This paper presents a boundary element method (BEM) analysis of linear elastic fracture mechanics in two-dimensional solids. The most outstanding feature of this new analysis is that it is a single-domain method, and yet it is very accurate, efficient and versatile: Material properties in the medium can be anisotropic as well as isotropic. Problem domain can be finite, infinite or semi-infinite. Cracks can be of multiple, branched, internal or edged type with a straight or curved shape. Loading can be of in-plane or anti-plane, and can be applied along the no-crack boundary or crack surface. Furthermore, the body-force case can also be analyzed. The present BEM analysis is an extension of the work by Pan and Amadei (1996a) and is such that the displacement and traction integral equations are collocated, respectively, on the no-crack boundary and on one side of the crack surface. Since in this formulation the displacement and/or traction are used as unknowns on the no-crack boundary and the relative crack displacement (i.e. displacement discontinuity) as unknown on the crack surface, it possesses the advantages of both the traditional displacement BEM and the displacement discontinuity method (DDM) and yet gets rid of the disadvantages associated with these methods when modeling fracture mechanics problems. Numerical examples of calculation of stress intensity factors (SIFs) for various benchmark problems were conducted and excellent agreement with previously published results was obtained.

https://blogs.uakron.edu/ernianpan/files/2014/09/030_1997IJFPan2DBemFract1.pdf

A general boundary element analysis of 2-D linear elastic fracture mechanics

A peridynamic model for dynamic fracture in functionally graded materials

Modeling method for a crack problem of functionally graded materials with arbitrary properties—piecewise-exponential model

Interaction integrals for thermal fracture of functionally graded materials

A theoretical treatment of mode I crack problem is put forward for a functionally graded orthotropic strip. The internal crack and edge crack perpendicular to the boundaries are investigated, respectively. The elastic property of the material is assumed to vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the boundaries of the strip. The singular integral equation for solving the problem and the corresponding asymptotic expression of the singular kernel are obtained. Three different loading conditions, namely crack surface pressure, fixed-grip loading and bending, are considered during the analysis. The influences of parameters such as the material constants and the geometry parameters on the stress intensity factors (SIFs) are studied.

Mode I crack problem for a functionally graded orthotropic strip

Transient dynamic stress intensity factors around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes

The stresses around a crack in an interfacial layer between two dissimilar elastic half-planes are obtained. The crack is parallel to the interfaces. The material constants of the layer vary continuously within a range from those of the upper half-plane to those of the lower half-plane. An internal gas pressure is applied to the surfaces of the crack. To derive the solution, the nonhomogeneous interfacial layer is divided into several homogeneous layers with different material properties. The boundary conditions are reduced to dual integral equations, which are solved by expanding the differences of the crack face displacements into a series. The unknown coefficients in the series are determined using the Schmidt method, and a stress intensity factor is calculated numerically for epoxy-aluminum composites.

Stress intensity factors around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes

Dynamic stress intensity factors around two parallel cracks in an infinite-orthotropic plane subjected to incident harmonic stress waves

Stress intensity factors are determined for a crack in an infinite orthotropic layer. The crack is situated parallel to the plane surfaces of the layer. Stresses are solved for two kinds of the boundary conditions with respect to temperature field. In the first problem, the upper surface of the layer is heated to maintain a constant temperature T
0, while the lower surface is cooled to maintain a constant temperature −T
0. In the other problem, uniform heat flows perpendicular to the crack. The surfaces of the crack are assumed to be insulated. The boundary conditions are reduced to dual integral equations using the Fourier transform technique. To satisfy the boundary conditions outside the crack, the difference in temperature at the crack surfaces and differences in displacements are expanded in a series of functions that vanish outside the crack. The unknown coefficients in each series are evaluated using the Schmidt method. Stress intensity factors are then calculated numerically for a steel layer that behaves as an isotropic material and for a tyrannohex layer that behaves as an orthotropic material.

Shouetsu Itou

Papers

Transient dynamic stress intensity factors around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes

Stress intensity factors around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes

Dynamic stress intensity factors around two parallel cracks in an infinite-orthotropic plane subjected to incident harmonic stress waves

Thermal stress intensity factors of an infinite orthotropic layer with a crack

Thermal stresses around a crack in the nonhomogeneous interfacial layer between two dissimilar elastic half-planes