Modeling Foam Growth in Semi-Crystalline Thermoplastics

Abstract

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.

Rheology and extrusion foaming of chain‐branched poly(lactic acid)

“…These cells undergo a growth stage fueled by the diffusion of the blowing agent from the polymer matrix into these newly formed gas cells. The next step is the foam stabilization which depends on nonlinear viscoelastic property (strainhardening), polymer deplasticization (i.e., the separation by diffusion of blowing agent phase out from polymer phase), polymer crystallization, and cooling rate [5,6]. The strainhardening is a rapid extensional viscosity increase in time that occurs when the polymer melt is highly oriented, i.e., during the cell growth stage in the particular case of polymer foaming.…”

Experimental observations and modelling relating to foaming and bubble growth from pentane loaded polystyrene melts

“…Many variables simultaneously influence the rheological and the microstructure of the product during the growth and its final stage. Investigations addressing the theoretical analysis of bubble growth in polymer foam have been reported (Shafi et al, 1996;Shafi and Flumerfelt, 1997;Koopmans et al, 2000;Den Doelder et al, 2002). Almost all previous work on polymer foaming involve the theoretical study of bubble growth and only few experiments were reported that address the dynamic behaviour of bubble growth in the molten polymer (Villamizar and Han, 1978a,b;Ramesh et al, 1991;Taki et al, 2003).…”

Numerical simulation of polypropylene foaming process assisted by carbon dioxide: Bubble growth dynamics and stability

“…The nonlinear parameter, on which the strain hardening property strongly depends, was varied to analyze the effects of the linear and nonlinear viscoelastic characteristics on bubble growth during isothermal extrusion foaming. It was found that the linear viscoelastic characteristics were more influential and Den Doelder et al (2002) investigated the nonisothermal foaming process for a L-PP and a LCBPP. Contrary to Otsuki and Kanai (2005), they concluded that the strain hardening should be one of the most important factors that stabilized the bubble growth.…”