High-order asymptotic field of tensile plane-strain nonlinear crack problems

In this paper, the governing equations and the analytical method of the secondorder asymptotic field for the plane-straln crack problems of mode I have been presented. The numerical calculation has been carried out. The amplitude coefficients k2 of the second term of the asymptotic field have been determined after comparing the present results with some fine results of the finite element calculation. The variation of coefficients k2 with changes of specimen geometry and developments of plastic zone have been analysed. It is shown that the second term of the asymptotic field has significant influence on the near-crack-tip field. Therefore, we may reasonably argue that both the J-integral and the coefficient k2 can beeome two characterizing parameters for crack initiation.

Wavefront conversion by local volume holograms between cylindrical and plane waves with reconstruction at a different readout wavelength

Based on the two-dimensional coupled-wave theory, the wavefront conversion between cylindrical and plane waves by local volume holograms recorded at 632.8 nm and reconstructed at 800 nm is investigated. The proposed model can realize the 90 degrees holographic readout at a different readout wavelength. The analytical integral solutions for the amplitudes of the space harmonics of the field inside the transmission geometry are presented. The values of the off-Bragg parameter at the reconstructed process and the diffracted beam's amplitude distribution are analysed. In addition, the dependences of diffraction efficiency on the focal length of the recording cylindrical wave and on the geometrical dimensions of the grating are discussed. Furthermore, the focusing properties of this photorefractive holographic cylindrical lens are analysed.

Geometrical learning, descriptive geometry, and biomimetic pattern recognition

Studies on learning problems from geometry perspective have attracted an ever increasing attention in machine learning, leaded by achievements on information geometry. This paper proposes a different geometrical learning from the perspective of high-dimensional descriptive geometry. Geometrical properties of high-dimensional structures underlying a set of samples are learned via successive projections from the higher dimension to the lower dimension until two-dimensional Euclidean plane, under guidance of the established properties and theorems in high-dimensional descriptive geometry. Specifically, we introduce a hyper sausage like geometry shape for learning samples and provides a geometrical learning algorithm for specifying the hyper sausage shapes, which is then applied to biomimetic pattern recognition. Experimental results are presented to show that the proposed approach outperforms three types of support vector machines with either a three degree polynomial kernel or a radial basis function kernel, especially in the cases of high-dimensional samples of a finite size. (c) 2005 Elsevier B.V. All rights reserved.

Dislocation theory of the fracture criterion for anisotropic solids

A dislocation theory of fracture criterion for the mixed dislocation emission and cleavage process in an anisotropic solid is developed in this paper. The complicated cases involving mixed-mode loading are considered here. The explicit formula for dislocations interaction with a semi-infinite crack is obtained. The governing equation for the critical condition of crack cleavage in an anisotropic solid after a number dislocation emissions is established. The effects of elastic anisotropy, crack geometry and load phase angle on the critical energy release rate and the total number of the emitted dislocations at the onset of cleavage are analysed in detail. The analyses revealed that the critical energy release rates can increase to one or two magnitudes larger than the surface energy because of the dislocation emission. It is also found elastic anisotropy and crystal orientation have significant effects on the critical energy release rates. The anisotropic values can be several times the isotropic value in one crack orientation. The values may be as much as 40% less than the isotropic value in another crack orientation and another anisotropy parameter. Then the theory is applied to a fee single crystal. An edge dislocation can emit from the crack tip along the most highly shear stressed slip plane. Crack cleavage can occur along the most highly stressed slip plane after a number of dislocation emissions. Calculation is carried out step by step. Each step we should judge by which slip system is the most highly shear stressed slip system and which slip system has the largest energy release rate. The calculation clearly shows that the crack orientation and the load phase angle have significant effects on the crystal brittle-ductile behaviours.

Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non-singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection-diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed.

Experimental Study on Vortex-Induced Vibrations of a Pipeline Near a Plane Boundary in Steady Flow

对单向水流作用下近壁管道横向涡激振动进行了实验模拟,重点探讨了管道与壁面间隙比(e/D)对管道涡激振动幅值和涡激振动频率响应特性的影响规律.实验结果表明,管道与壁面间隙宽度对管道涡激振动特性有较明显影响.在较大间隙比(e/D＞0.66)下,管道振幅随着Vr数的增大先快速增长到最大值,然后平缓下降;在振动初期(即Vr数较小时),管道振动频率变化基本符合Strouhal规律;在振动中后期(即Vr数较大时),管道振动频率变化不符合Strouhal规律,而在管道固有频率附近缓慢增长.在较小间隙比(e/D＜0.30)下,管道振幅随Vr数的增大先平缓上升到最大值,随后较快速下降;在振动初期,管道振动频率变化不遵循Strouhal规律;在整个振动范围内,与较大间隙比情况相比,随着Vr数增加,管道振动频率增长幅度明显较大.

Micro-shock waves generated inside a fluid jet impinging on plane wall

An Nd:glass laser pulse (18 ns, 1.38 J) is focused in a tiny area of about 100-mum diam under ambient conditions to produce micro-shock waves. The laser is focused above a planar surface with a typical standoff distance of about 4 mm, The laser energy is focused inside a supersonic circular jet of carbon dioxide gas produced by a nozzle with internal diameter of 2.9 mm and external diameter of 8 mm, Nominal value of the Mach number of the jet is around 2 with the corresponding pressure ratio of 7.5 (stagnation pressure/static pressure at the exit of the nozzle), The interaction process of the micro-shock wave generated inside the supersonic jet with the plane wall is investigated using double-pulse holographic interferometry. A strong surface vortex field with subsequent generation of a side jet propagating outward along the plane wail is observed. The interaction of the micro-shock wave with the cellular structure of the supersonic jet does not seem to influence the near surface features of the flowfield. The development of the coherent structures near the nozzle exit due to the upstream propagation of pressure waves seems to be affected by the outward propagating micro-shock wave. Mach reflection is observed when the micro-shock wave interacts with the plane wall at a standoff distance of 4 mm, The Mach stem is slightly deflected, indicating strong boundary-layer and viscous effects near the wall. The interaction process is also simulated numerically using an axisymmetric transient laminar Navier-Stokes solver. Qualitative agreement between experimental and numerical results is good.

Elasticity, stability, and ideal strength of beta-SiC in plane-wave-based ab initio calculations

On the basis of the pseudopotential plane-wave method and the local-density-functional theory, this paper studies energetics, stress-strain relation, stability, and ideal strength of beta-SiC under various loading modes, where uniform uniaxial extension and tension and biaxial proportional extension are considered along directions [001] and [111]. The lattice constant, elastic constants, and moduli of equilibrium state are calculated and the results agree well with the experimental data. As the four SI-C bonds along directions [111], [(1) over bar 11], [11(1) over bar] and [111] are not the same under the loading along [111], internal relaxation and the corresponding internal displacements must be considered. We find that, at the beginning of loading, the effect of internal displacement through the shuffle and glide plane diminishes the difference among the four Si-C bonds lengths, but will increase the difference at the subsequent loading, which will result in a crack nucleated on the {111} shuffle plane and a subsequently cleavage fracture. Thus the corresponding theoretical strength is 50.8 GPa, which agrees well with the recent experiment value, 53.4 GPa. However, with the loading along [001], internal relaxation is not important for tetragonal symmetry. Elastic constants during the uniaxial tension along [001] are calculated. Based on the stability analysis with stiffness coefficients, we find that the spinodal and Born instabilities are triggered almost at the same strain, which agrees with the previous molecular-dynamics simulation. During biaxial proportional extension, stress and strength vary proportionally with the biaxial loading ratio at the same longitudinal strain.

An Analytical Solution for Three-Dimensional Diffraction of Plane P-Waves by a Hemispherical Alluvial Valley with Saturated Soil Deposits

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot's dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot's dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

A Numerical Study of Indentation Using Indenters of Different Geometry

Finite element simulation of the Berkovich, Vickers, Knoop, and cone indenters was carried out for the indentation of elastic-plastic material. To fix the semiapex angle of the cone, several rules of equivalence were used and examined. Despite the asymmetry and differences in the stress and strain fields, it was established that for the Berkovich and Vickers indenters, the load-displacement relation can closely be simulated by a single cone indenter having a semiapex angle equal to 70.3degrees in accordance with the rule of the volume equivalence. On the other hand, none of the rules is applicable to the Knoop indenter owing to its great asymmetry. The finite element method developed here is also applicable to layered or gradient materials with slight modifications.

Deformation twinning and its effect on crack extension

Deformation twinning near a crack tip is observed in b.c.c. metal Mo based on molecular dynamics simulation at temperature T = 50 K and loading rate (K) over dot(II) = 0.0706 MPa m(1/2)/ps. The defor mation twinning is closely controlled by both the crystal geometry orientation and the stress distribution. The width of the deformation twin band is affected by the distance between the upper and lower crack surfaces. The twin plane and twin direction are (<1(1)over bar>2) and [(1) over bar 11], respectively. The initial crack extension occurs in the deformation twin region near the crack tip. The simulation shows that the extension direction of the crack is changed as the crack propagates over the twinning boundary.

The relationship of SIF between plate and plane fracture problems and the effect of the plate thickness on SIF

In the present paper, it is shown that the zero series eigenfunctions of Reissner plate cracks/notches fracture problems are analogous to the eigenfunctions of anti-plane and in-plane. The singularity in the double series expression of plate problems only arises in zero series parts. In view of the relationship with eigen-values of anti-plane and in-plane problem, the solution of eigen-values for Reissner plates consists of two parts: anti-plane problem and in-plane problem. As a result the corresponding eigen-values or the corresponding eigen-value solving programs with respect to the anti-plane and in-plane problems can be employed and many aggressive SIF computed methods of plane problems can be employed in the plate. Based on those, the approximate relationship of SIFs between the plate and the plane fracture problems is figured out, and the effect relationship of the plate thickness on SIF is given.

Finite Element Solutions for Plane Strain Mode I Crack with Strain Grading Effect

In this paper, a new phenomenological theory with strain gradient effects is proposed to account for the size dependence of plastic deformation at micro- and submicro-length scales. The theory fits within the framework of general couple stress theory and three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom mu(i). omega(i) is called micro-rotation and is the sum of material rotation plus the particles' relative rotation. While the new theory is used to analyze the crack tip field or the indentation problems, the stretch gradient is considered through a new hardening law. The key features of the theory are that the rotation gradient influences the material character through the interaction between the Cauchy stresses and the couple stresses; the term of stretch gradient is represented as an internal variable to increase the tangent modulus. In fact the present new strain gradient theory is the combination of the strain gradient theory proposed by Chen and Wang (Int. J. Plast., in press) and the hardening law given by Chen and Wang (Acta Mater. 48 (2000a) 3997). In this paper we focus on the finite element method to investigate material fracture for an elastic-power law hardening solid. With remotely imposed classical K fields, the full field solutions are obtained numerically. It is found that the size of the strain gradient dominance zone is characterized by the intrinsic material length l(1). Outside the strain gradient dominance zone, the computed stress field tends to be a classical plasticity field and then K field. The singularity of stresses ahead of the crack tip is higher than that of the classical field and tends to the square root singularity, which has important consequences for crack growth in materials by decohesion at the atomic scale. (C) 2002 Elsevier Science Ltd. All rights reserved.

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress,intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.