Analytical solutions of cracks emanating from an elliptical hole under shear

Based on the complex variable method, the analytical solutions of stress functions and stress intensity factors（SIFs） are provided for the plane problem of two collinear edge cracks emanating from an elliptical hole in an infinite plate under shear. The stress distribution along the horizontal axis is given in graphical forms, which conforms to Saint-Venant＇s principle. The influences of crack length and ellipse shape on the stress intensity factors are evaluated. Comparing the analytical solutions with finite element method（FEM） results shows good coincidence. These numerical examples show that the present solutions are accurate.     

Thermal Stresses and Cracks During the Growth of Large-sized Sapphire with SAPMAC Method

本文利用有限元法对冷心放肩微量提拉法(SAPMAC)生长大尺寸蓝宝石单晶过程中的热应力进行了模拟计算,应用临界缺陷理论解释了裂纹的萌生与扩展机理。研究表明,晶体内的热应力主要与晶体生长速率,环境温度和结晶取向有关;较大热应力多出现在结晶界面,放肩、收尾以及直径急剧变化等位置;最大热应力总是出现在籽晶与新生晶体的界面附近。裂纹将在临界缺陷位置产生,并在应力作用下沿a或m面扩展。计算结果与实验结果基本吻合,通过晶体生长系统和生长工艺的改进,对晶体的开裂问题得到了有效的抑制。