An Evaluation of Intensity of Stress Singularity at Interface of Three-Dimesnional Three-Layer Boded Joints (Evaluation of the Maximum Intensity of Singularity on Stress σθθ )

Abstract

Influence of interlayer thickness on singular stress fields around vertexes in 3-layered 3D-joints is evaluated through eigen analysis and BEM using fundamental solutions for two-phase materials. A model for analysis is three-layered joints consisting of Si, resin and FR-4.5. A relationship between singular stress fields and the resin thickness is precisely investigated. All stress components are expressed as spherical coordinate systems in which their origins are located at the vertex of each interface. They are derived from the transformation of coordinate system; from x-, y- and z-coordinates to r-, θ- and φ-coordinates. Here, θ is the angle from z-axis, φ is the angle from side surface and r is the distance from the stress singularity point. Angle, θmax, for the maximum of stress, σθθ, near the vertex of the interface is firstly searched for various angle φ. A coefficient of the power-law term in the expression of stress distribution for the r-direction is determined for the stress distributions in the θmax direction. The coefficient is referred to as the intensity of singularity in the r-direction. The intensity of singularity increases with the resin thickness, and attains to an upper limit in the case where the resin thickness is larger than the width of the model. Intensity of singularity in the φ-direction along θmax direction is also investigated. Values of the intensity of singularity in the φ-direction are a constant for Si-resin and resin-FR4.5 interfaces. Three-dimensional intensity of singularity at the vertex in three-dimensional joints is defined considering the intensities of singularity for the r- and φ-directions. Variation of the three-dimensional intensity of singularity at the vertex with the resin thickness is similar to that of the intensity of singularity for the interface.