A Multiscale Model for the Effective Thermal Conductivity Tensor of a Stratified Composite Material

Thermal modeling of composites has three essential objectives: (i) comprehension of their thermal behavior; (ii) composite scaling in order to satisfy specific requirements; and (iii) optimal analysis of experimental results from thermal characterization. For a complete study of the material, each of these three points must be taken into account at the fiber scale (≈10μm), the yarn scale (≈1 mm), and the composite scale (≈10 cm). This work presents multi-scale modeling of the effective thermal conductivity tensor of a stratified composite material made from carbon fibers, phenolic resin, and carbon loads. The longitudinal and transverse thermal conductivities of the yarn are computed from optical microscopic imaging of the material. The isotropic thermal conductivity of the loaded matrix is computed by the Bruggeman model. Then, the thermal conductivity tensor is determined by a finite element method taking into account the morphology of the fabric. Computed values are close to experimental values measured by classical methods. Finally, analytical relations are proposed to obtain an efficient model which can be used in a multiphenomenon simulation of the composite structure.