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.

Compressible laminar boundary-layer flows of a dusty gas over a semi-infinite flat-plate

The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions : the large-slip region near the leading edge, the moderate-slip region and the small-slip region far downstream. The asymptotic solutions for the two limiting regions are obtained by using a seriesexpansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes-interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.