钢化真空玻璃球形支撑的玻璃压痕应力场理论及分析

硅酸盐通报 ›› 2021, Vol. 40 ›› Issue (11): 3822-3828.

钢化真空玻璃球形支撑的玻璃压痕应力场理论及分析

蔺海晓, 刘志红, 岳高伟

河南理工大学土木工程学院,焦作 454000

收稿日期:2021-06-08 修回日期:2021-07-19 出版日期:2021-11-15 发布日期:2021-12-08
通讯作者: 岳高伟,博士,教授。E-mail:mxlygw@163.com
作者简介:蔺海晓(1978—),男,副教授。主要从事玻璃的研究。E-mail:lhxtmxy@163.com
基金资助:
河南省力学一级学科资助项目(教高[2018]119号)

Theory and Analysis of Glass Indentation Stress Field of Tempered Vacuum Glass with Spherical Support

LIN Haixiao, LIU Zhihong, YUE Gaowei

School of Civil Engineering, Henan Polytechnic University, Jiaozuo 454000, China

Received:2021-06-08 Revised:2021-07-19 Online:2021-11-15 Published:2021-12-08

摘要/Abstract

摘要： 针对钢化真空玻璃球形支撑物对玻璃压痕的应力场分布问题,采用接触力学,对Hertzian压痕方程进行了修正,推导了三维应力场方程,同时,对完全发展的锥形裂纹的应力强度因子进行了数值求解。结果表明,在球体与玻璃接触区域内,所有的主应力都是压应力,主应力σ₁导致了裂纹的萌生,而主应力σ₂形成了环形裂纹。与玻璃表面正交的最小主应力从接触边缘向外偏离,形成的近似平行的曲线即为锥形裂纹的形状,而最大拉应力总是垂直于这些曲线。因此,在最大主拉应力的作用下,球体加载后裂纹遵循最小主应力的轨迹。裂纹尖端的应力强度因子决定了断裂韧性,随着裂纹的扩展,应力强度因子减小,在离表面一定距离后,应力强度因子达到临界值,裂纹停止。不同压痕载荷下的归一化应力强度因子是一组具有相似形状的曲线。

关键词: 钢化真空玻璃, 支撑物, 压痕应力场, 断裂韧性, 应力强度因子

Abstract: In view of the stress field distribution of glass indentation caused by the spherical support of tempered vacuum glass, the Hertzian indentation equation was modified by using contact mechanics, and the three-dimensional stress field equations were derived. At the same time, the stress intensity factor of fully developed conical crack was numerically solved. The numerical results show that all the principal stresses inside the contact area between the sphere and the glass are compressive. The principal stress σ₁ leads to the initiation of the crack, while the principal stress σ₂ forms the annular crack. The minimum principal stress is perpendicular to the glass surface, and then deviates from the contact edge, which forms the approximately parallel curves. And the maximum tensile stress is always perpendicular to these curves. Therefore, under the action of the maximum principal tensile stress, the crack follows the trajectory of the minimum principal stress. The stress intensity factor at the crack tip determines the fracture toughness. With the crack propagation, the stress intensity factor decreases. After a certain distance from the surface, the stress intensity factor reaches the critical value and the crack stops. The normalized stress intensity factor under different indentation loads is a set of curves with similar shapes.

Key words: tempered vacuum glass, support, indentation stress field, fracture toughness, stress intensity factor

中图分类号:

TQ171

蔺海晓, 刘志红, 岳高伟. 钢化真空玻璃球形支撑的玻璃压痕应力场理论及分析[J]. 硅酸盐通报, 2021, 40(11): 3822-3828.

LIN Haixiao, LIU Zhihong, YUE Gaowei. Theory and Analysis of Glass Indentation Stress Field of Tempered Vacuum Glass with Spherical Support[J]. BULLETIN OF THE CHINESE CERAMIC SOCIETY, 2021, 40(11): 3822-3828.

参考文献

[1] 刘小根,包亦望,王秀芳,等.安全型真空玻璃构件功能一体化优化设计[J].硅酸盐学报,2010,38(7):1310-1317.
LIU X G, BAO Y W, WANG X F, et al. Optimization design of structural and function integration for safe vacuum glazing[J]. Journal of the Chinese Ceramic Society, 2010, 38(7): 1310-1317 (in Chinese).
[2] 唐健正,李洋,李楠.半钢化真空玻璃:高效节能玻璃研发的新突破[J].真空,2010,47(4):22-26.
TANG J Z, LI Y, LI N. Heat-strengthened vacuum glazing: a breakthrough in high energy efficiency glass[J]. Vacuum, 2010, 47(4): 22-26 (in Chinese).
[3] 郭卫,童树庭,朱雷波.玻璃钢化工艺过程与钢化应力的研究[J].建筑材料学报,2005,8(1):100-104.
GUO W, TONG S T, ZHU L B. Study of temper processing and temper stress in glass[J]. Journal of Building Materials, 2005, 8(1): 100-104 (in Chinese).
[4] BALAN B A, ACHINTHA M. Assessment of stresses in float and tempered glass using eigenstrains[J]. Experimental Mechanics, 2015, 55(7): 1301-1315.
[5] 程金树,朱连英,楼贤春.玻璃钢化方法的探讨[J].材料导报,2012,26(s2):135-137+162.
CHENG J S, ZHU L Y, LOU X C. Method discussion of glass tempering[J]. Materials Review, 2012, 26(s2): 135-137+162 (in Chinese).
[6] 李彦兵,岳高伟.钢化真空玻璃支撑点的排布方式[J].材料科学与工程学报,2016,34(6):955-959+966.
LI Y B, YUE G W. Support point arrangement of tempered vacuum glass[J]. Journal of Materials Science and Engineering, 2016, 34(6): 955-959+966 (in Chinese).
[7] 缪宏,张瑞宏,左敦稳,等.支撑柱对真空平板玻璃静态特性的影响[J].建筑材料学报,2013,16(1):153-158.
MIAO H, ZHANG R H, ZUO D W, et al. Effect of shore on static characteristics of vacuum plate glass[J]. Journal of Building Materials, 2013, 16(1): 153-158 (in Chinese).
[8] 张瑞宏,高建和,顾乡,等.真空平板玻璃支撑应力实验研究[J].真空科学与技术学报,2006,26(6):455-458.
ZHANG R H, GAO J H, GU X, et al. Experimental study on the braced stress of the vacuum glazing[J]. Chinese Journal of Vacuum Science and Technology, 2006, 26(6): 455-458 (in Chinese).
[9] 邹惠芬,王雪峰,孙阳,等.真空玻璃支撑柱处玻璃的应力分析[J].沈阳建筑大学学报(自然科学版),2010,26(2):355-359.
ZOU H F, WANG X F, SUN Y, et al. Stress analysis of vacuum glazing in the support pillar[J]. Journal of Shenyang Jianzhu University (Natural Science), 2010, 26(2): 355-359 (in Chinese).
[10] 冯毅,申惠东.真空绝热玻璃应力理论分析及数值计算[J].低温与超导,2009,37(7):78-80.
FENG Y, SHEN H D. Theoretical analysis and numerical calculation on the stress on vacuum insulation glass[J]. Cryogenics and Superconductivity, 2009, 37(7): 78-80 (in Chinese).
[11] 刘小根,包亦望,许海凤,等.真空玻璃支撑压痕控制准则[J].材料科学与工艺,2010,18(6):878-882.
LIU X G, BAO Y W, XU H F, et al. Propagation mechanism and control criterion of fracture indentation in vacuum glazing[J]. Materials Science and Technology, 2010, 18(6): 878-882 (in Chinese).
[12] 刘小根,万德田,孙景春,等.支撑物缺位对真空玻璃应力和变形影响分析[J].门窗,2016(4):42-45.
LIU X G, WAN D T, SUN J C, et al. Analysis of the influence of support absence on the stress and deformation of vacuum glass[J]. Doors & Windows, 2016(4): 42-45 (in Chinese).
[13] 李彦兵,岳高伟.支撑点间距对钢化真空玻璃力学特性的影响[J].硅酸盐通报,2016,35(4):1172-1176+1183.
LI Y B, YUE G W. Mechanical properties of tempered glass vacuum with different support point spacing[J]. Bulletin of the Chinese Ceramic Society, 2016, 35(4): 1172-1176+1183 (in Chinese).
[14] LOUAPRE D, BREDER K. Hertzian indentation stress field equations[J]. International Journal of Applied Ceramic Technology, 2015, 12(5): 1071-1079.
[15] MOUGINOT R, MAUGIS D. Fracture indentation beneath flat and spherical punches[J]. Journal of Materials Science, 1985, 20(12): 4354-4376.
[16] ZENG K, BREDER K, ROWCLIFFE D J. The Hertzian stress field and formation of cone cracks: I. Theoretical approach[J]. Acta Metallurgica et Materialia, 1992, 40(10): 2595-2600.