Multilayered piezomagnetic/piezoelectric composite with periodic interfacial Yoffe-type cracks under magnetic or electric field

The problem of periodic mode-III Yoffe-type cracks propagating subsonically along the interfaces in a multilayered piezomagnetic/piezoelectric composite under in-plane magnetic or electric field is studied. By means of periodic conditions, the analysis of the multilayered problem is simplified to a bilayer model with an interfacial Yoffe-type crack, which can be reduced to the Cauchy singular integration equation of the first kind, by utilizing the Fourier transform. The normalized dynamic stress intensity factor (NDSIF) can be obtained numerically. Results show that the NDSIF generally depends on the layer thickness ratio, crack moving speed, electric or magnetic loading as well as material properties. In regard to the curve monotony of the NDSIF versus the passive layer thickness, there generally exist three different cases distinguished by a parameter, θ, which depends on the crack moving speed as well as material mismatch parameters. Similar behavior has been reported for the periodic static cracks where the different monotonies are judged by the material mismatch parameter G (Wan et al. in Eng. Fract. Mech. 84:132–145, 2012). The present results reduce to those of periodic static cracks when considering the vanishing crack speed. As far as the curve monotony and the judging parameter are concerned, no matter what the crack moving speed is, the Yoffe-type crack problem is identical to the static crack problem when the piezomagnetic and piezoelectric layers share the same shear wave velocity. In addition, detailed analyses are also provided for NDSIF versus crack moving speed for different layer thickness ratio and material mismatch parameters. This study can be considered as an extension of the previous analysis of periodic static cracks problem and is expected together to provide some guidelines for the optimal design of a multilayered PM/PE composite.