Axisymmetric Elastic Deformations of a Finite Circular Cylinder with Application to Low Temperature Strains and Stresses in Solder Joints.

We consider an axially symmetric elastic problem for a finite circular cylinder whose end planes are subjected to identical radical deformations. The obtained solution is used to evaluate low temperature strains and stresses for solder joints in surface mounted assemblies having matched thermal expansion coefficients of the package and the substrate. The thermomechanical behavior of solder joints is determined in this case by the mismatch between the solder and the soldered materials. It is shown that the arising strains and stresses, especially in the axial, can be rather great and could possibly result in the ultimate or fatigue failure of the joint. They can be brought down by increasing the height-to-diameter ratio of the joint. The stresses can also be reduced flow modulus solder materials, such as 95% Pb/5% Sn solders or indium-based alloys, are used.