摘要
基于广义复变函数理论和保角映射技术,研究了磁电弹性体中具有穿透型的圆弧形裂纹和螺型位错的相互作用.为讨论磁电弹性体中裂纹尖端的位错、位错屏蔽效应和裂纹屏蔽效应,推导得到了力-电-磁场的场强度因子和作用在位错上的像力.当圆弧形裂纹退化为Griffith裂纹时,导出了应力和位移的显式解析表达式.利用解析解并结合数值算例,分析了磁电弹性材料中圆弧形裂纹和螺型位错的相互作用对场强度因子、位错力的影响.结果表明:圆弧形裂纹尖端到位错点的距离,以及它们连线与x_1轴正半轴所形成夹角的不断增大会引起场强因子屏蔽效应的降低,即位错对裂纹具有屏蔽作用;位错对圆弧形裂纹产生的影响比直线裂纹的影响更为明显;作用在位错上的像力会受到圆弧形裂纹表面状况的影响;螺型位错能降低圆弧形裂纹尖端的应力强度因子,且屏蔽效应随夹角的增加而迅速减弱,随位错点到裂尖的距离与圆弧形裂纹半弦长比值的增大,螺型位错对裂纹的屏蔽效应会加强.
The interaction between a penetrating-type circular-arc crack and a screw dislocation in magnetoelectric composites is studied.Firstly,according to the basic equations of magnetoelastic compos-ites and the theory of complex function,the relationship between the anti-plane shear stress,the normal component of the electric displacement,and the normal component of the magnetic induction along the boundary arc c is derived.Then,based on the conformal mapping technique,the complex form of the gen-eralized stress field is obtained by analyzing the stress conditions of the dislocation.In order to discuss the dislocation,dislocation shielding effect,and crack shielding effect at the crack tip,the force-electric-mag-netic field intensity factors and the image forces acting on the dislocation are further deduced.By analyzing the analytical solutions and numerical examples,the results show that the shielding effect of the field strength factor decreases with increasing the distance between the circular-arc crack tip and the dislocation point,and the angle formed by their connecting line and the positive half of the r-axis,indicating that the dislocation has a shielding effect on the crack.Additionally,the effect of dislocation on a circular-arc crack is more prominent than on a straight crack.Besides,the image force on the dislocation is affected by the surface properties of the circular-arc crack.Finally,the screw dislocation can reduce the stress intensity factor of the circular-arc crack tip,and the shielding effect rapidly weakens as the angle increases.The shielding effect of the screw dislocation on the crack tip is strengthened as the ratio between the distance from the dislocation point to the crack tip and the half-chord length of the circular-arc crack increases.These conclusions carry meaningful significance for fracture mechanics research and provide a theoretical basis for improving and evaluating the performance of electromagnetic devices.
作者
刘欣宇
刘官厅
Xinyu Liu;Guanting Liu(College of Mathematics Science,Inner Mongolia Normal University,Hohhot,O10022;Inner Mongolia Center for Applied Mathematics,Hohhot,O10022)
出处
《固体力学学报》
CAS
CSCD
北大核心
2024年第4期456-465,共10页
Chinese Journal of Solid Mechanics
基金
国家自然科学基金项目(12162027)
内蒙古自然科学基金重点项目(2024ZD21)
内蒙古自治区高等学校科学技术研究自然科学重点项目(NJZZ22574)
教育部重点实验室无穷维哈密顿系统及其算法应用(内蒙古师范大学)(2023KFZD02)
内蒙古师范大学基本科研业务费(2023JBZD005)资助。
关键词
螺型位错
磁电弹性体
圆弧形裂纹
相互作用
screw dislocation
magnetoelectroelastic composites
circular-arc crack
interaction
