C. L. Tan

Treatment of bimaterial interface crack problems using the boundary element method

Abstract Quadratic quarter-point crack-tip elements are introduced in the two-dimensional boundary element analysis of problems in which a crack lies along the interface of dissimilar elastic materials. Such problems present some modelling difficulties using conventional procedures because the stresses are oscillatorily singular in the neighbourhood of the crack-tip. Analytical expressions relating the stress intensity factor to the computed displacements of the crack-tip element or to the computed crack-tip nodal tractions are derived and their veracity demonstrated with some examples. Numerical results, compared with exact solutions where possible, are accurate even with relatively coarse mesh designs.

Boundary element analysis of interface cracks between dissimilar anisotropic materials

Abstract In this paper, the boundary element method (BEM) is applied to the analysis of interface cracks between dissimilar anisotropic materials in plane elasticity. It is based on the quadratic element formulation and special crack-tip elements which incorporate the proper O(r−12+1γ) oscillatory traction singularity are employed. A simple expression relating the stress intensity factors to the BEM computed traction coefficients is derived, and this procedure for determining stress intensity factors is validated by several examples. The numerical results obtained are shown to be very satisfactory even with relatively coarse mesh discretizations.

Anisotropic stress analysis of inclusion problems using the boundary integral equation method

Abstract Numerical methods for stress analysis are increasingly being employed in the micromechanics of solids. In this paper, the boundary integral equation (BIE) method for two-dimensional general anisotropic elasticity, based on the quadratic isoparametric element formulation, is extended to treating some inclusion problems. All the cases analysed involved an elliptical zirconia inclusion in an alumina matrix, noting that ZrO2–Al2O3 is an advanced ceramic increasingly used in structural applications. The BIE results are compared with those calculated using Eshelbys equivalent inclusion approach where possible, and excellent agreements between them are obtained. The present work demonstrates the suitability of using this numerical technique for analysing such problems and, in particular, the ease with which it may be used even in the case of general anisotropy.

Two-dimensional boundary element contact mechanics analysis of angled crack problems

Abstract In this paper, the boundary element method (BEM) for two-dimensional contact mechanics analysis is applied to a number of angle crack problems involving crack surfaces in contact. The formulation employed is based on the quadratic isoparametric boundary element, and the near-tip fields for both open and closed crack tips are properly modelled in the analysis using special crack tip elements with mid-side nodes. Stress intensity factor solutions are presented for a range of geometries and coefficients of friction in each of the problems treated. Where possible, the BEM results are compared with those available in the literature and good agreement between them is obtained. The study shows that friction between the crack surfaces in contact can have a significant effect indeed on the magnitude of the stress intensity factors for all the problems considered.

The use of quarter-point crack-tip elements for T-stress determination in boundary element method analysis

Abstract A simple formula for obtaining the elastic T-stress in boundary element method fracture mechanics analysis is presented in this communication. This formula is obtained by comparing the variation of the displacements along the quarter-point crack-tip element with the classical field solution for the crack-tip. Its validity is tested with four example problems for a range of crack sizes and good agreement with solutions in the literature is generally obtained.

Determination of characterizing parameters for bimaterial interface cracks using the boundary element method

Abstract The complex stress intensity factor, K = K I + iK II , which is used to characterize the near tip fields of a bimaterial interface crack may also be written as K = K 0 e iψ , and it has been shown that K 0 is directly related to the strain energy release rate. An efficient means of obtaining this quantity K 0 using the boundary element method (BEM) has been discussed in a recent paper by the present authors. However, some recent studies have suggested that fracture of such interfacial bonds is characterized by critical values of K 0 which may vary with the phase angle ψ. This note describes how ψ may also be determined using the BEM with quarter-point traction singular crack-tip elements. Results of some numerical experiments are presented to demonstrate the accuracy of the approach.

Boundary integral equation stress analysis of a rotating disc with a corner crack

Abstract The analytical and numerical formulation of the boundary integral equation (BIE) method are outlined for the general case in linear elasticity. Using this method, three-dimensional linear elastic fracture mechanics analyses of a rotating disc with a corner crack at its bore are carried out. The cases considered are for a disc with external to internal radius ratio of 8 and with thickness equal to the diameter of the central bore. Two different crack shapes, namely, a quarter-circular crack and a quarter-elliptical crack with ellipse aspect ratio of 0.75, are analysed. For each of these shapes, corner cracks penetrating 50 per cent and 75 per cent of the disc thickness are treated. Stress intensity factor solutions for these cracks are presented for the centrifugal loading condition, as well as when the disc is subjected to a radial tensile stress at its external circumferential periphery.

Boundary element analysis of orthotropic delamination specimens with interface cracks

Abstract The boundary element method (BEM) with special crack-tip elements is used to obtain the stress intensity factors, K1 and K2, and the strain energy release rates of interface cracks in bilayer double cantilever beam (DCB) and end-loaded-split (ELS) specimens. The material system considered is one in which an orthotropic, transversely isotropic layer is bonded to another layer of equal thickness and made of the same material, but the latter being in the plane of transverse isotropy. The effects of the mechanical properties of the orthotropic material are characterized by the parameters, η1 and η2, which correspond to the purely imaginary roots of the characteristic equation for the material. Calibration results showing the variations of the normalized strain energy release rates with the geometry of the specimens are presented for a range of values of these material parameters. They show the same qualitative trends as for a completely homogeneous beam specimen. To provide a complete characterization of the near-tip fields of the interface crack, the phase angle ψ = tan−1 (K2/K1), which denotes the degree of the mode mixity there, is also obtained for each case. The results show that ψ generally attains a constant value when the ratio of the crack length to the layer thickness reaches a value of less than eight.

Elastic-plastic stress analysis of a cracked thick-walled cylinder

Abstract The boundary integral equation (BIE) method for two-dimensional elastic-plastic stress analysis is applied to an internally pressurized thick-walled cylinder containing a radial crack. Two different types of material are considered, namely, an elastic-perfectly plastic material and a work-hardening material. The loading conditions applied include the case when the internal pressure also acts on the crack faces, and the case when it does not. Results are presented showing the plastic zone development in the cylinder and the variations of the fracture mechanics parameter, the J line integral, with increasing internal pressure.

Stress intensity factors for cracks at spherical inclusions by the boundary integral equation method

Abstract In this paper, the steps in the derivation of the analytical expressions, which could be used to evaluate directly stress intensity factors for cracks from the numerical results of boundary integral equation axisymmetric fracture mechanics analysis are reviewed. These expressions have been found previously to provide an efficient means by which stress intensity factors can be obtained without unnecessarily refined mesh discretisations. They include those which could be used to analyse interface cracks between dissimilar materials. Such crack problems present modelling difficulties when using conventional procedures for obtaining the fracture parameters because of the oscillatorily singular stresses in the vicinity of the interface crack tip. Three axisymmetric problems, each involving a crack at an elastic inclusion which, is embedded in an elastic matrix, are treated in this study, and stress intensity factors are obtained for a range of crack sizes. Both mechanical and thermal loading are considered, and the effects of the mismatch of the material properties of the inclusion and the matrix are also investigated. The numerical results are of interest to the study of, for example, microcracking in particulate composites.