Skript-basierte parametrische Modellierung zur numerischen Simulation des Einflusses von Poren auf lokale Spannungsüberhöhungen in keramischen Faserverbundwerkstoffen

Kurzfassung

This master thesis aims to use script-based parametric modelling for numerical simulation of the impact of pores on the stress distribution in ceramic fiber composites. These fiber compo-sites are designed to withstand mechanical forces under extreme heat, e. g. in aircraft engines, while being considerably lighter than nickel base super alloys. One such composite material, WHIPOX® (Wound Highly Porous Oxide Ceramic) has been developed at the German Aero-space Center (DLR). This particular composite features oxide ceramic fibers integrated into a porous oxide ceramic matrix. This combination allows for damage tolerant behavior not to be observed in monolithic ceramics. For production of WHIPOX® ceramic fiber bundles are in-filtrated with matrix slurry and wound onto a mandrel in specific angles. Once sufficient ma-terial has been accumulated, the pre-product can be removed from the mandrel and shaped into any form. After a pre-drying period, the material is sintered and can be used. During bending tests, large discrepancies between the strength data have been observed in identically manufactured samples. Images of cross sections revealed the presence of pores inside the fiber bundles which were thought to influence the strength of the material. Those pores were initially assumed to be ellipsoids with small aspect ratios. Computed X-ray tomography was used to determine the shape and distribution of those pores. Analysis of three-dimensional representation reconstructed from X-ray scans shows that the pores observed in cross sections are in fact ellipsoids with high aspect ratios. While the diam-eter of the pores ranges from 40 to well over 100 µm, the pore length varies between 100 µm and 1 mm. Further analysis shows, that the pores are evenly distributed within the fiber bun-dles and always aligned along the fiber direction. An algebraic distribution model for the ap-pearance of the voids inside the fiber bundles was derived and implemented into an ABAQUS FEM model using the programming language Python. This script places the pores inside a homogenized fiber bundle and can either be used to generate a pore from the statistical distributions determined from the analysis of the computed tomography images or a user defined pore. The above-mentioned script was then used to determine the influence of different pore shape characteristics on local stress concentration. A correlation between the length/diameter ratio and the stress concentration could be observed (between 48 and 2 percent higher stresses). The stress concentration is higher for smaller assigned ratios of both parameters. Neighboring pores also have a small influence on the stress concentration. A rather high influence could be observed upon variation of the load angle with respect to the fiber direction, which is parallel to the length axis of the pores. With the load oriented in 45° to the pore length axis, the stress concentration was found to be 50% higher than the induced nominal stress. With load oriented in the same direction as pore and fiber, stress concentration at the elongated ellipsoidal pores with an aspect ratio of 10 only reached 7.2% higher levels. Comparison between numerical and analytical computation of stress concentrations showed comparable levels. While analytical calculations with further homogenized isotropic material parameters resulted in 2.8% higher difference in stress levels, it is worth noting that the ho-mogenized transversal isotropic material parameters do not fulfill the requirements for which the analytical equations where derived. Verification using explicit modelling of the fibers embedded in homogenous matrix confirmed the findings for the homogenized models as levels of relative stress concentration at pores in matrix and homogenized composite, respectively turned out to be comparable (23% in matrix with explicitly modeled fibers and 26% in homogenized material models). While stress concentration in both type of models was similar, the stress level at the pores is much lower in the model with explicit fibers since most of the load is carried by the stiff fibers resulting in low stress level in the matrix. Since in the here evaluated bending test samples, the fiber bundles are oriented in 45° degrees relative to the applied stress, the observed pores are generating high stress concentrations and therefore are likely to influence the fracture stress. Consequently, measures to reduce the amount of the ellipsoidal pores may improve the performance of the composite material.