Computationally efficient algorithms for modelling thermal degradation and spiking phenomena in polymeric materials

Numerical study of the thermal degradation of isotropic and anisotropic polymeric materials

“…The reaction kinetics considered in this study is of firstorder in the monomer concentration and differs from that employed in other studies which assumed that the conversion of monomers [2], i.e., G = 1 − u, is governed by…”

“…Note that the formulation presented here assumes that the thermal capacity and the monomer and heat diffusion tensors are independent of both the temperature and monomer concentration. This assumption may not be a realistic one when considering the curing of polymeric materials where the thermal capacity is known to depend on the temperature, e.g., [2,6], but, as stated above, our main objective in this study is to examine the effects of the anisotropy of the monomer and heat diffusion tensors on the thermal degradation of polymeric materials. Moreover, the numerical method presented here can easily handle the dependence of the thermal capacity on temperature, monomer concentration, space and time, and calculations performed with more realistic, i.e., temperature-dependent, specific heats or thermal capacities may be performed in the future.…”

“…Note that most of the numerical studies on the curing of polymeric materials performed to-date, e.g., [2], have considered that D = 0, and, therefore, a comparison between results corresponding to D = 0 with those for D = 0 allows to determine the effects of the monomer mass diffusion on the thermal degradation of polymeric materials.…”

“…On the other hand, analytical methods fail in detecting chemical changes in polymers induced by their thermal degradation. Under these circumstances, the development of macroscopic mathematical models which incorporate the nonlinear coupling between chemical kinetics and heat transfer and allow for the prediction of thermal degradation as a function of space and time has become an important and challenging engineering task [2].…”

“…Since the polymerization kinetics in thermoset composites during the cure is a fairly complex process due to the fact that the curing kinetics is determined by cross-linking and the dynamics of the heat generation response, we consider here a polymerization kinetics model that takes into account the nonlinear coupling between heat and mass transfer, the anisotropic diffusion of both heat and monomer mass, and the quenching of the reaction if the temperature is not high enough. Current models of thermoset curing include heat diffusion, assume isotropic heat diffusion even in the case of composite materials, may consider the dependence of the thermal capacity or specific heat with temperature, and account for the resin cure or conversion by means of an ordinary differential equation for the resin conversion rate which depends in a polynomial fashion on the resin concentration, but they ignore the resin diffusion and consider isotropic heat diffusion [2,6].…”