A Creep/Relaxation Model Which Exhibits Chaotic Instability—Comparison With Solder Data

Abstract

A mathematical model of creep/relaxation was developed which allows non steady-state behavior, incorporates a modification of the customary steady-state stress versus creep rate power law in order to account for higher rate instability (super-plasticity effect), and uses a discrete time step which is assumed to depend crucially on the grainy structure of solder. In simplest form, the model is transformed into a classic discrete logistic model of population dynamics whose chaotic instability has been extensively studied. A “chaos parameter” is identified which is shown to depend upon time step (grain size) and relaxation of load (dwell). Dynamic behavior of Sn63-Pb37 solder was studied in both bulk and joint forms at various initial loads and constant temperatures. The prediction of instability after dwell was confirmed in both forms. Since both depend upon grain size, dwell time, and relate to instability, a close relationship between the chaos parameter and solder fatigue is suggested.