Multi-scale modeling of time-dependent thermal expansion and chemical shrinkage during the curing process of polymer matrix composites
Topic(s) : Material and Structural Behavior - Simulation & Testing
Co-authors :
Martin HIRSEKORN (FRANCE), Lionel MARCIN , Thierry GODONAbstract :
During the curing process of composites with thermosetting polymer matrices, residual stresses are generated within the material, due to the volume loss (chemical shrinkage) of the matrix during polymerization and the differences in the coefficients of thermal expansion (CTE) between the fibers and the matrix material. Since at small strains the mechanical behavior of the matrix is viscoelastic, these internal stresses cause creep and relaxation effects, which lead to a time-dependence of the average strain of the composite material. The homogenized constitutive behavior of the composite thus has to be formulated with time-dependent CTE and coefficients of chemical shrinkage (CCS) [1]. These coefficients are written in an integral form similar to the classical integral form of viscoelasticity [2]. The master curves of the time-dependent expansion coefficients are represented by a Prony series using the same relaxation times as for the viscoelastic behavior of the composite. In this way, strain-like internal variables are obtained that account for the temperature and cure history in the same way as the strain history is accounted for in the viscoelastic behavior.
A homogenization method for viscoelastic materials based on the Laplace-Carson transform [3] and its extension to parametric strains that depend on external properties such as temperature or cure [1] is presented. This method naturally yields time-dependent expansion coefficients for composite materials whose constituents have time-independent expansion coefficients, but a time-dependent viscoelastic behavior. With this method, a homogenized behavior of a carbon/epoxy composite with a 3D woven reinforcement is obtained by a two-step homogenization scheme, starting from the experimentally identified viscoelastic behavior of the matrix material [4]. Upon heating, the homogenized behavior predicts a sign inversion of the apparent CTE due to the accelerating stress relaxation at increasing temperature (see attached image and [1]).
The homogenized model is used in a thermo-mechanical Finite Element (FE) simulation of the evolution of the residual stresses in a composite part. The local evolution of temperature and cure is obtained from a coupled thermo-kinetic simulation of the resin transfer molding (RTM) process, taking into account the heat transfer and the heat generated by the exothermal polymerization reaction of the matrix. In this RTM process, the resin is injected at a high pressure, which is maintained during the curing cycle in order to partially compensate the chemical shrinkage of the resin. The injection pressure is taken into account through a parametric strain that simulates the additional volume of resin that is injected into the mold due to the applied pressure. The effect of the resin pressure on the stress state in the composite can be obtained using the same homogenization method as for the CTE and the CCS.
A homogenization method for viscoelastic materials based on the Laplace-Carson transform [3] and its extension to parametric strains that depend on external properties such as temperature or cure [1] is presented. This method naturally yields time-dependent expansion coefficients for composite materials whose constituents have time-independent expansion coefficients, but a time-dependent viscoelastic behavior. With this method, a homogenized behavior of a carbon/epoxy composite with a 3D woven reinforcement is obtained by a two-step homogenization scheme, starting from the experimentally identified viscoelastic behavior of the matrix material [4]. Upon heating, the homogenized behavior predicts a sign inversion of the apparent CTE due to the accelerating stress relaxation at increasing temperature (see attached image and [1]).
The homogenized model is used in a thermo-mechanical Finite Element (FE) simulation of the evolution of the residual stresses in a composite part. The local evolution of temperature and cure is obtained from a coupled thermo-kinetic simulation of the resin transfer molding (RTM) process, taking into account the heat transfer and the heat generated by the exothermal polymerization reaction of the matrix. In this RTM process, the resin is injected at a high pressure, which is maintained during the curing cycle in order to partially compensate the chemical shrinkage of the resin. The injection pressure is taken into account through a parametric strain that simulates the additional volume of resin that is injected into the mold due to the applied pressure. The effect of the resin pressure on the stress state in the composite can be obtained using the same homogenization method as for the CTE and the CCS.