Permeability describe the ability for fluids to flow through. The High permeability material generally allows faster filling. For anisotropic permeability, each component of tensor K indicates the easiness of filling in different direction. Permeability tensor is composed by fiber mat orientation and permeability. K22 and K11 are permeability of fiber mat in lateral direction, and K3 is permeability of fiber mat in normal direction.
where Kij (i, j = x, y, or z) are components of the permeability tensor, K11, K22, and K33 are principal permeability in porous media, lij are the directional cosines of local coordinates. The L1 and L2 are the orientation of fiber mat in lateral direction, and L3 is the orientation of fiber mat in normal direction.
The impregnation in fibrous material by a resin flow can be described by the Darcy’s law. Darcy's law is often used as model fluid flow in the porous media. It establishes a relation between velocity, pressure, permeability and viscosity which is used for the numerical simulation approach.
where u is the velocity vector, P is pressure, K is permeability tensor of the fibrous material, η is viscosity.
To consider permeability variation induced by the deformation of fabric, the relation between permeability and porosity and the relation between porosity and dimension can be introduced as:
where K is permeability,φis porosity, Vacuum means measured value with vacuum fabric, In-mold means actual value when placed into mold.
A volume fraction function f is introduced to track the evolution of the melt front. Here, f=0 is defined as the air phase, f=1 as the polymer melt phase, and then the melt front is located within cells with 0< f<1. The advancement of f over time is governed by the following transport equation:
The flow rate or injection pressure is prescribed at the mold inlet. No slip is assumed at the mold wall. Note that only inlet boundary condition is necessary for the hyperbolic transport equation of volume fraction function.
To invoke mechanical properties of both resin and fabric in Warp analysis, there are different ways to set ply material in Material Wizard: Composite and Fabric, simply meaning mechanical properties before or after filled with resin. The ply property is then coupled with fiber mat orientation for the generalized mechanical property to simulate part deformation following flow analysis. The deformation can be obtained through stress-strain relation within each composite part as:
where ǁǁis averages of generalized stress; averages of the generalized strain; material property submatrices; subscript of in-plane; subscript of out-of-plane; subscript of in-plane to the out-of-plane.