A J-based-fracture-testing method is presented for determining the bridging-stress-crack-opening-displacement (sigma-delta) relationship in fibre-reinforced composites where the crack-tip toughness is not negligible. The J-based technique originally proposed for concrete has been well-established for cementitious composites where the fracture process is primarily dominated by the formation of a fracture-process zone and the contribution of the crack-tip toughness is negligibly small. In this study, the J-based technique is further extended to cover materials for which the crack-tip stress singularity coexists with the fracture-process zone. This extended version of the J-based technique explicitly accounts for the crack-tip singularity while considering the fracture-process zone. This newly derived testing technique has been applied to a high-strength-mortar (HSM) reinforced with carbon and steel fibres where the fibre-bridging toughness can be of the same order of magnitude as the crack-tip toughness. The validity of the sigma-delta relationships deduced has been examined by comparing with results obtained from direct uniaxial tension tests. It is suggested that the J-based-fracture-testing technique can provide reasonable sigma-delta relationships and fracture parameters in a fibre-reinforced HSM.