| Plane strain and plane stress assumptions, although generally valid in the interior part of a wedge configuration, don't apply in the vicinity of corner points, at which stress and displacement fields are three-dimensional in nature. In this study a finite element procedure has been developed to compute singular eigenstates that characterize the exact solution of linear elastostatic problems in the vicinity of these threedimensional corners. The asymptotic stress field is composed of terms of the form r −λf(&thetas;,&phis;;λ), where r is the radial distance from the comer point, &thetas; and &phis; are spherical coordinates, and f(&thetas;,&phis;;λ) is the angular function defined on a spherical shell of unit radius which surrounds the corner (r → 0). The order of the singularity, λ, can be real or complex. The accuracy, completeness and efficiency of the method are fully demonstrated by taking into consideration of six rigid body motion modes.; The displacement eigenstates for the terminal point of an interfacial surface crack with and without contact consideration is fully investigated. The structure of all singular eigenstates are fully illustrated by plotting the eigen-displacements on the free surface and eigen-displacement jumps across the crack faces. It is found that in general three real eigenvalues exist without contact consideration and two otherwise. In all cases in-plane shear deformation dominates the displacement fields and it has a stronger singularity than the interior part of a perpendicular crack. Contact constraint changes little anti-symmetric mode asymptotics but it does dramatically change the behavior of the symmetric mode singularity. The study also shows that a critical intersection angle at the free surface can be determined so that the corner point has the same square root singularity as the interior part of the crack front.; For a typical Flip-Chip assembled Chip-on-Board (FCOB) package, it is shown that the stress singularities at three-dimensional comers are always more severe than those at the corresponding two-dimensional edges, which suggests that they are more likely to be the potential crack initiation or delamination sites. Based on the results obtained, several guidelines for minimizing edge stresses in IC packages are presented. |
