II.1.12 Moisture diffusion in laminates

The moisture conservation equation in a solid material is written as follows:

where $M$ is the moisture content (for example in [kg/m${}^3$]) and vector $q_M$ is the massic flux of moisture (in [kg/m${}^2$s]). When several materials are present in a structure, as often in laminates, it is more practical to work with moisture percentage $H$ (in [%w]). The moisture percentage is related to moisture content by the following expression:

where $c$ is the moisture coefficient in [kg/(m${}^3$%w)].

Generally, the moisture flux is related to the gradient of moisture by Fick’s law, and the moisture diffusion equation can be written:

Here ${\lambda }^H$ is the tensor of moisture conductivity coefficients. This expression is very similar to the equation of thermal diffusion:

• The components of ${\lambda }^H$ are defined the same way as the components of ${\lambda }^T$ depending on the type of material (isotropic, orthotropic or anisotropic).

• The calculation of laminate global conductivity properties is done the same way as for thermal conductivities:

  $${\left[{\Lambda }^H\right]}_{xy}=\sum _{k=1}^N{\left[S_{+}\right]}_{({\theta }_k)}\cdot {\left[{\lambda }_k^H\right]}_{12}\cdot {\left[S_{-}\right]}_{({\theta }_k)}{e}_k,$$

  $$R_{33}^H=\sum _{k=1}^N\frac{1}{{({\lambda }_{33}^H)}_k}{e}_k.$$

Since moisture percentages are used here, nothing equivalent to the laminate thermal capacity ${\left(\rho C_{p}h\right)}_{\text{lam}}$ is defined for moisture.