An Improved Closed-Form Solution for Shearing and Peeling Stresses of Trimaterial Assembly in Electronic Packaging
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Closed-form solutions for shearing and peeling stresses of trimaterial assembly were initially provided by Schmidt in 1999 [1] and Suhir in 2001 [2]. However, there exist some contradictions and inconsistencies the solutions of both Schmidt and Suhir. The contradiction arises in consideration of the exponent parameter k in the characteristic equation. Both Schmidt and Suhir showed that the exponent parameter k in the shearing stresses contains two roots, but for both cases they considered only one root for k; as a consequence, it leads to a mathematical inconsistency in the solution. In the present paper, a model for shearing stress for uniform temperature change is presented that considers both roots for k. Subsequently, a model for peeling stress is presented that considers moment equilibrium combined with the improved shearing stress model described above. The contradictions in Schmidt's and Suhir's solutions are highlighted in this paper. Analytical and FEM solutions are presented for the same trimate...
[1] E. Suhir. Analysis of interfacial thermal stresses in a trimaterial assembly , 2001 .
[2] Richard Ulrich,et al. Advanced electronic packaging , 2006 .