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A viscoelastic micor-mechanical analysis for dimensional stability of a composite layer

Coefficient of thermal expansion mismatch between the epoxy layer and composite substrate of «inner layers» can lead to large residual stresses during the manufacture of printed wiring boards (PWB). The viscoelastic nature of the polymeric resin (epoxy) leads to a relaxation of the stresses and a resulting change in dimensions of the inner layer over long periods of time. Here, we treat a micromechanical model using linear viscoelasticity in a finite element thermal stress analysis to demonstrate the time dependency of the ply dimensions upon cooling from near the glass transition temperature (T g ) of the resin to room temperature. The inner layer shrinkage reaches its highest value when room temperature is reached, but the part will continue to change dimensions (shrinkage recovery) for a long time as the in-plane residual stresses relax from their peak values. This evolution takes place over many decades of time. The results show that the long term behavior of dimensional changes is especially pronounced when the effects of time-temperature superposition (TTS) are included below T g