Fracture mechanics of an anisotropic elastic plane and its application

主要研究各向异性弹性体中裂纹、缺陷等原因引起的断裂。在本研究中，考虑了一个正交各向异性弹性平面，它与弹性模量之间存在一定的关系（称为准正交各向异性平面）。采用复应力函数和有理映射函数，分析了外边值问题。得到了应力分量和应力强度因子。然后得到了该应力强度因子与由仿射变换得到的各向同性平面应力强度因子之间的关系。我们可以利用已经得到的各向同性弹性平面的结果，这是非常有用的，因为各向同性弹性平面的许多应力强度因子已经得到。在正交各向异性平面主轴方向与裂纹轴线方向不同的情况下，得到了应力强度因子之间的关系。导出了准正交各向异性平面上混合边值问题的解析解，并分析了半平面边缘有细刚性线夹杂的半平面。由于夹杂体尖端存在一个奇异点，因此定义了应力强度因子。如果得到了仿射变换得到的相同形状的各向同性弹性平面的应力强度因子，则利用该结果可以得到应力强度因子。导出了准弹性平面和正交各向异性弹性平面模量之间的关系。

The main study is that of the fracture due to causes of existence of such as crack and defect in an anisotropic elastic body. For this study, an orthotropic elastic plane was considered, which has a relation among the elastic modulus ( called the quasi orthotropic plane ). Complex stress functions and a rational mapping function were used and an external boundary value problem was analyzed. The stress components and stress intensity factors were obtained. Then a relation between this stress intensity factors and those of the isotropic plane obtained by the Affinetransformation was obtained. We can use the results of the isotropic elastic plane which have already been obtained, and this is very useful because many stress intensity factors of the isotropic elastic plane have been obtained. Also a relation among the stress intensity factor was obtained in case that the directions of the principal axis of the orthotropic plane and of the crack are different.The analytical solution of the mixed boundary value problem on the quasi orthotropic plane was derived, And the half plane with a thin rigid line inclusion on the edge of the half plane was analyzed. Since there is a singularity at the tip of inclusion, the stress intensity factor was defined. If those of the isotropic elastic plane for the same shape obtained by the Affine transformation have been obtained, we use the results and can obtain the stress intensity factors. A relation among the moduli of the quasi and orthotropic elastic planes also was derived.