Effect of the Lüders plateau on the relationship between fracture toughness and constraint for pipeline steels

•The effect of the Lüders plateau on the fracture response for the steels is studied.•As the Lüders plateau length increases, the fracture toughness is more sensitive to the change of the constraint.•The larger the Lüders plateau length, the smaller the effect degree of the strain hardening exponent, yield stress and initial void volume fraction on the relationship between the fracture toughness and the constraint.•A constraint-based fracture failure criterion considering the Lüders plateau is proposed and validated.