层状非均匀材料边裂纹引起的J积分变化量分析

Analysis of J-integral changes caused by an edge crack in the layered material

均匀材料无裂纹时沿封闭路径的J积分为零,层状非均匀材料无裂纹时沿封闭路径的J积分通常不为零且与路径相关。在位移载荷保持不变条件下引入裂纹会使J积分改变,本文分析引入裂纹所导致的远场J积分变化量,即有裂纹时与无裂纹时沿同一远场路径的J积分之差,其值等于裂尖J积分与界面J积分变化量之和。对于层状非均匀材料,虽然无裂纹时和有裂纹时的远场J积分、界面J积分都与路径相关,但当积分路径远离裂尖后,有裂纹与无裂纹时的远场J积分之差、界面J积分之差与路径无关,引入裂纹所引起的远场J积分变化量等于边界应变能密度释放量沿边界的积分。对于均匀材料半无限大平面的边裂纹,裂纹能量释放率等于无裂纹时应变能密度与8倍裂纹长度的乘积;对于层状材料的边裂纹,裂纹能量释放率等于应变能密度释放量沿边界的积分减去界面J积分变化量。

The J-integral along a closed contour is zero in a homogeneous material without cracks, while in a layered material the J-integral is not zero and becomes path-dependent. The J-integral changes when a crack is introduced into a material under loading. In this paper, the difference of the far-field J-integral with and without a crack is analyzed. It equals to the crack tip J-integral plus the difference of the interface J-integral with and without a crack. In a layered material the far-field J-integrals and the interface J-integrals are path-dependent. However, when the far-field contour is far from the crack tip, the difference of the far-field J-integral with and without a crack becomes path-independent and equals to the integration of the released strain energy density along the boundary. For an edge crack in a homogeneous semi-infinite plate with unit thickness, the energy release rate of crack equals to eight times the product of the crack length and the strain energy density at the boundary when there is no crack. For an edge crack in a layered material, whether the energy release rate of crack extension is higher or lower than the integration of the released strain energy density along the boundary depends on the changes of the interface J-integrals when a crack is introduced into the material.