A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90degrees and 180degrees is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress sigma(infinity) and electric field E-infinity or (sigma(infinity), E-infinity) is replaced by strain e and electric displacement D-infinity or (epsilon(infinity), D-infinity). Mixed conditions (sigma(infinity),D-infinity) and (epsilon(infinity),E-infinity) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E-y(infinity),sigma(y)(infinity)) for negative E-y(infinity) and (D-y(infinity), epsilon(y)(infinity)) for positive D-y(infinity) while the mechanical conditions sigma(y)(infinity) or epsilon(y)infinity are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth. (C) 2002 Published by Elsevier Science Ltd.

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.

Rheological effect on thermocapillary flow of a liquid film jet painted on a moving boundary

In the present paper, a liquid (or melt) film of relatively high temperature ejected from a vessel and painted on the-moving solid film is analyzed by using the second-order fluid model of the non-Newtonian fluid. The thermocapillary flow driven by the temperature gradient on the free surface of a Newtonian liquid film was discussed before. The effect of rheological fluid on thermocapillary flow is considered in the present paper. The analysis is based on the approximations of lubrication theory and perturbation theory. The equation of liquid height and the process of thermal hydrodynamics of the non-Newtonian liquid film are obtained, and the case of weak effect of the rheological fluid is solved in detail.

Compact difference approximation with consistent boundary condition

For simulating multi-scale complex flow fields it should be noted that all the physical quantities we are interested in must be simulated well. With limitation of the computer resources it is preferred to use high order accurate difference schemes. Because of their high accuracy and small stencil of grid points computational fluid dynamics (CFD) workers pay more attention to compact schemes recently. For simulating the complex flow fields the treatment of boundary conditions at the far field boundary points and near far field boundary points is very important. According to authors' experience and published results some aspects of boundary condition treatment for far field boundary are presented, and the emphasis is on treatment of boundary conditions for the upwind compact schemes. The consistent treatment of boundary conditions at the near boundary points is also discussed. At the end of the paper are given some numerical examples. The computed results with presented method are satisfactory.

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.

Three-dimensional crack problem analysis using boundary element method with finite-part integrals

A set of hypersingular integral equations of a three-dimensional finite elastic solid with an embedded planar crack subjected to arbitrary loads is derived. Then a new numerical method for these equations is proposed by using the boundary element method combined with the finite-part integral method. According to the analytical theory of the hypersingular integral equations of planar crack problems, the square root models of the displacement discontinuities in elements near the crack front are applied, and thus the stress intensity factors can be directly calculated from these. Finally, the stress intensity factor solutions to several typical planar crack problems in a finite body are evaluated.

An improvement on the theoretical model for the large-scale coherent structures in the outer region of a turbulent boundary layer

According to the experimental results, there exist large-scale coherent structures in the outer region of a turbulent boundary layer, which have been studied by many authors.As experimental results, Antonia (1990) showed the phase- aver aged streamlines and isovorticity lines of the large-scale coherent structures in a turbulent boundary layer for different Reynolds numbers. Based on the hydrodynamic stability theory, the 2-D theoretical model for the large-scale structures was proposed by Luo and Zhou, in which the eddy viscosity was defined as a complex function of the position in the normal direction. The theoretical results showed in ref. were in agreement with those in ref. However, there were two problems in the results. One is that in the experimental results, there were divergent focuses between two saddle points in the streamlines, but in the theoretical results, there were centers. The other is that the stretched parts of the isovorticity lines appear at the location of centers in the theoretical results, while in the experimental results they located somewhere between the focuses and saddle points. The reason is that the computations were based on a 2-D model.

A finite deformation analysis of polycrystal by considering the influence of grain boundary

By combining grain boundary (GB) and its influence zone, a micromechanic model for polycrystal is established for considering the influence of GB. By using the crystal plasticity theory and the finite element method for finite deformation, numerical simulation is carried out by the model. Calculated results display the microscopic characteristic of deformation fields of grains and are in qualitative agreement with experimental results.

Molecular dynamics studies on the dislocation gliding near a tilt boundary

The gliding behavior of edge dislocation near a grain boundary(QB) in copper under pure shear stresses is simulated by using molecular dynamics(MD) method. Many-body potential incorporating the embedded atom method (EAM) is used. The critical shear stresses for a single disocation to pass across GB surface are obtained at values of sigma(c)=23MPa similar to 68 MPa and 137 MPa similar to 274 MPa for Sigma=165 small angle tilt GB at 300 K and 20 K, respectively. The first result agrees with the experimental yield stress sigma(y)(=42 MPa) quite well. It suggests that there might be one of the reasons of initial plastic yielding caused by single dislocation gliding across GB. In addition, there might be possibility to obtain yield strength from microscopic analysis. Moreover, the experimental value of sigma(y) at low temperature is generally higher than that at room temperature. So, these results are in conformity qualitatively with experimental fact. On the other hand, the Sigma=25 GB is too strong an obstacle to the dislocation. In this case, a dislocation is able to pass across GB under relatively low stress only when it is driven by other dislocations. This is taken to mean that dislocation pile-up must be built up in front of this kind of GB, if this GB may take effect on the process of plastic deformation.

Study of the shock motion in a hypersonic shock system turbulent boundary-layer interaction

Wall pressure fluctuations and surface heat transfer signals have been measured in the hypersonic turbulent boundary layer over a number of compression-corner models. The distributions of the separation shock oscillation frequencies and periods have been calculated using a conditional sampling algorithm. In all cases the oscillation frequency distributions are of broad band, but the most probable frequencies are low. The VITA method is used for deducing large scale disturbances at the wall in the incoming boundary layer and the separated flow region. The results at present showed the existence of coherent structures in the two regions. The zero-cross frequencies of the large scale structures in the two regions are of the same order as that of the separation shock oscillation. The average amplitude of the large scale structures in the separated region is much higher than that in the incoming boundary layer. The length scale of the separation shock motion region is found to increase with the disturbance strength. The results show that the shock oscillation is of inherent nature in the shock wave/turbulent boundary layer interaction with separation. The shock oscillation is considered to be the consequence of the coherent structures in the separated region.

Mechanical modeling of grain boundary sliding of polycrystals

Using a variational method, a general three-dimensional solution to the problem of a sliding spherical inclusion embedded in an infinite anisotropic medium is presented in this paper. The inclusion itself is also a general anisotropic elastic medium. The interface is treated as a thin interface layer with interphase anisotropic properties. The displacements in the matrix and the inclusion are expressed as polynomial series of the cartesian coordinate components. Using the virtual work principle, a set of linear algebraic equations about unknown coefficients are obtained. Then the general sliding spherical inclusion problem is accurately solved. Based on this solution, a self-consistent method for sliding polycrystals is proposed. Combining this with a two-dimensional model of an aggregate polycrystal, a systematic analysis of the mechanical behaviour of sliding polycrystals is given in detail. Numerical results are given to show the significant effect of grain boundary sliding on the overall mechanical properties of aggregate polycrystals.

Air flow over a mountain and the convective boundary-layer

In this paper, the analytical model coupling the convective boundary layer (CBL) with the free atmosphere developed by Qi and Fu (1992) is improved. And by this improved model, the interaction between airflow over a mountain and the CBL is further discussed. The conclusions demonstrate: (1) The perturbation potential temperatures in the free atmosphere can counteract the effect of orographic thermal forcing through entraining and mixing in the CBL. If u(M)BAR > u(F)BAR, the feedback of the perturbation potential temperatures in the free atmosphere is more important than orographic thermal forcing, which promotes the effect of interfacial waves. If u(M)BAR < u(F)BAR, orographic thermal forcing is more important, which makes the interfacial height and the topographic height identical in phase, and the horizontal speeds are a maximum at the top of the mountain. (2) The internal gravity waves propagating vertically in the free atmosphere cause a strong downslope wind to become established above the lee slope in the CBL and result in the hydraulic jump at the top of the CBL. (3) With the CBL deepening, the interfacial gravity waves induced by the potential temperature jump at the top of the CBL cause the airflow in the CBL to be subcritical.

A simple approach to solve boundary-value problems in gradient elasticity

We outline a procedure for obtaining solutions of certain boundary value problems of a recently proposed theory of gradient elasticity in terms of solutions of classical elasticity. The method is applied to illustrate, among other things, how the gradient theory can remove the strain singularity from some typical examples of the classical theory.

A new type of boundary integral-equation for plane problems of elasticity including rotational forces

Based on the idea proposed by Hu [Scientia Sinica Series A XXX, 385-390 (1987)], a new type of boundary integral equation for plane problems of elasticity including rotational forces is derived and its boundary element formulation is presented. Numerical results for a rotating hollow disk are given to demonstrate the accuracy of the new type of boundary integral equation.

Crack growth by grain boundary cavitation in the transient and extensive creep regimes

Crack growth due to cavity growth and coalescence along grain boundaries is analyzed under transient and extensive creep conditions in a compact tension specimen. Account is taken of the finite geometry changes accompanying crack tip blunting. The material is characterized as an elastic-power law creeping solid with an additional contribution to the creep rate arising from a given density of cavitating grain boundary facets. All voids are assumed present from the outset and distributed on a given density of cavitating grain boundary facets. The evolution of the stress fields with crack growth under three load histories is described in some detail for a relatively ductile material. The full-field plane strain finite element calculations show the competing effects of stress relaxation due to constrained creep, diffusion and crack tip blunting. and of stress increase due to the instantaneous elastic response to crack growth. At very high crack growth rates the Hui-Riedel fields dominate the crack tip region. However. the high growth rates are not sustained for any length of time in the compact tension geometry analyzed. The region of dominance of the Hui-Riedel field shrinks rapidly so that the near-tip fields are controlled by the HRR-type field shortly after the onset of crack growth. Crack growth rates under various conditions of loading and spanning the range of times from small scale creep to extensive creep are obtained. We show that there is a strong similarity between crack growth history and the behaviour of the C(t) and C(t) parameters. so that crack growth rates correlate rather well with C(t) and C(t). A relatively brittle material is also considered that has a very different near-tip stress field and crack growth history.