Time-domain viscoelastic constitutive model based on concurrent fitting of frequency-domain characteristics

A numerical procedure for constructing the multiaxial viscoelastic model for polymeric packaging material over a wide range of temperature is presented. By using the proposed best-fitting procedure, experimentally measured frequency-domain Young's and shear storage moduli are used to calculate the time-domain bulk and shear relaxation moduli which describe the three-dimensional constitutive behavior of a viscoelastic solid. The numerical procedure incorporates restrictions that ensure that the derived time-domain material function is physics compatible. The proposed procedure was applied to construct the viscoelastic constitutive models of epoxy molding compounds (EMCs), and compared to results obtained by using approximate-formula based direct conversion procedure. It was shown that, without using the proposed procedure, the directly calculated time-dependent Poisson's ratio oscillates significantly in the rubbery regime and is physically inadmissible. To validate the constitutive model constructed by using the proposed procedure, a numerical finite element model that incorporates the viscoelastic constitutive model of the EMC was applied to simulate warpage of an overmolded package under the solder reflow process and compared to experimental shadow Moiré measurements.