一维六方准晶纳米尺度孔边周期Ⅲ型裂纹断裂力学分析

Fracture Mechanics of Periodic Type-ⅢCracks Emanating from a Nano-hole in One-dimensional Hexagonal Quasicrystals

本文理论研究了一维六方准晶弹性体中孔边Ⅲ型周期多裂纹的断裂力学问题.基于表面弹性理论考虑纳米缺陷(孔洞和周期裂纹)的表面效应,利用解析函数边值问题理论并结合保角变换技术得到了问题的应力场,推导了裂纹尖端的声子场和相位子场应力强度因子和能量释放率的解析表达式.讨论了孔径尺寸、裂纹数量、裂纹长/孔径比、声子场-相位子场耦合系数和施加载荷对无量纲场强因子和无量纲能量释放率的影响.研究表明:不考虑表面效应时耦合系数、施加载荷和孔径尺寸对无量纲场强因子无影响;考虑表面效应时无量纲场强因子和无量纲能量释放率都存在着显著的尺寸依赖效应;声子场和相位子场之间有明显的耦合效应;裂纹数量对无量纲场强因子和能量释放率的影响受到缺陷尺寸的制约;施加的声子场和相位子场载荷对无量纲场强因子和能量释放率的影响不同.

The material properties of quasicrystals are significantly affected by defects due to high brittleness.Understanding the fracture behavior of quasicrystals is crucial for material applications.In this paper,the fracture mechanics of one-dimensional hexagonal quasicrystals with periodic Type-III multiple cracks emanating from a nanoscale hole is investigated theoretically.Based on complex elasticity theory and the Gurtin-Murdoch surface elasticity theory,stress fields of a nano-hole with periodic multiple cracks,considering surface effects,are obtained using boundary value problems of analytic function theory and the conformal transformation technique.Analytical expressions for stress intensity factors and energy release rates of the phonon field and phase field at the crack tip under the same conditions are further derived.The effects of aperture size,number of periodic cracks,crack-length/aperture ratio,coupling coefficient between phonon field and phase field,and applied loads on dimensionless stress intensity factors and dimensionless energy release rate are discussed.Results indicate that the coupling coefficient,applied loads,and aperture size do not affect dimensionless stress intensity factors without surface effects.Larger aperture sizes show stronger size dependence on dimensionless stress intensity factors and dimensionless energy release rate when considering surface effects.An obvious coupling effect between the phonon field and the phase field is observed.The influence of the number of periodic cracks on dimensionless stress intensity factors and energy release rate is restricted by defect size.The effects of phonon field loads and phase field loads on dimensionless stress intensity factors and energy release rate differ.This work reveals the specific influence of surface effects on the fracture behavior of multi-cracks at the hole edge,offering significant academic insights into quasicrystal fracture mechanics.