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斜裂纹是工程结构部件的“常见病”、“多发病”,它的受力状态是混合型的。这种混合型裂纹的扩展问题近年来已成为断裂力学的重要研究课题之一。本文从宏观断裂力学和微观物理模型相结合的观点,把宏观裂纹看成是微观位错的塞积,把加到裂纹尖端上的扩展力看成和加到塞积位错上的力一样;提出直接把裂纹尖端当作弹性场中的奇点模型来处理。本文应用能量动量张量方法得到了混合型裂纹扩展力的解析表达式,并提出了新的断裂判据。应用此模型进行的计算指出:混合型裂纹特征积分I_3≠0是偏离正常方向扩展的标志,其断裂偏离角α_0=arctg(-I_3/J),裂纹扩展力为Fl_0=J sec α_0。应用此式对单轴拉伸斜裂纹和压力容器斜裂纹进行了计算,所得结果和实验值相近。本文还将此结果和应变能密度因子等判据的结果进行了比较。
Oblique cracks are structural components of the “common disease”, “frequently-occurring disease,” its stress state is mixed. In recent years, the problem of this kind of mixed crack propagation has become one of the important research topics in fracture mechanics. In this paper, macroscopic cracks are regarded as the product of micro dislocations from the viewpoint of the combination of macroscopic fracture mechanics and microscopic physical model, and the expansive force added to the crack tip is regarded as the same as the force applied to the plug fault. It is proposed to treat the crack tip directly as a singularity model in the elastic field. In this paper, the analytic expression of the mixed crack propagation force is obtained by using the energy momentum tensor method, and a new fracture criterion is proposed. The calculation using this model points out that the characteristic integral I_3 ≠ 0 of the mixed crack is a sign deviating from the normal direction, and the fracture departure angle α_0 = arctg (-I_3 / J) and the crack propagation force is Fl_0 = J sec α_0. Applying this formula to calculate the oblique crack of uniaxial tension oblique pressure vessel and pressure vessel, the result is similar to the experimental value. This paper also compares the result with the criterion of strain energy density factor.