The debonding mode of failure, which is observed in concrete beams strengthened using externally attached CFRP composite sheets, is investigated using the direct shear test. The Mode II, cohesive stress-crack relative slip relationship is established using full-field displacements obtained from digital image correlation. The interface crack is associated with a cohesive stress-transfer zone of fixed length. The load capacity of the CFRP composite bonded to concrete is attained when the cohesive crack is fully established. The acoustic emission monitored during the interface fracture initiation and propagation indicates that microcracking events accumulate at a constant rate up to failure. The variations in the local fracture parameters are quantified and are adequately represented using the normal probability distribution. A numerical analysis of the direct-shear debonding response of CFRP composite attached to a concrete substrate is performed to study the influence of the variability of the local fracture parameters on the load-carrying capacity and the ultimate failure. An instability associated with a snapback in the load response resulting from a decrease in both load and displacement, is predicted close to failure. The variation in the local fracture properties does not influence the load-carrying capacity or the intensity of snapback instability at ultimate failure. © 2016 Informa UK Limited, trading as Taylor & Francis Group.