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At least 19 records

Mathematical modelling of the beam under axial compression force applied at any point – the buckling problem

The study is devoted to stability of simply supported beam under axial compression. The beam is subjected to an axial load located at any point along the axis of the beam. The buckling problem has been desribed and solved mathematically. Critical loads have been calculated. In the particular case, the Euler’s buckling load is obtained. Explicit solutions are given. The values of critical loads are collected in tables and shown in figure. The relation between the point of the load application and the critical load is presented.

97 MATHEMATICS AND COMPUTING↗

Experimental Investigation of Concrete Fatigue in Axial Compression

The use of concrete in fatigue critical structures, such as wind turbine towers, has necessitated the replacement of simplistic (and therefore insufficient) fatigue design recommendations with more accurate and advanced fatigue models that can consider a greater complexity of stress states and materials. As the first part of a multistage test series, an experimental investigation was conducted to determine the fatigue life of concrete subjected to axial compressive fatigue loading, focusing on the relatively high-cycle fatigue domain. Here, a wide range of values for maximum stress levels and stress ratios were considered. The experimental results were compared against existing predictive models, and the most applicable model was identified. Concrete strain and stiffness behavior during fatigue loading were also investigated and reported. Based on the observed behavior, a hypothesis for identifying the impending occurrence of fatigue failure, based on the monotonic stress-strain curve, is examined.

17 WIND ENERGY↗

On the bulk compaction of brittle granular materials, part I: SeS analysis of axial compression to 4000 MPa

The bulk compaction of granular materials has been studied for decades to interpret and manage responses for soils and powder-based component fabrication, and geophysical, celestial, and ballistic impact. Their bulk or macroscopic compaction response is limited by what occurs at the granular or microstructural scale. Motivation existed to more closely examine that association specific to granular brittle materials (e.g., ceramics and glasses). That examination is offered in a series of three companion papers where Part I describes a new supplemental analysis adopted to bulk compaction response involving relatively high compaction stresses (4000 MPa). Bulk compactions of vitreous silicates and crystalline quartzes were interpreted in three ways, including that of a new analysis that considers the product of void ratio (e) and stress (S) as a function of S, hereafter referred to as “SeS analysis”. In conclusion, the SeS analysis was found to be an informative supplement to conventional bulk compaction analyses because it provides more consistent higher sensitivity for the identification of bulk density rate increase with increasing compaction (softening); a rate increase that arises from the cumulative effect of the onsets and progression of compaction-induced yielding, fracture or comminution, densification, phase change, or combinations thereof occurring at the granular or microstructural scale.

compaction↗

Helical instability in MagLIF due to axial flux compression by low-density plasma

The MagLIF (Magnetized Liner Inertial Fusion) experiment at Sandia National Labs is one of the three main approaches to inertial confinement fusion. Radiographic measurements of the imploding liner have shown helical structuring that was not included in MagLIF scaling calculations but that could fundamentally change the viability of the approach. We present the first MagLIF linear dynamics simulations, using extended magnetohydrodynamical (XMHD) as well as standard MHD modeling, that reproduce these helical structures, thus enabling a physical understanding of their origin and development. Specifically, it is found that low-density plasma from the simulated power flow surfaces can compress the axial flux in the region surrounding the liner, leading to a strong layer of axial flux on the liner. The strong axial magnetic field on the liner imposes helical magneto-Rayleigh-Taylor perturbations into the imploding liner. A detailed comparison of XMHD and MHD modeling shows that there are defects in the MHD treatment of low-density plasma dynamics that are remedied by inclusion of the Hall term that is included in our XMHD model. In order to obtain fair agreement between XMHD and MHD, great care must be taken in the implementation of the numerics, especially for MHD. Even with a careful treatment of low-density plasma, MHD exhibits significant shortcomings that emphasize the importance of using XMHD modeling in pulsed-power driven high-energy-density experiments. As a result, the present results may explain why past MHD modeling efforts have failed to produce the helical structuring without initially imposing helical perturbations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Influence of weave architecture on mechanical response of SiC f -SiC m tubular composites

Due to their high resistance to radiation damage and elevated temperature, silicon carbide fiber-reinforced, silicon carbide matrix composites (SiC f -SiC m ) are identified as potential cladding structures for use in nuclear reactors. In this study, four composite architectures with varying ply numbers along the thickness direction and different biaxial or triaxial plain weave orientations at either 45° or 60°, were systematically evaluated under various stress states to assess the influence of weave architecture on mechanical performance. Experiments were conducted on SiC f -SiC m composite tubes under tensile hoop, axial compression, and rotating flexural loading to evaluate the mechanical response and investigate the failure modes using high-speed imaging and digital image correlation (DIC) techniques. It was found that for tensile hoop burst and flexural loading, the braiding angle had the most significant influence on the strength of the composite, whereas the effect of fiber angle was more limited for compression testing. Under axial compression a unique failure mode where a microcrack nucleates and grows only to a length equal to the thickness of a single yarn was identified. This crack growth behavior is reflected as periodic oscillations in the load-displacement response. For both axial and hoop loading, regardless of weave angle and number of plies, failure always initiated parallel to the tube axis in a single yarn and the cumulative interaction of these microcracks lead to either axial burst or fracture at an angle to the tube axis along a yarn. Furthermore, these results point to the importance of customizing the design of tube architecture for enhanced performance in specified nuclear applications.

36 MATERIALS SCIENCE↗

Magnetic moment collapse induced axial alternative compressibility of Cr 2 TiAlC 2 at 420 GPa from first principle

The electronic structure and thermo-dynamical properties of Cr 2 TiAlC 2 are studied by first principles under pressure. The obtained results observed that the ferromagnetic order is the most stable ground state and the magnetic moment will collapse at about 50GPa. As a result, the lattice a axis becomes stiffer above about 420GPa, ultimately presenting the same axial compressibility trends with those of nonmagnetic compounds Mo2TiAlC2 and hypothetical Cr2TiAlC2. The elastic constants and phonon dispersion curves demonstrate the structural stability during the disappearance of magnetic moment and occurrence of axial alternative compressibility. The density of states and energy band calculations confirmed the existence of magnetic moment of Cr2TiAlC2 at 0GPa and disappearance at high pressures above 50GPa. Evolutions of magnetic moment collapse with pressure are confirmed by a variety of properties. The obtained grüneisen parameter and thermal expansion coefficients show the maximum value among the known MAX phases, to date and to the author’s knowledge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Investigation of the High-Pressure Behaviors of Amblygonite by Single-Crystal X-ray Diffraction, Raman Spectroscopy, and DFT Calculations

In the present study, we extensively explored the high-pressure behaviors and vibrational properties of amblygonite LiAlPO 4 F with elevated pressures up to 34.3 GPa based on single-crystal X-ray diffraction measurements, Raman spectroscopy, and DFT calculations. The compressibility and elastic properties of amblygonite were determined first. Specifically, the obtained isothermal bulk modulus of LiAlPO 4 F is 128(4) GPa and the triclinic phase exhibited anisotropic compression with axial compressibility β c > β a > β b with a ratio of 1.11:1.00:1.20. The Raman spectra showed no indication of phase transformation and were used to obtained mode Grüneisen parameters. The average Grüneisen parameter for PO 4 tetrahedral sites was smaller than for the LiO 4 F sites. Our results provide new insights into the phase stability and elastic properties of lithium-fluorite granites at extreme conditions.

36 MATERIALS SCIENCE↗

A novel post-processing method for progressive failure analysis of brittle composite compression

Finite element analysis of brittle materials in axial compression typically uses element deletion to allow continued global deformation post-element-failure. However, element deletion produces cyclic load-displacement curves that underestimate energy absorption and are not representative of a continuum system. Two key observations support the conclusion that results from an appropriately discretized model can be an adequate representation of a continuum system. Specifically, the frequency of the oscillations in the load-displacement curve is directly dependent upon element length in the loading direction, and the peak amplitudes of oscillations are mesh size independent. A method of post-processing the analysis results, by connecting the peak amplitudes of oscillations, is proposed and applied to a series of continuous carbon fiber composite crush tubes. The load-displacement curve, stable crushing load, and specific energy absorption of the post-processed results compare well to an experimental study of crush tubes with similar layups.

Materials Science↗

X-ray diffraction strains in laser-ablated aluminum, nickel, sodium, and invar: Pressures to 475 GPa

Dynamically compressed materials in longitudinal waves are described by two physical models: hydrostatic pressure, with equal, normal, principal stresses or material uniaxially strained in the wave propagation direction. These models are disparate, so experimental comparisons and evaluations are important. Polycrystalline material in a state of hydrostatic pressure will have no eccentricity of x-ray-diffracted Debye–Scherrer rings. A general three-dimensional solution of Bragg diffracted x rays based on principal crystallographic strains in the compression wave was found. The distortion of x-ray diffraction beams has been used for strain measurements; the analysis developed incorporates a strained reciprocal lattice and the incident x-ray beam. Strain-distorted Polanyi surfaces form an annulus of compression with an ellipsoid of revolution in reciprocal space, which is intersected by Ewald's sphere for Bragg diffraction. The in situ measurements for strain describe nanosecond diffraction evaluated using two planes, (hkl) and (h′k′l′), both in the same crystallographic phase. Diffraction from Al, Ni, Na, and Invar quantifies the compression axial strains in these materials: The compression axial ratios are 0.65, 1.05, 0.88, and 1.58 at pressures of 291, 402, 409, and 367 GPa for the respective materials. Crystal structure transformations with homogeneous pressurized stresses, mandating equal normal strains, should not be anticipated to agree with heterogeneous, uniaxially strained, and sheared crystalline phases. Measurements support in-plane strains increasing with pressure, p , in fcc and hcp aluminum as ε 22 = −0.21 p /TPa.

Alloys↗

Negative viscosity from negative compressibility and axial flow shear stiffness in a straight magnetic field

Here, negative compressibility ITG turbulence in a linear plasma device (CSDX) can induce a negative viscosity increment. However, even with this negative increment, we show that the total axial viscosity remains positive definite, i.e. no intrinsic axial flow can be generated by pure ITG turbulence in a straight magnetic field. This differs from the case of electron drift wave (EDW) turbulence, where the total viscosity can turn negative, at least transiently. When the flow gradient is steepened by any drive mechanism, so that the parallel shear flow instability (PSFI) exceeds the ITG drive, the flow profile saturates at a level close to the value above which PSFI becomes dominant. This saturated flow gradient exceeds the PSFI linear threshold, and grows with $\nabla T_{i0}$ as $|\nabla V_\parallel| / |k_\parallel c_s| \sim|\nabla T_{i0}|^{2/3} / (k_\parallel T_{i0})^{2/3}$. This scaling trend characterizes the effective stiffness of the parallel flow gradient.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Compressional behavior of omphacite to 47 GPa

Omphacite is an important mineral component of eclogite. Single crystal synchrotron X-ray diffraction data on natural (Ca,Na)(Mg,Fe,Al)Si 2 O 6 omphacite have been collected at the Advanced Photon Source beamlines 13-BM-C and 13-ID-D up to 47 GPa at ambient temperature. Unit cell parameter and crystal structure refinements were carried out to constrain the isothermal equation of state and compression mechanism. The 3rd order Birch-Murnaghan equation of state (BM3) fit of all data gives V o = 423.9(3) Å3, K To = 116(2) GPa and K To ’ = 4.3(2). These elastic parameters are consistent with the general trend of the diopside-jadeite join. The eight-coordinated polyhedra (M2 and M21) are the most compressible, and contribute to majority of the unit cell compression, while the SiO 4 tetrahedra (Si1 and Si2) behave as rigid structural units and are the most incompressible. Axial compressibilities are determined by fitting linearized BM 3 equation of state to pressure dependences of unit cell parameters. Throughout the investigated pressure range, the b-axis is more compressible than the c-axis. Here, the axial compressibility of the α-axis is the largest among the three axes at 0 GPa, yet it quickly drops to the smallest at pressures above 5 GPa, which is explained by the rotation of the stiffest compression axis toward the a-axis with the increase of pressure.

36 MATERIALS SCIENCE↗

Diagnosing magnetic fields in cylindrical implosions with oblique proton radiography

Two experiments at the OMEGA Laser System used oblique proton radiography to measure magnetic fields in cylindrical implosions with and without an applied axial magnetic field. Although the goal of both experiments was to measure the magnitude of the compressed axial magnetic field in the core of the implosion, this field was obfuscated by two features in the coronal plasma produced by the compression beams: an azimuthal self-generated magnetic field and small length scale, high-amplitude structures attributed to collisionless effects. In order to understand these features, synthetic radiographs are generated using fields produced by 3D HYDRA simulations. These synthetic radiographs reproduce the features of the experimental radiographs with the exception of the small-scale structures. A direct inversion algorithm is successfully applied to a synthetic radiograph but is only partially able to invert the experimental radiographs in part because some protons are blocked by the field coils. The origins of the radiograph features and their dependence on various experimental parameters are explored. Furthermore, the results of this analysis should inform future measurements of compressed axial magnetic fields in cylindrical implosions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Stress–Strain State of Internal Rubber Shock-Absorbing Components in a Small Supporting Roller of a Caterpillar System

The stress–strain state of rubber components in the internal shock absorbers of a small-diameter supporting roller in a caterpillar system is analyzed. An algorithm for its calculation is proposed. The stress–strain states due to axial compression in roller assembly and the radial operational force are considered. The influence of axial compression of the rubber components on the radial rigidity of the supporting roller is determined.

42 ENGINEERING↗

High pressure structure studies of 6H-SrIrO{sub 3} and the octahedral tilting in 3C-SrIrO{sub 3} towards a post-perovskite

The high pressure behaviors of the two perovskite structures (hexagonal 6H-SrIrO{sub 3} and orthorhombic 3C-SrIrO{sub 3}) have been studied in diamond anvil cells to 43 and 60 GPa, respectively, using synchrotron powder X-ray diffraction. 6H-SrIrO{sub 3} was first synthesized at ambient pressure and subsequently transformed into 3C-SrIrO{sub 3} in a large volume press at 8.8 GPa and 1000 °C. Both polymorphs were found to retain the initial symmetry up to the highest pressures measured, but in the case of 6H-SrIrO{sub 3}, two anomalies were identified: a change in the axial compressibilities at 24 GPa and a change in both the axial and volume compressibilities at 32 GPa. Fitting a 3rd order Birch-Murnaghan equation of state to the obtained P-V data yielded bulk moduli of K{sub 0}=151.5(12) GPa (fitted range 0<P<30 GPa) for 6H-SrIrO{sub 3} and K{sub 0}=187.1(9) GPa for 3C-SrIrO{sub 3}. Analysis of the structural parameters for 6H-SrIrO{sub 3} aided by F-f plots suggests the anomalies are caused by changes in the compression mechanism. Comparison of the two polymorphs reveals that 6H-SrIrO{sub 3} becomes less compressible than 3C-SrIrO{sub 3} above 32 GPa as a result of the mechanistic change, and a crossing of their P-V curves is avoided. For 3C-SrIrO{sub 3}, analysis of the octahedral tilt angles shows that these increase monotonically from the ambient value of 7.23(6) to 23.0(2)° at 60 GPa suggesting that a transition to a post-perovskite is approached. - Graphical abstract: The structure of 3C-SrIrO{sub 3} synthesized at high pressure has been studied in a diamond anvil cell and is found to maintain its orthorhombic structure up to 60 GPa but distorts drastically due to octahedral tilting, strongly suggesting that a post-perovskite transition is possible. The compression is compared to 6H-SrIrO{sub 3} synthesized at ambient pressure, which is initially found to be more compressible but undergoes changes in its compression mechanism and 3C remains denser throughout compression. Display Omitted - Highlights: • Structures of 6H- and 3C-SrIrO{sub 3} were studied to pressures of 43 and 60 GPa, respectively. • Both structures maintain the initial symmetry up to the highest pressures measured. • 6H-SrIrO{sub 3} is initially more compressible than 3C-SrIrO{sub 3}. • Due to changes in the compression mechanism in 6H-SrIrO{sub 3} the 3C-SrIrO{sub 3} remains denser throughout. • 3C-SrIrO{sub 3} show large octahedral tilting, strongly suggesting a post-perovskite transition is imminent.

36 MATERIALS SCIENCE↗