徐华, 邓鹏, 蓝淞耀, 刘祖容, 杨绿峰. 曲线裂纹裂尖SIFs等效分析的广义参数Williams单元确定方法[J]. 工程力学, 2020, 37(6): 34-41. DOI: 10.6052/j.issn.1000-4750.2019.08.0455
引用本文: 徐华, 邓鹏, 蓝淞耀, 刘祖容, 杨绿峰. 曲线裂纹裂尖SIFs等效分析的广义参数Williams单元确定方法[J]. 工程力学, 2020, 37(6): 34-41. DOI: 10.6052/j.issn.1000-4750.2019.08.0455
XU Hua, DENG Peng, LAN Song-yao, LIU Zu-rong, YANG Lu-feng. THE DETERMINATION METHOD OF WILLIAMS ELEMENT WITH GENERALIZED DEGREES OF FREEDOM FOR EQUIVALENT ANALYSIS OF SIFS AT THE CURVED CRACK TIP[J]. Engineering Mechanics, 2020, 37(6): 34-41. DOI: 10.6052/j.issn.1000-4750.2019.08.0455
Citation: XU Hua, DENG Peng, LAN Song-yao, LIU Zu-rong, YANG Lu-feng. THE DETERMINATION METHOD OF WILLIAMS ELEMENT WITH GENERALIZED DEGREES OF FREEDOM FOR EQUIVALENT ANALYSIS OF SIFS AT THE CURVED CRACK TIP[J]. Engineering Mechanics, 2020, 37(6): 34-41. DOI: 10.6052/j.issn.1000-4750.2019.08.0455

曲线裂纹裂尖SIFs等效分析的广义参数Williams单元确定方法

THE DETERMINATION METHOD OF WILLIAMS ELEMENT WITH GENERALIZED DEGREES OF FREEDOM FOR EQUIVALENT ANALYSIS OF SIFS AT THE CURVED CRACK TIP

  • 摘要: 基于Williams级数建立的含直线裂纹平面弹性体裂尖应力强度因子(Stress Intensity Factors,简记SIFs)分析的广义参数Williams单元(简记W单元),因裂纹面必须满足σθ=0、τρθ=0(θ=±π)的边界条件,而曲线裂纹面无法满足该边界条件使得W单元不能直接适用。该文针对此问题,将含曲线裂纹平面弹性体裂尖局部区域进行等效处理,以裂尖为圆心,选取合适的半径建立等效区,即截取斜率呈单调变化的曲线微段,在微段两端引切线交叉成折线段,以该折线段近似代替曲线微段。算例分析表明:当等效区的尺寸取建议值时,该文方法的计算结果精度较高,证明了该文改进方法在分析曲线裂纹尖端SIFs的合理性,同时给出了等效区尺寸的建议值,即ψmin=5π/6,且等效区截取曲线长度宜大于原曲线长度的1/5。

     

    Abstract: The Williams element with generalized degrees of freedom (W element) for stress intensity factors (SIFs) analysis of the linear crack tip of plane elastic continuum based on Williams series must satisfy the boundary conditions that σθ=0 and τρθ=0(θ=±π) on a crack surface, but the curved crack surface does not meet it. Therefore, the application of the W element is limited to a curved crack. The local region of the curved crack tip of a plane elastic continuum is equivalently treated to solve the problem, where the crack tip is taken as the center to establish an equivalent region by selecting an appropriate radius, that is, the curved micro-segments where the slope changes monotonously is intercepted, the end of which the tangent line is guided to cross over into broken line that will approximately replace the curved micro-segment. The analysis of examples show that when the size of the equivalent region takes are commended value, the calculation of this method has high precision, which proves that the improved method is reasonable in analyzing the SIFs of curved cracks. Meanwhile, the recommended value of equivalent region size is developed, that is, ψmin=5π/6, and the length of the curve intercepted by the equivalent region should be greater than 1/5 length of the original curve.

     

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