复合材料平面断裂中的J积分
On J-lntegrals in the Plane Fracture of Composite Materials
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摘要: 本文采用复变函数方法,首先将裂纹尖端应力和位移代入J积分的一般公式得到了线弹性正交异性复合材料单向板复合型裂纹尖端的J积分的复形式,其次证明了该J积分的路径无关性,最后推出了该J积分的计算公式.作为特例,给出了线弹性正交异性复合材料单向板Ⅰ,Ⅱ型裂纹尖端的J积分的复形式,路径无关性和计算公式.Abstract: By using a complex function method in this paper, the complex form of J-integral of mixed mode crack tip for unidirectional plate of linear-elastic orthotropic composites is obtained first by substituting crack tip stresses and displacements into general formula of J-integral. And then, the path-independence of this J-integral is proved. Finally, the computing formula of this J-integral is derived. As special examples, the complex forms, path-independence and computing formulae of J-integrals of mode Ⅰ and mode Ⅱ crack tips for unidirectional plate of linear-elastic orthotropic composites are given.
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Key words:
- J-integral /
- crack tip /
- composite material /
- complex function method
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[1] Sih, G.C., P.C. Paris, and G.R. Inwin, On cracks in rectilinearly anisotropic bodies, International Journal of Fracture Mechanics, 1(1965), 189-203. [2] Sih, G.C.,ed, Mechanics of Fracture, Vol. 6, Crack in Compositc Materials, Martinus Nijhoff Publishers, Hague, (1981). [3] Rice, J.R., A path-independent integral and the approximate analysis of strain concentrations by notches and cracks, Journal of Applied Mechanics, 35 (1986), 379-386. [4] 杨维阳、张少琴,线弹性正交异性复合材料Ⅰ,Ⅱ型裂纹尖端的J积分,应用数学和力学, 11(7)(1990), 643-851. [5] 杨维阳、张少琴、陈华才,关于平面断裂中的J积分,应用数学和力学.11(6)(1990), 555-564. [6] Jiang Bo-zeng, Yang Wei-yang and Zhang Shao-qin,A pplication of the J-integral to mined mode fracture analysis of orthotropic composites,Engineering Fracture Mechanics, 36(3) (1990), 507-514, [7] Sih, G.C., ed, Mechanics of Fracture, Vol. 1, Methods of Analysis and Solutions of Crack Problems, Noordhoff International Publishing, Leyden, 1973. [8] Liebowitz, H. ed, Fracture, Vol.2, Mathematical Fundamentals, Academic Press, New York,1968. -
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