Explicit solution and invariance of the singularities at an interface crack in anisotropic composites

doi:10.1016/0020-7683(86)90031-4

International Journal of Solids and Structures

Volume 22, Issue 9, 1986, Pages 965-983

https://doi.org/10.1016/0020-7683(86)90031-4 Get rights and content

Abstract

Assuming that stress distribution near the tip of an interface crack in an anisotropic composite is proportional to r^δ, application of the interface and boundary conditions yields ||K(δ)|| = 0, where K is a 12 × 12 complex matrix. The surfaces of the crack can be free-free, fixed-fixed or free-fixed. For the cases of free-free and fixed-fixed cracks, explicit solutions for all δ's are obtained. For the case of free-fixed crack, the determinant of K is reduced to a 3 × 3 determinant which yields a sextic equation. Explicit solutions are obtained only for isotropic composites. The special cases of a homogeneous anisotropic material with a semi-infinite crack and the half-plane problems are also considered. Explicit solutions for δ's are obtained for all three boundary conditions. Finally, it is shown that δ is invariant with respect to the orientation of the plane boundary (in the case of half-plane problems), the semi-infinite crack (in the case of a crack in a homogeneous material) and the crack and interface (in the case of a composite with an interface crack) relative to the materials. This is a somewhat surprising result not expected of anisotropic materials.

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For assuring structural integrity, the study of interface cracks has remained to be an important topic in engineering analysis. It is well known to have stresses with oscillatory singularity in the vicinity of crack tips between dissimilarly adjoined anisotropic materials. The present works targets plane analysis of the stress intensity factors (SIF) of interface cracks by the boundary element method (BEM). For modeling multiply adjoined domains, the conventional sub-region technique in the BEM is applied. For calculating the SIF of interface cracks, the path-independent H-integral is evaluated by the solutions of stresses and displacements at internal points along the integration path in each irrespective domain. For resolving the problem of near singularity when the internal Gauss points are close to the interfaces or crack surfaces, all boundary integrals are regularized to calculate the displacements and stresses at the internal points. From a few examples tested, the approach is verified to be very efficient for accurate assessment of the SIFs of interface cracks between dissimilarly adjoined anisotropic materials.
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Explicit solution and invariance of the singularities at an interface crack in anisotropic composites

Abstract

Int. J. Eng. Sci.

Int. J. Solids Struct.

Int. J. Solids Struct.

Int. J. Solids Struct.

Int. J. Eng. Sci.

Eng. Fracture Mech.

Int. J. Solids Struct.

Acta Metall.

Int. J. Solids Struct.

Int. J. Solids Struct.

Adv. Appl. Mech.

Zur theorie des Druckversuchs

Zeit. Ang. Math. Mech.

Stress singularities resulting from various boundary conditions in angular corners of plates in extension

J. Appl. Mech.

The stresses around a fault or crack in dissimilar media

Bull. Seis. Soc. Am.

A crack between dissimilar media

J. Appl. Mech

Crack point stress singularities at a bi-materials interface

J. Appl. Mech

Two edge-bonded elastic wedges of different materials and wedge angles under surface tractions

J. Appl. Mech.

Stress analysis of a composite plate with circular hole under axisymmetric bending

J. Composite Mater.

On the singular behavior at the vertex of a bi-material wedge

J. Elasticity

On cracks in rectilineary anisotropic bodies

Int. J. Fracture Mech.

Mathematical theories of brittle fracture

The plane solution for anisotropic elastic wedges under normal and shear loading

J. Appl. Mech.

Plane solutions for the displacement and traction-displacement problems for anisotropic elastic wedges.

J. Appl. Mech.

Plane solutions for traction problems on orthotropic unsymmetrical wedges and symmetricallytwinned wedges

J. Appl. Mech.

Bonded orthotropic strips with cracks

Int. J. Fracture