Constraint conditional finite element method for off-axial interfacial sliding of fiber reinforced composite

The main toughening mechanism of Ceramics Matrix Composite (CMC) is the fiber/matrix interfacial debonding and sliding. To simulate of the contact problem (such as interfacial sliding), penalty method etc have been used in general finite element method. But, these method need the repeated calculations, thus the CPU time is long and the accuracy depends on the number of repetitions. On the other hand, in actual CMCs, the fibers are not necessarily oriented along the loading direction, and the fiber diameter also fluctuates along the axis. Therefore, in this study, Constraint Conditional Finite Element Method (CC-FEM) was formulated to analyze the "off-axis interfacial sliding" with high precision and in a short time without repeated calculations. In CC-FEM, the equality of nodal displacements at the interface and the equilibrium of contact forces are assumed as constraint conditions, in which Coulomb's friction law and equivalent friction coefficient were taken into account. In addition, the validity was verified especially for "off-axis interfacial sliding" by comparing with general-purpose finite element software ANSYS. In the both cases of on- and off-axial interfacial sliding, the resultant stress distributions of the fiber and matrix agreed well with those of ANSYS. As compared to the case of on-axial interfacial sliding, the matrix stress recovered more steeply because of the higher equivalent frictional coefficient. (paper)