Thermal Conduction in Composite Materials

Fiber-reinforced composites exhibit strong anisotropy. The thermal conductivity in the fiber direction is largely contributed by the fibers, while the transverse direction is dominated by the matrix (resin). As a result, the thermal conductivity (k) can differ by more than 10 times depending on the direction.

The effective thermal conductivity for the fiber direction (parallel model) and transverse direction (series model) are as follows.

Here, $V_f$ is the fiber volume fraction, $k_f$ is the thermal conductivity of the fiber, and $k_m$ is the thermal conductivity of the matrix.

For PAN-based carbon fiber ($k_f=10$ W/(mK)), epoxy resin ($k_m=0.2$ W/(mK)), and $V_f=0.6$:

• $k_{\parallel} = 0.6 \times 10 + 0.4 \times 0.2 = 6.08$ W/(mK)
• $k_{\perp} \approx 0.45$ W/(mK)

There is a difference of more than 13 times. Ignoring this and analyzing with isotropic properties will completely change the temperature distribution.

For more precise evaluation, the Hashin-Shtrikman upper and lower bounds are used.

Measured values fall within these upper and lower bounds. More precise predictions are possible using the Halpin-Tsai model or finite element homogenization (RVE analysis).

With random orientation, the material becomes nearly isotropic. However, in injection-molded parts, fibers align in the flow direction, resulting in partial anisotropy. Practical methods exist that export the fiber orientation tensor from injection molding simulations like Moldflow and map it to the thermal conductivity tensor.

Multi-scale analysis using a Representative Volume Element (RVE) is the standard method. An RVE is created with carbon fibers (7μm diameter) arranged in a hexagonal array, and an effective thermal conductivity tensor is obtained by applying temperature differences in each direction.

A guideline is 10 to 20 times the fiber diameter. If the results don't change when the RVE size is increased, it's sufficient. COMSOL and Digimat allow for automatic RVE generation and parametric homogenization.

For a laminate (e.g., [0/90/45/-45]s), the thermal conductivity tensor of each ply is rotated according to the stacking direction and superimposed. In Abaqus, the ply orientation angle is defined using ORIENTATION andSHELL SECTION.

Correct. However, the through-thickness direction remains low and matrix-dominated for all configurations. Ensuring thermal pathways in the through-thickness direction is the biggest challenge in thermal design of CFRP structures. Research is progressing on improvements through Z-pinning or through-thickness introduction of carbon nanotubes.

The most important thing is the correct definition of the material coordinate system. Since the fiber direction differs for each ply, the coordinate system for each element must be set accurately.

Using Ansys Composite PrepPost (ACP) automates the process from defining composite laminates to transferring data to the thermal analysis model.

1. Define the laminate configuration (ply sequence, orientation angle, thickness) in ACP

2. The material coordinate system is automatically generated

3. Data is transferred to Steady-State Thermal

4. The anisotropic k for each ply is automatically applied

In Abaqus, equivalent functionality is available via the Composite Layup feature in Abaqus/CAE. In COMSOL, the Composite Materials Module supports this.

The thermal conductivity of composite materials varies depending on the measurement method.

The Laser Flash method measures the thermal diffusivity in the through-thickness direction and converts it to thermal conductivity using $k = \alpha \rho c_p$. Measuring the in-plane direction is difficult due to sample preparation and has lower accuracy. This uncertainty must be considered when comparing analysis results with measurements.