Nonlinear viscoelastic constitutive model for organic laminate substrate

Organic laminate substrate is one of the largest constituent volume-wise in area array packages, and it plays a key role in overall package stress and warpage evolutions during fabrication process and in service conditions. In order to accurately estimate the influences of substrate on stress and warpage, it is important to characterize the time-dependent constitutive behavior of the organic substrate. In this study, a series of tensile creep and creep recovery experiments were performed to characterize the time-dependent behavior of a single-core laminate substrate. Nonlinear viscoelastic constitutive models including the Schapery model and a time-temperature-stress superposition model were developed based on the experimental characterization, and applied to simulate strain responses under cyclic loading conditions. It is shown that the predictions based on the nonlinear viscoelastic models give more accurate estimations on strain responses to creep and creep recovery loadings than the linear viscoelastic model does, in particularly for stress levels higher than 30% of the substrate's fracture strength.