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In this study, the angle-preserving transformation method is employed to establish a propagation model for I/II composite lip-shaped cracks under tensile loading conditions. Based on Irwin's 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 mode I and mode II at the tip of lip-shaped cracks within the plastic zone. Additionally, the stress distribution along the extension line of the lip-shaped crack tip is characterized. A tensile simulation model is developed, and the theoretical solution for stress distribution at the lip-shaped crack tip is compared with the elastoplastic and linear elastic simulation results. It is found that, based on Irwin's small-scale yielding equivalent hypothesis, the modified dimensions of lip-shaped cracks lead to increased crack sizes and greater equivalent SIFs. 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 basis of Irwin's small-scale yielding equivalent hypothesis, aligns well 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.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
|---|---|---|---|---|---|---|
| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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