Principal Shear Directions Research Articles

Investigating the structure under the Pingting Terrace from the co-seismic surface rupture of the 2022 Guanshan earthquake

AbstractOn September 17th and 18th, 2022, shallow earthquakes with magnitudes of 6.6 (ML) and 6.8 (ML) occurred in the eastern Taiwan Longitudinal Valley, which marks the collision zone between the Philippine Sea plate and the Eurasian plate, and led to noticeable surface deformation and ruptures within 70 km. This study primarily focuses on the southernmost section of the rupture zone—the Pingting Terrace. Surface rupture locations and behaviors correspond to changes in topography, providing mutual confirmation that the deformation behavior of Pingting Terrace is complex. Based on the distribution of surface ruptures and topography changes, this study roughly divides the Pingting Terrace into northern and southern segments, using the central concave feature as a boundary. The Riedel shear model analysis results show that the principal shear directions in the northern and southern segments are N–S trending and azimuth 20°, respectively. The maximum principal stress orientations are around 135° for the northern and 155° for the southern segments. These findings align with the fault mechanical investigation of the Lichi Mélange in the northern Muken River area of the Pingting Terrace. This suggests spatial changes in shear zone orientations within the Lichi Mélange, which contribute to developing pressure ridges due to transpressional forces. As a result, the Pingting Terrace experiences rapid uplift, causing the Luliao River to migrate southward into the Beinan River, while the eastern Beinan River turns to the eastward edge of the Pingting Terrace.

Close-Packed Spherical Morphology in an ABA Triblock Copolymer Aligned with Large-Amplitude Oscillatory Shear

A microphase-separated poly(styrene-b-(lauryl-co-stearyl acrylate)-b-styrene) (SAS) triblock copolymer exhibiting a disordered spherical microstructure with randomly oriented grains was aligned through the application of large-amplitude oscillatory shear (LAOS) at a temperature below the order–disorder transition temperature of the triblock copolymer, yet above the glass transition temperature of the polystyrene spherical domains. The thermoplastic elastomeric behavior of the SAS triblock copolymer provided a convenient means to observe the aligned morphology. Following application of LAOS, the specimen was quenched to room temperature (below the glass transition temperature of polystyrene), and small-angle X-ray scattering data were obtained in the three principal shear directions: shear gradient, velocity, and vorticity directions. The analysis revealed that the SAS triblock copolymer formed coexisting face-centered cubic and hexagonally close-packed spherical microstructures. The presence of a close-pa...

Microstructure and chemistry of an Al-4.7 wt.%Mg alloy subsurface after cold-rolling

During cold rolling, the surface and the near-surface region of a metal sheet are submitted to deformation states different from the bulk of the sheet. Indeed, the principal shear directions vary from the surface to different depths inside the sheet. The aim of the present study was to understand the influence of the working process on the nature and behavior of the surface and subsurface layers of a cold rolled Al-4.7wt.%Mg alloy. Features such as microstructure and texture have been investigated using Transmission Electron Microscopy (TEM) and electron micro-diffraction. Chemical characterization has been performed by using Energy Dispersive X-ray Spectroscopy (EDS), Secondary Ion Mass Spectroscopy (SIMS) and Glow-Discharge Optical Spectrometry (GDOS).

Determination of the Piezospectroscopic Coefficients for Chromium‐Doped Sapphire

The coefficients of the piezospectroscopic tensor for a 0.05 wt% ruby are evaluated by direct measurement of the frequency shift for uniaxial compression along the three principal crystallographic directions and for loading in the three principal shear directions. Although the numerical value of the trace of the tensor is the same äs previously reported, the piezospectroscopic coefficients along the c and m directions are slightly different. Contrary to expectation from the rotational symmetry of sapphire about the c axis, the coefflcient along the a direction was found to be different from that along the m direction. It also varies nonlinearly with strain in the a direction. The difference is attributed to the applied stress breaking the rotational symmetry about the c axis and is interpreted in terms of the relative motion of the Cr3+ ion with respect to the nearest‐neighbor oxygen ions. An additional finding is that there is a signiflcant difference in the piezospectroscopic tensor for the Rl and R2 lines. This will facilitate a more complete determination of the stress tensor from fluorescence measurements than has hitherto been possible.

Chain conformation in sheared polymer melts as revealed by SANS

The conformation of polymer chains in the melt during simple shear flow has been characterized by SANS on a narrow molecular weight distribution polystyrene sample. An apparatus has been designed which allows one to freeze-in by quenching uniform shear orientations in thick specimens on which the scattering experiments can be performed in the three principal shear directions. In the 1-2 shearing plane, the orientation of molecular anisotropy with respect to the shear axes is found to depend on the magnitude of the scattering vector and therefore on the considered length scale on the chin. A method has been proposed to analyze the data in this plane. The chin dimension in the neutral shear direction remains unaffected by the flow

Some Comments on the Optimization Problem for Shear Stress Magnitude

Directions of maximum and minimum shear stress magnitude at a point can be found as solutions to a Lagrange multiplier problem. All three principal shear directions are solutions to the optimization, but only the largest principal shear occurs at a local maximum. The other two principal shears correspond to saddle points for shear stress magnitude. These spurious solutions do not arise if the problem is recast as a Kuhn–Tucker optimization for inequality, rather than equality, constraints.

Rolling contact deformation, etching effects, and failure of high-strength bearing steel

This paper examines the connections between the continuing cyclic plastic deformation, the etching effects, and the fatigue life of a high-strength bearing steel under rolling contact. Etching effects, called the “dark etching regions” and the “white etching bands,” are observed after several million cycles. The inclinations of the white etching bands vary between 20 to 30 deg and 70 to 80 deg to the rolling direction, depending on the loading conditions and geometry of the rolling elements. The principal axes of stress and plastic strain rotate continuously as the rolling element translates over a fixed point below the running surface. At the same time, the cyclic plastic activity varies. A finite element model is used to calculate the inclinations and amounts of cyclic plastic strain as the roller translates over the running surface. The calculations are performed for both elastic linear kinematic-hardening plastic (ELKP) and elastic perfectlyplastic (EPP) material behaviors. Inclinations of concentrated plastic strain activity combined with low hydrostatic pressure are identified. There is a good correlation between the inclinations of the white etching bands and the inclinations of concentrated plastic activity calculated for the ELKP material behavior. No such correlation is obtained for the EPP behavior. Strain concentrations are intensified by the hydrostatic pressure dependence of the kinematic yield strength. While an equal amount of plastic strain activity occurs in the conjugate directions, no etching bands are observed at these inclinations. The reasons for this are not clear. The shakedown limit obtained for the two models is essentially the same. The fatigue lives under rolling contact are compared with the lives obtained in simple cyclic torsion experiments with the same cyclic plastic strain amplitudes. The rotation of the principal shear direction and the high hydrostatic pressure attending rolling contact may be responsible for the seven orders-of-magnitude longer contact lives.

Rolling contact deformation and microstructural changes in high strength bearing steel

This paper examines the connections between the continuing cyclic plastic deformation, the etching effects and the fatigue life of high strength bearing steel under rolling contact. A finite element model is used to calculate the increments of cyclic plastic strain as the roller translates over the running surface. The cyclic plastic strain is related to the plasticity-induced microstructural changes observed in bearings. The calculations are performed for both elastic linear kinematic hardening plastic and elastic-perfectly plastic material behaviors. Observed fatigue lives under rolling contact are compared with the lives obtained in simple cyclic torsion experiments with the same cyclic plastic strain amplitudes. The rotation of the principal shear direction, the smaller strained volume, and the high hydrostatic pressure attending rolling contact may be responsible for the contact lives, which are seven orders of magnitude longer.