JEC COMPOSITES MAGAZINE - Issue #114 - July 2017 - 54

TECHNOLOGY software

A novel physics node for Nakamura
crystallization kinetics

arthur LevY,
Lecturer
Laboratoire de
Thermique et Energie de Nantes

The Nakamura kinetics law is commonly used to model the evolution of crystallization. A novel physics node, freely available, was developed using the
COMSOL Physics Builder, accounting for the resolution of Nakamura kinetics.
The new physics node can be used in any COMSOL multiphysical model. An example of composite forming simulation, including coupling with a heat transfer
node, is presented in this paper.

he new physics node is efficient at automatically handling
couplings (with built-in physical magnitudes) but also calls
for physical material properties with consistent units. Thus,
this novel physics node will prevent mistakes when developing
new models. It is available under GPL opensource license at
http://github.com/arthurlevy/ComsolPhysics.
Introduction
Thermoplastic polymer forming
Due to their good specific properties, advanced polymers and the
corresponding composite materials tend to replace traditional
materials such as metals in industrial applications. Thermoplastic
polymers and their composites offer new possibilities for the industry. Large structures can be processed rapidly and more cost
effectively than with thermoset materials, which need to undergo lengthy curing reactions. Advanced thermoplastic composites
very often have a semi-crystalline matrix. This is the case for PET
and polyamide, but also for advanced polymers such as PAEK.
In this case, the cooling, solidification and final properties are
determined by the crystallization phenomenon, which is usually
thermally induced [1].

Predicting crystallization
For these materials, crystallization, which occurs during the forming process and especially during the solidification phase, plays a
critical role in the final part quality. For instance, in the case of
injection moulding, crystallization determines the liquid/solid
transition and thus establishes the ejection criteria. In addition,
crystallization induces shrinkage and residual stresses.
Therefore, polymer forming simulation software programs have
to accurately predict crystallization effects, especially during the

jec composites magazine / N°114 July 2017

cooling phase. An accurate quantitative prediction is a prerequisite for predicting solidification (or gel) time.
Crystallization depends on both temperature and flow histories.
Typically at the macroscopic scale, one defines a scalar variable,
the degree of crystallization, which quantifies the advancement
of the crystallization transformation and varies between 0 and 1.
Paper outlines
This paper describes the development of a novel physics node in
COMSOL using the Physics Builder. It contains the crystallization rules presented in the following section.
This work focuses on thermal quiescent crystallization. Indeed,
temperature history appears to play the dominant role in crystallization effects during forming processes. In essence, this problem
is thus multiphysical since heat transfer and crystallization effects
both have to be predicted simultaneously (see Figure 1). A typical model, including a heat transfer node and the newly developed crystallization node, was then developed in COMSOL (see
the Application section).

Fig. 1: Heat transfer and crystallization coupling is a typical multiphysical
problem when dealing with the solidification of semi-crystalline polymers

Robust modelling of polymer crystallization
Crystallization kinetics
The evolution of the degree of crystallization, α, is ruled by crystallization kinetics. The first kinetics models were based on geometrical, nucleation and growth rate assumptions [2]. Nakamura
[3] extended these models to account for non-isothermal conditions. The Nakamura law is written as follows:

http://www.github.com/arthurlevy/ComsolPhysics

Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #114 - July 2017