Abstract：In this study, the preservation of angles transformation method is employed to establish a propagation model for I/II composite lip-shaped cracks under tensile loading conditions. Grounded in the Irwin small-scale yielding equivalent hypothesis, a plastic propagation zone model is formulated for I-II composite lip-shaped cracks under tensile loading. This model provides expressions for the stress intensity factors (SIFs) of the mode I and mode II at the tip of lip-shaped cracks within the plastic zone. Additionally, stress distribution along the extension line of the lip-shaped crack tip is characterized. A tensile simulation model is developed, and comparisons are drawn between the theoretical solution for stress distribution at the lip-shaped crack tip and elastoplastic and linear elastic simulation results. It is found that, based on the Irwin small-scale yielding equivalent hypothesis, the modified dimensions of lip-shaped cracks lead to increased crack sizes and greater equivalent stress intensity factors. Geometric alterations in lip-shaped crack parameters also influence the plastic zone, with larger semi-lengths resulting in larger plastic zones under equivalent width-to-length ratios. Conversely, greater width-to-length ratios lead to smaller plastic zones under equivalent semi-lengths. Moreover, an increase in the inclination angle of the lip-shaped crack corresponds to a proportional increase in the plastic zone size. The plastic correction theory at the lip-shaped crack tip, founded on the Irwin small-scale yielding equivalent hypothesis, exhibits notable alignment with plastic finite element simulations. As the inclination angle of the lip-shaped crack rises, stress levels at the crack tip diminish. On the one hand, this phenomenon arises from the transition from mode I crack extension to I-II composite crack extension, coupled with stress yielding at the concave region of the lip-shaped crack for larger inclination angles, on the other hand, this stress yielding serves to mitigate stress concentration at the crack tip, ultimately resulting in reduced stress levels at the crack tip.
2024, Vol. 45 
