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 radial deformations. The obtained solution is used to evaluate low temperature strains and stresses for solder joints in assemblies having matched thermal expansion coefficients of the components. 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 direction, can be rather great and could possibly result in the failure of the joint. They can be brought down by increasing its height-to-diameter ratio. The stresses can also be reduced if low modulus solder materials, such as 95 percent Pb/5 percent Sn solders or indium-based alloys, are used.