Statistical prediction of cracking paths: application to cementitious materials

The ageing of French nuclear power plants raises many research issues in nuclear safety analysis. The phenomena involved in the ageing of structures are mainly due to the development of pathologies, in particular internal swelling reactions. They can lead to concrete degradation and more specifically to the cracking of the corresponding structures. In order to study these pathologies and to be able to predict further degradation, it is necessary to carry out numerical simulations using full-field mechanical codes at mesoscopic scale. However, each simulation is costly in term of computational time. This remains a strong limitation for industrial applications where a large number of simulations are often required to perform the whole mechanical analysis. Therefore, in order to circumvent this limitation, this work is devoted to the construction of a new fast-to-evaluate mathematical model to predict the cracking trajectory in a microstructure. This construction is performed in two steps. Starting from mechanical considerations, the first one concerns the introduction of indicators that provide information on the local behavior of a crack. In the second step, these indicators are integrated in a Markov Chain prediction model whose parameters are estimated from a learning set coming from computer code simulations. The model is then integrated in a cracking propagation algorithm that provides a set of trajectory realizations. This set can be exploited to derive a single cracking trajectory and to quantify the prediction uncertainty. The analysis of the performances of the new model is then conducted. It exhibits the agreement between the predictions and the computer code simulations (XPER in our study). Moreover, one can observe a significant reduction of the computational time, a few minutes on a processor to obtain the complete cracking path with a reasonable uncertainty whereas the XPER simulation can take several days on a few dozen of processors. The new model is finally applied to a three-point bending beam test. It requires coupling the model to a Finite Elements mechanical code to derive the local cracking direction based on the local stress fields. The results show that the model is able to accurately predict the crack simulated by the XPER code. Moreover, the prediction is performed in few hours whereas the simulation takes about 100 days on 81 processors. (author)