T应力对立方准晶中含十字交叉型裂纹的影响  

Effect of T-Stress on Cubic Quasicrystals with Unequal Arm Cracks

作　　者：索亚茹 周彦斌[1] 刘官厅[1] Yaru Suo;Yanbin Zhou;Guanting Liu(Mathematics Science College Inner Mongolia Normal University,Hohhot,010022)

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《固体力学学报》2022年第1期95-110,共16页Chinese Journal of Solid Mechanics

基　　金：内蒙古自然科学基金项目(2020LH01011);内蒙古师范大学高层次人才引进科研项目(2019YJRC005)资助。

摘　　要：论文研究了立方准晶中含十字交叉型裂纹尖端附近的T应力.采用了积分变换法,将相关边值问题转换为求解奇异积分方程,得到声子场和相位子场的T应力,且可以表示为裂纹张开位移和施加在无穷远处的载荷之和.裂纹张开位移在确定声子场和相位子场的T应力中起着主导作用.同时强调了T应力在立方准晶脆性断裂中的作用.此外,还研究了裂纹臂长度比b/a对十字交叉型裂纹T应力的影响.The T-stress near the tips of a cruciform crack with unequal arms in cubic quasicrystals is analyzed. First, similar to the determination of stress intensity factors, the T-stresses considering phonon field and phason field at crack tips are derived using the integral transformation technique, through which the related boundary value problem is convert to singular integral equations. According to the stress difference method, T-stresses can be expressed as the sum of integrals involving the crack opening displacement and the loads applied at infinity. The obtained results indicate that, in addition to the applied loads, the T-stresses at the horizontal/vertical crack tips depend on the crack opening displacement of the vertical/horizontal crack surface. The crack opening displacement plays a leading role in determining the T-stress, especially for a cruciform crack of two crack-arm lengths of the same order. Moreover, the T-stresses for a single-crack limiting case can be recovered from the present results as the length of one arm approaches zero. The T-stresses for a cruciform crack under biaxial tension of the same magnitude show that, when the crack length ratio is fixed, the stress at the crack tip will not disappear. Finally, for several cases of interest, the T-stresses for a cruciform crack are evaluated and compared with those of a single crack, and the influences of the ratio of two crack-arm lengths b/a and the crack opening displacement on the T-stress of a cruciform crack is examined. The numerical analysis shows that the T-stress with phason field is always greater than that of no phason field, meaning that considering the phason field will increase the T-stress, and indicating that the cubic quasicrystal is more brittle as compared with isotropic elastic materials, and the brittle fracture in cubic quasicrystals can be a consequence of both singular stresses and T-stresses.

关 键 词：T应力 立方准晶 十字交叉型裂纹 裂纹张开位移 

分 类 号：O753.3[理学—晶体学] O346.1