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Buckling of circular cylindrical shells under axial compression.
The infinitely long cylindrical shell under axial compression with axisymmetric sinusoidal imperfections is considered. The bifurcation problem is formulated exactly, and a complete family of buckling modes is identified. Koiter's (1963) upper bound pertains to the critical stress associated with one restricted set of modes, and the critical stress for a set of long wavelength modes reproduces some numerical results obtained by Almroth (1966). The initial postbuckling analysis is also formulated exactly. An exact analytical solution is obtained for the limiting case of modes with infinitely long wavelengths, and numerical analysis is used to solve the equations for the other cases. An appendix gives the details of the analysis.
Orientation-selected micro-pillar compression of additively manufactured 316L stainless steels: Comparison of as-manufactured, annealed, and proton-irradiated variants
In this work, irradiation response and deformation mechanisms of additively manufactured (AM) 316L stainless steel were studied by atomic scale characterization and micro-pillar compression. The AM 316L stainless steels were fabricated by direct energy deposition, a laser-based additive manufacturing process. Irradiation with 2 MeV protons at 360°C was performed to create ~1.8 displacements-per-atom (dpa) damage in AM 316L. Deformation behaviors of the as-manufactured, annealed, and proton-irradiated variants were studied, focusing on the effects of manufacturing-induced pores, residual stress, and irradiation-introduced defects (dislocation loops and voids). Micro-pillars were prepared from grains of pre-selected orientation, avoiding contributions of grain boundaries and allowing determination of resolved shear stress on {111} glide planes. Transmission electron microscopy was used to characterize the pre- and post-deformation microstructure. It was found that in the as-manufactured alloy variant, moving dislocations were the major deformation carrier, with noticeable blocking by fabrication-induced pores, In the annealed variant, hardness was reduced, and deformation was also accomplished by dislocation gliding. In the proton-irradiated variant, significant twinning was observed. Comparing measured resolved shear stress and predicted critical stress for dislocation dissociation, we conclude that irradiation hardening became high enough to activate twinning. Therefore, the deformation mechanism changes from dislocation gliding to twinning. The study is important for both processing optimization and performance evaluation of AM alloys for reactor applications.
Structural Analysis of Pyrolytic Graphite Optics for the HiPEP Ion Thruster
The long lifetime requirements of interplanetary exploration missions is driving the need to develop long-life components for the electric propulsion thrusters that are being targeted for these missions. One of the primary life-limiting components of ion thrusters are the optics, which are continuously eroded during the operation of the thruster. Pyrolytic graphite optics are being considered for the High Power Electric Propulsion (HiPEP) ion thruster because of their very high resistance to erosion. This paper describes the structural analysis of the HiPEP pyrolytic graphite. A description of the development of the grid model, as well as the development of the effective properties and stress concentrations in the apertured area of the grids is included. An evaluation of the use of curved grids shows that the increased stiffness (compared to flat grids) prevents intergrid impact during launch, however, the residual stresses introduced by curving the grids pushes the resulting peak stresses beyond the critical stress. As a result, flat grids are recommended as the design solution. Thermally induced grid displacements during normal thruster operation are also presented.
A Simplified Method of Elastic-Stability Analysis for Thin Cylindrical Shells
This paper develops a new method for determining the buckling stresses of cylindrical shells under various loading conditions. In part I, the equation for the equilibrium of cylindrical shells introduced by Donnell in NACA report no. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. In part II, a modified form of Donnell's equation for the equilibrium of thin cylindrical shells is derived which is equivalent to Donnell's equation but has certain advantages in physical interpretation and in ease of solution, particularly in the case of shells having clamped edges. The question of implicit boundary conditions is also considered.
Subcritical crack growth in two titanium alloys.
Measurement of subcritical crack growth during static loading of precracked titanium alloys in salt water using samples too thin for plane strain loading to predominate was examined as a method for determining the critical stress intensity for crack propagation in salt water. Significant internal crack growth followed by arrest was found at quite low stress intensities, but crack growth rates were relatively low. Assuming these techniques provided a reliable measurement of the critical stress intensity, the value for annealed Ti-4Al-1.5Mo-0.5V alloy was apparently about 35 ksi-in. to the 1/2 power, while that for annealed Ti-4Al-3Mo-1V was below 45 ksi-in. to the 1/2 power. Crack growth was also observed in tests conducted in both alloys in an air environment. At 65 ksi-in. to the 1/2 power, the extent of crack growth was greater in air than in salt water. Ti-4Al-3Mo-1V showed arrested crack growth in air at a stress intensity of 45 ksi-in. to the 1/2 power.
Damage growth in composite laminates with interleaves
The influence of interleaves on the fracture behavior of laminated composites is investigated. The geometry of the composite consists of a cracked layer, bonded between two half-planes, which is separated by thin, low modulus, interleaves. The interleaves are modeled as uncoupled tension and shear springs. A stress analysis is carried out for a crack which may grow up to and spread along the interface. Integral transform techniques are used to develop the solution in terms of singular integral equations. An asymptotic analysis reveals logarithmic singularities in the critical stresses for the case of a broken layer. The equations are solved numerically and the effect of damage on critical stresses is studied. Initial results indicate that the interleaf gives a significant reduction in stresses in the adjacent regions and, if properly selected, should result in a more damage tolerant laminate.
Thermal stress analysis of ceramic gas-path seal components for aircraft turbines
Stress and temperature distributions were evaluated numerically for a blade-tip seal system proposed for gas turbine applications. The seal consists of an abradable ceramic layer on metallic backing with intermediate layers between the ceramic layer and metal substrate. The most severe stresses in the seal, as far as failure is concerned, are tensile stresses at the top of the ceramic layer and shear and normal stresses at the layer interfaces. All these stresses reach their maximum values during the deceleration phase of a test engine cycle. A parametric study was carried out to evaluate the influence of various design parameters on these critical stress values. The influences of material properties and geometric parameters of the ceramic, intermediate, and backing layers were investigated. After the parametric study was completed, a seal system was designed which incorporated materials with beneficial elastic and thermal properties in each layer of the seal. An analysis of the proposed seal design shows an appreciable decrease in the magnitude of the maximum critical stresses over those obtained with earlier configurations.
Exploration Extra-Vehicular Mobility Unit (xEMU) Composite Hard Upper Torso (CHUT) Development
The xEMU is the Exploration Mobility Unity or space suit designed for microgravity (cislunar and low earth orbit (LEO)) and lunar surface operations. This suit design allows crewmembers to perform extravehicular exploration, science, construction, maintenance, and contingency operations while unattached to a vehicle for life support in pressure and thermal environments that exceed human capability. The xEMU provides life support, environmental protection, and communications capabilities to the EVA crewmember while allowing sufficient mobility and visibility to perform dexterous EVA tasks. The effort documented in this paper, addressed the design, analysis, manufacturing, full-scale test article testing and validation for a Composite Hard Upper Torso(CHUT)unit. Design and analysis of the CHUT was based on measured B-basis properties of the selected S-glass/epoxy composite, and established final geometry, composite layup and interface details that met requirements. A complete manufacturing and assembly protocol was established for the CHUT starting from composite layup in the tool, to final assembly of all interface metal hardware prior to delivery to NASA for suit integration. Full-scale CHUT test articles underwent static and fatigue pressure testing (2 lifetimes), impact testing at critical stress locations for tool drop/microgravity scenarios, followed by post-impact fatigue testing. Effect of manufacturing defects was evaluated by manufacturing a full-scale CHUT with 0.375”/0.5” defects at critical stress locations, followed by static and life-cycle fatigue testing. In all cases, the CHUT design met or exceeded mass, structural, interface and functional requirements. Two (2) complete CHUT articles were delivered to NASA for full-scale suit integration and testing.
Composite Hard Upper Torso (CHUT) for xEMU Space Suit
The xEMU is the Exploration Mobility Unity or space suit designed for microgravity (cislunar and low earth orbit (LEO)) and lunar surface operations. This suit design allows crewmembers to perform extravehicular exploration, science, construction, maintenance, and contingency operations while unattached to a vehicle for life support in pressure and thermal environments that exceed human capability. The xEMU provides life support, environmental protection, and communications capabilities to the EVA crewmember while allowing sufficient mobility and visibility to perform dexterous EVA tasks. The effort documented in this paper, addressed the design, analysis, manufacturing, full-scale test article testing and validation for a Composite Hard Upper Torso(CHUT)unit. Design and analysis of the CHUT was based on measured B-basis properties of the selected S-glass/epoxy composite, and established final geometry, composite layup and interface details that met requirements. A complete manufacturing and assembly protocol was established for the CHUT starting from composite layup in the tool, to final assembly of all interface metal hardware prior to delivery to NASA for suit integration. Full-scale CHUT test articles underwent static and fatigue pressure testing (2 lifetimes), impact testing at critical stress locations for tool drop/microgravity scenarios, followed by post-impact fatigue testing. Effect of manufacturing defects was evaluated by manufacturing a full-scale CHUT with 0.375”/0.5” defects at critical stress locations, followed by static and life-cycle fatigue testing. In all cases, the CHUT design met or exceeded mass, structural, interface and functional requirements. Two (2) complete CHUT articles were delivered to NASA for full-scale suit integration and testing.
Stress-controlled medium-amplitude oscillatory shear (MAOStress) of PVA–Borax
We report the first-ever complete measurement of MAOStress material functions, which reveal that stress can be more fundamental than strain or strain rate for understanding linearity limits as a function of Deborah number. The material used is a canonical viscoelastic liquid with a single dominant relaxation time: polyvinyl alcohol (PVA) polymer solution cross-linked with tetrahydroborate (Borax) solution. We outline experimental limit lines and their dependence on geometry and test conditions. These MAOStress measurements enable us to observe the frequency dependence of the weakly nonlinear deviation as a function of stress amplitude. The observed features of MAOStress material functions are distinctly simpler than MAOStrain, where the frequency dependence is much more dramatic. The strain-stiffening transient network model was used to derive a model-informed normalization of the nonlinear material functions that accounts for their scaling with linear material properties. Moreover, we compare the frequency dependence of the critical stress, strain, and strain-rate for the linearity limit, which are rigorously computed from the MAOStress and MAOStrain material functions. While critical strain and strain-rate change by orders of magnitude throughout the Deborah number range, critical stress changes by a factor of about 2, showing that stress is a more fundamental measure of nonlinearity strength. This work extends the experimental accessibility of the weakly nonlinear regime to stress-controlled instruments and deformations, which reveal material physics beyond linear viscoelasticity but at conditions that are accessible to theory and detailed simulation.
Assessing Seismic Risk for CO2 Geologic Storage: Comparative Analysis of the Delaware Basin and Basin and Range Province Projects
ABSTRACT: Effective management of induced seismicity is critical for safe and sustainable CO2 storage. This study evaluates fault slippage risks in the Delaware Basin (Texas) and Basin and Range Province (Utah), integrating geological, operational, and geomechanical parameters to assess fault stability and seismic hazard mitigation. In the Delaware Basin, two sites were analyzed under an injection rate of 20,000 bbl/day over 25 years. One site showed low fault slip risk, while the other exhibited higher reactivation potential due to proximity to critically stressed faults. Sensitivity analysis revealed that increased pore pressure significantly heightened slip potential, highlighting the necessity of precise pressure control and real-time monitoring. In the Basin and Range Province, fault stability was evaluated at Neck of the Desert, Escalante Desert, Parowan, and Beaver sites under injection rates of 8,750 bbl/day per site over 30 years. Minimal fault slip risk was observed at Neck of the Desert and Escalante Desert sites, whereas Parowan and Beaver sites exhibited elevated slip potential due to semi-critically stressed faults sensitive to modest pore pressure increases. The findings demonstrate that fault slippage analysis, combined with sensitivity analysis of pore pressure and friction coefficients, is essential for understanding seismic risks. Continuous monitoring, adaptive injection management, and rigorous geomechanical analysis are key strategies for minimizing induced seismicity in CO2 sequestration projects.
Simple Formulas and Results for Buckling-Resistance and Stiffness Design of Compression-Loaded Laminated-Composite Cylinders
Simple formulas for the buckling stress of homogeneous, specially orthotropic, laminated-composite cylinders are presented. The formulas are obtained by using nondimensional parameters and equations that facilitate general validation, and are validated against the exact solution for a wide range of cylinder geometries and laminate constructions. Results are presented that establish the ranges of the nondimensional parameters and coefficients used. General results, given in terms of the nondimensional parameters, are presented that encompass a wide range of geometries and laminate constructions. These general results also illustrate a wide spectrum of behavioral trends. Design-oriented results are also presented that provide a simple, clear indication of laminate composition on critical stress, critical strain, and axial stiffness. An example is provided to demonstrate the application of these results to thin-walled column designs.
Two-dimensional numerical simulation of sediment transport using improved critical shear stress methods
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Chart for critical compressive stress of flat rectangular plates
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Critical shear stress of long plates with transverse curvature
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Critical shear stress of curved rectangular panels
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Critical shear stress of an infinitely long plate in the plastic region
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