Ⅰ-Ⅱ复合型唇形裂纹尖端塑性区分析  

Analysis of Plastic Zone at theⅠ/ⅡComposite Lip-Shaped Crack Tip

作　　者：陈建良 张鸿[1] 胡雪兰[1] 李湘萍[1] 唐云冰 谢小虎 Jianliang Chen;Hong Zhang;Xuelan Hu;Xiangping Li;Yunbing Tang;Xiaohu Xie(Sino-European Institute of Aviation Engineering,Civil Aviation University of China,Tianjin,300300;Changzhou E&E Turbo-Power Co.,Ltd.,Changzhou,213002)

机构地区：[1]中国民航大学中欧航空工程师学院,天津300300 [2]常州环能涡轮动力股份有限公司,常州213002

出　　处：《固体力学学报》2024年第2期266-278,共13页Chinese Journal of Solid Mechanics

基　　金：中央高校基本科研业务费专项(3122019180)资助。

摘　　要：本文采用保角变换方法,建立了拉伸载荷下Ⅰ/Ⅱ复合型唇形裂纹的扩展模型,基于Irwin小屈服等效假设,建立了拉伸载荷下Ⅰ-Ⅱ复合型唇形裂纹尖端塑性扩展区模型,得到了唇形裂纹尖端塑性区Ⅰ型和Ⅱ型应力强度因子的表达式、基于该模型,进一步得到了唇形裂纹尖端延长线上的应力分布,并建立拉伸仿真模型,将唇形裂纹尖端应力分布理论解与弹塑性仿真解以及线弹性仿真解进行对比,研究结果表明:基于Irwin小屈服等效假设修正后的唇形裂纹尺寸会变大,唇形裂纹等效应力强度因子变大;唇形裂纹的形状参数的改变会对塑性区产生影响,相同宽长比情况下,半长越大,塑性区尺寸越大,相同半长情况下,宽长比越大,塑性区尺寸越小,且伴随唇形裂纹倾斜角越大,塑性区尺寸也会相应增加;基于Irwin小屈服等效假设的唇形裂纹尖端塑性修正理论与塑性有限元仿真具有较好的一致性,伴随唇形裂纹倾斜角增加,裂纹尖端的应力水平降低,一方面,这是由于裂纹扩展形式由Ⅰ型向Ⅰ-Ⅱ复合型的转变造成的影响,另一方面,对于大倾斜角情况下,唇形裂纹腹部出现应力屈服现象,对唇形裂纹裂纹尖端的应力集中产生分担的影响,造成裂纹尖端应力水平的降低.In this study,the preservation of angles transformation method is employed to establish a propagation model forⅠ/Ⅱcomposite lip-shaped cracks under tensile loading conditions.Grounded in the Irwin small-scale yielding equivalent hypothesis,a plastic propagation zone model is formulated forⅠ-Ⅱcomposite lip-shaped cracks under tensile loading.This model provides expressions for the stress intensity factors(SIFs)of the modeⅠand modeⅡat 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 modeⅠcrack extension toⅠ-Ⅱcomposite 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,ultimat

关 键 词：唇形裂纹 复变函数 保角映射 Ⅰ-Ⅱ复合型裂纹 裂纹尖端塑性区 

分 类 号：O346.1[理学—固体力学]