Modeling foam growth in semi-crystalline thermoplastics

The accurate description of the rapidly changing viscoelastic character of the gas-laden polymer melt during the expansion phase of foam development is one of the main challenges in modeling thermoplastic foam processing. A general model addressing this challenge for amorphous and semi-crystalline polymers is presented here. Key model elements include the capturing of strain hardening in extensional flow and flow-induced crystallization. The extensional rheology is modeled using the Lodge constitutive equation. The crystallization is modeled using the Avrami equation enhanced with a flow-induced Jay-factor. The model is applied to two isotactic polypropylene materials. The results show the complex non-linearity of foam expansion. The calculated foaming window is in good agreement with experimental data.