The present paper deals with the J‐A concept in two‐parameter elastic–plastic approaches of fracture mechanics. The cumulative damage rule in a solid is employed to construct the quantitative elastic–plastic J‐A fracture criterion. As a result, the constraint corrected elastic–plastic fracture toughness
as a function of the crack‐tip constraint parameter A, the yield stress, the strain hardening exponent and the failure stress has been proposed. The significant effect of the strain hardening exponent on the normalized constraint corrected fracture toughness is observed. The value of the normalized constraint corrected fracture toughness decreases with the increase of the applied failure stress and the decrease of the crack aspect ratio to a certain values, and then it stabilizes.