两条等长共线裂纹尖端塑性区扩展理论研究
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摘要
采用Kachanov法基本思想求解2条等长共线裂纹相互作用下裂纹的应力强度因子,分别基于Mises屈服准则和D-P屈服准则推导了裂纹尖端塑性区半径的表达式,并求得裂纹相互作用下塑性区半径的扩大倍数,其值为2条裂纹相互作用下的应力强度因子与单裂纹状态下应力强度因子比值的平方。在此基础上,分析了裂纹间距对塑性区扩展的影响。研究发现,同一裂纹倾角下裂纹间距与裂纹长度比值越小,2条裂纹尖端的塑性区半径越大,裂纹尖端塑性区扩展速度越快,直至塑性区发生接触,且不同的裂纹倾角,裂纹尖端塑性区发生接触的条件不同。
Based on the basic idea of the Kachanov method, the stress intensity factors for the interaction of isometric collinear cracks are computed. Moreover, according to the Mises failure criterion and the D-P failure criterion, the expression of the plastic zone radius at the crack tip and the expansion ratio of plastic zone radius under the crack interaction are derived based on the small-area yield condition under the uniaxial tension. The radius enlargement of the plastic zone is the square of the ratio of the stress intensity factor under the interaction of two cracks to the stress intensity factor of a single crack. And, the influence of crack spacing on the plastic zone expansion is also analyzed. The results show that, for a same inclining angle of crack, the plastic zone radius of crack tip increases with the decrease of crack spacing, and its increasing rate increase as well. For different crack angles, the contact conditions at the plastic zone of crack tip are also different. Therefore, the combination conditions of double cracks need to be determined according to the inclining angle of crack.
Based on the basic idea of the Kachanov method, the stress intensity factors for the interaction of isometric collinear cracks are computed. Moreover, according to the Mises failure criterion and the D-P failure criterion, the expression of the plastic zone radius at the crack tip and the expansion ratio of plastic zone radius under the crack interaction are derived based on the small-area yield condition under the uniaxial tension. The radius enlargement of the plastic zone is the square of the ratio of the stress intensity factor under the interaction of two cracks to the stress intensity factor of a single crack. And, the influence of crack spacing on the plastic zone expansion is also analyzed. The results show that, for a same inclining angle of crack, the plastic zone radius of crack tip increases with the decrease of crack spacing, and its increasing rate increase as well. For different crack angles, the contact conditions at the plastic zone of crack tip are also different. Therefore, the combination conditions of double cracks need to be determined according to the inclining angle of crack.
引文
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[16]OCHI Y,ISHII A,SASAKI S K.An experimental and statistical investigation of surface fatigue crack initiation and growth[J].Fatigue&Fracture of Engineering Materials&Structures,1985,8(4):327-339.
[2]石路杨,余天堂.多裂纹扩展的扩展有限元法分析[J].岩土力学,2014,38(1):263-272.(SHI Luyang,YU Tiantang.Analysis of multiple crack growth using extended finite element method[J].Rock and Soil Mechanics,2014,38(1):263-272.(in Chinese))
[3]周小平,杨海清,董捷.压应力状态下多裂纹扩展过程数值模拟[J].岩土工程学报,2010,32(2):192-197.(ZHOUXiaoping,YANG Haiqing,DONG Jie.Numerical simulation of multiple-crack growth under compressive loads[J].Chinese Journal of Geotechnical Engineering,2010,32(2):192-197.(in Chinese))
[4]陈小翠,杜成斌,江守燕.基于XFEM的主次裂纹间应力强度因子相互作用[J].河海大学学报(自然科学版),2014,42(4):327-331.(CHEN Xiaocui,DU Chengbin,JIANG Shouyan.Study of interaction between stress intensity factors of main and secondary cracks based on XFEM[J].Journal of Hohai University(Natural Sciences),2014,42(4):327-331.(in Chinese))
[5]HAERI H,SHAHRIAR K,MARJI M F,et al.Cracks coalescence mechanism and cracks propagation paths in rock-like specimens containing pre-existing random cracks under compression[J].Journal of Central South University,2014,21(6):2404-2414.
[6]CAO P,LIU T,PU C,et al.Crack propagation and coalescence of brittle rock-like specimens with pre-existing cracks in compression[J].Engineering Geology,2015,187:113-121.
[7]IRWIN G R.Fracture dynamics[C]//ASTM STP.Fracturing of metals seminar.Chicago:American Society for Metals,1948:147-166.
[8]IRWIN G R,KIES J A,SMITH H L.Fracture strengths relative to onset and arrest of crack propagation[J].Proceedings of the American Society for Tesiing Materials,1958,58:551-589.
[9]IRWIN G R.Analysis of stresses and strains near the end of a crack traversing a plate[J].Journal of Applied Mechanics,1957,24:361-364.
[10]李世愚,和泰名,尹祥础.岩石断裂力学[M].北京:科学出版社,2015:11-29.
[11]SWIFT T.Damage tolerance capacity[J].International Journal of Fatigue,1994,16(1):75-94.
[12]KACHANOV M.Elastic solids with many cracks:a simple method of analysis[J].International Journal of Solids and Structures,1987,23(1):23-43.
[13]KACHANOV M.Elastic solids with many cracks and relate problems[J].Advances in Applied Mechanics,1993,30:259-445.
[14]席婧仪,陈忠辉,朱帝杰,等.岩石不等长裂纹应力强度因子及起裂规律研究[J].岩土工程学报,2015,37(4):727-733.(XI Jingyi,CHEN Zhonghui,ZHU Dijie,et al.Stress intensity factors and initiation of unequal collinear cracks in rock[J].Chinese Journal of Geotechnical Engineering,2015,37(4):727-733.(in Chiniese))
[15]张显余,付长安.断裂问题研究中裂尖塑性区的影响及处理原则[J].飞机设计,2010,30(1):34-37.(ZHANG Xianyu,FU Zhang’an.Effect of plastic zone around crack-tip and its criterion in fracture analysis[J].Aircraft Design,2010,30(1):34-37.(in Chiniese))
[16]OCHI Y,ISHII A,SASAKI S K.An experimental and statistical investigation of surface fatigue crack initiation and growth[J].Fatigue&Fracture of Engineering Materials&Structures,1985,8(4):327-339.