Unified constraint parameter based on crack-tip opening displacement

•A new constraint parameter Ad based on crack-tip opening displacement (CTOD) was proposed.•The parameter Ad can quantify both in-plane and out-of-plane constraints.•A unified correlation line between normalized fracture toughness and Ad can be obtained.•The parameter Ad may be an appropriate engineering unified constraint parameter. To develop new fracture assessment methodology to incorporate both in-plane and out-of-plane constraints, it is desirable to develop unified constraint parameters convenient for engineering calculation and application. In this work, a new unified constraint parameter Ad based on crack-tip opening displacement (CTOD) was proposed, and the capability of Ad to characterize both in-plane and out-of-plane constraints has been investigated by a comparison with the unified constraint parameter Ap. The results indicate that the parameter Ad can quantify both in-plane and out-of-plane constraints and their change with load levels. A unified correlation line between the normalized fracture toughness JC/Jref and Ad (toughness locus) can be established for both ductile and brittle fracture. The parameter Ad based on CTOD has clear physical and geometric meaning, and it can be easily measured and determined in FEM analyses. Therefore, the Ad may be an appropriate engineering unified constraint parameter, and it may be adopted in fracture assessments of cracked structures for incorporating both in-plane and out-of-plane constraints.