[SY-J1] Symposium J-1

[SY-J1] Analysis for the Plane Problem of Layered Magnetoelectric Composite with Collinear Interfacial Cracks

^○Wenxiang Tian¹, Zheng Zhong^1,2 (1.School of Aerospace Engineering and Applied Mechanics,Tongji Univ, China, 2.School of Science, Harbin Institute of Technology, China)

A fracture problem of collinear interfacial cracks in layered magnetoelectric composites is studied. The magnetic permittivity of the piezoelectric material and the dielectric constant of the piezomagnetic material are considered. The poling axis of the piezoelectric and piezomagnetic material are all assumed to be perpendicular to the interfacial cracks and an in-plane magnetic potential difference or voltage is applied along the poling axis, which results in in-plane deformation of the composite. Thus, a plane fracture problem is studied in the present paper. A system of singular integral equation of the second kind with Cauchy kernel is obtained by means of Fourier transform and further solved by using Jacobi polynomials. The primary interfacial fracture mechanics parameters, such as the stress intensity factors, the electric displacement intensity factors, the magnetic inductions intensity factors and the energy release rates are then obtained. Analysis reveals that the material combination and the thickness ratio of piezomagnetic/ piezoelectric layer has significant influences on the stress, the electric displacement and the magnetic inductions on the interface versus the thickness of the active response layer. In terms of the defined dimensionless parameters Z_sigma, Z_B, Z_D, which represent the interface material mismatch under in-plane deformation, three different cases can be categorized for each parameter, i.e. Z_sigma>1,Z_sigma<1 and Z_sigma=1; Z_B>1, Z_B<1 and Z_B=1; Z_D>1, Z_D<1 and Z_D=1; where the stress curves, magnetic inducions curves and electric displacement curves display different monotony, respectively. Based on the three dimensionless parameters, we can define another four dimensionless parameters C_KI,C_KII,C_KD,C_KB, which represent the cracked interface material mismatch under in-plane deformation, different cases can be categorized for different parameters, where the corresponding intensity factor curves display different monotony.