• ceramic
• fitting
• optimization
• scaling
• test
• matlab
• patran
• nastran

Ceramic materials represent a remarkable resource for space applications, given their very peculiar properties. In particular, their large stiffness, low density and incredibly small thermal expansion makes them specifically suitable to give thermoelastic stability to payloads.
Nevertheless, their brittle behavior makes it impossible to study and design ceramic structures as the typical metallic ones. Consequently, statistical considerations are needed to predict the failure of these materials, in order to take into account all the factors involved in the breakage.
The purpose of this work, which represents a work package of the mission "Ceramic structures sizing and verification method improvements", funded by ESA, is to define a proper way to fit the test data to a 3-parameter Weibull distribution, which seems the best one capable to describe the great failure scattering typical of ceramic materials. Further, one of the three parameters defines a threshold stress, and can be directly used in the design phases of a project.
After a brief introduction on ceramics and on the Weibull distribution, the various methods proposed to derive the 3 parameters of a Weibull distribution are discussed. Next, the results of these methods, obtained with an algorithm implementation in MATLAB, are presented. Several analyses, including Montecarlo simulations and sensitivity studies, have been performed, to identify the best approaches in different situations.
Chapter 3 is focused on the definition of confidence intervals for the obtained data, especially for the three derived Weibull parameters, through the application of resampling techniques. The main outcome of this part has been an user-friendly tool specifically designed to find the three Weibull parameters and the associated confidence bounds, additionally plotting useful graphical results as outputs.
The subsequent chapter consists in an evaluation of an existing software, called Weibull ++, to understand if its range of applicability may be extended to the matter in hand. Weibull++ features have been compared with the ones of the designed tool, to test the performances of both softwares.
Finally, a scaling methodology to extend the data fitted from tests to complex ceramic structure has been developed. In particular, a procedure to obtain the failure probability of a ceramic structure starting from test data and FE analyses has been defined. It is presented in the final chapter, together with a practical example on a real silicon carbide structure.