Small-Strain Shear Modulus of Calcareous Sand under Anisotropic Consolidation

In this study, the small strain shear modulus of a calcareous sand was investigated by conducting bender element tests on both horizontal and vertical planes. The effects of sample preparation method, stress path and stress history on the developing of void ratio, the parameters in the modified Hardin equation and the stiffness anisotropy were examined. The test results show that the moist tamping samples have the least void ratio variation among the five samples. The void ratio recovery in σ'h = 100 kPa tests is higher than that in the σ'v = 100 kPa tests. The samples prepared in dry state have lower stiffness than those prepared in moisture state, which is not influenced by the anisotropic stress state. The stiffness anisotropy induced by the sample preparation method is significant under anisotropic consolidation. In σ'h = 100 kPa tests, the stiffness ratios at the end of the unloading stage are lower than the initial values at the loading stage, which is not found in the σ'v = 100 kPa tests, meaning that the stress history and stress path could affect the stiffness anisotropy and cover the impact of fabric anisotropy.

RADIAL STIFFNESS ANISOTROPY OF BODY BORING FOR LATHE SPINDLE BEARINGS

In the paper there are considered problems connected with the radial stiffness anisotropy of body borings for lathe spindle bearings. Factors having an influence upon stability of its operation characteristics of a machine-tool during idling are considered. The analysis of force factors having an influence upon bearings of a spindle unit during lathe idling is carried out. The work purpose is to determine a quantitative and qualitative situation in the changes of boring forms for spindle bearings under the impact of loads mentioned. As an object of investigations there is chosen the lathe “Vector” manufactured at the Middle-Volga machine-tool plant. A finite element modeling is carried out for deformation investigations in the body boring of the spindle unit under the impact of forces caused by weight and imbalance of the rotating spindle. There is shown a geometrical model of a spindle carrier body, the peculiarities of a finite element model formation and a procedure for the fulfillment of a numerical experiment are described, and approaches of boundary conditions setting are also considered. As a result of a finite element there are obtained values of finite element unit displacements lying on the surface of the body boring of the spindle carrier under the impact of the mentioned power factors. The results found are presented for illustration in the form of solid and flat graphical dependences. The analysis of numerical experiment results has confirmed the presence of the stiffness anisotropy in spindle unit bearings. The phenomenon of stiffness anisotropy in bearings was already under consideration in investigations carried out earlier. But the results of the numerical experiments carried out by us have shown that along with other factors the imbalance forces together with design peculiarities of body parts have an influence upon the constancy of elastic characteristics of bearings. The matter obtained can be used during development of measures for design changes in a spindle unit body with the purpose of stiffness anisotropy decrease in the borings for bearing.

Stiffness and strength anisotropy of overconsolidated Bootlegger Cove clays

This paper presents the evaluation of the stiffness and strength anisotropy of overconsolidated (OC) Bootlegger Cove Formation (BCF) clays at the Port of Alaska, formerly known as the Port of Anchorage. The stiffness and strength anisotropic material response was evaluated based on triaxial samples equipped with internal instrumentation including a submersible load cell and three subminiature linear variable displacement transducers (LVDTs). Three sets of bender elements were used in this research to measure shear wave velocities for different propagation and polarization directions. The effects of reproducing the stress history of the soil deposit on the stiffness cross-anisotropic behavior of the material are discussed. The laboratory test results are compared with in situ measurements of shear wave velocities based on suspension logging and crosshole and downhole soundings. The results of the experimental program showed that BCF clay is a cross-anisotropic material. Mean stiffness anisotropy ratios ranged from 0.90 to 1.22 and 0.93 to 1.46 for lightly OC and OC conditions, respectively. Strength anisotropy ratios, defined as the ratio of undrained shear strength under triaxial extension to compression, varied between 0.8 and 0.5. It is found that reproducing the stress history of the OC soil deposit during the laboratory reconsolidation stage did not have a significant impact on the initial stiffness anisotropy ratios of the BCF clay.

Quantifying static and dynamic stiffness anisotropy and nonlinearity in finely laminated shales: Experimental measurement and modeling

Sedimentary rocks contain layers and a wide range of microstructures that may produce mechanical complexities including dynamic and quasistatic stiffness anisotropy and nonlinearity. However, most applications in geophysics and geomechanics disregard these mechanical complexities, which can lead to significant error and uncertainty in rock properties and may increase the risk associated with cost-intensive drilling and completions operations in shales. We have conducted simultaneous triaxial stress tests and ultrasonic wave propagation monitoring to measure and model stiffness anisotropy and nonlinearity of Mancos Shale plugs with varying bedding orientations. Results highlight the need for different sets of nonlinear coefficients to describe different stress loading paths, in which isotropic loading exhibits larger increases in stiffness for a given change in mean stress (and strain) than deviatoric loading. The vertical transverse isotropic (VTI) nonlinear model helps to account for the appreciable anisotropy and nonlinearity of Mancos samples, in which the dynamic Young’s moduli [Formula: see text] are more than 25% higher than [Formula: see text] and [Formula: see text] increases by approximately 35% during deviatoric stress loading. Measured static moduli are typically less than 50% of their dynamic equivalent and exhibit separate anisotropic and nonlinear relationships. Therefore, we have developed anisotropic stress-dependent dynamic-static transforms to estimate the static moduli from the nonlinear VTI model. Although heterogeneity and discontinuities cause samples to deviate from VTI symmetry, our modified dynamic-static transforms provide an excellent fit to the experimentally measured Young’s moduli and Poisson’s ratios. Post-test X-ray micro-CT imaging evidences the impact of sample layering and heterogeneity on rock failure and failure geometry. Bedding planes can act as preferential failure planes, whereas layering-induced mechanical stratigraphy can cause fractures to reorient due to changes in lithology. Our combined experimental, modeling, and imaging results provide insight into the complex deformational and failure behavior of shales. The analysis and results also highlight the need to consider the elastic and plastic deformations in shales.

Design of bending dominated lattice architectures with improved stiffness using hierarchy

Micro-architectured lattices are a promising subclass of cellular solids whose inner topologies can be tailored to enhance their stiffness. Generally, enhancing lattices' stiffness is achieved by increasing their connectivity. This strategy gives rise to a stiffer response by forcing lattices' ligaments to deform mainly in an axial manner. Conversely, this work is interested in developing micro-architectured lattices with enhanced stiffness, but whose cell walls deform in a flexural manner. Such structures can be more ductile and exhibit better energy mitigation abilities than their stretching dominated counterparts. Enhancing the stiffness of bending dominated lattices without increasing their connectivity can be realized by transforming them to hierarchical ones. This work explores, using experimentally verified finite element simulations, the effect of fractal-inspired hierarchy and customized nonfractal-based hierarchy on stiffness, anisotropy, and deformation mechanisms of an anisotropic bending dominated diamond lattice. Results show that fractal-inspired hierarchy can significantly enhance the stiffness of bending dominated lattices without affecting their deformation mechanisms or anisotropy level; ill-designed hierarchy can have a detrimental effect on lattice's stiffness; and customized hierarchy are more effective than fractal-inspired hierarchy in enhancing lattices' stiffness as well as can be more compatible with traditional, reliable, mass-producing manufacturing processes.

Finite Element Analysis and Experimental Validation of Transfer Function of Rotating Shaft System With Both an Open Crack and Anisotropic Support Stiffness

In this paper, transfer function of rotating shaft system for detecting transverse open crack is developed. Rotating shaft system is modeled using one-dimensional finite element method (1D-FEM), and quantitative analysis is performed. Open crack is modeled as weak asymmetry rotating with shaft's rotation. It is known that, when both open crack and support stiffness anisotropy coexist, various frequency components of shaft's vibration are generated through their successive interaction. This paper evaluates the order of these components, and concludes that first five main components are enough to investigate interaction of open crack and support stiffness anisotropy. Then, five sets of transfer functions for these components are derived. The validity of this set of transfer functions is confirmed by numerical simulation. Moreover, excitation experiment utilizing active magnetic bearing (AMB) is performed, and the validity of derived transfer function was verified experimentally.

Characterization of Mechanical Property Distributions on Tablet Surfaces

Powder densification through uniaxial compaction is governed by a number of simultaneous processes taking place on a reduced time as the result of the stress gradients within the packing, as well as the frictional and adhesive forces between the powder and the die walls. As a result of that, a density and stiffness anisotropy is developed across the axial and radial directions. In this study, microindentation has been applied to assess and quantify the variation of the module of elasticity ( E m o d ) throughout the surface of cylindrical tablets. A representative set of deformation behaviors was analyzed by pharmaceutical excipients ranging from soft/plastic behavior (microcrystalline cellulose) over medium (lactose) to hard/brittle behavior (calcium phosphate) for different compaction pressures. The results of the local stiffness distribution over tablet faces depicted a linear and directly proportional tendency between a solid fraction and E m o d for the upper and lower faces, as well as remarkable stiffness anisotropy between the axial and radial directions of compaction. The highest extent of the stiffness anisotropy that was found for ductile grades of microcrystalline cellulose (MCC) in comparison with brittle powders has been attributed to the dual phenomena of overall elastic recovery and Poisson’s effect on the relaxation kinetics. As a reinforcement of this analysis, the evolution of the specific surface area elucidated the respective densification mechanism and its implementations toward anisotropy. For ductile excipients, the increase in the contact surface area as well as the reduction and closing of interstitial pores explain the reduction of surface area with increasing compaction pressure. For brittle powders, densification evolves through fragmentation and the subsequent filling of voids.