Viscoplastic Formulation
Viscoplastic constitutive equations characterize the rate-dependent deformation of solder joints subjected to thermal cycling and mechanical stress. The Anand creep model represents this behavior by relating stress to plastic strain rate and internal state variables. It describes the rate-dependent plastic flow of solder alloys under conditions of high homologous temperature, which are typical during PCB thermal cycling.
Material Characterization
Determining the parameters for this mathematical model requires isothermal tensile or shear testing at multiple temperatures and strain rates. Nine material constants must be extracted from the experimental data, which describe the rate sensitivity, hardening, and dynamic recovery of the alloy. Circuit board assembly engineers load these constants into finite element software to predict the deformation behavior of surface-mount components.
Accurate extraction of these variables allows for reliable simulation of creep strain accumulation in SAC305 and other lead-free alloys. Poor parameter calibration leads to inaccurate simulations of the joint mechanical stress profile.
Operational Constraint
The simulation limits are defined by the temperature range and strain rate of the calibration tests. This viscoplastic approach assumes isotropic behavior, which does not hold for solder joints dominated by a few large grains. Over long exposure times, microstructural changes in the alloy can invalidate the initial model parameters.
