Fatigue and constraint are two important factors affecting fracture behavior of materials and life of structures. Some researchers have attempted to describe the fatigue crack propagation (FCP) behavior based on the two-parameter constraint theory. However, there is still no consensus regarding the effect of the constraint on the FCP rate. A correlation between the constraint and the FCP rate must be established. Thus, in this study, a new FCP model was developed by numerical simulations and verified by experiments. Then, the FCP behavior for compact tension (CT) and single edge-notched tensile (SENT) specimens with different in-plane and out-of-plane constraints was studied by numerical simulations using the new FCP model. The trends and essence of the FCP behavior under different constraints were finally clarified. In detail, a linear correlation of the FCP rate with the constraint was established for the first time by using the unified constraint parameter, Ap. Ap was not only extended for use in both monotonic and fatigue loading, but this paper also emphasizes that the FCP rate was largely dependent on the area surrounded by the equivalent plastic strain (εp) isoline at the crack tip rather than the length of the plastic zone. The results show that Ap can be employed to reveal the constraint effect in fatigue deeply and extensively.

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