Modelling of critical fibre length and interfacial debonding in the fragmentation testing of polymer composites

Micro-mechanical models based on a unidimensional load transfer approximation are used to predict the critical fibre length as a function of applied strain in the fragmentation testing of polymer matrix composites. Conditions of perfect adhesion, partial debonding, and total debonding are considered in turn. Situations are identified where the critical length cannot be viewed as a material constant, i.e. where it remains strain dependent as the applied strain increases. Numerical results based on the partial debonding model are given for the critical fibre length and the extent of the debonding zone as a function of applied strain. The prediction of the total debonding model is recovered asymptotically for large strains. We find, however, that the critical length predicted by the partial debonding model can be lower than the one predicted by the total debonding model if the interfacial bond strength is sufficiently larger than the frictional shear stress. These theoretical results show that both bond strength and frictional shear stress must be taken into account in the interpretation of the fragmentation test data.