交叉裂纹各裂尖应力强度因子同时快速求解的Williams单元

Williams element quickly solving the stress intensity factors of cross crack tip simultaneously

为了研究交叉裂纹各裂尖应力强度因子之间的相互影响,建立了交叉裂纹各裂尖应力强度因子同时快速求解的Williams单元,以十字交叉裂纹为例,分别对正交十字裂纹或斜十字裂纹各裂尖应力强度因子相关参数进行研究,分析了薄板尺寸、裂纹夹角与奇异区尺寸等相关参数对十字交叉裂纹各裂尖应力强度因子的影响,其中KⅠ、KⅡ为裂尖Ⅰ、Ⅱ型应力强度因子。算例分析表明,当板宽与裂纹长度满足W/a≥13时,能够忽略板的尺寸对正交十字裂纹裂尖应力强度因子的影响,可视为无限大板;对于斜十字裂纹情况,当水平裂纹长度不变时,随着斜裂纹长度参数d的增大,KⅠ,A、KⅡ,C和KⅠ,D逐渐递减,而KⅡ,A、KⅠ,B、KⅡ,B和KⅠ,C逐渐递增,对于KⅡ,D则出现先减后增的趋势;当斜裂纹长度参数d=0时,随着裂纹夹角γ的变化,KⅠ,A、KⅠ,B大小相等,符号相同,KII,A、KⅡ,B则大小相等,符号相反,且各裂尖应力强度因子对裂尖奇异区尺寸不敏感。证明了Williams单元能够同时快速求解交叉裂纹各裂尖应力强度因子,且具有较高的计算精度。

In order to study the interaction between the stress intensity factor at the crack tips of cross crack,Williams element is established to solve the stress intensity factors of cross crack tip simultaneously.Taking cross fracture as an example,the parameters related to stress intensity factors of orthogonal cruciform crack or oblique cruciform crack are studied respectively.The influence of the size of thin plate,the angle of crack and the size of singular region on the stress intensity factors of cruciform crack tip is analyzed.KI and KII are stress intensity factors of type I and II.The analysis of the example shows that when the plate width and crack length meet W/a≥13,the influence of plate size on stress intensity factors of orthogonal cruciform crack tip can be ignored,and can be regarded as infinite plate.For the oblique cruciform crack,when the horizontal crack length is constant,the KI,A、KII,C and KI,D decrease gradually with the increase of the oblique crack length parameter d,while the KII,A、KI,B、KII,B and KI,C increase gradually,and as for KII,D,it decreases at first and then increases.When the oblique cruciform crack length parameter d=0,with the change of crack angle γ,the KI,A and KI,Bis equal with the same sign;the KII,A、KII,B is equal with the opposite sign.Moreover,the stress intensity factor of each crack tip is not sensitive to the size of the singular region of the crack tip,which proves that the Williams element can solve the stress intensity factor of each crack tip with relatively high accuracy.