Date of Award
Master of Science
The growing risk that tin whiskers pose to the reliability of electronic assemblies has driven the need for a risk assessment tool. In this paper a mathematical model has been developed to calculate the displacement and stress response of a tin whisker to a harmonic input. The model is based on Euler-Bernoulli beam theory and utilizes the method of eigenfunction expansion to calculate the forced response solution. The model was then coded into Matlab to calculate numerical solutions for a variety of parameters. To enhance the accuracy of the model tin whisker samples were prepared and measured with a microtribometer. The whiskers were loaded traversly with a rigid probe tip and the normal and tangential forces were measured. The whiskers appeared very rigid and did not grossely fracture remaining attached to the substrate. They deformed near the root or in the surrounding tin plating where the whisker grew. The mean deformation stress calculated was 505 MPa although there were not enough measurements for statistical significance. The range of values was quite large relative to the mean. The high variability was primarily attributed to the small sample size of 3 valid measurements, the small magnitude of the forces relative to the tolerance of the microtribometer and the crystal orientation of the whisker itself.
Matthew James Spitzner
Spitzner, Matthew James, "Response of tin whiskers to dynamic input: Mathematical modeling and experimental property measurement" (2009). Graduate Theses and Dissertations. 10633.