正交异性介质中定常扩展裂纹尖端应力、应变场

STRESS AND STRAIN FIELDS NEAR A STEADY GROWTH CRACK TIP IN AN ORTHOTROPIC SOLID

本文将正交异性材料视为理想弹塑性材料,采用R.Hill屈服准则及与之相关的流动法则,推导了平面应变Ⅰ型定常扩展裂纹的基本方程。在假定材料不可压缩的条件下,获得了泊桑系数间的相互关系v_(31)+v_(32)=1,进一步还假定了v_(31)=G/(F+G),v_(32)=F/(F+G),因而获得了问题的分析解。结果表明,应变场具有ln(A/r)的奇异性。

By applying R. Gill yield criterion for orthotropic materials regarded as elastic perfectly-plastic, the foundation formulae of the steady growth crack of Mode Ⅰ under the plane strain condition are deduced. On the assumption of imcompressibility of the materials the relation of Poison ratios v_(31)+v_(32)=1 is obtained, further it can be assumed that v_(31)=G/(F+G) and v_(32)=F/(F+G). Therefore, the problem can be solved analytically. The result shows that there is singularity of ln(A/r) for the strain field.