含力磁屈服区的压磁材料硬币型裂纹问题研究  

On the Problem of Penny-Shaped Crack of Piezomagnetic Material with Mechanical and Magnetic Yield Zone

作　　者：李梦涵 吴琼 万永平[1] LI Menghan;WU Qiong;WAN Yongping(School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《力学季刊》2021年第3期538-549,共12页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(12072240)。

摘　　要：本文利用Hankel变换及Copson求解方法,得到了在无穷远处磁荷载以及对称力荷载作用下的无限大压磁材料中,硬币型裂纹在裂纹尖端含有环状力磁双屈服区情况下的相关解析解.本文考虑了磁屈服区尺寸小于、大于、等于力屈服区尺寸的三种情况.结果表明:屈服区尺寸不仅与外荷载及材料常数相关,更与力磁屈服区尺寸的相对大小有关;其中,较大尺寸的屈服区仅受同性质单一荷载影响,与材料常数无关;而较小尺寸屈服区受力磁两荷载与材料常数共同影响;裂纹张开位移、磁势跳变均沿裂纹面径向增大而减小;裂尖张开位移、裂尖磁势跳变与材料常数相关,且随外荷载增大而增大.The analytical solutions of penny-shaped crack in an infinite piezomagnetic material subjected to remote magnetic and axisymmetric mechanical loadings with annular mechanical and magnetic yield zones are obtained by using the Hankel transform and the method of Copson.Three different cases,i.e,the magnetic yield zone is shorter than,longer than,or equal to the domain of mechanical yielding are considered in this article respectively.The results show that the size of yield zone is not only related to the loadings and material constants,but also to the relative size of mechanical and magnetic yield zones.The larger-sized yield zone is only affected by the single load of the same style and is irrelevant with the material constants,while the smaller-sized yield zone is affected by both the mechanical and the magnetic loads as well as the material constants.The crack opening displacement and magnetic potential jump decrease as the radial direction of crack surface increases.The crack opening displacement and the jump of magnetic potential of crack tip are related to the material constants,and increase as the loading rises.

关 键 词：HANKEL变换 Copson方法 压磁材料 硬币型裂纹 力磁屈服区 

分 类 号：O346.1[理学—固体力学]