纯弯曲矩形截面梁Ⅰ型单边裂纹端部的应力应变场及裂纹失稳扩展临界应力的计算
Stress-Strain Field near Crack Tip and Calculation of Critical Stress of Crack Propagation in a Pure Bending Beam of Rectangular Section with One-Sided Mode I Crack
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摘要: 本文应用文[1]的分析方法,研究了纯弯曲矩形载面梁Ⅰ型单边裂纹端部的应力应变场,给出了裂纹尖端的应力应变分量和计算裂纹端部弹性变形区和变形强化区宽度的公式以及计算裂纹失稳扩展临界应力的方程组。最后用计算实例对裂纹失稳扩展临界应力方程组进行了验证,最大误差不超过0.18%.Abstract: This paper studies the stress-sirain field near crack tip in a pure bending beam of rectangular section with one-sided mode I crack by the analytic method of Ref [1],then it gives the stress and strain components at the crack tip when the crack propagates and further it obtains the formulas of calculating the elastic deformed area width, the deformed intensity, area width and the equation groups of calculating the critical stress of crack propagation, last the equation group of calculating critical stress of crack propagation is verified by calculating instance. The maximum error is 0.18%.
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[1] Liu Hanchi, Stress-strain field near crack tip and calculation of critical stress of crack propagation in a single tension finite width thin sheet with central mode I piercing crack, Advances in Applied Mathematics and Mechanics in China, 4,IAP(1992), 171-184. [2] Liu Hanchi, Stress-strain Geld near crack tip and calculation of critical stress of crack propagation in a single tension finite sheet with one-side mode I crack, Advances in Applied Mathematics and Mechanics in China, 4, IAP (1992), 135-146. [3] 陈境等.K工程断裂力学》，国防工业出版社(1977). [4] 单辉祖主编.《材料力学教程》，国防工业出版社(1965). [5] 工程材料实用手册编辑委员会，《工程材料实用手册》.1，中国标准出版社(1988). -
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