Prediction of first matrix cracking in micro/nanohybrid brittle matrix composites

The classical Aveston–Cooper–Kelly shear-lag model for predicting the first matrix cracking strength in a brittle matrix composite is extended to the case of a hybrid brittle matrix composite containing both micro-scale and nano-scale fibers. First, closed-form solutions for the stresses in the two types of fibers and the matrix are derived. These are then used along with an energy analysis to predict the matrix cracking stress as a function of relevant material parameters. The analysis is applied to a typical Nicalon-SiC/CVI-SiC ceramic matrix composite containing additional nanofibers, for a wide range of nanofiber properties. A few volume percent of small diameter, moderate-stiffness nanofibers is predicted to provide significant strengthening and reduced crack opening while maintaining acceptable post-cracking fiber stresses. Various issues in the design of such micro/nanohybrid composites are then discussed.