无限体中受均匀拉伸的椭圆片状裂纹周界上各点应力强度因子的讨论
Discussion on the SIF for Points on Border of Elliptical Flat Crack inside Infinite Solid under Uniform Tension
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摘要: 本文从Green-Sneddon解[1]的裂纹表面位移场结果出发,应用坐标变换推出了无限体中受均匀拉伸的椭圆片状裂纹周界上任意点、任意方位上的应力强度因子K1(x1,z1,α)表达式.从而补充了Irwin的工作[3],证明了对椭圆周界上某一确定点而言,沿法线平面上所得的应力强度因子为最大值.并指出了一些著作中,对[3]中有关内容所作的错误解释.还推荐了一个更为直观的以极角来表示的椭圆周界上任意点处的应力强度因子表达式.Abstract: Using the results of crack surface displacement field in Green-Sneddon's solution[1] and coordinate transformation, this paper has derived an expression K1(x1,z1,a) for SIF at any point and at any orientation on the border of elliptical flat crack inside infinite solid under uniform tension. As a complement of Irwin's work[3], it is shown that for any pointed point on the elliptical border the SIF defined on normal plane takes the maximum value. And it should be pointed out that in some works some idea concerning Irvin's contents is open to question. An expression K1 in terms of polar angle which is more intuitional than centrifugal angle is proposed for SIF at any point on the elliptical border.
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[1] Green,A.E.,Sneddon.I.N,,The stress distrib utioa in the neighborhood of a flat elliptic crack in an elastic solid,Proc,Camb.Phil.Soc,,46(1950).159. [2] 陈跪等编著,《工程断裂力学》(上册)国防工业出版社,(1977).28-29. [3] Irwin,G,R Crack-estettsion force for a part-through crack in a plate,,J,Appl,Mech,,29,4,Dec,(1962),65I-654. [4] 通用机械研究所等编,《压力容器国外技术进展》(上册),通用机械研究所出版,(1974) 196-199. [5] 老亮,椭圆裂纹K1式中常见的一些错误,上海力学,2.2,(1981).58-59. [6] Broek,D.Elementarg Engineering Fracture Mechanics,Sijthoff & Noordhoff,(1978).2nd.Ed,81. -
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