二维位错裂纹的稳定性分析

在已有的一维穿透位错裂纹模型及能量计算的基础上，将其推广为二维椭圆盘状裂纹模型，并计算了其能量．根据能量平衡原理，给出了位错裂纹模型的裂纹平衡尺寸、裂纹扩展临界应力．并与不考虑位错影响的宏观断裂力学中Ⅰ型穿透裂纹的Ｇｒｉｆｉｔｈ解及椭圆盘裂纹的Ｇｒｉｆｉｔｈ解加以比较．给出的位错裂纹模型解在位错数目ｎ＝０时与宏观断裂力学解一致

STABILITY ANALYSIS OF A TWO-DIMENTIONAL DISLOCATION CRACK MODEL

Based on the one-dimensional dislocation crack model and the energy calculations, a two-dementional dislocation crack model is presented,which is an elliptical crack caused by the dislocation pile-up groups.The total potential energy of this model is obtained. Following the principle of conservation of energy, the equilibrium length of the crack and the critical stresses for growing cracks are given. All results are compared with Griffith's solutions for Mode-I through crack and the elliptical embedded crack, which get in macroscopic fracture mechanics.When the number of dislocation tends to zero, the results obtained in this paper are reduced to that of macroscopic fracture mechanics.