Analysis of thermomechanical interactions in a miniature solder under cyclic fatigue loading

This paper discusses the possible thermomechanical interaction (coupling) phenomena of a miniature solder system in electronic packaging application similar to those which have been identified for some metallic material systems in aerospace and nuclear structures under cyclic fatigue loads at different frequencies. The main objective is to investigate the heat generated by the viscoplastic deformations, and vice versa, especially on the thermal transient and the gradient induced viscoplastic ratchetting response of cyclic creep. A literature review was conducted to focus on the temperature-dependent, strain rate-sensitive stress-strain response of the eutectic or near-eutectic lead-tin (Pb37-Sn63 or Pb40-Sn60) solder alloys. The result was used to develop and apply a simple overstress constitutive theory for modeling the coupled, isotropic thermoviscoplasticity of the eutectic lead-tin solder alloy. A fully coupled heat transfer and mechanical finite element model is used to simulate possible thermal-mechanical interactions of temperature rise and viscoplastic ratchetting of the miniature solder systems in a C4/BGA chip scale package (CSP) under cyclic fatigue loads at different frequencies. The results of analysis are discussed to compare between a coupled thermomechanical model and that of a pure mechanical model.