Deformation Length Scale Research Articles

Plasticity in pentacene thin films

We have investigated the structure, defects and plasticity of thermally evaporated thin films of the organic molecular semiconductor pentacene using X-ray Diffraction (XRD), Optical microscopy (OM), Transmission Electron Microscopy (TEM), Electron Diffraction (ED), and High Resolution Electron Microscopy (HREM). Using XRD the degree of (001) texturing present in the as-grown films was characterized. The nature of pentacene plasticity and deformation-induced molecular alignment was investigated using rubbing and scratching techniques, as well as nanoindentation. Rubbing of the bulk powder produced thin oriented films, and a deformation length scale dependence was seen. Under stress pentacene crystals initially fail by cracking, until they reach a critical size of about one micron, when they tend to plastically deform into thin sheets. Alignment of thermally evaporated films was achieved under a controlled load scratch, and the degree of molecular orientation inside the scratched region was directly imaged using HREM. Finally, using nanoindentation we measured pentacene's plastic hardness to be 0.25 GPa at a loading rate 0.05 mN/s. A loading rate dependence of the hardness and stiffness was measured, with thin films behaving harder and stiffer at faster indentation rates.

Cross-shelf variations of near-inertial current oscillations

Observations and numerical simulations show that cross-shelf variations of current oscillations at near-inertial frequencies increase exponentially in amplitude from nearshore to waters with depths of 100–200 m. An assessment of a semi-analytical theory of the cross-shelf variation of near-inertial current oscillations (Chen and Xie, 1997, Journal of Geophysical Research 102(C7), 15,583–15,593) indicates that, although instructive, the theory does not capture all the elements seen in numerical simulations. Here a purely analytical approach is taken. It assumes only that the cross-shelf currents are of the form AB cos ft, where B is an amplitude modifier (a function of the distance offshore) and f is the Coriolis parameter. The solution to the governing equations gives B=1−e − x/ L , where x is the distance offshore and L is a radius of deformation length scale. The solutions show that exponentially increasing current oscillations over continental shelves are actually a form of inertial-gravity waves. In non-equatorial regions, the effect of the sea surface pressure gradient is found to be in phase with that of the Coriolis effect but with a much larger magnitude over the inner continental shelves. The kinematic boundary condition results in the oscillating sea level setup and setdown, the resulting pressure gradient drives the oscillatory cross-shelf currents over the inner continental shelf, and the Coriolis effect results in a corresponding oscillatory flow in the longshore direction. One of the more notable findings is that the length scale L, referred to here as the inertial-gravity barotropic radius of deformation, is found to be significantly larger than the classical barotropic radius of deformation.

Jetlet Formation from Diabatic Forcing with Applications to the 1994 Palm Sunday Tornado Outbreak

Abstract The three-dimensional responses of simple stably stratified barotropic and baroclinic flows to prescribed diabatic forcing are investigated using a dry, hydrostatic, primitive equation numerical model (the North Carolina State University Geophysical Fluid Dynamics Model). A time-dependent diabatic forcing is utilized to isolate the effects of latent heat release in a midlatitude convective system. Examination of the mass-momentum adjustments to the diabatic forcing is performed with a focus on the development of an isolated midlevel wind maximum. The results of both cases suggest the formation of a midlevel wind maximum in the form of a perturbation meso-β-scale cyclone, which later propagates downstream as the heating is decreased. The scale of the perturbation cyclone remains at a sub-Rossby radius of deformation length scale. Therefore, the mass perturbations adjust to the wind perturbations as the mesocyclone propagates downstream. Transverse vertical circulations, which favor ascent on the r...

On the role of strain gradients in adiabatic shear banding

The effect of higher order strain gradients on adiabatic shear banding is investigated by considering the simple shearing of a heat conducting thermoviscoplastic material with a gradient-dependent flow stress. The competition between the gradient-dependent plastic flow and heat conduction and their influence on the shear band width and structure are examined. Two internal length scales, i.e., the deformation internal length and the thermal internal length, are incorporated into the linear stability analysis, which shows that the band width size scales either with the square root of the strain gradient coefficient (in the absence of heat conduction) or the thermal conductivity (in the absence of strain gradients), respectively. The numerical computation for the nonlinear problem reveals that the “diffusive” effect of the strain gradient is much stronger than that of the heat conduction and dictates the constitutive response of the material in the postlocalization regime, and shows that the deformation length scale is much larger than the termal length scale. The band width predicted by the gradient theory agrees reasonably well with the experimental observations found in the literature.

Measurements of strain at plate boundaries using space based geodetic techniques

We have used the space based geodetic techniques of Satellite Laser Ranging (SLR) and Very Long Baseline Interferometry (VLBI) to study strain along subduction and transform plate boundaries and have interpreted the results using a simple elastic dislocation model. Six stations located behind island arcs were analyzed as representative of subduction zones while 13 sites located on either side of the San Andreas fault were used for the transcurrent zones. The length deformation scale was then calculated for both tectonic margins by fitting the relative strain to an exponentially decreasing function of distance from the plate boundary. Results show that space‐based data for the transcurrent boundary along the San Andreas fault help to define better the deformation length scale in the area while fitting nicely the elastic half‐space earth model. For subduction type boundaries the analysis indicates that there is no single scale length which uniquely describes the deformation. This is mainly due to the difference in subduction characteristics for the different areas, and the use of an elastic stress model then helps us understand some of these differences.

Diffuse continental deformation: length scales, rates and metamorphic evolution

In contrast with the oceanic portions of the plates, continents may deform hundreds of kilometres away from any plate boundary. Calculations that treat the continents as continuous media suggest that the across-strike length scale of deformation associated with a convergent boundary is proportional to the along-strike length of the boundary, the constant of proportionality depending on the rheology of the lithosphere. The dependence on convergent boundary length implies that, for fixed velocity of convergence, strain rates decrease with increasing length of the orogen. The dependence on rheology is less straightforward, but it appears from laboratory determination of flow laws that the scale length of compressional deformation decreases as the fraction of the lithospheric strength supported by friction on faults increases; that fraction depends on the thermal profile of the continental lithosphere and will change during the evolution of an orogenic belt. The thermal development of a diffusely deforming compressional belt is nearly independent of its strain history unless the strain rates are less than about 10 -15 s -1 . If erosion terminates the heating phase of such an orogenic belt, the dominant control on the metamorphic history is the heat supply to the continental lithosphere. In contrast, if extension of the thickened crust ends metamorphism, peak metamorphic conditions depend only on the rheological properties of the lithosphere. Metamorphism in crust that is subject to major extension following compressional orogenesis should be nearly independent of the initial thermal conditions of the crust, and may be distinguished from metamorphism terminated by erosion by a final stage of isobaric cooling from temperatures close to the maximum experienced.

Continuum calculations of continental deformation in transcurrent environments

A thin viscous sheet approximation is used to investigate continental deformation near a strike‐slip boundary. The vertically averaged velocity field is calculated for a medium characterized by a power law rheology with stress exponent n. Driving stresses include those applied along boundaries of the sheet and those arising from buoyancy forces related to lateral differences in crustal thickness. Calculations are performed with either velocity or stress prescribed on the transcurrent boundary. Exact and approximate analytic solutions for a region with a sinusoidal strike‐slip boundary condition are compared with solutions for more geologically relevant boundary conditions obtained using a finite element technique. The across‐strike length scale of the deformation is approximately 1/[4π(n)1/2] times the dominant wavelength of the imposed strike‐slip boundary condition for both the analytic and the numerical solutions; this result is consistent with length scales observed in continental regions of large‐scale transcurrent faulting. An approximate, linear relationship between displacement and rotation is found that depends only on the deformation length scale and the rheology. Calculated displacements, finite rotations, and distribution of crustal thicknesses are consistent with those observed in the region of the Pacific‐North America plate boundary in California.

Finite strain calculations of continental deformation: 1. Method and general results for convergent zones

A finite element method is used to calculate stresses and strain rates in a thin viscous sheet, representing the continental lithosphere, that is bordered in one part by an indenting boundary. We calculate solutions for velocity fields, crustal thickness distributions, strain rates, rotation (time‐integrated vorticity), and finite strain ellipsoids to show the dependence of these quantities on the controlling parameters: the stress‐strain exponent n and the strength of the sheet relative to the gravitational forces (which may be expressed as a dimensionless number: the Argand number Ar). For n > 3 and Ar between 1 and 10 a plateau of thickened crust is formed in front of the indenter. The strain histories of individual elements within the viscous sheet may be quite complex, and the finite strain at the end of deformation may bear no obvious relation to the principal stress orientations during the deformation. The strain rate fields are interpreted in terms of the style of faulting that would be expected in the brittle upper crust if it were coupled to the ductile, but stronger, upper mantle. In general, the length scale of deformation increases with Ar and time since the start of the collision and decreases with n; for Ar ≃ 3, the increase in length scale is accompanied by a change in the style of deformation: from predominantly crustal thickening (with thrust faulting in the brittle layer) to predominantly transcurrent deformation (strike‐slip faulting in the brittle layer).