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1.
Summary A problem of partial sliding along a planar crack with a local drop in frictional resistance is investigated. A sliding zone initiates in the area of reduced friction, and then propagates as the applied shear load is monotonously increased. The problem is formulated in general terms, and then solved for the case when sliding spreads as a penny-shaped zone. Conditions under which the front of the zone stays circular during sliding are analyzed. It is observed that the axisymmetry of the profile of frictional resistance does not necessarily guarantee uniform propagation of sliding in the radial direction. The circular shape becomes the most favorable growth condition only if the shear modes are related in a certain way. The problem is studied based on the criterion of propagation that stress intensity factors(SIFs) for II and III modes vanish on the boundary of the sliding zone. The singular integrals in expressions for the SIFs are reduced to non-singular ones. Analytical solutions are derived for a number of special cases where the radius of the sliding zone is related to the applied shear load.This work is supported by the National Science Foundation through grant DGE-0209543 to the University of New Mexico. 相似文献
2.
Considered is the tandem emission of dislocations and dislocation dipoles from a crack under in-plane shear in one slip system as well as multiple slip systems. Effective stress intensity factors are determined by considering zones of local distortion similar to that in macro-plasticity. The dislocation free zone (DFZ) is also obtained which is analogous to the core region in fracture mechanics. Studied are effects of dislocation emission or development of plastic zone in front of the crack tip on the potential crack propagation based on the strain energy density factor criterion. 相似文献
3.
An investigation of fatigue crack propagation in rectangular AM60B magnesium alloy plates containing an inclined through crack is presented in this paper. The behavior of fatigue crack growth in the alloy is influenced by the fracture surface roughness. Therefore, in the present investigation, a new model is developed for estimating the magnitude of the frictional stress intensity factor, kf, arising from the mismatch of fracture surface roughness during in-plane shear. Based on the concept of kf, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δkeff. Subsequently, the proposed model is applied to predict crack growth due to fatigue loads. Experiments for verifying the theoretical predictions were also conducted. The results obtained are compared with those predicted using other employed mixed mode fracture criteria and the experimental data. 相似文献
4.
Scattering of monochromatic elastic waves on an isolated planar crack of arbitrary shape is considered. The 2D-integral equation for the crack opening vector is discretized by Gaussian approximating functions. For such functions, the elements of the matrix of the discretized problem have forms of standard one-dimensional integrals that can be tabulated. For regular grids of approximating nodes, the matrix of the discretized problem has the Toeplitz structure, and the corresponding matrix–vector products can be calculated by the fast Fourier transform technique. The latter strongly accelerates the process of iterative solution of the discretized problem. Examples of calculations of crack opening vectors, dynamic stress-intensity factors, and differential cross-sections of circular (penny-shaped) and non-circular cracks for various incident wave fields are presented. For a penny-shaped crack and longitudinal incident waves normal to the crack plane, an efficient semi-analytical method of the solution of the scattering problem is developed. The results of both methods are compared in a wide frequency region of the incident field. 相似文献
5.
Effect of electric displacement saturation on the stress intensity factor for a crack in a ferroelectric ceramic 总被引:3,自引:0,他引:3
A crack in a ferroelectric ceramic with perfect saturation under electric loading is analyzed. The boundary of the electric displacement saturation zone ahead of the crack tip is assumed to be ellipse in shape. The shape and size of ferroelectric domain switching zone near a crack tip is determined based on the nonlinear electric theory. The stress intensity factor induced by ferroelectric domain switching under small-scale conditions is numerically obtained as a function of the electric saturation zone parameter and the ratio of the coercive electric field to the yield electric field. It is found that the stress intensity factor increases as the ratio of the semi-axes of the saturation ellipse increases. 相似文献
6.
Elastic field in an infinite medium of one-dimensional hexagonal quasicrystal with a planar crack 总被引:1,自引:0,他引:1
This present work is concerned with planar cracks embedded in an infinite space of one-dimensional hexagonal quasicrystals. The potential theory method together with the general solutions is used to develop the framework of solving the crack problems in question. The mode I problems of three common planar cracks (a penny-shaped crack, an external circular crack and a half-infinite crack) are solved in a systematic manner. The phonon and phason elastic fundamental fields along with some important parameters in crack analysis are explicitly presented in terms of elementary functions. Several examples are given to show the applications of the present fundamental solutions. The validity of the present solutions is discussed both analytically and numerically. The derived analytical solutions of crack will not only play an important role in understanding the phonon–phason coupling behavior in quasicrystals, but also serve as benchmarks for future numerical studies and simplified analyses. 相似文献
7.
Variation of the stress intensity factor along the front of a 3-D rectangular crack subjected to mixed-mode load 总被引:3,自引:0,他引:3
Summary The singular integral equation method is applied to the calculation of the stress intensity factor at the front of a rectangular
crack subjected to mixed-mode load. The stress field induced by a body force doublet is used as a fundamental solution. The
problem is formulated as a system of integral equations with r
−3-singularities. In solving the integral equations, unknown functions of body-force densities are approximated by the product
of polynomial and fundamental densities. The fundamental densities are chosen to express two-dimensional cracks in an infinite
body for the limiting cases of the aspect ratio of the rectangle. The present method yields rapidly converging numerical results
and satisfies boundary conditions all over the crack boundary. A smooth distribution of the stress intensity factor along
the crack front is presented for various crack shapes and different Poisson's ratio.
Received 5 March 2002; accepted for publication 2 July 2002 相似文献
8.
The effect of a non-uniform parallel high magnetic field on flow control characteristics is investigated experimentally for a magnetic fluid single-phase flow and an air—magnetic fluid two-phase flow in a vertical channel. It is found that as the magnetic field strength is increased, the friction factor of the single-phase flow increases significantly. For the two-phase flow, the friction pressure loss and the head pressure loss, which is smaller than the friction loss, are negligibly small compared with the magnetic pressure loss. In the case where air is injected 27.9d upstream from the maximum magnetic field, the air flow is blocked by the magnetic force in the entrance of the magnetic field, which leads to increases in both local void fraction and pressure drop there. In the case where air is injected 1.43d downstream from the maximum magnetic field, the air flow is accelerated, resulting in a decrease in void fraction and an increase in pressure rise. In the latter case and under the present range of experimental conditions, the magnetic pumping head reaches 0.02 MPa at the highest, and the maximum circulation flow rate reaches twice as high as non-magnetically driven flow rate. 相似文献
9.
The mechanical model was established for the anti-plane fracture problem of a functionally graded coating–substrate system
with a coating crack inclined to the weak/micro-discontinuous interface. The Cauchy singular integral equation for the crack
was derived using Fourier integral transform, and the Lobatto–Chebyshev collocation method put up by Erdogan and Gupta was
used to get its numerical solution. Finally, the effects of the weak/micro-discontinuity of the interface on SIFs were analyzed,
the “affected regions” corresponding to the two crack tips have been obtained and their engineering significance was discussed.
It was indicated that, for the crack tip in the corresponding “affected region”, to reduce the weak-discontinuity of the interface
and to make the interface micro-discontinuous are the two effective ways to reduce the SIF, and the latter way always has
more remarkable SIF-reduction effect. For the crack tip outside the “affected region”, its SIF is mainly influenced by material
stiffness, and to prevent such a tip from growing toward the interface “softer coating and stiffer substrate” is a more advantageous
combination than “stiffer coating and softer substrate”. 相似文献
10.
When rewriting the governing equations in Hamiltonian form, analytical solutions in the form of symplectic series can be obtained by the method of separation of variable satisfying the crack face conditions. In theory, there exists sufficient number of coefficients of the symplectic series to satisfy any outer boundary conditions. In practice, the matrix relating the coefficients to the outer boundary conditions is ill-conditioned unless the boundary is very simple, e.g., circular. In this paper, a new two-level finite element method using the symplectic series as global functions while using the conventional finite element shape functions as local functions is developed. With the available classical finite elements and symplectic series, the main unknowns are no longer the nodal displacements but are the coefficients of the symplectic series. Since the first few coefficients are the stress intensity factors, post-processing is not required. A number of numerical examples as well as convergence studies are given. 相似文献
11.
V. V. Mykhas’kiv I. Ya. Zhbadynskyi 《Journal of Applied Mechanics and Technical Physics》2008,49(3):510-518
The dynamic behavior of a circular crack in an elastic composite consisting of two dissimilar half-spaces connected by a thin
compliant interlayer is studied. One half-space contains a defect aligned perpendicular to the interlayer; the defect surfaces
are loaded by normal harmonic forces, which ensures the symmetry of the stress-strain state. The thin interlayer is modeled
by conditions of a nonideal contact of the half-spaces. The problem is reduced to a boundary integral equation with respect
to the function of dynamic opening of the defect. The numerical solution of this equation yields frequency dependences of
the mode I stress intensity factor in the vicinity of the crack for different values of interlayer thickness and relations
between the moduli of elasticity of the composite components.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 197–207, May–June, 2008. 相似文献
12.
V. S. Kirilyuk 《International Applied Mechanics》2008,44(7):757-768
The paper establishes a relationship between the solutions for cracks located in the isotropy plane of a transversely isotropic
piezoceramic medium and opened (without friction) by rigid inclusions and the solutions for cracks in a purely elastic medium.
This makes it possible to calculate the stress intensity factor (SIF) for cracks in an electroelastic medium from the SIF
for an elastic isotropic material, without the need to solve the electroelastic problem. The use of the approach is exemplified
by a penny-shaped crack opened by either a disk-shaped rigid inclusion of constant thickness or a rigid oblate spheroidal
inclusion in an electroelastic medium
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 47–60, July 2008. 相似文献