Method to determine the required microstructure size to be represented by a second order fibre orientation tensor using X-ray micro computed tomography to evaluate compression moulded composites

Abstract The second order fibre orientation tensor has been used to predict the mechanical response of injection and compression moulded composites with the capability to couple mould filling with structural finite element simulations to account for the microstructure. In order to accurately model these materials the mesh size used simulations must be representative of the actual microstructure of the composite. Herein a method to determine the microstructure size required to achieve a near constant value of the orientation tensor based on its derivative is presented. The method is demonstrated with the microstructure of a sheet moulding compound composite which has been evaluated using X-ray micro computed tomography. The average values of the derivative of the orientation tensor and its standard deviation approach constant values with increasing microstructure size. For the material considered a microstructure size of 5 mm square is sufficient to achieve a near constant value of the fibre orientation tensor, which is called a microstructural unit.