Prediction of interfacial crack path: a direct boundary integral approach and experimental study

Abstract

This paper presents the development of a higher-order direct boundary integral-displacement discontinuity method for crack propagation in layered elastic materials. The method is based on the dual boundary integral equations of linear elasticity which are solved by means of a quadratic boundary element formulation. The analytical solution for a point force within a bonded half-plane region is used to derive the kernel functions of the boundary integral equations. Square-root displacement-discontinuity elements are used to model the crack tips, and stress intensity factors may be computed using the numerically predicted values of the displacement discontinuity components at the midpoints of these crack-tip elements. An algorithm based on the maximum tensile-stress criterion is then developed and incorporated into the boundary element model to predict the paths of cracks propagating in layered elastic materials.In the experimental part of this study, crack profiles for straight-through-cracked, compact-tension specimens of the anodically bonded silicon/Pyrex glass system are measured by profilometry. The plane strain prediction of the crack-propagation path is compared with the experimentally measured crack profiles. Consistent with the prediction, the interfacial crack is observed to kink away from the strong, anodicaUy-bonded interface and propagate into the more compliant glass layer. The predicted initial kink angle of 26 ° agrees very well with the average measured value of 280 . The measured path of the crack is also in very good agreement with the predicted path over about the first 120 microns of crack growth with increasing deviation observed beyond that.

Symmetric Galerkin boundary integral fracture analysis for plane orthotropic elasticity

“…collocating 1 interior to the element instead of at the endpoints (e.g. Selcuk et al 1994). However, this adds signi®cantly to the number of unknowns, especially in three-dimensions, and is therefore also quite expensive.…”

“…Recently, methods based on HBIEs have been developed to overcome the problems inherent in the multi-domain method. There are a number of hypersingular approaches, and each approach has been developed independently by several groups, see for example Bonnet and Bui (1993);Cruse (1988);Chang and Mear (1995); Gray, Martha and Ingraffea (1990); Guimara Äes and Telles (1994); Hong and Chen (1988); Paulino (1995); Selcuk et al (1994). Although successful, the common problem for these methods is that, when employed in conjunction with a collocation approximation, a smoothness constraint is necessarily imposed on the boundary displacement (Gray 1991;Martin and Rizzo 1996).…”

Crack Tip Interpolation, Revisited

“…(2) Note that this equation simply states that there is no linear term present in the expansion of the crack opening displacements, ∆u(r) = u(r, π) − u(r, −π). Thus, incorporating (2) into a computational algorithm should be an especially easy task within the displacement discontinuity method [15,47] or the recent combination of the hypersingular equation method with a symmetric-Galerkin approximation [24]. In both approaches, ∆u(r) is dealt with directly.…”

“…It is well established that use of special elements at the crack tip significantly improves the accuracy of stress intensity factor calculations [3,8,37,49], and many refinements and extensions of the original quarter point element technique have been developed [32,36] (see also the extensive list of references in [3]). Note that for boundary integral fracture analysis, whether using an approach which combines the displacement and traction boundary integral equations [22,27,31] or using the displacement discontinuity method [15,16,18,47], only the displacement on the crack surfaces, θ = ±π, is approximated in the calculation. The near tip crack surface interpolation of the displacement is therefore crucial for accurate SIF calculations using these methods.…”

On crack path stability in a layered material

“…By using boundary element methods the time consuming rediscretisation is reduced. Some recent investigations utilising boundary element methods for crack path prediction are; Bower and Fleck (1994), investigating growth of edge cracks formed in an in®nite half-plane at a sliding contact, and Selcuk et al (1994), studying fracture trajectories from cracks close to the interface in bimaterial specimens applied to tensile loading perpendicular to the interface.…”