Fracture tests, especially at lower testing temperatures, have become quite popular in quantifying low-temperature cracking. However, current fracture testing analysis methods often use a single number, such as fracture energy or fracture toughness, to quantify cracking resistance. These tests do not capture both the initiation and propagation of the crack. The Resistance Curve, or R-curve, is widely applied in many fields, such as metal, polymer and composites. The R-curve considers cracking resistance as a function of crack extension, which includes initiation and propagation. In this research, three asphalt concrete mixtures, including hot mix, hot mix with reclaimed asphalt pavement (RAP) and warm mix with RAP were tested at two temperatures, three levels of ageing and two levels of moisture condition by the Semi-Circular Bend fracture test. R-curves were constructed using the data from the fracture test, and digital images were utilised to capture the crack extension. In addition to capturing the traditional fracture energy, two new parameters were explored using the R-curves: the cohesive energy and the propagation parameter energy rate. It was found that cohesive energy was always in a narrow range (approximately 500–1000 J/m2) compared to the fracture energy range (approximately 500–1700 J/m2) over all combinations of ageing and moisture conditions, which indicates that the crack initiation may not be as sensitive to temperature, ageing and moisture as fracture energy. The results of energy rate indicated that moisture and short-term ageing impact the crack propagation by reducing the resistance of crack growth. These results proved that R-curves are a potentially useful tool to quantify the cracking resistance of asphalt concrete in both crack initiation and propagation.