一维六方准晶非周期平面内中心开口裂纹的平面热弹性问题
The Plane Thermoelastic Problem of a Central Opening Crack in the 1D Hexagonal Quasicrystal Non-Periodic Plane
赵雪芬 1卢绍楠 2马园园 2张保文2
作者信息
- 1. 宁夏大学 信息工程学院,银川 750021;宁夏大学新华学院,银川 750021
- 2. 宁夏大学 数学统计学院,银川 750021
- 折叠
摘要
考虑裂纹内部介质的热传导率,研究了一维六方准晶非周期平面内含中心开口裂纹的平面热弹性问题.利用Fourier积分变换技术,得到了热应力、裂纹尖端处的热应力强度因子和应变能密度因子的封闭解.数值结果讨论了裂纹内部介质的热传导率、外载荷及声子场-相位子场耦合系数对热应力强度因子和应变能密度因子的影响.结果表明,声子场-相位子场耦合系数对裂纹扩展影响较大.当声子场载荷较小或热流密度较大时,裂纹不易扩展,热流密度在裂纹尖端处会出现集中热效应.随着裂纹内部介质热传导率的增大,热流密度逐渐增加而热应力强度因子逐渐减小.该文所得结果为准晶热力学性质的实际应用提供了理论依据,进而可用于优化准晶元器件的设计和制备.
Abstract
Considering the thermal conductivity of the medium inside the crack,the plane thermoelastic prob-lem of the 1D hexagonal quasicrystal with a central open crack in an aperiodic plane,was studied.With the Fourier integral transformation technology,the closed form solutions of thermal stresses,thermal stress inten-sity factors and strain energy density factors were obtained.Numerical examples were used to analyze the effects of the thermal conductivity,the external load,and the phonon field-phason field coupling coefficient on the thermal stress intensity factor and the strain energy density factor at the crack tip.The results indicate that,the heat flux density gradually increases but the thermal stress intensity factor gradually decreases with the ther-mal conductivity.The phonon field-phason field coupling coefficient has a significant impact on the crack propa-gation.When the phonon field load is relatively small or the heat flux density is relatively high,the crack is not easy to propagate.The heat flux density exhibits a concentration effect at the crack tip.The work provides a theoretical basis for the application of thermodynamic properties of quasicrystals,and the optimization of de-sign and preparation of quasicrystal components.
关键词
一维六方准晶/中心开口裂纹/Fourier积分变换/热应力强度因子/应变能密度因子Key words
1D hexagonal quasicrystal/central opening crack/Fourier integral transformation/thermal stress intensity factor/strain energy density factor引用本文复制引用
基金项目
国家自然科学基金(12062021620620571226203312062022)
出版年
2024
国家科技期刊平台
NSTL
万方数据