Ⅰ型裂纹的连续位错模型

An Analysis of Mode Ⅰ Crack Based on the Continuous Dislocation Model

用连续位错分布模拟裂纹和裂尖塑性区，建立了中心对称有限长Ⅰ型裂纹的无位错区（ＤＦＺ）模型．对一个主裂纹和四个对称滑移带情形推导出基本方程．计算表明，随着外加应力的增大，位错密度增大，位错活动明显加剧，在滑移带，位错密度在紧接ＤＦＺ的塑性区中某点达最大。

A DFZ model for mode Ⅰ crack of centrosymmetry and finite length is developed on the basis of the continuous model of dislocation. The crack and the plastic zone of the crack tip are simulated by continuous distribution of dislocation. A simultaneous set of singular integral equations are derived for the case where there are a crack and two pairs of symmetrical slip bands. Numerical results show that an increase in the externally applied stress will increase the dislocation density and intensify the dislocation activities. In the slip bands, the dislocation density reaches a maximum at a certain point near the plastic portion of DFZ. For c/e =100, the distribution of dislocation is very close to the case of semi infinite crack when c→∞ . According to the DFZ condition derived, the measurement of experimental parameters is simplified.