Curing Method

The curing method applies to viscous flows that change physical and chemical properties during the course of the simulation.

The reaction within the curing process is tracked using the empirical kinetic model proposed by Kamal and Sourour [932]. In this model, the degree of curing $\alpha$ at time $t$ is:

where:

• $H\left(t\right)$ is the heat of curing released until time $t$ .
• $H_{\mathrm{\Sigma }}$ is the total heat of curing.

The progress of the curing phenomenon for an incompressible fluid is:

where:

• $m$ and $n$ are constant model parameters.
• $k_1$ and $k_2$ are the kinetic rate constants.

$k_1$ and $k_2$ depend on the temperature $T$ according to the Arrhenius law:

where:

• $i$ =1 or 2.
• $K_i$ is the pre-factor.
• $E_i$ is the activation energy.
• $R$ is the universal gas constant.
• $T$ is the absolute temperature.

The parameters associated with the Kamal and Sourour model are determined by fitting the model against experimental data governed by Differential Scanning Calorimetry (DSC). [927]

The degree of curing can also alter the viscosity of the material. For the case of epoxy resin, Castro and Macosko [925] propose a viscosity model describing the dependency of viscosity on curing, shear rate and temperature according to:

where:

• ${\mu }_0(\dot{\gamma },T)$ is the zero shear viscosity which can depend on shear rate $\dot{\gamma }$ (according to one of the generalized Newtonian models) and temperature $T$ (according to one of the time-temperature superposition laws).
• ${\left(\frac{{\alpha }_g}{{\alpha }_g-\alpha }\right)}^{C_1+C_2\alpha }$ is the viscosity factor.
  • ${\alpha }_g$ is the degree of cure (∼0.65−0.73) at the gel point.
  • $C_1$ and $C_2$ are the fitted constants.

The temperature distribution is found by solving with the energy conservation:

where:

• $C_p$ is the specific heat capacity.
• $k$ is the thermal conductivity of the material.