3D front tip fields in creeping solids under constraint effects: a higher-order asymptotic solution

As one of the most important topics studied in creep fracture mechanics, mechanics fields at three-dimensional (3D) sharp V-notches and crack tip have drawn tremendous attentions. With many years efforts on constraint theory developed in creeping solids, there still seems dense fog on how in-plane and out-of-plane constraint effects are interacted for 3D sharp V-notch and crack in creeping solids. To shed lights on this topic, a 3D higher-order termed solution for sharp V-notches in creeping materials subjected to mode 1 loading is established by introducing the out-of-plane factor, which is the out-of-plane stress divided by the sum of in-plane normal stress. The solution can naturally be degenerated to a 3D crack. Based on the 3D higher-order term solution, a new fracture parameter is proposed and combined with to characterize 3D constraint effect. It is found that the stress exponents and angular distribution of higher-order term for 3D notches and cracks are highly related to . The proposed higher order termed solutions show better agreement with the FEA results than the 3D leading-term and 2D two-term solutions, especially for smaller notch angles and ligament width. Moreover, the presented 3D constraint theory shows that effects of and are highly interlinked rather than simply separated. It implies that the 3D constraint level may be significantly influenced by . The 3D mathematical solutions discussed in this paper could enhance the understanding of the 3D effect and has the potential to explain the 3D constraint effect on the notches and cracks under creep conditions.