Debonding along the interface of composites (Q1822555)

The fibrous composites have some internal behaviours under loading. When the matrix is cracked the fibres may still be intact, and the composite can continue to sustain additional load. But, during the loading process the fibres near the crack-surface should be debonded and protruded to certain extent to enable the crack open. On the other hand, the fibres debonding and slipping will be resisted by the interface bond and friction. Therefore, the ultimate fracture strength of the composite is controlled by the mechanism of fibre-matrix interaction. Thus, the relation between fibre protruding and pull-force becomes a important problem. This relation is also called gradual fibre debonding criterion. In the article of \textit{H. Stang} and \textit{S. P. Shah}, Failure of fibre- reinforced composites by putt-out fracture [J. Material Sci. 21, 953-957 (1986)], the debonding criterion was discussed based on fracture mechanics, but the interface friction was not considered. \textit{B. Budiansky, J. W. Hutchinson} and \textit{A. G. Evans} [(*) J. Mech. Phys. Solids 34, 167-189 (1986; Zbl 0575.73106)] considered the matrix fracture of fibre-reinforced ceramic. In such a problem, the debonding criterion was needed, but to avoid this obstacle, (*) gave a special assumption that the average stresses behind and ahead of the crack-tip keep the same value. In this paper, the fibre debonding, slipping, and protruding is investigated and a new debonding criterion is given. Using this debonding criterion, the basic relation between fibre protruding and pull-force is obtained.