Ceramic Matrix Composites (CMCs) are a class of advanced materials that are drawing attention for their potential application as hot structures or reusable lightweight Thermal Protection Systems (TPS), especially after Liquid Silicon Infiltration (LSI) significantly reduced the production cost [1]. This work developed a FE non-linear material model for a LSI produced CMC consisting in a Silicon Carbide (SiC) matrix reinforced by a 2x2 twill fabric of carbon fibres. The aim of this material model, formulated at the ply level, is to support the calibration of macroscale failure criteria and the identification of allowables and design values to be used in more conventional linear analyses for the design of real-world CMC structures. The development of the model relied on a campaign of tensile and three-point-bending tests that involved specimens with different lamination sequences, including cross-ply, angle-ply and quasi-isotropic lay-ups. The experiments highlighted a considerably non-linear behavior and the predominant role of the LSI-produced matrix material in determining the response and the failure of the laminates. It was also observed that the strength that can be attributed to the plies in flexural tests was higher than the one in tensile tests. To capture the response of the laminates and the damage mechanisms of interest, the model was based on a bi-phasic decomposition of the material into an idealized fibres phase and an effective medium for matrix, in a similar way to the techniques adopted in binary models [2-3]. The constitutive law attributed to the matrix phase was based on a Continuum Damage Mechanics approach, with a single scalar damage variable whose evolution and threshold functions were shaped as an in-plane Tsai-Wu criterion. Finally, fibre failure in the fabric was modelled by two additional damage variables to obtain a quasi-brittle response. A fundamental aspect of the proposed numerical approach is that all the parameters related to the activation of strain softening regimes in matrix and fibres were statistically distributed in the volume of the FE models of the tensile and bending specimens according to a normal distribution. The mean value and the standard deviation of such parameters were identified through a Monte-Carlo like approach, defining as the performance index the distance between numerical and experimental failure points in the stress-strain plane for tensile specimens. On the other hand, the parameters that describe the non-linear behaviour of the material were identified through calibration algorithms. Eventually, the FE simulations of the experiments achieved a remarkable correlation with the stress vs. strain non-linear curves for all the investigated lay-ups, predicting the failure stress for all tensile tests and grasping with good accuracy the bending-to-tensile strength ratio.

Acknowledgements
The present activity was part of the Am3aC2a project, funded by the Italian Space Agency (ASI).

References
[1] Krenkel, W. Ceram. Eng. Sci. Proc. (2001) 22, 443-454
[2] Cox, B. N. et al. Acta Metall. Mater. (1994) 42(10), 3463-3479
[3] Flores, S. et al. Compos. Part A Appl. Sci. Manuf. (2010) 41(2), 222-229