“Deborah Numbers”, Coupling Multiple Space and Time Scales and Governing Damage Evolution to Failure

Two different spatial levels are involved concerning damage accumulation to eventual failure. nucleation and growth rates of microdamage nN* and V*. It is found that the trans-scale length ratio c*/L does not directly affect the process. Instead, two independent dimensionless numbers: the trans-scale one * * ( V*)including the * **5 * N c V including mesoscopic parameters only, play the key role in the process of damage accumulation to failure. The above implies that there are three time scales involved in the process: the macroscopic imposed time scale tim = /a and two meso-scopic time scales, nucleation and growth of damage, (* *4) N N t =1 n c and tV=c*/V*. Clearly, the dimensionless number De*=tV/tim refers to the ratio of microdamage growth time scale over the macroscopically imposed time scale. So, analogous to the definition of Deborah number as the ratio of relaxation time over external one in rheology. Let De be the imposed Deborah number while De represents the competition and coupling between the microdamage growth and the macroscopically imposed wave loading. In stress-wave induced tensile failure (spallation) De* < 1, this means that microdamage has enough time to grow during the macroscopic wave loading. Thus, the microdamage growth appears to be the predominate mechanism governing the failure. Moreover, the dimensionless number D* = tV/tN characterizes the ratio of two intrinsic mesoscopic time scales: growth over nucleation. Similarly let D be the “intrinsic Deborah number”. Both time scales are relevant to intrinsic relaxation rather than imposed one. Furthermore, the intrinsic Deborah number D* implies a certain characteristic damage. In particular, it is derived that D* is a proper indicator of macroscopic critical damage to damage localization, like D* ∼ (10–3~10–2) in spallation. More importantly, we found that this small intrinsic Deborah number D* indicates the energy partition of microdamage dissipation over bulk plastic work. This explains why spallation can not be formulated by macroscopic energy criterion and must be treated by multi-scale analysis.

Failure process analysis of cement under explosive loading with a generalized driven nonlinear threshold model

The microstructural heterogeneity and stress fluctuation play important roles in the failure process of brittle materials. In this paper, a generalized driven nonlinear threshold model with stress fluctuation is presented to study the effects of microstructural heterogeneity on continuum damage evolution. As an illustration, the failure process of cement material under explosive loading is analyzed using the model. The result agrees well with the experimental one, which proves the efficiency of the model.

Mechanisms of thermal shock failure for ultra-high temperature ceramic

The materials considered in our analysis were ZrB2 ceramic matrix composites. Effect of two different additives (graphite and AlN) on thermal shock stability for the materials was measured by water quench test. It showed that it may provide more stable thermal shock properties with additives of graphite. It was explained by different thermal properties and crack resistance of the two materials in detail. Surface oxidation was one of main reasons for strength degradation of ceramic with additives of graphite after quenched in water, and surface crack was one of main reasons for strength degradation of ceramic with additives of AlN after quenched in water. It was presented that it was a potential method for improving thermal shock stability of ZrB2 ceramic matrix composites by introducing proper quantities of graphite.

Effects of rainfall infiltration on deep slope failure

With the finite element method and the limit equilibrium method, a numerical model has been estab-lished for examining the effects of rainfall infiltration on the stability of slopes. This model is able to reflect the variations in pore water pressure field in slopes, dead weight of the soil, and soil softening caused by rainfall infiltration. As a case study, an actual landslide located at the Nongji Jixiao in Chongqing was studied to analyze the effects of rainfall infiltration on the seepage field and slope sta-bility. The simulated results showed that a deep slope failure is prone to occur when rainfall infiltration leads to a remarkable variation in the seepage field, especially when the pore water pressure in slopes increases in a large range.

Transmission spectrum of a double quantum-dot-nanocavity system in photonic crystals

We investigate the optical transmission properties of a combined system which consists of two quantum-dot-nanocavity subsystems indirectly coupled to a waveguide in a planar photonic crystal. A Mollow-like triplet and the growth of sidebands are found, reflecting intrinsic optical responses in the complex microstructure.

Self-induced transmission on intersubband resonance in multiple quantum wells

We investigate the nonlinear propagation of ultrashort pulses on resonant intersubband transitions in multiple semiconductor quantum wells. It is shown that the nonlinearity rooted from electron-electron interactions destroys the condition giving rise to self-induced transparency. However, by adjusting the area of input pulse, we find the signatures of self-induced transmission due to a full Rabi flopping of the electron density, and this phenomenon can be approximately interpreted by the traditional standard area theorem via defining the effective area of input pulse.

Reflection and transmission of Gaussian beam from a uniaxial crystal slab

We investigate the characteristics of Gaussian beams reflected and transmitted from a uniaxial crystal slab with an arbitrary orientation of its optical axis. The formulas of the total electric and magnetic fields inside and outside the slab are derived by use of Maxwell's equations and by matching the boundary conditions at the interfaces. Numerical simulations are presented and the field values as well as the power densities are computed. Negative refractions are demonstrated when the beam is transmitted through a uniaxial crystal slab. Beam splitting of the reflected beam is observed and is explained by the resonant transmission for plane waves. Dependences of the lateral shift on the incident angle and beam width are discussed. Negative and positive lateral shifts are observed due to the spatial anisotropic properties.

Transmission area and correlated imaging

The relationship between transmission area of an object imaged and the visibility of correlated imaging is investigated in a lensless system. We show that they are not in simple inverse proportion, as usually depicted. The changes of the visibility will be quite different when the transmission area is varied by different manners, which may motivate people to seek a new understanding about the influence factors of the visibility. (C) 2007 Optical Society of America

Composite second-order performance improvement in optical fibre CATV transmission system using chirped fibre grating

Theoretically, we analyse the dispersion compensation characteristics of the chirped fibre grating (CFG) in an optical fibre cable television (CATV) system and obtain the analytic expression of the composite second-order (CSO) distortion using the time-domain form of the field envelope wave equation. The obtained result is in good agreement with the numerical simulation result. Experimentally, we verify the result by making use of the tunable characteristics of CFG to change the dispersion compensation amount and obtain an optimal CSO performance in a 125km fibre transmission link. Both the theoretical and experimental results show that the CSO performance can be improved by properly choosing the dispersion compensation amount for a certain fibre transmission link.

Coma measurement using a PSM and transmission image sensor

As feature size decreases, especially with the use of resolution enhancement technique, requirements for the coma aberrations in the projection lenses of the lithographic tools have become extremely severe. So, fast and accurate in situ measurement of coma is necessary. In the present paper, we present a new method for characterizing the coma aberrations in the projection lens using a phase-shifting mask and a transmission image sensor. By measuring the image positions at multiple NA and partial coherence settings, we are able to extract the coma aberration. The simulation results show that the accuracy of coma measurement increases approximately 20% compared to the previous straightforward measurement technique. (c) 2005 Elsevier GmbH. All rights reserved.

Deep-etched high-density fused-silica transmission gratings with high efficiency at a wavelength of 1550 nm

We describe the design, fabrication, and excellent performance of an optimized deep-etched high-density fused-silica transmission grating for use in dense wavelength division multiplexing (DWDM) systems. The fabricated optimized transmission grating exhibits an efficiency of 87.1% at a wavelength of 1550 nm. Inductively coupled plasma-etching technology was used to fabricate the grating. The deep-etched high-density fused-silica transmission grating is suitable for use in a DWDM system because of its high efficiency, low polarization-dependent loss, parallel demultiplexing, and stable optical performance. The fabricated deep-etched high-density fused-silica transmission gratings should play an important role in DWDM systems. (c) 2006 Optical Society of America.

DIFFERENTIAL GEOMETRICAL METHODS IN THE STUDY OF OPTICAL-TRANSMISSION (SCALAR THEORY) .1. STATIC TRANSMISSION CASE

Static optical transmission is restudied by postulation of the optical path as the proper element in a three-dimensional Riemannian manifold (no torsion); this postulation can be applied to describe the light-medium interactive system. On the basis of the postulation, the behaviors of light transmitting through the medium with refractive index n are investigated, the investigation covering the realms of both geometrical optics and wave optics. The wave equation of light in static transmission is studied modally, the postulation being employed to derive the exact form of the optical field equation in a medium (in which the light is viewed as a single-component field). Correspondingly, the relationships concerning the conservation of optical fluid and the dynamic properties are given, and some simple applications of the theories mentioned are presented.