The single fibre fragmentation test is commonly used to characterise the interfacial properties, a.o. the interfacial fracture toughness. Fibre fracture in the fragmentation test is, in many fibre-matrix systems, followed by debonding at the interface. The debonded interface is under radial compression due to residual strain and a mismatch in Poisson’s ratios. The debond crack surfaces are hence in contact and the debond crack propagation is pure mode II. Two previously derived, rigorous stress-based variational models, associated with a recently derived expression for the energy release rate due to a frictional crack growth, have been applied to the fragmentation test data to calculate the values of interfacial fracture toughness for two and three phase systems. It was found that the calculated values of interfacial fracture toughness are profoundly influenced by the value of the friction coefficient at the debonded interface and the accuracy of the used model.