Yang Wei-yang, Zhang Shao-qin, Jia Yuan-duo. On J-lntegrals in the Plane Fracture of Composite Materials[J]. Applied Mathematics and Mechanics, 1992, 13(3): 263-269.
 Citation: Yang Wei-yang, Zhang Shao-qin, Jia Yuan-duo. On J-lntegrals in the Plane Fracture of Composite Materials[J]. Applied Mathematics and Mechanics, 1992, 13(3): 263-269.

# On J-lntegrals in the Plane Fracture of Composite Materials

• Publish Date: 1992-03-15
• 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.
•  [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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