Analytical and numerical shear-lag models describing probabilistic ruptures in ceramic matrix mini-composites.
Topic(s) : Material and Structural Behavior - Simulation & Testing
Co-authors :
Claire MOREL (FRANCE), Emmanuel BARANGER (FRANCE)Abstract :
Ceramic matrix composites (CMC) are being considered for various high-temperature applications, such as in aerospace and nuclear industries, thanks to their excellent thermo-mechanical properties. However, each component independently exhibits brittle-elastic behavior. To address this issue, weak interphase can be deposited in order to provide brittle-damaging behavior to the composite and allow matrix cracks to be deflected at the fiber/matrix interface. A decohesion zone is created around a matrix crack, which enables progressive load transfer between the fiber and matrix by shear transfer [1,2]. Writing the local equilibrium allows us to determine the evolution of stresses and strains in the matrix and fibers, commonly known as the shear lag model. It can describe unidirectional composites' brittle tensile damage behavior or the ply tensile behavior of more complex structures. Load transfer between the fiber and the matrix enables matrix multi-cracking of the composite [3]. The overall mechanical behavior will then depend on the rate of matrix cracking. Therefore, it is essential to predict the appearance of new matrix cracks accurately.
Probability laws, particularly the Weibull law and Poisson Point Process (PPP), are studied, in order to predict new matrix crack and used to develop two mechanical models. The influence of modeling choice on mechanical behavior is investigated based on experimental data from the literature of a SiC/SiC unidirectional composite with pyrocarbon interphase [4]. In particular, the influence of material properties, matrix failure properties and size effect are studied.
First model is based on Weibull’s law, which is widely used to describe the fracture of ceramic materials. Weibull's law calculates the probability of having at least one crack in a given volume at a given load. It is based on the weakest link hypothesis. A spatial discretization of the composite is be carried out, and, at each time step, we determined which volume elements are cracked. The discretization must be fine to represent overall behavior, well below the minimum inter-crack distance at saturation. From the point of view of multi-scale modeling of a CMC composite, this fine discretization of ply (i.e., the unidirectional composite) on a mesoscopic scale can be time-consuming.
The second model is based on PPP, which can determine the probability of k crack(s) in a given volume at a given loading. It does not rely on the weakest link hypothesis. Thanks to PPP, the second model does not need a fine discretization. However, it is then necessary to impose the position of the cracks. The influence of the relative position of cracks on mechanical behavior is also studied. In particular, the periodic or random distribution of cracks is compared.
Probability laws, particularly the Weibull law and Poisson Point Process (PPP), are studied, in order to predict new matrix crack and used to develop two mechanical models. The influence of modeling choice on mechanical behavior is investigated based on experimental data from the literature of a SiC/SiC unidirectional composite with pyrocarbon interphase [4]. In particular, the influence of material properties, matrix failure properties and size effect are studied.
First model is based on Weibull’s law, which is widely used to describe the fracture of ceramic materials. Weibull's law calculates the probability of having at least one crack in a given volume at a given load. It is based on the weakest link hypothesis. A spatial discretization of the composite is be carried out, and, at each time step, we determined which volume elements are cracked. The discretization must be fine to represent overall behavior, well below the minimum inter-crack distance at saturation. From the point of view of multi-scale modeling of a CMC composite, this fine discretization of ply (i.e., the unidirectional composite) on a mesoscopic scale can be time-consuming.
The second model is based on PPP, which can determine the probability of k crack(s) in a given volume at a given loading. It does not rely on the weakest link hypothesis. Thanks to PPP, the second model does not need a fine discretization. However, it is then necessary to impose the position of the cracks. The influence of the relative position of cracks on mechanical behavior is also studied. In particular, the periodic or random distribution of cracks is compared.