Simulations of oil spread on a water surface

Numerical simulation of an oil slick spreading on still and wavy surfaces is described in this paper. The so-called sigma transformation is used to transform the time-varying physical domain into a fixed calculation domain for the water wave motions and, at the same time, the continuity equation is changed into an advection equation of wave elevation. This evolution equation is discretized by the forward time and central space scheme, and the momentum equations by the projection method. A damping zone is set up in front of the outlet boundary coupled with a Sommerfeld-Orlanski condition at that boundary to minimize the wave reflection. The equations for the oil slick are depth-averaged and coupled with the water motions when solving numerically. As examples, sinusoidal and solitary water waves, the oil spread on a smooth plane and on still and wavy water surfaces are calculated to examine the accuracy of simulating water waves by Navier-Stokes equations, the effect of damping zone on wave reflection and the precise structures of oil spread on waves.

Torsional impact of transversely isotropic solid with functionally graded shear moduli and a penny-shaped crack

The torsional impact response of a penny-shaped crack in an unbounded transversely isotropic solid is considered. The shear moduli are assumed to be functionally graded such that the mathematics is tractable. Laplace transform and Hankel transform are used to reduce the problem to solving a Fredholm integral equation. The crack tip stress fields are obtained. Investigated are the influence of material nonhomogeneity and orthotropy on the dynamic stress intensity factor. The peak value of the dynamic stress intensity factor can be suppressed by increasing the shear moduli's gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface.

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress,intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.

Transition to Chaos in the Floating Half Zone Convection

The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge. The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos. The measured Feigenbaum numbers are delta(2) = 4.69 and delta(4) = 4.6, which are comparable with the theoretical asymptotic value delta = 4.669.

Martensitic transformation under impact with high strain rate

This paper deals with the quantitative prediction of the volume fraction of martensitic transformation in a austenitic steel that undergoes impact with high strain rate. The coupling relations between strain, stress, strain rate, transformation rate and transformed fraction were derived from the OTC model and modified Bodner-Partom equations, where the impact process was considered as an adiabatic and no entropy-increased process (pressure less than or equal to 20GPa). The one-dimensional results were found to model and predict various experimental results obtained on 304 stainless steel under impact with high strain rate.

The instability analysis of saturated soil under shear load

A theoretical description of shear instability is presented in a system of equations. It is shown that two types of instability may exist. One of them is dominated by pore pressure softening while the other by strain softening. A criterion combining pore pressure softening, strain hardening, and volume strain coefficient is obtained and practical implications are discussed.

Two bifurcation transitions of the floating half zone convection in a fat liquid bridge of larger Pr

The transient process of the thermocapillary convection was obtained for the large Pu floating half zone by using the method of three-dimensional and unsteady numerical simulation. The convection transits directly from steady and axisymmetric state to oscillatory flow for slender liquid bridge, and transits first from steady and axisymmetric convection to the steady and non-axisymmetric convection, then, secondly to the oscillatory convection for the fatter liquid bridge. This result implies that the volume of liquid bridge is not only a sensitive critical parameter for the onset of oscillation, but also relates to the new mechanism for the onset of instability in the floating half zone convection even in case of large Prandtl number fluid.

A new model of thermocapillary convection in floating half zone

A new model of thermocapillary convection in floating half zone was suggested in the present paper. The liquid bridge floats between two co-axis rods, the lower rod consists of metal with constant temperature and the upper rod consists of thermal insulating materials, where the normal gradient of temperature is nearly zero. In this case, the new model is relatively closer to simulate a half part of floating full zone in microgravity environment in comparison with the usual model of floating half zone. Basic features of the new model were studied by both numerical simulation and experiments, and the comparisons with the usual model were also discussed.

Dynamic stress intensity factor of a functionally graded material under antiplane shear loading

The dynamic response of a finite crack in an unbounded Functionally Graded Material (FGM) subjected to an antiplane shear loading is studied in this paper. The variation of the shear modulus of the functionally graded material is modeled by a quadratic increase along the direction perpendicular to the crack surface. The dynamic stress intensity factor is extracted from the asymptotic expansion of the stresses around the crack tip in the Laplace transform plane and obtained in the time domain by a numerical Laplace inversion technique. The influence of graded material property on the dynamic intensity factor is investigated. It is observed that the magnitude of dynamic stress intensity factor for a finite crack in such a functionally graded material is less than in the homogeneous material with a property identical to that of the FGM crack plane.

Weak Zone Related Seismic Cycles in Progressive Failure Leading to Collapse in Brittle Crust

Until quite recently our understanding of the basic mechanical process responsible for earthquakes and faulting was not well known. It can be argued that this was partly a consequence of the complex nature of fracture in crust and in part because evidence of brittle phenomena in the natural laboratory of the earth is often obliterated or obscured by other geological processes. While it is well understood that the spatial and temporal complexity of earthquakes and the fault structures emerge from geometrical and material built-in heterogeneities, one important open question is how the shearing becomes localized into a band of intense fractures. Here the authors address these questions through a numerical approach of a tectonic plate by considering rockmass heterogeneity both in microscopic scale and in mesoscopic scale. Numerical simulations of the progressive failure leading to collapse under long-range slow driving forces in the far-field show earthquake-like rupture behavior. $En Echelon$ crack-arrays are reproduced in the numerical simulation. It is demonstrated that the underlying fracturing induced acoustic emissions (or seismic events) display self-organized criticality------from disorder to order. The seismic cycles and the geometric structures of the fracture faces, which are found greatly depending on the material heterogeneity (especially on the macroscopic scale), agree with that observed experimentally in real brittle materials. It is concluded that in order to predict a main shock, one must have extremely detailed knowledge on very minor features of the earth's crust far from the place where the earthquake originated. If correct, the model proposed here seemingly provides an explanation as to why earthquakes to date are not predicted so successfully. The reason is not that the authors do not understand earthquake mechanisms very well but that they still know little about our earth's crust.

Behavior of Multiple Shear Bands in Zr-Based Bulk Metallic Glass

The deformation behavior of Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass was studied by in situ scanning electron microscopy (SEM) quasi-static uniaxial compression tests at room temperature. Multiple shear bands were observed with a large plasticity. Microscopic examination demonstrates that slipping, branching and intersecting of multiple shear bands are the main mechanisms for enhancing the plasticity of this metallic glass. Additionally, nano/micro-scale voids and cracks at the intersecting sites of shear bands and preferential etching of shear bands were observed as well. These observations demonstrated that the formation of shear bands in bulk metallic glasses is resulted mainly from local free volume coalescence.

Gamma -> Epsilon Martensite Transformation and Twinning Deformation in fcc Cobalt During Surface Mechanical Attrition Treatment

The deformation microstructure of face-centered cubic cobalt subjected to surface mechanical attrition treatment was studied as a function of strain levels. Strain-induced gamma --> epsilon transformation and twinning deformation were evidenced by transmission electron microscopy and were found to progress continuously in ultrafine and nanocrystalline grains as the strain increased.

Shear localization and recrystallization in dynamic deformation of 8090 Al-Li alloy

The microstructural evolution in localized shear deformation was investigated in an 8090 Al-Li alloy by split Hopkinson pressure bar (strain rate of approximately 10(3) s(-1)) at ambient temperature and 77 K. The alloy was tested in the peak-, over-, under-, and natural-aged conditions, that provide a wide range of microstructural parameters and mechanical properties. Two types of localized shear bands were distinguished by optical microscopy: the deformed shear band and the white-etching shear band. They form at different stages of deformation during localization. There are critical strains for the occurrence of deformed and white-etching localized shear deformation, at the imposed strain rate. Observations by transmission electron microscopy reveal that the white-etching bands contain fine equiaxed grains; it is proposed that they are the result of recrystallization occurring during localization. The deformed-type bands are observed after testing at 77 K in all heat treatment conditions, but they are not as well defined as those developed at ambient temperature. Cracking often occurs along the localized shear at ambient temperature. The decrement in temperature is favorable for the nucleation, growth and coalescence of the microcracks along the shear bands, inducing fracture.

A Thermodynamic Constitutive Model for Stress Induced Phase Transformation in Shape Memory Alloys

In this paper a thermodynamic constitutive model is developed for stress induced phase transformation in single crystalline and polycrystalline shape memory alloys (SMAs). Volume fractions of different martensite variants are chosen as internal variables to describe the evolution of microstructure state in the material. This model is then used in prediction the transformation behavior of a SMA (Cu-Al-Zn-Mn) under complex thermomechanical load (including complete and incomplete transformation in mechanical cycling, and proportional/non-proportional loading). (C) 2002 Elsevier Science Ltd. All rights reserved.

Instability from steady and axisymmetric to steady and asymmetric floating half zone convection in a fat liquid bridge of larger Prandtl number

The linear instability analysis of the present paper shows that the thermocapillary convection in a half floating zone of larger Prandtl number has a steady instability mode w(i) = 0 and m = 1 for a fat liquid bridge V = 1.2 with small geometrical aspect ratio A = 0.6. This conclusion is different from the usual idea of hydrothermal instability, and implies that the instability of the system may excite a steady and axial asymmetric state before the onset of oscillation in the ease of large Prandtl number.