A constraint theory in fracture mechanics is used to analyze the test data of 18G2A steels using single edge-notched bend (SENB) specimens with various crack depth to specimen width ratios ( a/ W). A bending correction factor is included in the two-parameter ( J– A 2) asymptotic solution to improve the theoretical prediction of the stress field for deep cracks under large-scale yielding condition, where J is the J-integral and A 2 is the constraint parameter, which depends on the in-plane geometry of the cracked body ( a/ W). As a result, the valid region for a traditional J-controlled crack growth is extended, and the ASTM specimen size requirements for fracture toughness testing can be relaxed. In addition, it is shown that the functional dependence of J– R curves on A 2 for 18G2A steels is established with test data; and the predicted J– R curves agree very well with the experimental curves. This ensures the transferability of laboratory test data to an actual structure provided the constraint level ( A 2) of the cracked structure is known or determined. This procedure allows an appropriate J– R curve with the same constraint level to be constructed and used in flaw stability analysis of any cracked body.