王强胜,张启洞,蒋哲亮,李乐毅,江晓禹.基于分布位错法研究多条微裂纹对偏折主裂纹的影响[J].表面技术,2023,52(10):439-447.
WANG Qiang-sheng,ZHANG Qi-dong,JIANG Zhe-liang,LI Le-yi,JIANG Xiao-yu.Effect of Multiple Micro-cracks on Kinked Macro-cracks Based on the Distributed Dislocation Method[J].Surface Technology,2023,52(10):439-447
基于分布位错法研究多条微裂纹对偏折主裂纹的影响
Effect of Multiple Micro-cracks on Kinked Macro-cracks Based on the Distributed Dislocation Method
投稿时间:2022-08-03  修订日期:2023-02-17
DOI:10.16490/j.cnki.issn.1001-3660.2023.10.040
中文关键词:  偏折主裂纹  微裂纹  分布位错法  应力强度因子  裂纹扩展
英文关键词:kinked macro-crack  micro-crack  distribution dislocation  stress intensity factor  crack propagation
基金项目:国家自然科学基金资助项目(11472230)
作者单位
王强胜 四川建筑职业技术学院,四川 德阳 618000 
张启洞 中国兵器工业试验测试研究院,陕西 华阴 714200 
蒋哲亮 联合微电子中心有限责任公司,重庆 401332 
李乐毅 四川建筑职业技术学院,四川 德阳 618000 
江晓禹 西南交通大学 力学与航空航天学院,成都 610031 
AuthorInstitution
WANG Qiang-sheng Sichuan College of Architectural Technology, Sichuan Deyang 618000, China 
ZHANG Qi-dong Test and Measuring Academy of Norinco Group, Shaanxi Huayin 714200, China 
JIANG Zhe-liang United Microelectronics Center, Chongqing 401332, China 
LI Le-yi Sichuan College of Architectural Technology, Sichuan Deyang 618000, China 
JIANG Xiao-yu School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 610031, China 
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中文摘要:
      目的 采用理论方法求解多条微裂纹对偏折主裂纹的影响,重点分析偏折主裂纹尖端的力学行为及微裂纹对主裂纹扩展角度和闭合区域的影响等问题,为实际的工程应用提供理论依据。方法 运用叠加原理将主问题分解成2个子问题,通过材料力学方法求解子问题一;基于分布位错方法求解子问题二。进一步建立关于位错密度的奇异积分方程,利用Gauss-Chebyshev数值求积分法解决位错密度方程的奇异性问题,并通过计算机编写程序,最终得到相关力学参量的数值解。结果 得到了偏折主裂纹附近的应力场以及微裂纹长度、微裂纹个数对偏折主裂纹尖端应力强度因子的影响等相关力学参量。分析了主裂纹不同偏折角度时的闭合区域,以及微裂纹的方位角、微裂纹个数等对偏折主裂纹扩展角度的影响。结论 裂纹面对拉应力有屏蔽作用,导致拉应力在裂纹面附近应力松弛,而裂纹尖端对拉应力有放大作用,随着应力增加将导致裂纹的扩展。一条微裂纹位于主裂纹尖端约–30°<θ<50°时,将使主裂纹尖端应力强度因子增加,促进主裂纹的扩展,而微裂纹位于50°<θ<90°或–90°<θ<–30°时,将使主裂纹尖端应力强度因子减小,抑制主裂纹的扩展。主裂纹尖端应力强度因子随微裂纹长度的增加而变大,随微裂纹与主裂纹间距离的增加而减小。
英文摘要:
      The work aims to study the problem of the effect of multiple micro-cracks on the kinked macro-crack by a theoretical method. In this paper, the mechanical behavior of the kinked macro-crack tip and the effect of multiple micro-cracks on the kinked macro-crack propagation angle and the closed regions of the kinked macro-crack were analyzed mainly. The obtained results will provide a theoretical basis for practical engineering applications. When solving the problem studied in this paper through theoretical analysis, it was divided into two steps. Firstly, the problem considered in this paper was divided into two sub-problems based on the superposition principle, and then solved one by one. Secondly, the first sub-problem was solved by material mechanics and the second sub-problem was solved by the distributed dislocation technique. Further, a singular integral equation about the dislocation density function was established. The singularity problem of the dislocation density equation was solved based on the Gauss-Chebyshev integration method and the numerical solution of the equation was obtained by means of computer programming. Finally, a series of valuable mechanical parameters about the kinked macro-crack were obtained. In this paper, some results were obtained which will provide a theoretical basis for practical engineering applications. For example, the stress field near the kinked macro-crack and the related mechanical parameters of the macro-crack tip were obtained. Specifically, these mechanical parameters affected the micro-crack length and the number of micro-cracks on the stress intensity factor at the tip of the macro-crack. The closed regions of the macro-crack with different kinked angles, and the effect of the orientation of micro-cracks and the number of micro-cracks on the propagation angle of the kinked macro-crack were analyzed. Several practical conclusions were obtained in this paper. It is concluded that the regions near the kinked macro-crack surface has a shielding effect on the tensile stress, which will lead to stress relaxation of the tensile stress near the crack surface. The regions near the crack tip will amplify the tensile stress. In other words, the stress will be concentrated near the crack tip, and the kinked macro-crack tip will further propagate as the increased of the applied load. When only one micro-crack is located at the macro-crack tip about –30°<θ<50°, the stress intensity factor at the kinked macro-crack tip will increase, which will promote the propagation of the macro-crack. When the micro-crack is located at 50°<θ<90° or –90°<θ<–30°, the stress intensity factor at the tip of the macro-crack will decrease, which will inhibit the propagation of the macro-crack. The stress intensity factor at the tip of the macro-crack will become larger with the increase of the micro-crack length, and decrease with the increase of the distance between the micro-crack and the macro-crack.
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