JEC COMPOSITES MAGAZINE - Issue #67 - August/September 2011 - 51

higher for the second part.

Numerical model
Simulation of curing process is realized using a simulation tool based on the general Finite Element purpose SYSPLY 11.0, which is a part of SYSWORLD software environment (ESI group product) [8]. A macro-mechanical approach is used to solve the manufacturing problem and to predict distortions and residual stresses. The chosen model is based on two weakly coupled submodels: a thermochemical one and a mechanical one. This type of thermochemical model describes the curing behaviour of the resin. A mechanical viscoelastic model is used to calculate the residual stresses. One of the main difficulties faced when setting up such a numerical model is the number of material parameters that need to be determined in both the rubbery and glassy states. The governing equation of the thermochemical model is: (1) where ρ is the laminate density, Cp its specific heat capacity, Q the heat flux, and q the internal heat generation (latent heat). To complete Eq. 1, constitutive Eqs. 2 - 3 are used to close the thermochemical problem to be solved. The heat flux can be described using Fourier’s heat law: (2) where kij is the thermal conductivity tensor.

chemical shrinkage coefficients, respectively. These are thermodependent as well. The glass transition temperature is defined by DiBenedetto equation. The viscoelastic behaviour of composite materials is typically represented by rheological schemes, where n Maxwell elements are in parallel with m springs. The Maxwell element is used to simulate a boundary condition between the rubbery and the glassy state. It is assumed that the material is stress free in the rubbery state. Boundary conditions The mesh geometry of the composite part corresponds to the L shape used in the experiments (Figure 4 (a)). It consists of 300 eightnode brick elements. Different boundary conditions (thermal and mechanical) have to be applied to simulate the curing process. The cure cycle resulting from the experiment is used as an initial BC representing the process parameters. The resulting temperature values are applied to the nodes of the "TOOL" and "BAG" surfaces of the mesh (Figure 4). The mechanical boundary conditions are changed during simulation in order to simulate an in-mould process and a demoulding process. The in-mould cure is modelled by applying zero degree of freedom to the nodes situated on the skin of

The latent heat is the energy released by the resin during cure: (3)

where q(χ, T) is the latent heat (energy per unit volume), ρr the resin density, Htot the total heat released during cure (energy per unit mass), ∂χ/∂t the chemical reaction rate, or cure kinetics, and Vf the fibre volume fraction.

Along this thermochemical model, a mechanical phenomenological-like model proposed earlier by Svanberg [6] is used in a second step. This model only captures the main features of the reaction kinetics. The constitutive equation for an anisotropic linear viscoelastic material is usually written as: (4)

where σij are the stress components, the relaxation moduli, and the total strain and the free thermochemical strain, respectively (i, j, k, l = 1, 2, 3).

The expansion strain consists of a thermal and a chemical component , which depend on the thermal expansion and

No67 August - September 2011 / jec composites magazine
Fig.4: (a) Part dimensions in [mm]; (b) mechanical boundary conditions created to observe only the displacements of the upper side of the Lshaped part, representing the simulation of the demoulding process

Research & development

JEC COMPOSITES MAGAZINE - Issue #67 - August/September 2011

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