The problem of an elastic plane containing an elastic inclusion is considered. It is assumed that both the plane and the inclusion contain a radial crack and the two cracks are collinear. The problem is formulated in terms of a system of singular integral equations. In the interesting limiting cases in which the crack tips approach the interface from either one or both sides, the dominant parts of the kernels become generalized Cauchy kernels giving rise to stress singularities of other than 13-1 power. For these unusual cases of a crack terminating at or crossing the interface stress intensity factors are defined and some detailed results are given for various crack-inclusion geometries and material combinations.RésuméOn considère le problème d'un plan élastique comportant une inclusion élastique. On suppose que et le plan et l'inclusion contiennent une fissure radiale, et que les deux fissures sont alignées l'une sur l'autre. Le problème est formulé sous la forme d'un système d'équations à intégrales singulières. Dans les cas limites intéressants où les extrémités des fissures se rapprochent, d'un côté ou des deux côtés, de l'interface du plan et de l'inclusion, les portions principales des noyaux deviennent des noyaux généralisés du Cauchy, ce qui donne lieu à des singularités de la tension d'un ordre différent que la puissance −1/2. Dans les cas inhabituels d'une fissure aboutissant à l'interface ou le traversant, les facteurs d'intensité des contraintes sont déterminés, et quelques résultats détaillés sont fournis, pour diverses géométries d'inclusions et de fissures et diverses combinaisons de matériaux.ZusammenfassungMan untersucht das Problem einer elastischen Ebene die eine elastische Inklusion enthält. Man nimmt an daß beide die Ebene und die Inklusion einen radialen Riß enthalten, und daß beide Risse kolinear sind. Das Problem wird in Form von Singularitätsintegralgleichungen gestellt. Für die interessanten Grenzfälle wo die Rißspitzen sich von einer oder von beiden Seiten der Übergangsfläche nähern, werden die Hauptteile der Kerne verallgemeinerte Cauchykerne die Spannungssingularitäten erzeugen mit einer Potenz verschieden von −1/2. Für diese ungewöhnliche Fälle eines Risses der sich an der Übergangsfläche beendet oder sie durchquert werden Spannungsintensitätsfaktore bestimmt und einige detaillierte Ergebnisse werden für verschiedene Riß-Inklusionsgeometrien und Materialzusammensetzungen gegeben.

The inclusion problem with a crack crossing the boundary. [of an elastic plane

A numerical method has been developed to study the interaction between a crack and second phase particles in a discontinuously reinforced composite material. The simulation is achieved using a ‘dual’ boundary integral method, coupled with a maximum energy release rate criterion for determining the direction of crack propagation. The method has been applied to a composite material composed of components having the elastic properties of Aluminium (matrix) and Silicon Carbide (reinforcement). In particular, the method is used to investigate the crack trajectory and energetics as it interacts with a single particle and with clusters consisting of two particles or a random distribution of ten particles. It is found that although the energy release rate is affected by the particle(s) at relatively large distances, the crack trajectory is not substantially altered until the crack is very close to the particle(s). A pre-existing interface flaw is observed to attract the crack and substantially increase the energy release rate.

The interaction between a crack and a particle cluster

Due to the singularity nature of delamination, the fundamental concept of fracture mechanics was applied. However, the oscillatory characteristics near the delamination tip prohibited the use of conventional definition assuming the crack embedded into a homogeneous solid. A proper definition for the stress intensity factors and energy release rates of bimaterial interface cracks was introduced in this paper to study the fracture criterion for delamination. To measure the delamination fracture toughness, the test specimen usually used for the unidirectional composites was redesigned to suit for the cases that the delamination lies between two laminae with different fiber orientations. The test results show that the double cantilever beam (DCB) test is near to pure Mode I and the end-notched flexural (ENF) test is near to pure Mode II. Therefore, like the cracks in homogeneous materials, the test methods DCB and ENF are useful for the measurement of delamination fracture toughness GC and G11,. Based upon th...

Delamination Fracture Criteria for Composite Laminates

Two-dimensional time domain BEM for scattering of elastic waves in solids of general anisotropy

http://users.cecs.anu.edu.au/~Qinghua.Qin/publications/pap65E-EFM.pdf

BEM for crack-hole problems in thermopiezoelectric materials

Green's functions of two-dimensional anisotropic plates containing an elliptic hole

By combining the method of Stroh`s formalism, the concept of perturbation, the technique of conformal mapping and the method of analytical continuation, a general analytical solution for the elliptical anisotropic elastic inclusions embedded in an infinite anisotropic matrix subjected to an arbitrary loading has been obtained in this paper. The inclusion as well as the matrix are of general anisotropic elastic materials which do not imply any material symmetry. The special cases when the inclusion is rigid or a hole are also studied. The arbitrary loadings include in-plane and antiplane loadings. The shapes of ellipses cover the lines or circles when the minor axis is taken to be zero or equal to the major axis. The solutions of the stresses and deformations in the entire domain are expressed in complex matrix notation. Simplified results are provided for the interfacial stresses along the inclusion boundary. Some interesting examples are solved explicitly, such as point forces or dislocations in the matrix and uniform loadings at infinity. Since the general solutions have not been found in the literature, comparison is made with some special cases of which the analytical solutions exists, which shows that our results are exact and universal.

On the anisotropic elastic inclusions in plane elastostatics

The problems of a crack inside, outside, penetrating or lying along the interface of an anisotropic elliptical inclusion are considered in this paper. Because the crack may be represented by a distribution of dislocation, integrating the analytical solutions of dislocation problems along the crack and applying the technique of numerical solution on the singular integral equation, we can obtain the general solutions to the problems of interactions between cracks and anisotropic elliptical inclusions. Since there are no analytical solutions existing for the general cases of interactions between cracks and inclusions, the comparison is made with the numerical results obtained by other methods or with the analytical results for the special cases which can be reduced from the present problems. These results show that our solutions are correct and universal

Interactions between inclusions and various types of cracks

The plane elasticity problem of dislocation inside, outside, or on the interface of an anisotropic elliptical inclusion in an unbounded anisotropic matrix is considered. A general solution for the stresses and deformations in the entire domain is obtained by applying the Stroh’s formalism and the method of analytical continuation. Since the general solutions have not been found in the literature, in order to verify the present solution, comparison is made with some special cases of which the analytical solutions exist, which shows that our results are exact and universal.

Dislocation Inside, Outside, or on the Interface of an Anisotropic Elliptical Inclusion

Stroh's formalism and the Muskhelishvili's method of analytical continuation are used. The solutions are valid for general elastic anisotropic media under two dimensional deformation. The interaction energy between dislocations and elastic inclusions is obtained explicitly. The solutions in general are expressed in series form for elastic inclusions. However, for the special cases when the elastic inclusions are replaced by a hole or rigid inclusion, simple closed form solutions are derived

Wen J. Yen

Papers

Green's functions of two-dimensional anisotropic plates containing an elliptic hole

On the anisotropic elastic inclusions in plane elastostatics

Interactions between inclusions and various types of cracks

Dislocation Inside, Outside, or on the Interface of an Anisotropic Elliptical Inclusion

Interactions Between Dislocations and Anisotropic Elastic Elliptical Inclusions