摘要
用有裂纹与无裂纹时的远场J积分之差分析了无限大平面中心裂纹的能量释放率,材料形式分别为均匀和层状材料,裂纹垂直于拉伸方向,层状材料界面平行于拉伸方向.有裂纹与无裂纹J积分之差表示载荷作用下的无裂纹材料引入裂纹所导致的J积分变化.对于均匀材料无限大平面中心裂纹,能量释放率等于对称轴处应变能密度释放量沿对称轴的积分,其值等于无裂纹时的应变能密度乘以一个以裂纹半长为半径的圆周长.对于层状材料无限大平面中心裂纹,能量释放率等于对称轴处应变能密度释放量沿对称轴的积分减去界面J积分的改变量.
The difference between the J-integrals with and without a crack along a far-field contour was considered to analyze the energy release rate of the crack extension in an infinite plane. Two material cases were studied： a homogeneous material and a layered material. The constant displacement load was applied far from the crack,the crack was assumed to be perpendicular to the load,and the interfaces of the layered material were parallel to the load. The difference between the J-integrals with and without a crack represents the change of the far-field J-integral when a crack is introduced into the loaded material. For the central crack in a homogeneous infinite plane with a unit thickness,the energy release rate is the integral of the released strain energy density along the symmetry axis,and equals the product of the strain energy density without a crack and the perimeter of a circle,where the diameter of the circle is the crack length.For the central crack in an infinite plane of the layered material with a unit thickness,the energy release rate of crack extension equals the integral of the released strain energy density along the symmetry axis minus the change of the interface J-integral.
作者
陈昌荣
CHEN Changrong(School of Air Transportation,Shanghai University of Engineering Science,Shanghai 201520,P.R.China)
出处
《应用数学和力学》
CSCD
北大核心
2018年第10期1172-1179,共8页
Applied Mathematics and Mechanics
基金
国家自然科学基金(51175321)~~
作者简介
陈昌荣（1964-），男，教授，博士（E-mail：13761742152@163．com）．
