Miller, Robert A.↗
NASA NTRS1956

Impingement of Droplets in 60 Deg Elbows with Potential Flow

Trajectories were determined for water droplets or other aerosol particles in air flowing through 600 elbows especially designed for two-dimensional potential motion. The elbows were established by selecting as walls of each elbow two streamlines of a flow field produced by a complex potential function that establishes a two-dimensional flow around. a 600 bend. An unlimited number of elbows with slightly different shapes can be established by selecting different pairs of streamlines as walls. Some of these have a pocket on the outside wall. The elbows produced by the complex potential function are suitable for use in aircraft air-inlet ducts and have the following characteristics: (1) The resultant velocity at any point inside the elbow is always greater than zero but never exceeds the velocity at the entrance. (2) The air flow field at the entrance and exit is almost uniform and rectilinear. (3) The elbows are symmetrical with respect to the bisector of the angle of bend. These elbows should have lower pressure losses than bends of constant cross-sectional area. The droplet impingement data derived from the trajectories are presented along with equations so that collection efficiency, area, rate, and distribution of droplet impingement can be determined for any elbow defined by any pair of streamlines within a portion of the flow field established by the complex potential function. Coordinates for some typical streamlines of the flow field and velocity components for several points along these streamlines are presented in tabular form. A comparison of the 600 elbow with previous calculations for a comparable 90 elbow indicated that the impingement characteristics of the two elbows were very similar.

Hacker, Paul T.↗
NASA NTRS1978

The point mutation process in proteins

An optimized scoring matrix for residue-by-residue comparisons of distantly related protein sequences has been developed. The scoring matrix is based on observed exchanges and mutabilities of amino acids in 1572 closely related sequences derived from a cross-section of protein groups. Very few superimposed or parallel mutations are included in the data. The scoring matrix is most useful for demonstrating the relatedness of proteins between 65 and 85% different.

Schwartz, R. M.↗
DOE OSTI2020

Crossing symmetry, transcendentality and the Regge behaviour of 1d CFTs

We develop the technology for Polyakov-Mellin (PM) bootstrap in one- dimensional conformal field theories (CFT 1 ). By adding appropriate contact terms, we bootstrap various effective field theories in AdS 2 and analytically compute the CFT data to one loop. The computation can be extended to higher orders in perturbation theory, if we ignore mixing, for any external dimension. We develop PM bootstrap for O(N) theories and derive the necessary contact terms for such theories (which also involves a new higher gradient contact term absent for N = 1). We perform cross-checks which include considering the diagonal limit of the 2d Ising model in terms of the 1d PM blocks. As an independent check of the validity of the results obtained with PM bootstrap, we propose a suitable basis of transcendental functions, which allows to fix the four-point correlators of identical scalar primaries completely, up to a finite number of ambiguities related to the number of contact terms in the PM basis. We perform this analysis both at tree level (with and without exchanges) and at one loop. We also derive expressions for the corresponding CFT data in terms of harmonic sums. Finally, we consider the Regge limit of one-dimensional correlators and derive a precise connection between the latter and the large-twist limit of CFT data. Exploiting this result, we study the crossing equation in the three OPE limits and derive some universal constraints for the large-twist limit of CFT data in Regge-bounded theories with a finite number of exchanges.

1/N expansion↗
DOE OSTI2025

A cross-platform execution engine for the quantum intermediate representation

Hybrid languages like the quantum intermediate representation (QIR) are essential for programming systems that mix quantum and conventional computing models, while execution of these programs is often deferred to a system-specific implementation. Here, we develop the QIR Execution Engine (QIR-EE) for parsing, interpreting, and executing QIR across multiple hardware platforms. QIR-EE uses LLVM to execute hybrid instructions specifying quantum programs and, by design, presents extension points that support customized runtime and hardware environments. We demonstrate an implementation that uses the XACC quantum hardware-accelerator library to dispatch prototypical quantum programs on different commercial quantum platforms and numerical simulators, and we validate execution of QIR-EE on IonQ, Quantinuum, and IBM hardware. Our results highlight the efficiency of hybrid executable architectures for handling mixed instructions, managing mixed data, and integrating with quantum computing frameworks to realize cross-platform execution.

LLVM↗
DOE OSTI2022

Form factors and spectral densities from Lightcone Conformal Truncation

We use the method of Lightcone Conformal Truncation (LCT) to obtain form factors and spectral densities of local operators $\mathcal{O}$ in $\phi^4$ theory in two dimensions. We show how to use the Hamiltonian eigenstates from LCT to obtain form factors that are matrix elements of a local operator $\mathcal{O}$ between single-particle bra and ket states, and we develop methods that significantly reduce errors resulting from the finite truncation of the Hilbert space. We extrapolate these form factors as a function of momentum to the regime where, by crossing symmetry, they are form factors of $\mathcal{O}$ between the vacuum and a two-particle asymptotic scattering state. We also compute the momentum-space time-ordered two-point functions of local operators in LCT. These converge quickly at momenta away from branch cuts, allowing us to indirectly obtain the time-ordered correlator and the spectral density at the branch cuts. We focus on the case where the local operator $\mathcal{O}$ is the trace Θ of the stress tensor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Survey of Surveys: I. The largest compilation of radial velocities for the Galaxy

In the present-day panorama of large spectroscopic surveys, the amount, diversity, and complexity of the available data continuously increase. The overarching goal of studying the formation and evolution of our Galaxy is hampered by the heterogeneity of instruments, selection functions, analysis methods, and measured quantities. Here, we present a comprehensive catalogue, the Survey of Surveys (SoS), built by homogeneously merging the radial velocity (RV) determinations of the largest ground-based spectroscopic surveys to date, such as APOGEE, GALAH, Gaia-ESO, RAVE, and LAMOST, using Gaia as a reference. This pilot study serves to prove the concept and to test the methodology that we plan to apply in the future to the stellar parameters and abundance ratios as well. We have devised a multi-staged procedure that includes: (i) the cross match between Gaia and the spectroscopic surveys using the official Gaia cross-match algorithm, (ii) the normalisation of uncertainties using repeated measurements or the three-cornered hat method, (iii) the cross calibration of the RVs as a function of the main parameters on which depend (magnitude, effective temperature, surface gravity, metallicity, and signal-to-noise ratio) to remove trends and zero point offsets, and (iv) the comparison with external high-resolution samples, such as the Gaia RV standards and the Geneva-Copenhagen survey, to validate the homogenisation procedure and to calibrate the RV zero-point of the SoS catalogue. We provide the largest homogenised RV catalogue to date, containing almost 11 million stars, of which about half come exclusively from Gaia and half in combination with the ground-based surveys. We estimate the accuracy of the RV zero-point to be about 0.16–0.31 km s –1 and the RV precision to be in the range 0.05–1.50 km s –1 depending on the type of star and on its survey provenance. We validate the SoS RVs with open clusters from a high resolution homogeneous samples and provide the systemic velocity of 55 individual open clusters. Additionally, we provide median RVs for 532 clusters recently discovered by Gaia data. The SoS is publicly available and ready to be applied to various research projects, such as the study of star clusters, Galactic archaeology, stellar streams, or the characterisation of planet-hosting stars, to name a few. We also plan to include survey updates and more data sources in future versions of the SoS.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Abrasion-fission reactions at intermediate energies

The availability of high-intensity, heavy-ion beams coupled to sensitive, large solid-angle acceptance spectrometers has enabled a detailed examination of the fission fragments produced in induced-fission reactions. The abrasion fission process involves the formation of projectile-like prefragments in violent nuclear collisions at relative energies in excess of 100 MeV/u. At intermediate energies below this threshold, experiments suggest a change in the prefragment kinematic qualities. Information regarding the influence of this transitional phase upon the evolution of nuclei approaching the point of scission is scarce. In this article, data are presented for over 200 nuclei from nickel to palladium produced in abrasion-fission reactions of a 80 MeV/u 238 U beam. Cross sections were obtained following yield measurements performed for the principal charge states of the identified fission fragments and a detailed analysis of the ion transmission. A full kinematic analysis of the fission fragments has been performed using the LISE ++ software package, where the trajectory of an ion passing through a spectrometer can be reconstructed based upon measurements at the focal plane. Furthermore, the results obtained at the S800 spectrograph are compared with predictions obtained with a three-fission progenitor (3EER) model. Systematic studies of fission-fragment properties continue to provide a valuable experimental benchmark for theoretical efforts directed toward describing this complex decay channel, that is important in the context of planning experiments to explore the neutron-rich region of the nuclear chart at rare-isotope beam facilities.

59 ≤ A ≤ 8990 ≤ A ≤ 149↗
DOE OSTI2023

Constructing Regulatory Networks to Compare Axenic and Interspecies Microbial Gene Transcription

In this preliminary study, we constructed gene regulatory networks (GRNs) from transcriptional expression data of axenic and interspecies microbial cultures with the goal of predicting how cocultivation affected greenhouse gas respiration by these species. The specific strains of Methylotuvimicrobium alkaliphilum 20Z, a methylotroph, and Cyanobacterium stanieri HL-69, a phototroph, were chosen for their viability in industrial bioprocessing. We ranked directed interactions between gene pairs based on the ability of the input gene to predict the expression of a target gene relative to their transcriptomes. While we were able to identify topological differences between conditions, our initial findings require validation through experimental analysis and further modeling. We aimed to develop a systematic thresholding approach to optimize the accuracy of our networks. We filtered out trial networks separately from top gene interactions of the scored rankings. Parameters of unfiltered and filtered networks were used to test and develop thresholding approaches. Knee point detection of edge weight distributions was explored as an approach for separating significant interactions from insignificant interactions in unfiltered networks. While knee detection failed to produce analogous networks for broad cross-condition comparisons, the results informed us about the proportions of significant edges present in unfiltered networks. We also calculated the average mean degree for nodes in a selection of trial networks to find a thresholding value characteristic to all groups. While we did not reach a definitive conclusion, we gained insight into the coregulatory structures of our groups and made critical evaluations of systematic methods for filtering networks. We recommend an iterative process for the inference of GRNs, where the most significant results from preliminary explorations are used to improve the efficiency with which regulatory motifs are chosen for experimental characterization. Experimental results can then inform the framework of adjusted models to improve broad interpretations of GRNs.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1974

Antiplane shear crack terminating at and going through a bimaterial interface

The antiplane shear problem of two bonded elastic half-planes containing a crack perpendicular to the interface is considered. The cases of a semiinfinite crack terminating at the interface, a finite crack away from and terminating at the interface, two cracks one on each side of the interface, and a finite crack crossing the interface are separately investigated. The nature of the stress singularity for the crack terminating at and going through the interface is studied, and it is shown that at the irregular point on the interface, for the former the power of singularity is not -1/2 and for the latter the stresses are bounded. For a material pair of aluminum-epoxy some numerical results giving the stress intensity factors, the density functions, and the crack opening displacements are presented.

Erdogan, F.↗
NASA NTRS1979

Handbook on astronaut crew motion disturbances for control system design

The analyses and results pertinent to the characterization of the disturbances imparted to the Skylab vehicle by the T-013 crew motion experiments are summarized. Guidelines to help control system designers assess anticipated crew motion disturbances during the design cycle of a new manned spacecraft control system are provided. These guidelines, in conjunction with the T-013 characterizations outlined, begin with the control system conceptual design and conclude with preliminary expectations for pointing performance as affected by crew motions. Block diagrams to highlight the contents so that the reader can easily identify the information and data flow are used. These diagrams provide a handy cross reference of related topics.

Kullas, M. C.↗
NASA NTRS1986

Comment on electric field evidence on the viscous interaction at the magnetopause, by F. S. Mozer

In his paper on ISEE-1 electric field measurements in the low-latitude boundary layer (LLBL), Mozer (1984) concluded that LLBL contributes only about 10 percent of the average cross-tail potential difference Delta phi, and thus that viscous effects associated with the boundary layer are not very important as compared to the competing process of magnetic reconnection. Here, it is pointed out that Mozer may not have recognized an important feature of the LLBL, in that the maximum or minimum values of Delta phi (BL) may have occurred tailward of the spacecraft orbit. It is also pointed out that the sum of the viscous interaction potentials across the dawn and dusk low latitude boundary layers is closer to 30 kV than the 6 kV reported by Mozer. In his reply, Mozer gives reasons why the values he used are correct and that his earlier conclusions need no revision.

Heikkila, W. J.↗
NASA NTRS1988

ISEE 1 and 2 observation of the oscillating magnetopause

The ISEE 1 and 2 magnetometer data for 10 years between October 1977 and September 1987 were used to identify magnetopause crossings that occurred in this period in the northward, horizontal, and southward IMFs and to determine the dependence of the oscillation amplitude of surface waves with periods greater than about 2 min on latitude, local time, and the direction of the IMF. The IMP 8 and ISEE 3 data were used to determine the IMF in the geocentric solar magnetosphere coordinates during the crossings. More than 1000 magnetopause passes were identified, with half of them with multiple crossings. The number of crossings per pass and the inferred average amplitude of the oscillation under southward conditions were nearly three times higher than under northward conditions. The amplitude increased with increasing angle from the subsolar point, when under southward, but not when under northward, conditions. The results suggest that the Kelvin-Helmholtz instability plays a very minor role in causing the surface waves on the dayside magnetopause.

Song, PU↗
NASA NTRS1960

Fatigue-Crack Propagation in Aluminum-Alloy Tension Panels

Results are presented of a series of fatigue tests to study crack propagation and the resulting stress distributions in tension panels. The panels were all of the same general design, and configurations varied mainly in the relative amount of cross-sectional area in the skin, stiffeners, and flanges. The panels were constructed of 2024-T3 and 7075-T6 aluminum alloys. It was found that the average rate of crack growth was slower in panels made of 2024-T3 aluminum alloy than in panels made of 7075-T6 aluminum alloy. All cracks initiated in the skin, and the slowest crack growth was measured in configurations where the highest percentage of cross-sectional area was in the stiffeners. Strain-gage surveys were made to determine the redistribution of stress as the crack grew across the panels. As a crack approached a given point in the skin, the stress at that point increased rapidly. The stress in the stiffeners also increased as the crack approached the stiffeners. During the propagation of the crack the stress was not distributed uniformly in the remaining area.

Whaley, Richard E.↗