On the single fibre pull-out problem: effect of loading method

The loading method in single fibre pull-out experiments would influence the stress distributions in the constituents which, in turn, determine the fibre debond and frictional pull-out stresses. The difference in these stresses for three loading conditions (i.e. the fixed matrix bottom, fixed fibre and matrix bottom and the restrained matrix top conditions) has been identified in a newly-developed analytical model that is based on a fracture mechanics approach. It is shown that the restrained matrix top condition induces a lower initial debond, maximum debond and frictional pull-out stresses compared with the fixed bottom conditions. This is explained by the observation that the potential energy release rate calculated for a given external stress with respect to incremental debond crack propogation is always higher, thereby allowing easy debonding, for the restrained top loading condition. After complete debonding, the interfacial frictional shear stress is significantly lower for the restrained top condition, requiring a low external stress to overcome the interfacial friction for fibre pull-out. The difference in the debond and pull-out stresses increases with increasing embedded fibre length and decreases with increasing ratio of matrix to fibre radii (or fibre volume fraction). A systematic way of evaluating the difference in theoretical predictions against experiments is also presented.