The instability of the diffusion-controlled grain-boundary void in stressed solid

As atoms migrate along a void surface and grain-boundary, driven by various thermodynamic forces, the grain-boundary void changes its shape and volume. When the void changes its configuration, the free energy of the system also changes. In this article, the free energy is calculated for an evolving grain-boundary void filled with gas in a stressed solid. Then the instability conditions and the equilibrium shape of the void are determined as a function of the grain-boundary and surface energies, the void volume, the externally applied stresses, as well as the internal pressure built up by the gas filled in the void. The project supported by the National Natural Foundation of China (10272075 and 19972053)     

The dynamic growth of a single void in a viscoplastic material under transient hydrostatic loading

We have examined the problem of the dynamic growth of a single spherical void in an elastic-viscoplastic medium, with a view towards addressing a number of problems that arise during the dynamic failure of metals. Particular attention is paid to inertial, thermal and rate-dependent effects, which have not previously been thoroughly studied in a combined setting. It is shown that the critical stress for unstable growth of the void in the quasistatic case is strongly affected by the thermal softening of the material (in adiabatic calculations). Thermal softening has the effect of lowering the critical stress, and has a stronger influence at high strain hardening exponents. It is shown that the thermally diffusive case for quasistatic void growth in rate-dependent materials is strongly affected by the initial void size, because of the length scale introduced by the thermal diffusion. The effects of inertia are quantified, and it is demonstrated that inertial effects are small in the early stages of void growth and are strongly dependent on the initial size of the void and the rate of loading. Under supercritical loading for the inertial problem, voids of all sizes achieve a constant absolute void growth rate in the long term. Inertia first impedes, but finally promotes dynamic void growth under a subcritical loading. For dynamic void growth, the effect of rate-hardening is to reduce the rate of void growth in comparison to the rate-independent case, and to reduce the final relative void growth achieved.     

Vapor pressure and void size effects on failure of a constrained ductile film

To achieve certain properties, semiconductor adhesives and molding compounds are made by blending filler particles with polymer matrix. Moisture collects at filler particle/polymer matrix interfaces and within voids of the composite. At reflow temperatures, the moisture vaporizes. The rapidly expanding vapor creates high internal pressure on pre-existing voids and particle/matrix interfaces. The simultaneous action of thermal stresses and internal vapor pressure drives both pre-existing and newly nucleated voids to grow and coalesce causing material failure. Particularly susceptible are polymeric films and adhesives joining elastic substrates, e.g. Ag filled epoxy. Several competing failure mechanisms are studied including: near-tip void growth and coalescence with the crack; extensive void growth and formation of an extended damaged zone emanating from the crack; and rapid void growth at highly stressed sites at large distances ahead of the crack, leading to multiple damaged zones. This competition is driven by the interplay between stress elevation induced by constrained plastic flow and stress relaxation due to vapor pressure assisted void growth.A model problem of a ductile film bonded between two elastic substrates, with a centerline crack, is studied. The computational study employs a Gurson porous material model incorporating vapor pressure effects. The formation of multiple damaged zones is favored when the film contains small voids or dilute second-phase particle distribution. The presence of large voids or high vapor pressure favor the growth of a self-similar damage zone emanating from the crack. High vapor pressure accelerates film cracking that can cause device failures.     

Analysis of the Time Behaviour of a Diffusive Transport in a Stratified Medium

The paper presents a study of the diffusive transport of passive solute plumes in a two-dimensional non-homogeneous depth stratified flow domain. All the properties of the process are expressed by depth dependent deterministic functions. The method of moments, combined with the method of Green functions are chosen to determine the relevant characteristics of the flow (mass, center of mass, variance, etc.) used to describe the behaviour of the transient motion. General relationships for the n-order concentration moments are proved. Further, it is derived that the transient motion defined by time-dependent parameters tends asymptotically at large time to a stable regime whose characteristics are determined. Consequently, under certain hypotheses, an equivalence between the mean original process and a Fickian diffusive transport at large time may be established. The time required by the process to reach its asymptotic behaviour is also calculated.     

Evolution of material voids for highly anisotropic surface energy

In this paper we consider the evolution by surface diffusion of material voids in a linearly elastic solid, focusing on the evolution of voids with large surface energy anisotropy. It is well known that models for the time evolution of similar material surfaces can become mathematically ill-posed when the surface energy is highly anisotropic. In some cases, this ill-posedness has been associated with the formation of corners along the interface. Here the ill-posedness is removed through a regularization which incorporates higher order terms in the surface energy. Spectrally accurate numerical simulations are performed to calculate the steady-state solution branches and time-dependent evolution of voids, with a particular emphasis on inferring trends in the zero regularization (c→0) limit. For steady voids with large anisotropy we find that apparent corners form as c→0. In the presence of elastic stresses σ the limiting corner angles are most often found to differ from angles found on the (σ=0) Wulff shape. For large elastic stresses we find that steady solutions no longer exist; instead the void steadily lengthens via a filamenting instability referred to as tip streaming.     

The role of the configurational force balance in the nonequilibrium epitaxy of films

We discuss the epitaxial growth of an elastic film, allowing for stress and diffusion within the film surface as well as nonequilibrium interactions between the film and the vapor. Our approach, which relies on recent ideas concerning configurational forces, is based on: (i) standard (Newtonian) balance laws for forces and moments together with an independent balance law for configurational forces; (ii) atomic balances, one for each species of mobile atoms; (iii) a mechanical version of the second law that accounts for temporal changes in free energy, energy flows due to atomic transport, and power expended by both standard and configurational forces; (iv) thermodynamically consistent constitutive relations for the film surface and for the interaction between the surface and the vapor environment. The normal component of the configurational force balance at the surface represents a generalization, to a dynamical context involving dissipation, of a condition that would arise in equilibrium by considering variations of the total free energy with respect to the configuration of the film surface. Our final results consist of partial differential equations that govern the evolution of the film surface.     

Theoretical analysis on capillary adhesion of microsized plates with a substrate

The stiction of a thin plate induced by the capillary force has attracted much attention in the broad range of applications. A novel method is presented to calculate the capillary adhesion problem of the plate through analytical method. The expressions of the surface energy, the strain energy and the total potential energy of the plate-substrate system have been analyzed and delineated. By means of continuum mechanics and the principle of minimum potential energy, the governing equation of the plate with an arbitrary shape and the corresponding transversality boundary condition due to the moving bound have been derived. Then the critical adhesion radius of the circular plate has been solved according to the supplementary transversality condition. Thus the deflections of the plates are analytically calculated with different critical adhesion radii. The results may be beneficial to the engineering application and the micro/nanomeasurement.     

Analysis of dislocation nucleation from a crystal surface based on the Peierls-Nabarro dislocation model

Dislocation nucleation from a stressed crystal surface is analyzed based on the Peierls-Nabarro dislocation model. The variational boundary integral approach is used to obtain the profiles of the embryonic dislocations in various three-dimensional nucleation configurations. The stress-dependent activation energies required to activate dislocations from their stable to unstable saddle point configurations are determined. Compared to previous analyses of this type of problem based on continuum elastic dislocation theory, the present analysis eliminates the uncertain core cutoff parameter by allowing for the existence of an extended dislocation core as the embryonic dislocation evolves. Moreover, atomic information can be incorporated to reveal the dependence of the nucleation process on the profile of the atomic interlayer potential as compared to continuum elastic dislocation theory in which only elastic constants and Burgers vector are relevant. Finally, the presented methodology can also be readily used to study dislocation nucleation from the surface heterogeneities such as cracks, steps, and quantum structures of electronic devices.     

Spatial distribution of void fraction within a liquid slug and some other related slug parameters

The structure of vertical upward slug flow in a pipe is studied. The distribution of the phases in the Taylor bubble zone and the liquid slug zone is investigated by simultaneous measurements with two optical fiber probes. In the Taylor bubble zone the shape of the Taylor bubble and the distribution of the bubble length is reported. In the liquid slug region, the distribution of the void fraction is obtained over a dense grid in both the axial and radial directions. These experimental results shed some light on the hydrodynamics of the two-phase slug flow, in particular regarding the production of the dispersed bubbles and their distribution along the liquid slug.     

A numerical study of a rectangular jet along a shear free boundary: Surface jet

A numerical simulation of a rectangular surface jet is performed at a Reynolds number of ${\mathit{Re}}_j=4400$. The global parameters of the jet e.g. maximum velocity decay, jet surface normal and lateral spread rates, entrainment, jet momentum flux and turbulent momentum flux are in agreement with several other studies reported in the literature. It is shown that the mean velocity and Reynolds stress profiles scale with the maximum local streamwise velocity and jet half width in the surface normal and lateral directions. The current simulation provides balance, explicitly calculated budgets for the turbulence kinetic energy, Reynolds normal and shear stresses. The surface jet develops a thin layer of fast moving fluid in the lateral direction near the surface. This layer is called the ‘surface current’. It has been suggested that the surface current arises due to the Reynolds stress anisotropy in the near surface region. The current study shows that this explanation is incomplete. The turbulence production for the Reynolds stress in the lateral direction is negative, which can drive the mean flow in the lateral direction. The higher level of negative production in the near surface region is responsible for the development of the surface current.     

Simulations of the spreading of a vesicle on a substrate surface mediated by receptor-ligand binding

A continuum model was introduced for the adhesion of vesicles to substrate surfaces. In the model, the vesicle membrane was assumed to be a closed shell with hyperelasticity. The vesicle cavity is filled with a liquid of fixed volume. The receptors on the membrane are mobile and initially uniformly distributed while the ligands on the substrate surface are fixed and also uniformly distributed. The formation of localized regions of tight binding between receptors and ligands, results in vesicle adhesion to the substrate surface. An adhesive model was introduced to describe the adhesive interaction between the receptors and the ligands. The growth of the adhesion area occurs via recruiting receptors from the non-adhered region through diffusion. Finite-element methods were used to solve the governing equations for the deformation of the vesicle and the receptor diffusion on the membrane surface. Effects of the membrane stiffness, the cohesive parameters and the receptor density on the adhesion kinetics of the vesicle were studied. In addition, the instability of the advancing front of the adhesion was also analyzed.     

Acceleration of chemical reactions within a shock wave front

The aim of the present numerical study was to illustrate the possible influence of translational nonequilibrium in the front of a shock wave on the rate of the threshold chemical reaction. The Monte Carlo method of nonstationary statistical simulation with variable weighting factors was used. Gas mixtures which contained, ahead of the front, two chemically interacting small additives , and an inert light main component were considered. A chemical reaction of the additives started in the front of a shock wave and led to formation of two new low-concentration components and . It was shown that for the ratio of molecular number densities of the additives , and an inert component of 1:10:200 and for the molecular mass ratio of components , , , , of 34.5:8:38.5:4:1 the value of the direct reaction rate obtained in the front exceeds its equilibrium value behind the wave by more than 100 times. As a result, the reaction occurs more intensively in the zone of translational nonequilibrium. It was also shown that for the cases of an exothermic reaction and a weak endothermic reaction, a small amount of the light reaction product has the velocity of the shock wave and is carried by the front. Received 13 June 1997/ Accepted 13 July 1998     

Diffusion of magnetic nanoparticles in a multi-site injection process within a biological tissue during magnetic fluid hyperthermia using lattice Boltzmann method

In this study the lattice Boltzmann model (LBM) has been used to simulate diffusion of magnetic nanoparticles (MNPs) injected at multiple sites inside a biological tissue during magnetic fluid hyperthermia (MFH). To validate the numerical results, diffusion in infinite one and two dimensional domains have been compared with the analytical solutions. Agreement were excellent. Also diffusion of a water based nanofluid containing magnetite MNPs (ferrofluid) for mono and multi-site injection in the tissue has been studied. Moreover, the effects of ferrofluid injection volume as well as infusion flow rate of ferrofluid on the distribution of MNPs have been investigated.     

Evolution of roughness on the surface of a strained elastic material due to stress-driven surface diffusion

The free energy of a stressed crystal is assumed to consist of elastic strain energy and surface energy, and the chemical potential for surface diffusion at constant temperature is obtained under this assumption. A gradient in chemical potential results in diffusive mass transport along the surface. The result is applied in considering the phenomena of instability of a flat surface in a stressed material under fluctuations in surface shape, and the transient evolution of surface roughness due to an initial perturbation in the nearly flat free surface of the material, both under plane strain conditions.     

Measuring Fracture Energy in a Brittle Polymeric Material: Application of a High-Speed Optical Extensometer

The brittle fracture of polymethyl methacrylate (PMMA) was studied using a high-speed extensometer, which consisted of an optical fiber and a position-sensing detector (PSD). Single-edge-cracked tensile specimens were pin-loaded with a special jig so that they could split and fly in the loading direction after fracture. The flying height and residual deformation of the split specimen were measured to estimate the elastic energy E _e and non-elastic energy E _n, respectively. By subtracting E _e and E _n from the external work U _ex applied to the specimen, the fracture energy E _f for creating a new fracture surface was evaluated. The results showed that E _e, E _n, and E _f increased with U _ex, and the ratio E _f/U _ex was about 45% over a wide range of U _ex. Energy release rate was also estimated using U _ex or E _f, and the results suggested that it was overestimated if E _e and E _n were included.     

Steady accretion of an elastic body on a hard spherical surface and the notion of a four-dimensional reference space

Taking the cue from experiments on actin growth on spherical beads, we formulate and solve a model problem describing the accretion of an incompressible elastic solid on a rigid sphere due to attachment of diffusing free particles. One of the peculiar characteristics of this problem is that accretion takes place on the interior surface that separates the body from its support rather than on its exterior surface, and hence is responsible for stress accumulation. Simultaneously, ablation takes place at the outer surface where material is removed from the body. As the body grows, mechanical effects associated with the build-up of stress and strain energy slow down accretion and promote ablation. Eventually, the system reaches a point where internal accretion is balanced by external ablation. The present study is concerned with this stationary regime called “treadmilling”.The principal ingredients of our model are: a nonstandard choice of the reference configuration, which allows us to cope with the continually evolving material structure; and a driving force and a kinetic law for accretion/ablation that involves the difference in chemical potential, strain energy and the radial stress. By combining these ingredients we arrive at an algebraic system which governs the stationary treadmilling state. We establish the conditions under which this system has a solution and we show that this solution is unique. Moreover, by an asymptotic analysis we show that for small beads the thickness of the solid is proportional to the radius of the support and is strongly affected by the stiffness of the solid, whereas for large beads the stiffness of the solid is essentially irrelevant, the thickness being proportional to a characteristic length that depends on the parameters that govern diffusion and accretion kinetics.     

Observations of acoustically generated cavitation bubbles within typical fluids applied to a scroll expander lubrication system

An experimental study to evaluate the dynamic performance of three different types of cavitation bubbles is conducted. An ultrasonic transducer submerged into the working fluids of a scroll expander is utilised to produce cavitation bubbles and a high speed camera device is used to capture their behaviour. Three critical regions around the ultrasonic source, between the source and the solid boundary, and across the solid boundary were observed. Experimental results revealed that refrigerant bubbles sustain a continuous oscillatory movement, referenced as “wobbling effect”, without regularly collapsing. Analytical results indicate the influence of several factors such as surface tension/viscosity ratio, Reynolds number and Weber number which interpret that particular behaviour of the refrigerant bubbles. Within the refrigerant environment the bubbles obtain large Reynolds numbers and low Weber numbers. In contrast, within the lubricant and the water environment Weber number is significantly higher and Reynolds number substantially lower. The bubble radius and velocity alterations are accurately calculated during the cavitation process. Lubricant bubbles achieve the highest jet velocity while refrigerant bubbles having the lowest jet velocity are not considered as a destructive mean of cavitation for scroll expander systems.     

Propagation of longitudinal and transverse waves in a multimodulus elastic medium

A problem of propagation of longitudinal and transverse waves in a multimodulus elastic isotropic medium is considered. In the model used, the medium is described by a potential depending on three invariants of strains, which allows the influence of preliminary deformation of the medium on the longitudinal and transverse velocities to be taken into account. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 176–182, July–August, 2009.