Finite-Element Analysis of Current-Induced Thermal Stress n a Conducting Sphere

Understanding the electrothermal-mechanical behavior of electronic inter-
connects is of practical importance in improving the structural reliability of
electronic devices. In this work, we use the finite-element method to analyze
the Joule-heating-induced thermomechanical deformation of a metallic sphere
that is sandwiched between two rigid plates. The deformation behavior of the
sphere is elastic–perfectly plastic with Young’s modulus and yield stress
decreasing with temperature. The mechanical stresses created by Joule
heating are found to depend on the thermal and mechanical contact conditions
between the sphere and the plates. The temperature rise in the sphere for the
diathermal condition between the sphere and the plates deviates from the
square relation between Joule heat and electric current, due to the tempera-
ture dependence of the electrothermal properties of the material. For large
electric currents, the simulations reveal the decrease of von Mises stress near
the contact interfaces, which suggests that current-induced structural damage
will likely occur near the contact interfaces.