高温循环载荷下石英坩埚气孔-裂纹应力强度因子数值模拟

摘要/Abstract

摘要： 连续拉晶用石英坩埚的内壁会随拉晶次数的增多而形成更多的气泡,易在晶体中产生位错和侵蚀性硅熔体,导致坩埚随时间溶解和腐蚀等。为研究侵蚀性硅熔体与气泡相互作用对坩埚的影响,研究人员期望对石英坩埚的性能进行原位观察,然而,单晶炉内的极端高温环境使得很难通过实验手段对其内部进行研究。本文以石英坩埚内表面气孔-裂纹为研究对象,采用有限元模拟获得了高温循环载荷下石英坩埚不同气孔形态、裂纹形状和裂纹倾斜角度的各拉晶阶段应力强度因子(K_Ⅰ、K_Ⅱ、K_Ⅲ),分析了总应力强度因子的分布规律。结果表明:随着裂纹倾斜角的增加,K_Ι值呈现逐渐减小的趋势,K_Ⅲ值呈现先增大后减小的趋势,且K_Ⅲ值沿倾斜角45°对称;随气孔深径比增大,K_Ι值呈现减小趋势,且减小速率以深径比等于1为界有明显的增大,K_Ⅲ«K_Ι,说明裂纹主导形式为Ⅰ型;裂纹形状比对K_Ι或K_Ш值影响显著,形状比越小,裂纹尖端应力强度因子值越大;当倾斜角为0°时,总应力强度因子K值最大,此时裂纹扩展趋势最强,对石英坩埚危害最高;此外,连续拉晶下放肩阶段的总应力强度因子总是大于等径、收尾、冷却阶段。仿真结果对实际生产有一定的理论指导意义。

关键词: 石英坩埚, 气孔, 深径比, 裂纹形状, 应力强度因子, 有限元模拟

Abstract: The inner wall of the quartz crucible for continuous Czocharlski will form more bubbles with the increase of Czocharlski times, and it is easy to generate dislocations in the crystal and the erosive silicon melt, which will cause the crucible to dissolve and corrode over time. In order to study the effect of the interaction of erosive silicon melt with bubbles on the crucible, in situ observations of the performance of quartz crucibles are expected. However, the extremely high temperature environment inside single crystal furnaces makes it difficult to investigate their interiors experimentally. In this paper, the pore-crack on the inner surface of the quartz crucible are taken as the research object, and the finite element simulation is used to obtain the stress intensity factor values of different pore shapes, crack shapes and crack inclination angles of the quartz crucible under high temperature cyclic loading at different Czocharlski stages. The results show that with the increase of the crack inclination angle, the K_Ι value shows a trend of gradually decreasing, the K_Ⅲ value shows a trend of first increasing and then decreasing, and the K_Ⅲ value is symmetrical distributed along 45°; furthermore, with the increase of the pore depth/diameter ratio, K_Ι value shows a decreasing trend, and the rate of reduction when the depth/diameter ratio is equal to 1 as the boundary has a significant increase, K_Ⅲ is much smaller than K_Ι value, indicating that the dominant form of cracking is type Ⅰ; the crack shape ratio has a significant impact on the value of K_Ι or K_Ⅲ, and the smaller the shape ratio, the greater the value of the stress intensity factor at the crack tip; when the inclination angle is 0°, the total stress intensity factor K value is the largest, which will make the crack most likely to expand and the most harmful to the quartz crucible. Finally, in the case of continuous Czocharlski, the total stress intensity factor of the crown growth process is always greater than that of the equal diameter growth, cone and cooling growth process. Simulation results bring certain theoretical guiding significance for production.

Key words: quartz crucible, pore, depth/diameter ratio, crack shape, stress intensity factor, finite element simulation

中图分类号:

O782
TB321

赵国彦, 瞿立, 李进, 马润. 高温循环载荷下石英坩埚气孔-裂纹应力强度因子数值模拟[J]. 人工晶体学报, 2023, 52(3): 493-500.

ZHAO Guoyan, QU Li, LI Jin, MA Run. Numerical Simulation of Stress Intensity Factor for Pore-Crack in Quartz Crucible under High Temperature Cyclic Loading[J]. JOURNAL OF SYNTHETIC CRYSTALS, 2023, 52(3): 493-500.

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