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.

A BIEM optimization method for fracture dynamics inverse problem

In the present paper, based on the theory of dynamic boundary integral equation, an optimization method for crack identification is set up in the Laplace frequency space, where the direct problem is solved by the author's new type boundary integral equations and a method for choosing the high sensitive frequency region is proposed. The results show that the method proposed is successful in using the information of boundary elastic wave and overcoming the ill-posed difficulties on solution, and helpful to improve the identification precision.

Elimination of loading reverberation in the split hopkinson torsional bar

The loading reverberation is a multiple wave effect on the specimen in the split Hopkinson torsional bar (SHTB). Its existence intensively destroys the microstructure pattern in the tested material and therefore, interferes with the study correlating the deformed microstructure to the macroscopic stress-strain response. This paper discusses the problem of the loading reverberation and its effects on the post-mortem observations in the SHTB experiment. The cause of the loading reverberation is illustrated by a stress wave analysis. The modification of the standard SHTB is introduced, which involves attaching two unloading bars at the two ends of the original main bar system and adopting a new loading head and a couple of specially designed clutches. The clutches are placed between the main bar system and the unloading bars in order to lead the secondary loading wave out of the main bar system and to cut off the connection in a timely manner. The loading head of the standard torsional bar was redesigned by using a tube-type loading device associated with a ratchet system to ensure the exclusion of the reflected wave. Thus, the secondary loading waves were wholly trapped in the two unloading bars. The wave recording results and the contrasting experiments for examining the post-mortem microstructure during shear banding both before and after the modification highly support the effectiveness of the modified version. The modified SHTB realizes a single wave pulse loading process and will become a useful tool for investigating the relation between the deformed microstructure and the macroscopic stress-strain response. It will play an important role especially in the study of the evolution of the microstructure during the shear banding process. (C) 1995 American Institute of Physics.

Elastodynamic stress intensity factor history for a semi-infinite crack under three-dimensional transient loading

The dynamic stress intensity factor history for a semi-infinite crack in an otherwise unbounded elastic body is analyzed. The crack is subjected to a pair of suddenly-applied point loadings on its faces at a distance L away from the crack tip. The exact expression for the mode I stress intensity factor as a function of time is obtained. The method of solution is based on the direct application of integral transforms, the Wiener-Hopf technique and the Cagniard-de Hoop method. Due to the existence of the characteristic length in loading this problem was long believed a knotty problem. Some features of the solutions are discussed and graphical result for numerical computation is presented.

High order asymptotic field for plane stress crack problem

This paper presents an exact analysis for high order asymptotic field of the plane stress crack problem. It has been shown that the second order asymptotic field is not an independent eigen field and should be matched with the elastic strain term of the first order asymptotic field. The second order stress field ahead of the crack tip is quite small compared with the first order stress field. The stress field ahead of crack tip is characterized by the HRR field. Hence the J integral can be used as a criterion for crack initiation.

The plane problem of collinear rigid lines under arbitrary loads

The elastic plane problem of collinear rigid lines under arbitrary loads is dealt with. Applying the Riemann-Schwarz symmetry principle integrated with the analysis of the singularity of complex stress functions, the general formulation is presented, and the closed-form solutions to several problems of practical importance are given, which include some published results as the special cases. Lastly the stress distribution in the immediate vicinity of the rigid line end is examined.

Plane strain problem of growing crack for a perfectly plastic solid

In this paper, fundamental equations of the plane strain problem based on the 3-dimensional plastic flow theory are presented for a perfectly-plastic solid The complete governing equations for the growing crack problem are developed. The formulae for determining the velocity field are derived.The asymptotic equation consists of the premise equation and the zero-order governing equation. It is proved that the Prandtl centered-fan sector satisfies asymptotic equation but does not meet the needs of hlgher-order governing equations.

Complete solution of the columbus problem for large-disturbance cases

The Columbus problem has been rigorously solved by Lyapunov's direct approach to the continuous system in gencral cases of large disturbance and the theory has proved to be in strict consistency with Kelvin's experiments.

The thermal and mechanical structure of a two-dimensional plume in the earths mantle

On the condition that the distribution of velocity and temperature at the mid-plane of a mantle plume has been obtained (pages 213–218, this issue), the problem of determining the lateral structure of the plume at a given depth is reduced to solving an eigenvalue problem of a set of ordinary differential equations with five unknown functions, with an eigenvalue being related to the thermal thickness of the plume at this depth. The lateral profiles of upward velocity, temperature and viscosity in the plume and the thickness of the plume at various depths are calculated for two sets of Newtonian rheological parameters. The calculations show that the precondition for the existence of the plume, δT/L 1 (L = the height of the plume, δT = lateral distance from the mid-plane), can be satisfied, except for the starting region of the plume or near the base of the lithosphere. At the lateral distance, δT, the upward velocity decreases to 0.1 – 50% of its maximum value at different depths. It is believed that this model may provide an approach for a quantitative description of the detailed structure of a mantle plume.

Variational approach to the closure problem of turbulence theory

A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963).

On the non-linear stability theory of spinning solid bodies with liquid-filled cavities and its application to the columbus problem

In this paper, we first present a system of differential-integral equations for the largedisturbance to the general case that any arbitrarily shaped solid body with a cavity contain-ing viscous liquid rotates uniformly around the principal axis of inertia, and then develop aweakly non-linear stability theory by the Lyapunov direct approach. Applying this theoryto the Columbus problem, we have proved the consistency between the theory and Kelvin'sexperiments.

Analysis of micro-indentation problem of a soft film on a hard substrate

Two stages have been observed in micro-indentation experiment of a soft film on a hard substrate. In the first stage, the hardness of the thin film decreases with increasing depth of indentation when indentation is shallow; and in the second stage, the hardness of the film increases with increasing depth of indentation when the indenter tip approaches the hard substrate. In this paper, the new strain gradient theory is used to analyze the micro-indentation behavior of a soft film on a hard substrate. Meanwhile, the classic plastic theory is also applied to investigating the problem. Comparing two theoretical results with the experiment data, one can find that the strain gradient theory can describe the experiment data at both the shallow and deep indentation depths quite well, while the classic theory can't explain the experiment results.

Controllable Kerr nonlinearity with perfect transparency in the existence of spontaneously generated coherence

We investigate the Kerr nonlinearity of a V-type three-level atomic system where the upper two states decay outside to another state and hence spontaneous generated coherence may exist. It is shown that dark state and hence perfect transparency present under certain conditions. Meanwhile, the Kerr nonlinearity can be controlled by manipulation of the decay rates and the splitting of the two excited states. Therefore, enhanced Kerr nonlinearity without absorption can be obtained under proper parameters.

Existence of the transverse relaxation time in optically excited bulk semiconductors

Two basic types of depolarization mechanisms, carrier-carrier (CC) and carrier-phonon (CP) scattering, are investigated in optically excited bulk semiconductors (3D), in which the existence of the transverse relaxation time is proven based on the vector property of the interband transition matrix elements. The dephasing rates for both CC and CP scattering are determined to be equal to one half of the total scattering-rate-integrals weighted by the factors (1 - cos chi), where chi are the scattering angles. Analytical expressions of the polarization dephasing due to CC scattering are established by using an uncertainty broadening approach, and analytical ones due to both the polar optical-phonon and non-polar deformation potential scattering (including inter-valley scattering) are also presented by using the sharp spectral functions in the dephasing rate calculations. These formulas, which reveal the trivial role of the Coulomb screening effect in the depolarization processes, are used to explain the experimental results at hand and provide a clear physical picture that is difficult to extract from numerical treatments.