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Influence of interlayer thickness on stress fields at the vertices in three-dimensional joints with three layers is evaluated using eigen analysis formulated by finite element method (FEM) and boundary element method (BEM). A model for analysis is a three-layered joint consisting of Si, resin and FR-4.5. Singular stress fields for mechanical loading and residual thermal stress are investigated. All stress components are expressed in spherical coordinate systems where their origins are located at the vertices of each interface. Expressions for stress field near the vertex on the interface are derived from the result of eigen analysis. The order of singularity at Si-resin interface is larger than that at resin-FR-4.5 interface. A coefficient of a power law term of stress distribution in a radial direction from the vertex increases with increasing the thickness of interlayer in cases of mechanical loading and residual thermal stress. A coefficient of a power law term in the angular function of stress obtained from BEM is almost agreed with the value obtained from the angular function derived by eigen analysis. Three-dimensional intensity of singularity at the vertex of interface is defined using the intensities of singularity in the radial direction and that in the angular direction. The three-dimensional intensity of singularity at the vertex varies with the interlayer thickness in a similar way to the intensity of singularity in the radial direction from the vertex.

Effect of interlayer thickness on stress singularity field near a vertex in three-dimensional joints under thermal and mechanical loadings