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Analysis of Fibre Orientation using μCT Data

Integrative simulations are based on a calculated bre orientation from which the local material properties can be derived in several ways. For instance the micro-mechanical model proposed by Tandon and Weng may be used coupled with an orientation averaging approach to include the bre orientation. This approach then gives the elastic properties of the bre matrix compound with a strong dependency, of e.g. the elastic modulus, on the bre orientation. Modeling failure for nite element simulations, e.g. crash, also requires knowledge of the bre orientation, because the failure strains and energy dissipation also depend on the orientation of the bres [1, 2]. The accuracy of the calculated bre orientation depends on several simulation input parameters, which are not necessarily physical properties. The most important example is the bre interaction coecient (c). This parameter allows the user to modify the calculated bre orientation from isotropic to transversely isotropic [3]. In this paper a new experimental method to determine the bre interaction coecient is presented. The classical approach to validate the calculated bre orientation would be the usage of optical microscope images of cut surfaces of the specimen and the calculation of the bre orientation by measuring the cut ellipsis dimensions. This method is very time consuming and with respective to the necessary magnication not very accurate, because not all bres can be accounted for. The new method is using a model based algorithm to analyze three-dimensional micro computer tomography measurements. This enables the identication of up to 90% of the bres within the specimen and calculate a second order orientation tensor and the bre length distribution in any arbitrary space. Due to the fact that a model based algorithm is used, the bre detection can also be performed, if the density of the matrix polymer is near to the density of the bre material. This is a novelty to existing bre orientation measurements with computer tomography. To obtain reliable data which can be directly compared with injection moulding simulations, several steps had to be taken. First of all a representative volume must be dened, in which the bre orientation will be evaluated. This representative volume must be the same in the injection moulding simulation and the μCT measurement. As the injection moulding model is already discretized, the representative volume is set as a stack of nite elements over the part thickness. To calculate the second order orientation tensor in exactly the same geometrical space and the same coordinate system as in the injection moulding simulation, it was necessary to develop a method which allows a reconstruction of the original part from which the μCT specimen was taken. A special painting and evaluation procedure were implemented into the existing method to recalculate the original position and orientation of the specimen, enabling us to achieve the desired measurements. At the moment the determination of the bre interaction coecient requires still many injection moulding simulations, which then are compared to the measured values. This allows for a more realistic bre coecient in comparison to the default parameter. The next steps are to automate the described procedure and to correlate the measured bre orientations directly with the bre interaction coecient to avoid unnecessary simulations.