Frontal polymerization of unidirectional carbon-fiber-reinforced composites

doi:10.1016/j.compositesa.2019.105689

Composites Part A: Applied Science and Manufacturing

Volume 130, March 2020, 105689

https://doi.org/10.1016/j.compositesa.2019.105689 Get rights and content

Abstract

We formulate a homogenized thermo-chemical model to simulate the manufacturing of unidirectional composites made of carbon fibers embedded in a thermosetting dicyclopentadiene (DCPD) matrix using frontal polymerization (FP). The reaction-diffusion model is then solved using the finite element method to investigate the evolution of the temperature and degree of cure during the fabrication process. The results reveal two different processing regimes: At lower fiber volume fractions, the polymerization front speed increases with the fiber volume fraction due to the increase in the effective thermal conductivity of the composite. At higher fiber volume fractions, the front velocity decreases with increasing fiber content due to the reduced heat source generated by the exothermic reaction. The 1-D simulations are complemented with 2-D studies that include heat losses to the surroundings. The model predictions are validated with experiments conducted on carbon/DCPD composite panels manufactured through frontal polymerization.

Introduction

Current autoclave-based manufacturing methods for fiber-reinforced thermosetting-polymer-matrix composites are both time and energy intensive [1], [2], with the cost increasing exponentially with the part size [3]. To address these challenges, various out-of-autoclave methods have been proposed, including Vacuum Assisted Resin Transfer Molding (VARTM) [4], [5], Vacuum Bag Only (VBO) consolidation [6], [7], and Thermal Press Curing (TPC) [8]. In a recent publication [9], a new out-of-autoclave/out-of-oven method for fiber-reinforced polymer composites (FRPC) based on Frontal Polymerization (FP) has been introduced to greatly speed up and substantially reduce the energy cost of the manufacturing process. FP is a self-propagating reaction driven by exothermic polymerization, where an advancing front is formed by a local thermal stimulus applied to a solution of monomer and initiator. The heat generated by the exothermic reaction diffuses forward to advance the propagating front, resulting in a self-sustained process.

Frontal polymerization of neat resins has been extensively investigated analytically. However, these studies have been mostly restricted to 1-D domains and simple cure kinetic models. Goldfeder et al. [10] predicted the degree of monomer conversion and front velocity in an adiabatic acrylate FP system based on the concentrations of reactants and initial solution temperature. They also re-examined the FP process in a nonadiabatic environment [11]. Viner et al. [12] modified the solution to include non-polymerizing fillers that undergo a phase change. Other analytical studies based on mathematical models of FP are found in [13], [14], [15], [16]. FP has also been investigated numerically, allowing for a wider range of reaction kinetics and more complex domains. In this line of work, Frulloni et al. [17] employed an axisymmetric finite difference model using an alternate-direction implicit method to model FP in epoxy and investigate the influence of the physico-chemical properties of the resin and the boundary conditions on the evolution of FP. Goli et al. [18] recently used an adaptive finite element scheme to investigate the 1-D transient and steady-state propagation of a polymerization front in dicyclopentadiene (DCPD).

In this study, we propose a continuum-level homogenized model to study the FP-based processing of unidirectional carbon-fiber-reinforced DCPD composites. The finite element method is used to solve the proposed model and obtain the evolution of the temperature and degree of cure fields during the manufacturing process. Of particular interest is the impact of the fiber volume fraction on the characteristics of the front, i.e., speed and maximum temperature. The analysis is first performed in a 1-D adiabatic setting. This 1-D study is then complemented by a 2-D analysis that incorporates the heat losses to the surroundings and their effect on the propagation of the polymerization front. The model is validated against experimental measurements of front speed and maximum temperature for DCPD/carbon fiber composites with varying fiber volume fractions.

Section snippets

Problem description

In the absence of fiber reinforcements, the initiation and 1-D propagation of a polymerization front in DCPD is mathematically described by the following coupled system of partial differential equations (PDEs) for the degree of cure $α (x, t)$ and the temperature $T (x, t)$ (with $0 ⩽ x ⩽ L, t ⩾ 0$ ): $\{\begin{matrix} κ \frac{\partial^{2} T}{\partial x^{2}} + ρ H_{r} \frac{\partial α}{\partial t} = ρ C_{p} \frac{\partial T}{\partial t}, \\ \frac{\partial α}{\partial t} = A \exp (- \frac{E}{RT}) {(1 - α)}^{n} α^{m} \frac{1}{1 + \exp [C (α - α_{c})]}, \end{matrix}$ where $κ$ (in $\frac{W}{m \cdot K}$ ) denotes the thermal conductivity, $ρ$ (in $\frac{kg}{m^{3}}$ ) the density, $C_{p}$ (in $\frac{J}{kg \cdot K}$ ) the specific heat, and $H_{r}$ (in $\frac{J}{kg}$ ) the total enthalpy of

Effect of carbon fiber tow on polymerization front

The presence of more thermally conductive carbon fibers is expected to influence the propagation of the polymerization front. In a recent study [23], we found that the presence of continuous conductive elements made of copper and steel affects the shape and speed of the front. Building on these results, we present in this section the results of experimental and numerical studies that illustrates in a qualitative way the effect of a carbon fiber tow inserted in a channel of DCPD monomer solution

Frontal polymerization in unidirectional composites: homogenized model

To simulate the evolution of the temperature and degree of cure fields in uni-directional fiber-reinforced composites cured by FP, we adopt the following homogenized thermo-chemical model: $\{\begin{matrix} \overline{κ_{ij}} \frac{\partial^{2} T}{\partial x_{i} \partial x_{j}} + \overline{ρ} H_{r} (1 - ϕ) \frac{\partial α}{\partial t} = \overline{ρ} \overline{C_{p}} \frac{\partial T}{\partial t}, (sum over i and j) \\ \frac{\partial α}{\partial t} = A \exp (- \frac{E}{RT}) {(1 - α)}^{n} α^{m} \frac{1}{1 + \exp [C (α - α_{c})]}, \end{matrix}$ where $ϕ$ is the volume fraction of fibers. Overbars denote the homogenized properties of the composite described by the extended Rayleigh model [24], [25] as $\{\begin{matrix} \overline{κ_{11}} = κ_{m} (1 - ϕ) + κ_{f} ϕ, \\ \overline{κ_{22}} = \overline{κ_{33}} = κ_{m} + \frac{2 ϕ κ_{m}}{\frac{κ_{f} + κ_{m}}{κ_{f} - κ_{m}} - ϕ + \frac{κ_{f} - κ_{m}}{κ_{f} + κ_{m}} (0.30584 ϕ^{4} +)} \end{matrix}$

Model validation

We developed a controlled method for FP-based fabrication of carbon/DCPD FRPCs to validate the numerical simulations. An open mold processing technique was used to insulate the layup thermally and produce FRPCs with a pre-determined thickness for tailoring the fiber volume fraction of the composites. The mold (Fig. 7) was constructed using two thermally insulating rigid foam panels (448-D, Fibre Glast Development Corp.) sandwiched between two fiberglass tool plates. The surface of the foam was

Sensitivity analysis on cure kinetics parameters

The reaction-diffusion model described by (5) provides a link between the cure kinetic parameters and the characteristics of the polymerization front. It can therefore be utilized to tailor the polymer chemistry for a specific application of FP. For example, when higher volume fractions of carbon fibers are needed, a parametric study of the effect of activation energy, E, on the $ϕ$ -dependence of the front velocity reveals that a 2% reduction in the activation energy increases the applicability

Conclusions

A homogenized thermo-chemical model has been proposed and implemented in a multiphysics nonlinear finite element solver to investigate the FP-based manufacturing of unidirectional carbon/DCPD composites. 1-D numerical simulations of the initiation and propagation of the polymerization front obtained for a range of fiber volume fractions have yielded two distinct regimes. In the first one, which corresponds to low values of fibers volume fraction, the front velocity increases with the fiber

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was supported by the Air Force Office of Scientific Research through Award FA9550-16-1-0017 (Dr. B. ‘Les’ Lee, Program Manager) as part of the Center for Excellence in Self-Healing, Regeneration, and Structural Remodeling. The authors would like to acknowledge Prof. Scott White for his insights and guidance regarding this work.

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View full text

Frontal polymerization of unidirectional carbon-fiber-reinforced composites

Abstract

Introduction

Section snippets

Problem description

Effect of carbon fiber tow on polymerization front

Frontal polymerization in unidirectional composites: homogenized model

Model validation

Sensitivity analysis on cure kinetics parameters

Conclusions

Declaration of Competing Interest

Acknowledgement

Compos Sci Technol

Compos Part A: Appl Sci Manuf

Compos Part A: Appl Sci Manuf

Compos Part A: Appl Sci Manuf

Phys D: Nonlinear Phenomena

Phys D: Nonlinear Phenomena

Chem Eng Sci

Nucl Eng Des

J Comput Phys

Modelling heat transfer inside an autoclave: effect of radiation

J Reinf Plast Compos

An experimental study of temperature distribution in an autoclave

J Reinf Plast Compos

Curing methods for advanced polymer composites-a review

Polym Polym Compos