A new method is presented to determine the crack-tip plastic zone size (Ry) that along the direction of plate thickness for the center cracked plate with biaxial uniform tension load by considering the thickness effect. Firstly, Introducing out of plane constraint factor Tz and maximum opening displacement (MCOD), based on the series of calculation results by elastic plastic finite element simulation and theoretical derivation, the distribution of Tz in the plastic zone is studied at the mid-plane position. It is found that the Tz value at the position of 0.75Ry can represent the comprehensive thickness effect in the plastic zone, and the function expression of Tz (0.75Ry) is obtained by MCOD. Next, an function expression for the Ry at the mid-plane position is determined by Tz (0.75Ry) and MCOD. In order to improve the scope of application of the formula, at different plate thickness positions, the thickness reduction factor fB is proposed, finally, the plastic zone size along the plate thickness can be calculated by MCOD, except for the area near the plane surface.


During the service period for ships and marine engineering structures, the penetrating fatigue cracks will be generated due to the accumulation of fatigue damage on sheet metal components. The response state of the crack tip area can be described based on the elastic-plastic fracture mechanics (EPFM) with mature assessment methodologies (Sharif et al., 2000; Do-Jun Shim et al., 2002). The crack-tip plastic zone size (Ry) (Nakamura T et al., 1990; Guo W et al., 1999 ; Paul S K et al., 2015) had been suggested for characterizing fatigue crack propagation behaviors. And many researchers considered that Ry was the most suitable parameter to describe the propagation of fatigue cracks (Brown M W et al., 1988; Wang G S et al., 1991; Wang G S et al., 1993), because it not only facilitates correlation of fast growing cracks but also has an obvious physical interpretation. Therefore, it is important to determine the value of Ry to assess the safety state of cracked component in practice.

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