Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

We present a slice-sampling method and study the ensemble evolution of a large finite nonlinear system in order to model materials failure. There is a transitional region of failure probability. Its size effect is expressed by a slowly decaying scaling law. In a meso-macroscopic range (similar to 10(5)) in realistic failure, the diversity cannot be ignored. Sensitivity to mesoscopic details governs the phenomena. (C) 1997 Published by Elsevier Science B.V.

Features of the supercritical transition in the wake of a circular cylinder

The features of the wake behind a uniform circular cylinder at Re = 200, which is just beyond the critical Reynolds number of 3-D transition, are investigated in detail by direct numerical simulations by solving 3-D incompressible Navier-Stokes equations using mixed spectral-spectral-element method. The high-order splitting algorithm based on the mixed stiffly stable scheme is employed in the time discretization. Due to the nonlinear evolution of the secondary instability of the wake, the spanwise modes with different wavelengths emerge. The spanwise characteristic length determines the transition features and global properties of the wake. The existence of the spanwise phase difference of the primary vortices shedding is confirmed by Fourier analysis of the time series of the spanwise vorticity and attributed. to the dominant spanwise mode. The spatial energy distributions of various modes and the velocity profiles in the near wake are obtained. The numerical results indicate that the near wake is in 3-D quasi-periodic laminar state with transitional behaviors at this supercritical Reynolds number.

Evolution of thermoplastic shear localization and related microstructures in Awl/SiCp composites under dynamic compression

The localized shear deformation in the 2024 and 2124 Al matrix composites reinforced with SiC particles was investigated with a split Hopkinson pressure bar (SHPB) at a strain rate of about 2.0x10(3) s(-1). The results showed that the occurrence of localized shear deformation is sensitive to the size of SiC particles. It was found that the critical strain, at which the shear localization occurs, strongly depends on the size and volume fraction of SiC particles. The smaller the particle size, the lower the critical strain required for the shear localization. TEM examinations revealed that Al/SiCp interfaces are the main sources of dislocations. The dislocation density near the interface was found to be high and it decreases with the distance from the particles. The Al matrix in shear bands was highly deformed and severely elongated at low angle boundaries. The Al/SiCp interfaces, particularly the sharp corners of SiC particles, provide the sites for microcrack initiation. Eventual fracture is caused by the growth and coalescence of microcracks along the shear bands. It is proposed that the distortion free equiaxed grains with low dislocation density observed in the center of shear band result from recrystallization during dynamic deformation.

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

Micromechanics analysis on evolution of crack in viscoelastic materials

A preliminary analysis on crack evolution in viscoelastic materials was presented. Based on the equivalent inclusion concept of micro-mechanics theory, the explicit expressions of crack opening displacement delta and energy release rate G were derived, indicating that both delta and G are increasing with time. The equivalent modulus of the viscoelastic solid comprising cracks was evaluated. It is proved that the decrease of the modulus comes from two mechanisms: one is the viscoelasticity of the material; the other is the crack opening which is getting larger with time.

Analysis and application of ellipticity of stability equations on fluid mechanics

By using characteristic analysis of the linear and nonlinear parabolic stability equations (PSE), PSE of primitive disturbance variables are proved to be parabolic intotal. By using sub-characteristic analysis of PSE, the linear PSE are proved to be elliptical and hyperbolic-parabolic for velocity U, in subsonic and supersonic, respectively; the nonlinear PSE are proved to be elliptical and hyperbolic-parabolic for relocity U + u in subsonic and supersonic, respectively. The methods are gained that the remained ellipticity is removed from the PSE by characteristic and sub-characteristic theories, the results for the linear PSE are consistent with the known results, and the influence of the Mach number is also given out. At the same time, the methods of removing the remained ellipticity are further obtained from the nonlinear PSE.

Effects of adiabatic exponent on Richtmyer-Meshkov instability

We present a systematical numerical study of the effects of adiabatic exponent gamma on Richtmyer-Meshkov instability (RMI) driven by cylindrical shock waves, based on the gamma model for the multi-component problems and numerical simulation with high-order and high-resolution method for compressible Euler equations. The results show that the RMI of different gamma across the interface exhibits different evolution features with the case of single gamma. Moreover, the large gamma can hold back the development of nonlinear structures, such as spikes and bubbles.

Microstructural evolution and formation of nanocrystalline intermetallic compound during surface mechanical attrition treatment of cobalt

Nanocrystalline intermetallic Co3Fe7 was produced on the surface of cobalt via surface mechanical attrition (SMA). Deformationinduced diffusion entailed the formation of a series of solid solutions. Phase transitions occurred depending on the atomic fraction of Fe in the surface solid solutions: from hexagonal close-packed (<4% Fe) to face-centered cubic (fcc) (4-11% Fe), and from fcc to body-centered cubic (>11% Fe). Nanoscale compositional probing suggested significantly higher Fe contents at grain boundaries and triple junctions than grain interiors. Short-circuit diffusion along grain boundaries and triple junctions dominate in the nanocrystalline intermetallic compound. Stacking faults contribute significantly to diffusion. Diffusion enhancement due to high-rate deformation in SMA was analyzed by regarding dislocations as solute-pumping channels, and the creation of excess vacancies. Non-equilibrium, atomic level alloying can then be ascribed to deformation-induced intermixing of constituent species. The formation mechanism of nanocrystalline intermetallic grains on the SMA surface can be thought of as a consequence of numerous nucleation events and limited growth. (C) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Dynamic equations for curved submerged floating tunnel

In virtue of reference Cartesian coordinates, geometrical relations of spatial curved structure are presented in orthogonal curvilinear coordinates. Dynamic equations for helical girder are derived by Hamilton principle. These equations indicate that four generalized displacements are coupled with each other. When spatial structure degenerates into planar curvilinear structure, two generalized displacements in two perpendicular planes are coupled with each other. Dynamic equations for arbitrary curvilinear structure may be obtained by the method used in this paper.

Energy principle of ferroelectric ceramics and single domain mechanical model

Many physical experiments have shown that the domain switching in a ferroelectric material is a complicated evolution process of the domain wall with the variation of stress and electric field. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of ferroelectric ceramic and used to study the nonlinear constitutive behavior of ferroelectric body in this paper. The principle of stationary total energy is put forward in which the basic unknown quantities are the displacement u (i) , electric displacement D (i) and volume fraction rho (I) of the domain switching for the variant I. Mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion. On the basis of the domain switching criterion, a set of linear algebraic equations for the volume fraction rho (I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. Then a single domain mechanical model is proposed in this paper. The poled ferroelectric specimen is considered as a transversely isotropic single domain. By using the partial experimental results, the hardening relation between the driving force of domain switching and the volume fraction of domain switching can be calibrated. Then the electromechanical response can be calculated on the basis of the calibrated hardening relation. The results involve the electric butterfly shaped curves of axial strain versus axial electric field, the hysteresis loops of electric displacement versus electric filed and the evolution process of the domain switching in the ferroelectric specimens under uniaxial coupled stress and electric field loading. The present theoretic prediction agrees reasonably with the experimental results given by Lynch.

Numerical analysis of spatial evolution of the small signal gain in a chemical oxygen-iodine laser operating without primary buffer gas

A chemical oxygen iodine laser (COIL) that operates without primary buffer gas has become a new way of facilitating the compact integration of laser systems. To clarify the properties of spatial gain distribution, three-dimensional (3-D) computational fluid dynamics (CFD) technology was used to study the mixing and reactive flow in a COIL nozzle with an interleaving jet configuration in the supersonic section. The results show that the molecular iodine fraction in the secondary flow has a notable effect on the spatial distribution of the small signal gain. The rich iodine condition produces some negative gain regions along the jet trajectory, while the lean iodine condition slows down the development of the gain in the streamwise direction. It is also found that the new configuration of an interleaving jet helps form a reasonable gain field under appropriate operation conditions. (c) 2007 Elsevier Ltd. All rights reserved.