Formulation of off-axial interfacial debonding and sliding problem by constrained conditional finite element method

In ceramics matrix composites (CMCs), fiber-matrix interfacial debonding and sliding are the main toughening mechanisms. An interfacial debonding and sliding problem was formulated in this study, using the constrained conditional finite-element method (CC-FEM). In this formulation, the equivalence of nodal displacements at the interface and the equilibrium of contact forces are assumed as constrained conditions in which Coulomb’s law of friction is taken into account. As a distinguished advantage, numerical solutions are obtainable by a single calculation without an iterative algorism. We earlier treated a case in which fibers were oriented along the loading direction. In actual CMCs, however, fibers are not necessarily oriented along the loading direction. The fiber diameter also fluctuates along the axis. In this study, therefore, the off-axial interfacial debonding and sliding problem based on CC-FEM was formulated. Its validity was discussed by comparison with ANSYS. In both cases of on-axis and off-axis, the resultant fiber and matrix stress distributions agreed well with those of ANSYS. Comparison between on-axis and off-axis cases showed that the matrix stress in the latter recovered more steeply because of the higher equivalent friction coefficient.