Constraint can be divided into two conditions of in‐plane and out‐of‐plane, and each of them has its own parameter to characterize. However, in most cases, there exists a compound change of both in‐plane and out‐of‐plane constraint in structures, a unified measure that can reflect both of them is needed. In this paper, the finite element method (FEM) was used to calculate the equivalent plastic strain (ɛp) distribution ahead of crack tips for specimens with different in‐plane and out‐of‐plane constraints, and the FEM simulations based on Gurson–Tvergaard–Needleman (GTN) damage model and a small number of tests were used to obtain fracture toughness for the specimens with different constraints. Unified measure and characterisation parameter of in‐plane and out‐of‐plane constraints based on crack‐tip equivalent plastic strain has been investigated. The results show that the area APEEQ surrounded by the ɛp isoline ahead of crack tips can characterize both in‐plane and out‐of‐plane constraints. Based on the area APEEQ, a unified constraint characterisation parameter Ap was defined. It was found that there exists a sole linear relation between the normalised fracture toughness JIC/Jref and regardless of the in‐plane constraint, out‐of‐plane constraint and the selection of the ɛp isolines. The unified JIC/Jref−reference line can be used to determine constraint‐dependent fracture toughness of materials. The FEM simulations with the GTN damage model (local approach) can be used in obtaining the unified JIC/Jref−reference line for materials with ductile fracture.

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In this paper, the specimens with different geometries and loading configurations were used to study the unified correlation of in‐plane and out‐of‐plane constraints with fracture toughness by using numerical simulation method. The results show that the unified constraint parameter Ap which was defined on the basis of the areas surrounded by the equivalent plastic strain isolines ahead of crack tip can characterise both in‐plane and out‐of‐plane constraints induced by different specimen geometries and loading configurations. A sole linear relation between the normalised fracture toughness JIC/Jref and Ap was obtained. The JIC/Jref ‐Ap line is a unified correlation line of in‐plane and out‐of‐plane constraints with fracture toughness of a material, and the constraint dependent fracture toughness of a material can be determined from the unified correlation line. The results also demonstrate that the out‐of‐plane constraint effect is related to the in‐plane constraint effect, and there exists interaction between them. The higher in‐plane constraint strengthens the out‐of‐plane constraint effect, whereas the lower in‐plane constraint is not sensitive to the out‐of‐plane constraint effect.

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