摘要
研究了一维六方准晶中纳米尺度开裂孔洞的Ⅲ型断裂力学问题.基于复变弹性理论和表面弹性理论获得了考虑表面效应时椭圆孔边裂纹的应力场、应力强度因子和能量释放率的解析表达;讨论了缺陷尺寸、裂纹/孔洞比、耦合系数和施加载荷对应力强度因子和能量释放率的影响.研究表明:考虑表面效应且缺陷的尺寸在纳米尺度时,声子场和相位子场的无量纲应力强度因子以及无量纲能量释放率具有明显的尺寸依赖;裂纹相对尺寸较小时,表面效应对声子场和相位子场的无量纲应力强度因子影响较小;纳米尺度时无量纲能量释放率随耦合系数的增加而增大;耦合系数一定时,无量纲能量释放率受到椭圆孔尺寸影响;随着声子场载荷的增大,无量纲能量释放率先减小后增加,最后趋于稳定;无量纲能量释放率随相位子场载荷的增大单调减小,非常小和非常大的声子场载荷(或相位子场载荷)屏蔽了相位子场载荷(或声子场载荷)的影响.
The type III fracture mechanics of a nanoscale cracked elliptical hole in one-dimensional hexagonal quasicrystals is investigated.Based on the complex elasticity theory and the surface elasticity theory,the analytical expressions of stress fields,stress intensity factors and energy release rate of an elliptical hole with edge crack considering surface effects are presented,and the degraded results are consistent with those from the literature.The influences of defect size,crack/hole ratio,coupling coefficient and applied loads on stress intensity factors and energy release rate are discussed.The results show that the dimensionless stress intensity factors of the phonon field and the phase field and the dimensionless energy release rate are significantly size-dependent when considering the surface effects of the nanoscale defects.When the relative size of the crack is very small,the surface effect has little impact on the dimensionless stress intensity factors of the phonon field and the phase field;on the contrary,the surface effect is significant.The dimensionless energy release rate increases with the increase of the coupling coefficient at the nanoscale.When the coupling coefficient is constant,the dimensionless energy release rate is affected by the size of the elliptical hole;and the larger is the defect,the higher is the dimensionless energy release rate.With the increase of the phonon field loads,the dimensionless energy release rate decreases first,then increases and finally stabilizes.The dimensionless energy release rate monotonously decreases with the increase of the phase field loads;that is,very small and very large phonon field loads(or phase field loads)shield the effects of phase field loads(or phonon field loads).This work shows that the Gurtin-Murdoch surface elasticity theory can be theoretically extended to the quasicrystal material,which can be helpful in the development of quasicrystal fracture mechanics.
作者
苏梦雨
肖俊华
冯国益
Mengyu Su;Junhua Xiao;Guoyi Feng(Key Laboratory of Mechanical Reliability for Heavy Equi pments and Large Structures of Hebei Province,Yanshan University,Qinhuangdao,066004)
出处
《固体力学学报》
CAS
CSCD
北大核心
2020年第3期281-292,共12页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金项目(11302186)资助。
关键词
一维六方准晶
椭圆孔边裂纹
表面效应
尺寸依赖效应
应力强度因子
能量释放率
one-dimensional hexagonal quasicrystals
elliptical hole edge crack
surface effect
size-dependent effect
stress intensity factors
energy release rate
