**A numerical method to simulate the intra-tows mechanical behaviour of oxide/oxide CMCs: coupling of a lattice with a FE continuum**

__CANET T. ^{1}__, DUSSERRE G.

^{1} Institut Clement Ader (ICA) ; Université de Toulouse ; CNRS, IMT Mines Albi, INSA, ISAE-SUPAERO, UPS, Albi, France

Oxide/oxide Ceramic Matrix Composites (CMCs) are used in many technical applications, including the manufacture of aircraft engine tailpipes [1]. It is essential to well understand the impact of the manufacturing process on the properties of such a material. Essentially, it is necessary to be able to anticipate the mechanical behaviour of the porous matrix but also of its bonding with the fibres.

For this purpose, a multi-scale numerical method was developed to mechanically model the microstructure of a porous ceramic elaborated from submicron alumina particles and nanometric silica ones, based on its characteristics in terms of porosity and composition. This microstructure modelling by a lattice makes it possible to determine the mechanical behaviour of the matrix alone. It can also be directly coupled with a finite element model of alumina fibres.

This numerical method is mainly based on the assumption that a network of silica bridges is formed between the alumina particles due to the decrease in silica viscosity and the effect of surface tension during the sintering of the green body [2]

Firstly, a large cluster of independent particles, placed in contact with each other, is numerically built and a selected area of this cluster is retained. This subcluster is then subjected to an homothecy to consider the desired porosity and composition. In parallel, a series of silica bridges of different sizes are modelled using a finite element method and subjected to four mechanical loading modes (tension, shear, torsion, bending). These results are then compiled in the form of stiffness response surfaces as a function of the distance between the particles and of the involved volume of silica. A Representative Elementary Volume (REV) of the ceramics microstructure is then formed as a network of connectors whose positions and stiffnesses are determined by the two previous simulations.

Once the REV has been formed, it can be used to determine the mechanical properties of the matrix via the application of modal analysis. It can also be linked to a finite element model of the alumina fibre in order to reconstruct a REV of a CMC and analyse it mechanically either via virtual tensile tests or modal analysis.

Thus, this method makes it possible to determine the mechanical properties of an alumina/silica sintered material from its composition and porosity. In order to investigate the effect of manufacturing processes on the properties, further developments will focus on relating microstructure to sintering.

References:

[1] Ceramic Matrix Composites. Fiber Reinforced Ceramics and their Applications, Walter Krenkel, Wiley-VCH Verlag GmbH&Co. KGaA. 2008.

[2] Review: liquid phase sintering, R. M. German et al. Journal of Materials Science, vol. 44, no. 1, pp. 1–39, Jan. 2009.