关于平面断裂中的J积分
On J Integrals in the Plane Fracture
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摘要: 本文利用复变函数和微积分的理论讨论线弹性各向同性均匀材料板和正交异性复合材料板Ⅰ、Ⅱ型裂纹尖端附近的J积分,得到了下列结果: (1)将各个J积分统一化为对坐标的曲线积分的标准形式:J=∫rP(x,y)dx+Q(x,y)dy (2)证明了各个J积分的路径无关性. (3)推出了各个J积分的具体计算公式.Abstract: In this paper, we discuss J-integrals near models Ⅰ and Ⅱ crack tips for the plates of linear-elastic isotropic homogeneous material and orthotropic composite material, using the theories of complex function and calculus, and obtain the result as follows:(1) The various J-integrals are transformed into standard form of line integrals with respect to coordinates: J=∫rp(x,y)dx+Q(x,y)dy (2) Independence of path of the various J-integrals is proved.(3) Computing formulae of J-integrals are derived.
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[1] 褚武扬编著,《断裂力学基础》,科学出版社(1979) 265-267. [2] Corten,H.T.,Fracture Mechanics of Composites,Fracture,Ed.H.Liebowitz,7,Academic Press,New York(1972),690-691,695-703. [3] 李濒、陈树坚、郭碧坚,《断裂力学与复合材料力学》,华中工学院出版社(1986).337-348. [4] 杨维阳、张少琴,关于复合材料单层板I型裂纹尖端应力场的探讨,太原重型机械学院学报,7, 3(1986), 46-53. [5] 杨维阳、张少琴,关于复合材料单层板I型裂纹尖端附近应变场与位移场的探讨,太原重型机械学院学报,8. 1(1987), 77-87. [6] 杨维阳、张少琴,复合材料单层板I型裂纹尖端附近应力场、应变场和位移场的解析解,太原重型机械学院学报,9, 2 (1988), 46-58. [7] Rice,J.R.,A path-independent integral and the approximate analysis of strain concentrations by notches and cracks,J.Applied Mechanics,35,2(1968).379-386. -
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