软铁磁材料平面裂纹问题的耦合场

COUPLING FIELD IN AN INFINITE SOFT FERROMAGNETIC ELASTIC PLANE WITH A THROUGH CRACK

由磁弹性问题的线性化理论导出磁场下平面软铁磁体问题的控制方程和复势解．利用复势解和奇异积分方程方法，对面内磁场和远场载荷作用下的含裂纹无限大软铁磁平面问题进行了求解，得到耦合场的解．并对不同磁力模型的结果和磁场与机械载荷共同作用下的裂尖应力强度因子进行了讨论．

Magnetoelastic coupling of ferromagnetic elastic solids with cracks was received growing interest because of its possible applications in nondestructive detection and smart materials. In this paper, an infinite soft ferromagnetic elastic plane with a through crack subject to load and magnetic field is conducted. Based on the foundational theory of magnetomechanics and the linear model proposed by Pao and Yeh, the controlling equations of the magnetoelastic field are derived. A general solution for the plane problem is obtained and three cases of diffrent theoretical models of magnetic force are considered. The analytic solution of the coupling field in the cracked soft ferromagnetic material is then obtained by using the method of singular integral equation. The special value of far-field magnetic induction that may induce very strong magnetoelastic interaction in the region near the crack is also deduced. The result for the case of magnetic field normal to the crack is same as the one solved by employing Fourier transform in Shindo's paper. The far-field magnetic induction responding to strong magnetoelastic interaction by applying diffrent theoretical models of magnetic force is analyzed. Finally, the singularity of stress field near the crack tip and the effect of magnetic field on the stress singularity are discussed.