Resin transfer molding (RTM) is among the most used manufacturing processes for composite parts. Initially, the resin cure is initiated by heat supply to the mold. The supplementary heat generated during the reaction can cause thermal gradients in the composite, potentially leading to undesired residual stresses which can cause shrinkage and warpage. In the present numerical study of these processes, a one-dimensional finite difference method is used to predict the temperature evolution and the degree of cure in the course of the resin polymerization; the effect of some parameters on the thermal gradient is then analyzed, namely: the fiber nature, the use of multiple layers of reinforcement with different thermal properties and also the temperature cycle variation. The validity of this numerical model is tested by comparison with experimental and numerical results in the existing literature.

In resin transfer molding (RTM) process, a thermoset resin is injected into a dry fiber preform placed in a closed mold cavity in order to produce a polymer composite. When the resin impergnate the reinforcement, an exothermic reaction is declenced which cross-links the resin and the composite solidifies [

By managing the mold walls temperature, it is become possible to control the cure reaction and consequently to reduce the thermal gradients in composite. The results of Choi et al. [

In this work, we present a strategy to control and minimize the temperature gradients caused by the exothermic reaction of curing. The method accuracy is examined by studying the reticulation process in a rectangular mold using different types of fiber preforms impregnated with a polyester resin.

The equation that Governs heat transfer in the composite laminate is given as follows [

The thermal properties k, ρ and C_{p} are respectively expressed as follows [

The mass fractions wr, wp and wf are respectively given by the following expressions [

The volume fraction_{p} and v_{f} are given respectively by [

The equation of the curing rate reactions used in our case is defined as follows [

With:

Initial condition (t = 0): _{0}

The side wall: _{w}(

The center of the wall:

The initial condition for resin curing is [_{0} at t = _{0}

The room temperature is equal to 25°C, and the imposed condition for the degree of cure at (t = 0) is set to zero.

In our study we have opted with the explicit finite difference method to discretize the two

For this explicit scheme, the stability condition is given as follows [

By means of the finite difference method, the discretization of the energy equation is presented as:

This results on:

In this study we have considered a mold with rectangular shape as it is presented in

_{1}(1/ |
5.68667 ^{12} |

_{2}(1/ |
8.61167 ^{8} |

_{1}(cal/mol) |
25570 |

_{2}(cal/mol) |
17930 |

n | 1.42 |

m | 0.58 |

ΔH (cal/mol) | 47.8 |

Materials | ^{3}) |
_{p} (cal/g.K) |
K (cal/cm.s.K) |
---|---|---|---|

Uncured polyester | 1.10 | 0.45 | 4.0510^{−4} |

Cured polyester | 1.20 | 0.45 | 1.5410^{−4} + 9.4610^{−7} |

Glass fiber | 2.54 | 0.199 | 2.0710^{−3} |

The numerical model that we developed for the polyester resin and fiber glass system is based on the resolution of the energy equation and the degree of the curing reaction. This coupling allows us to determine both the temperature and the degree of curing α (T, α) at each point in the thickness laminate in the mold and at each moment [

From the results illustrated in

One can deduce from the

In almost all of the applications we use one ply of reinforcement with uniform properties, but in the case of low thermal conductivity the thermal gradient is highly pronouced, to resolve this situation one can increase the conductivity of the whole reinforcement, which is not practical since it increases the cost of the final product. To overcome this restriction we have suggested to use a multiple plies of reinforcement (Three plies) (

The

^{3}) |
Cp (J/kg) | k (W/m.K) | |
---|---|---|---|

Fiberglass | 1900 | 1500 | 0.31 |

Aramide fiber | 1450 | 1030 | 0.29 |

Carbone fiber | 1700 | 710 | 0,26 |

By our numerical sudy, we first used the fiber glass in the three layers with the conductivity is higher at the center.

From

In this case by using fiberglass the gradient is considerably reduced and the maximum temperature is 379.8103 K and the degree of cure reaches 0.96.

By changing the nature of fiber, we noted that the thermal gardients has slightly changed, in fact, the maximun temperature was 379.7801 K in aramide and 379.6887 with carbone.

To more increase the degree of cure in the case of fiberglass in order to guarantee a complete reticulation for the composite. We increase the temperature of the mold wall to 390 K, and contrary to what can happen in the normal condition, the temperature does not surpass its value on the mold borders (

In the other hand, and by using the mold wall tempertaure 378 K, when we combine between aramide and glass fiber (i.e., the inner ply is in aramide and the two extenal plies are in fibergalss), we obtain the minimun gradient of 379.65 K by comparison with using only glass or aramide or carbone in the three plies of the reinforcement.

El Yousfi et al. [

Elsemore, it was proved by many researches [

A series of numerical modeling was carried out for differentes possible scenarios, this allows us finally to opte for a particular temperature cycle (

We can observe from

In this numerical sudy, we have opted for the explicit finite difference methods in the one-dimensional case applied to composite laminate. The developped program allows us to determine both the coupled temperature and the degree of curing in the composite. Furthermore, and following particular strategies, namely the best selection of fiber and reinforcement structure and the judicious control of the imposed temperature, we have shown that the thermal gradient could be reduced by a big margin. We have proved that our numerical results agree well with some experimental and numerical results in the litterature.

The obtained results prove that our numerical method permit to reduce the thermal gradients effeciently in composite pieces produces by resin transfer molding. This study can afford a robust tool to help engineers and designers in manufacturing composite with good mechanical performace.

Temperature (K).

Density (g/cm^{3}).

_{p}

Specific heat (cal/g.K).

_{p}

Volume fraction of the cured product.

_{f}

Volume fraction of the fibers.

_{r}

Volume fraction of the resin.

_{r}

Mass fraction of the resin.

_{p}

Mass fraction of the cured product.

_{f}

Mass fraction of the fibers.

Degree of cure.

Thermal conductivity (cal/cm.s.K).

_{i}

Activation energy (cal/mol).

_{i}

Frequency factors of reaction (s^{−1}).

Gas constant (j/mol.K).

Time (s).

Empirical exponents in the cure kinetic model.

_{r}

Total heat of reaction (cal/mol).

Rectangular coordinate (cm).