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Introduction to Heat Transfer During the Forming of Organic Matrix Composites

In this chapter, we present some very illustrative examples of advances obtained in the analysis of the heat transfer in the forming processes of composites. These examples highlight at the same time the difficulties and scientific issues, as well as some simplified approaches to obtain, in an accessible way, a rapid estimation of the times of cooling or heating of a composite part. We also point out some preconceived ideas, in particular on the nature of transfers during the filling of molds in injection process, and for this we propose a new criterion to determine the transition between the thermal shock regime and the one of established convection, which is validated by experimental results. The selected processes are the injection of composites with short fibers (thermoplastic and thermosets), and the injection on a fabric. The examples are illustrated by results issued of more than 25 years of analysis of heat transfer in the processes, during thesis led within the framework of partnership programs with companies of the plastics processing industry. Finally, some directions for new developments are proposed.

1.1. Introduction

The mastery of composite forming processes raises a number of challenges on heat transfer and how to take them into account adequately. Indeed, the nature of these materials itself induces peculiarities. First, they have at least two components, which poses the problem of determining their effective properties according to those constituents. Composites are also multi-scale materials: the fibers are gathered into tows, which are woven to make a fabric. Reinforcements, but sometimes also the matrices, are anisotropic. The coupled phenomena introduce complex physics difficult to interpret without thorough knowledge of them and their interactions. Furthermore, the operating conditions in the process can be often considered as extreme. High cooling rates are frequently encountered, such as for the contact between a cold mold and a hot composite. Shear rates can be very large at the wall of an injection mold, or in the micro channels between fibers (even if the flow rates are low). To compensate the shrinkages due to the cooling or the transformations, pressures are sometimes very high in the molding cavity (up to 200 MPa for injection). Low-conductive polymers and composites are in some cases subjected to overheating as a result of heat source release induced by transformation. An additional issue is the fact that the temperature measurement is very difficult because it is intrusive. It is not yet well known how to experimentally determine the temperature fields within a molded part or inside of the plies in a reinforcement stack. The size of thermocouples, which should be at least as small as the fibers, makes them very fragile, especially in a viscous fluid flow. To date, the precise determination of the inlet temperature in the injection channel of a mold is an open problem. Another particularly characteristic example is the location of the filling fronts and the saturation distribution in a composite made by liquid composite molding (LCM) since it is coupled to heat transfer. In addition, solving a heat transfer problem requires the accurate knowledge of the boundary conditions, which may be difficult. We can also give the example of the determination of the thermal contact resistance (TCR) to the wall of a molding cavity or between plies during the consolidation of a composite.

Temperatures are important to know, but the dynamics of a thermal system may be assessed only by measuring the heat flux. How to make a heat flux sensor nonintrusive and accurate in the environment of forming processes? The main question is ultimately whether a fine thermal knowledge is essential to achieve quality parts.

In this chapter, we will show, from a few illustrative examples, that the couplings involved at all levels must be adequately taken into account from the point of view of heat transfer, since they induce consequences on the quality of the final product appearance, size, shape and properties. The thermal scientific problem appears as inevitable, especially since productivity requires short cycles in mass production: there is indeed cycles of about 1 min for automotive parts. Everyone can easily understand that the heating and cooling of a part by varying its temperature sometimes several hundred degrees in very short times, with the objective to control the temperature fields and to obtain uniform final properties for complex shapes, requires a non-trivial strategy.

1.2. Examples of injection of short fiber reinforced composites

1.2.1. Heat transfer during the filling phase

1.2.1.1. Case of semi-crystalline polymer matrices

We will first discuss the injection of a polymer reinforced with glass fibers, taking the example of a widely distributed poly-aramid, whose trade name is IXEF [PIN 09]. The scope of this study is a collaborative program ("FISH" program) involving LTN, IMP (Lyon), PIMM (ENSAM Paris) laboratories and Moldflow, Legrand, and Solvay companies.

An injection cycle is typically divided into four phases: the filling step (few seconds) is short compared to the total cycle time, during which high shear rates may occur. The packing phase consists of applying a pressure on the polymer/composite to compensate the thermal and crystallization shrinkages. The third step is the isochoric cooling under pressure after the gel of the injection gate, preventing the entry or exit of polymer from the molding cavity and finally the cooling at atmospheric pressure after the possible unsticking of the part. At the end of the cooling, the solid polymer part is ejected and the new cycle can begin.

Figure 1.1. Heat flux to the wall of a molding cavity in injection process

The thermal behavior of the mold is periodic: the heat flux exchanged between the part and the mold is very large at the beginning of the cycle, decreases and finally is negative at the ejection, as shown in Figure 1.1. This particularity has to be taken into account since an established periodic state is required for constant quality parts. The typical example of heat flux at the wall of a molding cavity displayed in Figure 1.1 highlights a dramatic and very quick decrease. How can we interpret this behavior? Let us consider the flow in the channel formed by the molding cavity. If we assume legitimately that the forced convection is in the steady state, it is possible under these conditions to evaluate a local Nusselt number at the distance x from the entry of the molding cavity using a conventional correlation for a prescribed wall temperature [PIN 09], for a shear thinning fluid with a rheological power law type:

The Peclet number is defined as Pe = VDh/a; Dh is the hydraulic diameter of the channel, here twice its thickness, a is the diffusivity of melt, n is the index of the power law viscosity. For the considered instrumented molding cavity [LEG 06] (incomplete part is shown in Figure 1.2 and instrumented cavity in Figure 1.10), we obtain the position of the sensor near the gate a value of 20 for the Nusselt number, which corresponds to a constant heat flux during the filling phase close to 1.105 W/m2. The heat flux obtained as such (see detailed calculations in section 1.2.1.2 applied for bulk molding compound (BMC) processing) is the good order of magnitude (see Figure 1.1) but the experimental one decreases very quickly and we do not observe a constant value even during a short time. The analysis is thus invalidated: the evolution of the heat flux does not correspond to a regime of established convective exchange between the polymer and the wall of the molding cavity. Here is a preconceived idea, which constitutes an approach nevertheless classic but erroneous.

Let us test then the hypothesis that the heat flux decrease is due to the coupling with the conduction in the mold. There is an analytical solution [CAR 59] to the problem of a flowing fluid, which is suddenly put into contact with a wall. In this solution, exchanges by convection are based on a constant convective heat transfer coefficient h. This latter, calculated from the equations [1.1] and [1.11], is in this case approximately equal to 660 W/m2/K (we take the value n = 0.308). The heat flux density is given by F(t) = h F(t/t) (Tm-Ti). Tm is the average temperature of the melt, and Ti is the initial temperature of the mold. F is a decreasing function of time [CAR 59]. t is given by t = ?2/h2a, where ? is the mold thermal conductivity and a is the melt diffusivity. For the molding cavity studied, we find t = 35586 s, which corresponds to about 10 h. The rapid decrease in the observed heat flux is completely incompatible with this law since for t = t the value of the function F is approximately 0.4. The result of this analysis using a reductio ad absurdum that convective heat transfer during the filling phase is not the key to analyze the heat transfer with the mold.

Let us consider the incomplete part shown in Figure 1.2. The energy equation for the filling of the molding cavity may under certain simplifying assumptions (constant thermophysical properties in particular) be written as:

Figure 1.2. Incomplete part obtained with the SWIM mold [LEG 06]

In this equation, D/Dt is the operator...