A novel unified constraint parameter based on plastic strain energy

•A novel unified constraint parameter λ based on the plastic strain energy is proposed.•A series of uniaxial and biaxial bending experiments using BS1501-224 28B steel were conducted to capture the biaxiality effect.•An investigation of the constraint parameters Q, φ and Ad* for the changes in constraint level, caused by the multi-axiality effect, is discussed.•The parameter λ not only can characterize crack-tip constraint but is effective in the multi-axiality effect.•A high order relationship can be established between parameter λ and fracture toughness.