Crack propagation and branching are modeled using nonlocal peridynamic theory. One major advantage of this nonlocal theory based analysis tool is the unifying approach towards material behavior modeling- irrespective of whether the crack is formed in the material or not. No separate damage law is needed for crack initiation and propagation. This theory overcomes the weaknesses of existing continuum mechanics based numerical tools (e.g. FEM, XFEM etc.) for identifying fracture modes and does not require any simplifying assumptions. Cracks grow autonomously and not necessarily along a prescribed path. However, in some special situations such as in case of ductile fracture, the damage evolution and failure depend on parameters characterizing the local stress state instead of peridynamic damage modeling technique developed for brittle fracture. For brittle fracture modeling the bond is simply broken when the failure criterion is satisfied. This simulation helps us to design more reliable modeling tool for crack propagation and branching in both brittle and ductile materials. Peridynamic analysis has been found to be very demanding computationally, particularly for real-world structures (e.g. vehicles, aircrafts, etc.). It also requires a very expensive visualization process. The goal of this paper is to bring awareness to researchers the impact of this cutting-edge simulation tool for a better understanding of the cracked material response. A computer code has been developed to implement the peridynamic theory based modeling tool for two-dimensional analysis. A good agreement between our predictions and previously published results is observed. Some interesting new results that have not been reported earlier by others are also obtained and presented in this paper. The final objective of this investigation is to increase the mechanics knowledge of self-similar and self-affine cracks.

Cette thèse avait pour objectif de mettre en place et d’appliquer les techniques de mesure de champs de déplacements et de déformations (corrélation d’images numériques CIN) pour caractériser le comportement mécanique non linéaire de matériaux réfractaires. L’étude a été réalisée sur différents types de matériaux présentant des degrés variables de flexibilité : un matériau modèle monophasé à base de titanate d’aluminium (TA VF) et des matériaux industriels multi-phasés à base de magnésie. La flexibilité dans le cas du TA VF est obtenue grâce à l’anisotropie de la dilatation thermique entre les trois axes cristallographiques, et dans le cas des matériaux industriels grâce à la différence de coefficients de dilatation entre les agrégats de spinelle et la matrice magnésienne. Ces matériaux industriels ayant une déformation à rupture plus faible, la technique de corrélation d’images a dû être optimisée en ajustant au mieux les conditions expérimentales.La CIN et la méthode de suivi de marqueurs ont permis de mettre en évidence le caractère dissymétrique du comportement mécanique en flexion du TA VF entre la zone de l’éprouvette sollicitée en traction et celle en compression et d’investiguer le déplacement relatif des rouleaux du dispositif de flexion. Cette dissymétrie de comportement engendre un déplacement progressif de la fibre neutre au fur et à mesure que la charge appliquée augmente. Cette technique a ensuite été étendue à d’autres essais tels que l’essai brésilien et le Wedge Splitting appliqués aux matériaux industriels magnésiens. La CIN a ainsi permis d’illustrer les mécanismes de rupture (initiation et propagation de fissures) et de mettre en évidence la présence de phénomènes de « crack branching » obtenus grâce au réseau initial de microfissures volontairement généré au sein du matériau par différentiel de dilatation entre phases dans le but d’améliorer sa résistance aux chocs thermiques. Enfin, à partir des champs de déplacements obtenus par corrélation d’images, la méthode de recalage par éléments finis a été développée et utilisée pour déterminer l’évolution des propriétés élastiques du matériau pendant l’essai. / The present thesis aimed to apply digital image correlation (DIC) used for kinematic fields’ measurements as a support for the experimental characterization of refractory materials with specific non-linear behaviour. Model and industrial materials with different degrees of flexibility were studied. The first type of materials was a single phase model flexible aluminium titanate material (AT VF) developed for academic purposes by improving the grain growth. Its non-linear mechanical behaviour was obtained thanks to the thermal expansion mismatch of its grains according to the different crystallographic axis. The second one is multi-phased magnesia based industrial materials, whose flexibility is less accentuated, and for which the non-linear mechanical behaviour is obtained thanks to the thermal expansion coefficients mismatch between spinel aggregates and magnesia matrix. In order to apply the optical methods on these materials which exhibit lower strain-to-rupture, it was necessary to optimize the accuracy of these techniques by improving experimental conditions.In the case of AT VF, DIC and mark tracking method have been applied on four-points bending test at room temperature to underline the material asymmetric mechanical behaviour which induces a significant shift of the neutral fibre and to evaluate the relative displacement of rolls. The application of DIC has been extended to other experimental testing method such as Brazilian and Wedge Splitting test using the multi-phased magnesia based materials. This highlighted fracture mechanisms (crack occurrence and propagation) and the presence of crack branching phenomenon promoted thanks to an initial micro-cracks network voluntary introduced by thermal expansion mismatch between the different phases so as to improve their thermal shock resistance. From displacement experimentally obtained by DIC, a finite element method updating (FEMU-U) has been developed to determine material properties.

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