Analysis of Plastic Zone at the Ⅰ/Ⅱ Composite Lip-shaped Crack Tip
In this study,the angle-preserving transformation method is employed to establish a propa-gation 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 distri-bution along the extension line of the lip-shaped crack tip is characterized.A tensile simulation model is de-veloped,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 e-quivalent 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 in-crease 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 phenome-non 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 re-duced stress levels at the crack tip.
lip crackcomplex functionconformal mappingⅠ-Ⅱ composite crackcrack tip plastic zone
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