Damage analysis of tetragonal perovskite structure ceramics implicated by asymptotic field solutions and boundary conditions

Cracking of ceramics with tetragonal perovskite grain structure is known to appear at different sites and scale level. The multiscale character of damage depends on the combined effects of electromechanical coupling, prevailing physical parameters and boundary conditions. These detail features are exhibited by application of the energy density criterion with judicious use of the mode I asymptotic and full field solution in the range of r/a = 10(-4) to 10(-2) where r and a are, respectively, the distance to the crack tip and half crack length. Very close to the stationary crack tip, bifurcation is predicted resembling the dislocation emission behavior invoked in the molecular dynamics model. At the macroscopic scale, crack growth is predicted to occur straight ahead with two yield zones to the sides. A multiscale feature of crack tip damage is provided for the first time. Numerical values of the relative distances and bifurcation angles are reported for the PZT-4 ceramic subjected to different electric field to applied stress ratio and boundary conditions that consist of the specification of electric field/mechanical stress, electric displacement/mechanical strain, and mixed conditions. To be emphasized is that the multiscale character of damage in piezoceramics does not appear in general. It occurs only for specific combinations of the external and internal field parameters, elastic/piezoelectric/dielectric constants and specified boundary conditions. (C) 2002 Published by Elsevier Science Ltd.

Coupling effects of heterogeneity and stress fluctuation on rupture

The coupling of mesoscopic strength distribution and stress fluctuation on damage evolution and rupture are examined. The numerical simulations show that there is only weak stress fluctuation at the initial damage stage when the mean field approximation is in effect. As the damage fraction becomes larger than the threshold value, the fluctuation is amplified significantly, and damage localization appears. The coupling between stress fluctuation, disordered heterogeneity and the damage localization may play an essential role in catastrophic rupture. (C) 2003 Elsevier Ltd. All rights reserved.

Two-way coupling model for shock-induced laminar boundary-layer flows of a dusty gas

The present paper describes a numerical two-way coupling model for shock-induced laminar boundary-layer flows of a dust-laden gas and studies the transverse migration of fine particles under the action of Saffman lift force. The governing equations are formulated in the dilute two-phase continuum framework with consideration of the finiteness of the particle Reynolds and Knudsen numbers. The full Lagrangian method is explored for calculating the dispersed-phase flow fields (including the number density of particles) in the regions of intersecting particle trajectories. The computation results show a significant reaction of the particles on the two-phase boundary-layer structure when the mass loading ratio of particles takes finite values.

Toward an understanding of the turbidity measurement of fleterocoagulation rate constants of dispersions containing particles of different sizes

Our previous studies have shown that the determination of coagulation rate constants by turbidity measurement becomes impossible for a certain operating wavelength (that is, its blind point) because at this wavelength the change in the turbidity of a dispersion completely loses its response to the coagulation process. Therefore, performing the turbidity measurement in the wavelength range near the blind point should be avoided. In this article, we demonstrate that the turbidity measurement of the rate constant for coagulation of a binary dispersion containing particles of two different sizes (heterocoagulation) presents special difficulties because the blind point shifts with not only particle size but also with the component fraction. Some important aspects of the turbidity measurement for the heterocoagulation rate constant are discussed and experimentally tested. It is emphasized that the T-matrix method can be used to correctly evaluate extinction cross sections of doublets formed during the heterocoagulation process, which is the key data determining the rate constant from the turbidity measurement, and choosing the appropriate operating wavelength and component fraction are important to achieving a more accurate rate constant. Finally, a simple scheme in experimentally determining the sensitivity of the turbidity changes with coagulation over a wavelength range is proposed.

A dynamic coupling model for hybrid atomistic-continuum computations

A dynamic coupling model is developed for a hybrid atomistic-continuum computation in micro- and nano-fluidics. In the hybrid atomistic-continuum computation, a molecular dynamics (MD) simulation is utilized in one region where the continuum assumption breaks down and the Navier-Stokes (NS) equations are used in another region where the continuum assumption holds. In the overlapping part of these two regions, a constrained particle dynamics is needed to couple the MD simulation and the NS equations. The currently existing coupling models for the constrained particle dynamics have a coupling parameter, which has to be empirically determined. In the present work, a novel dynamic coupling model is introduced where the coupling parameter can be calculated as the computation progresses rather than inputing a priori. The dynamic coupling model is based on the momentum constraint and exhibits a correct relaxation rate. The results from the hybrid simulation on the Couette flow and the Stokes flow are in good agreement with the data from the full MD simulation and the solutions of the NS equations, respectively. (c) 2007 Elsevier Ltd. All rights reserved.

A new expression of hardening coefficients for fcc-crystal and calibration of the material constants

In order to describe the effect of latent hardening on the macro-plastic behavior of foc-crystal, a new expression for hardening coefficient is proposed in which there are 12 material constants, each having clear physical meaning. And a method of material constant calibration is suggested and used to determine the material constants of copper and aluminum crystal. The simulated load-elongation curves along various crystallographic orientations are comparable with the experimental ones.

Coupling of melting-solidification phase-change convection with floating-zone convection under microgravity

A finite element algorithm is used to analyze the process of floating zone crystal growth under microgravity. The effect of phase change convection coupled with surface tension convection is considered. The results show that the rate of crystal growth is very important. The single-crystal-melt interface is steeper than the feed-melt interface during the process of crystal growth. When the rate exceeds a critical value, the Marangoni vortex near the feed-melt interface will become so large that a secondary vortex will exist.

“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.

Mechanisms underlying two kinds of surface effects on elastic constants

ABSTRACT Recently, people are confused with two opposite variations of elastic modulus with decreasing size of nano scale sample: elastic modulus either decreases or increases with decreas- ing sample size. In this paper, based on intermolecular potentials and a one dimensional model, we provide a unified understanding of the two opposite size effects. Firstly, we analyzed the mi- crostructural variation near the surface of an fcc nanofilm based on the Lennard-Jones potential. It is found that the atomic lattice near the surface becomes looser in comparison with the bulk, indicating that atoms in the bulk are located at the balance of repulsive forces, resulting in the decrease of the elastic moduli with the decreasing thickness of the film accordingly. In addition, the decrease in moduli should be attributed to both the looser surface layer and smaller coor- dination number of surface atoms. Furthermore, it is found that both looser and tighter lattice near the surface can appear for a general pair potential and the governing mechanism should be attributed to the surplus of the nearest force to all other long range interactions in the pair po- tential. Surprisingly, the surplus can be simply expressed by a sum of the long range interactions and the sum being positive or negative determines the looser or tighter lattice near surface re- spectively. To justify this concept, we examined ZnO in terms of Buckingham potential with long range Coulomb interactions. It is found that compared to its bulk lattice, the ZnO lattice near the surface becomes tighter, indicating the atoms in the bulk located at the balance of attractive forces, owing to the long range Coulomb interaction. Correspondingly, the elastic modulus of one- dimensional ZnO chain increases with decreasing size. Finally, a kind of many-body potential for Cu was examined. In this case, the surface layer becomes tighter than the bulk and the modulus increases with deceasing size, owing to the long range repulsive pair interaction, as well as the cohesive many-body interaction caused by the electron redistribution.

Space-frequency coupling, conical waves, and small-scale filamentation in water

Numerical simulations of fs laser propagation in water have been made to explain the small-scale filaments in water we have observed by a nonlinear fluorescence technique. Some analytical descriptions combined with numerical simulations show that a space-frequency coupling mainly from the interplay among self-phase modulation, dispersion and phase mismatching will reshape the laser beam into a conical wave which plays a major role of energy redistribution and can prevent laser beam from self-guiding over a long distance. An effective group velocity dispersion is introduced to explain the pulse broadening and compression in the filamentation. (c) 2005 American Institute of Physics.

Relativistic channel-coupling focusing enhanced nonlinear guiding of an intense laser beam in a plasma channel

We employ the variational method to study the optical guiding of an intense laser beam in a preformed plasma channel without using the weakly relativistic approximation. Apart from the dependence on the laser power and the nonlinear channel strength parameter, the beam focusing properties is shown also to be governed by the laser intensity. Relativistic channel-coupling focusing, arising from the coupling between relativistic self-focusing and linear channel focusing, can enhance relativistic self-focusing but its strength is weaker than that of linear channel focusing. (C) 2008 Elsevier B.V. All rights reserved.

Influence of birefringence dispersion on distributed measurement of polarization coupling in birefringent fibers

A white light interferometer is developed to measure the distributed polarization coupling in high-birefringence polarization-maintaining fibers (PMFs). Usually the birefringence dispersion between two orthogonal eigenmodes of PMFs is neglected in such systems. Theoretical analysis and experimental results show that the birefringence dispersion becomes a nonnegligible factor in a long-fiber test. Significant broadening of interferograms and loss of longitudinal coherence are observed. The spatial resolution and measurement sensitivity of the system decrease correspondingly. Optimum spectrum width selection is presented for better spatial resolution and measurement range. c 2007 Society of Photo-Optical Instrumentation Engineers.