Stress intensity factors for a semi-infinite plane crack under a pair of point forces on the faces

Static three-dimensional stress intensity factors of a semi-infinite plane crack are investigated in this paper. The deformations are caused by a pair of normal and tangential point forces acting on the crack faces but located away from the crack front. Cases of symmetric and anti-symmetric loadings with respect to the crack plane are both considered. Analytic solutions are obtained by the application of Fourier transforms together with the Wiener-Hopf technique. The formulation departs significantly from the Papkovich-Neuber formulation used in previous works. This alternative formulation reduces the complexity of the calculations involved and has the same potential in regard to the elastodynamic problem. Several misprints in previous works are also noted.     

On the response to point forces suddenly applied to a semi-infinite crack

The solution to the title problem is presented in detail for the case of anti-plane deformation and compared with the more restricted solution available for the plane problem. When instantaneous point forces are applied to the crack's faces the stress ahead of the crack shows a delta-function singularity. It is shown that this result could be derived from a result first obtained by Friedlander.     

Point forces and point charge applied to a circular crack in a transversely isotropic piezoelectric space

Interaction between an arbitrarily located and oriented point force and point charge with a circular crack is considered. Obtained are the exact expressions for the stress intensity factors (SIFs) k_j (j=1,2,3) and electric displacement intensity factor (EDIF) k_D; they are given in terms of elementary functions. The results are also presented in graphical form.     

High frequency scattering due to a pair of time-harmonic antiplane forces on the faces of a finite interface crack between dissimilar anisotropic materials

The high-frequency elastodynamic problem involving the excitation of an interface crack of finite width lying between two dissimilar anisotropic elastic half-planes has been analyzed. The crack surface is excited by a pair of time-harmonic antiplane line sources situated at the middle of the cracked surface. The problem has first been reduced to one with the interface crack lying between two dissimilar isotropic elastic half-planes by a transformation of relevant co-ordinates and parameters. The problem has then been formulated as an extended Wiener–Hopf equation (cf. Noble, 1958) and the asymptotic solution for high-frequency has been derived. The expression for the stress intensity factor at the crack tips has been derived and the numerical results for different pairs of materials have been presented graphically.     

Stress-intensity factors for a semi-infinite plane crack with a wavy front

The stress-intensity factors for a semi-infinite plane crack with a wavy front are determined when the crack faces are subjected to normal and shearing tractions. The results are derived using asymptotic methods and are valid to O(²) where =A/1; A is the amplitude and is the wavelength of the wavy front. The normal and shearing tractions are in the form of line loads parallel to the crack front.The results are then used to evaluate, in a qualitative manner, the growth characteristics of a semi-infinite plance crack with a wavy front under combined mode loading. This provides a possible explanation of crack front segmentation observed experimentally.     

Elastic interaction between edge dislocation,concentrated force,point heat source and edge crack in a semi-infinite plane

We investigate the interaction between edge crack and edge dislocation as well as concentrated force and point heat source. The stress intensity factors at the edge crack tip and the image forces acting on the edge dislocation are calculated. The influence of the concentrated force, point heat source and edge dislocation on the shielding and anti-shielding effects to edge crack as well as the glide and climb forces acting on the edge dislocation is examined in detail. The results indicate that the shielding and anti-shielding effects increase acutely with the increment of concentrated force and point heat source. In addition, the glide and climb forces increase acutely with the decrement of the distance between dislocation and crack tip.     

NEAR CRACK LINE ELASTIC－PLASTIC ANALYSIS FOR A CRACK LOADED BY ANTIPLANE POINT FORCES

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On a pair of axisymmetric forces inside a sphere

In this paper, the stresses in a sphere under a pair of concentrated forces acting axisymmetrically inside the sphere are solved by using a Love's stress function. The method of solution is also applied to solve the problem of a pair of ring forces acting axisymmetrically inside the sphere. In either problem, the solution covers the limiting case in which the pair of forces or ring forces is acting on the sphere.     

Dynamic problem of elasticity theory for a space with a moving semi-infinite crack

Taganrog Pedagogical Institute, Russia. Translated from Prikladnaya Mekhanika, Vol. 28, No. 12, pp. 56–63, December, 1992.     

Diffraction of a plane stress wave by a semi-infinite crack in a general anisotropic elastic material

The problem of a semi-infinite crack subjected to an incident stress wave in a general anisotropic elastic solid is considered. The plane wave impinges the crack at a general oblique angle and is of any of the three types propagating in that direction. A related problem of a semi-infinite crack loaded by a pair of concentrated forces moving along the crack surfaces is also considered. In contrast to the conventional approach by Laplace transforms, a Stroh-like formalism is employed to construct the solution directly in the time domain. The solution is shown to depend on a Wiener–Hopf factorization of a symmetric matrix. Closed-form solution of the stress intensity factors is derived. A remarkably simple expression for the energy release rate is obtained for normal incidence.     

Circular crack in a transversely isotropic piezoelectric space under point forces and point charges

In this paper, two kinds of circular crack including external circular crack and penny-shaped crack in a transversely isotropic piezoelectric space are considered. Firstly, we obtain the solution to the problem of an external circular crack in a transversely isotropic piezoelectric space subjected to antisymmetric normal point forces and point charges. Based on this, the solution of one-sided loading of an external circular crack is constructed. Secondly, the real shape of an external circular crack and the opening displacement of a penny-shaped crack under an arbitrary point force and point charge are further obtained. At last, the results are presented in a graphical form. The project supported by the National Natural Science Foundation of China (19872060 and 69982009) and the Postdoctoral Foundation of China     

The 3-D stress intensity factor for a half plane crack in a transversely isotropic solid due to the motion of loads on the crack faces

Three-dimensional analysis of a half plane crack in a transversely isotropic solid is performed. The crack is subjected to a pair of normal point loads moving in a direction perpendicular to the crack edge on its faces. Transform methods are used to reduce the boundary value problem to a single integral equation that can be solved by the Wiener-Hopf technique. The Cagniard-de Hoop method is employed to invert the transforms. An exact expression is derived for the mode I stress intensity factor as a function of time and position along the crack edge. Some features of the solution are discussed through numerical results. The project supported by the Guangdong Provincial Natural Science Foundation and the Science Foundation of Shantou University     

Differentiation of energy functionals in the problem of a curvilinear crack in a plate with a possible contact of the crack faces

A problem of equilibrium of a cracked plate is considered within the framework of the Kirchhoff-Love model. Non-penetration conditions in the form of inequalities (Signorini-type conditions) are set on the crack faces. The behavior of the energy functional is studied for the case of a rather smooth perturbation of the domain of the general form. Sufficient conditions for the existence of the energy functional derivative with respect to the parameter of domain perturbation are derived. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 153–168, September–October, 2008.     

New solution of the plane problem for an equilibrium crack

We consider the classical plane problem of elasticity about a crack in an isotropic elastic unbounded plane resulting in a singular solution for the stresses near the crack edge. Relations of generalized elasticity with a small parameter characterizing the medium microstructure are derived, and the higher order of these relations permits eliminating the singularity of the classical solution. An experimental method for determining the medium parameter is proposed, and the corresponding experimental results are given.     

On a semi-infinite crack penetrating a piezoelectric circular inhomogeneity with a viscous interface

We investigate a semi-infinite crack penetrating a piezoelectric circular inhomogeneity bonded to an infinite piezoelectric matrix through a linear viscous interface. The tip of the crack is at the center of the circular inhomogeneity. By means of the complex variable and conformal mapping methods, exact closed-form solutions in terms of elementary functions are derived for the following three loading cases: (i) nominal Mode-III stress and electric displacement intensity factors at infinity; (ii) a piezoelectric screw dislocation located in the unbounded matrix; and (iii) a piezoelectric screw dislocation located in the inhomogeneity. The time-dependent electroelastic field in the cracked composite system is obtained. Particularly the time-dependent stress and electric displacement intensity factors at the crack tip, jumps in the displacement and electric potential across the crack surfaces, displacement jump across the viscous interface, and image force acting on the piezoelectric screw dislocation are all derived. It is found that the value of the relaxation (or characteristic) time for this cracked composite system is just twice as that for the same fibrous composite system without crack. Finally, we extend the methods to the more general scenario where a semi-infinite wedge crack is within the inhomogeneity/matrix composite system with a viscous interface.     

On the problem of vortex interaction with a plane

We consider the well-known problem of the interaction of a vortex filament with a perpendicular plane in a viscous incompressible fluid. In this study, the vortex filament is represented by a semi-infinite rotating needle. Different models are considered: a zero-radius needle and fixed and movable in the axial direction needles of a finite radius. The ranges of the existence of the solution are found, and the correspondence of the flow around a finite-radius needle to that around a zero-radius needle, as the needle radius decreases, is studied.     

On the matched-asymptotic solution to the diffraction of a plane elastic wave by a semi-infinite stress-free boundary of finite width

The diffraction of a plane elastic compressional wave by a semi-infinite rectangular stress-free boundary of finite width is investigated using the method of matched-asymptotics. The outer problems are solved in terms of Wiener-Hopf functions while the inner problems by the Kolosov-Muskhelishvili complex potentials. The two are matched to derive the stress behavior away from the edge of the strip. Numerical results are presented for various angles of incidence of the plane wave.