A new interfacial imperfection coupling model (IICM) and its effect on the facture behavior of a layered multiferroic composite: Anti-plane case

Abstract

Abstract The across-interface diffusion and permeation of the ingredients in the manufacturing process inevitably induce magneto-electro-mechanical couplings in the interfacial regions of multiferroic composites that consist of alternate ferromagnetic (FM) and ferroelectric (FE) layers. Therefore, it is impossible for the mechanical, the magnetic and the electric interfacial imperfections to occur and grow independently. Up till now, the imperfection couplings have not been investigated. By extending the classical spring model, this article presents a new one to formulate these three kinds of imperfections and their inter-couplings in the anti-plane deformation case. Six coefficients are proposed to construct the model, three representing the imperfections and the other three characterizing the inter-couplings. On this basis, fracture analysis is further performed on a bi-layered multiferroic composite with two groups of cracks parallel to the imperfect interfacial region and each in a layer. Numerical results of the stress intensity factor (SIF) are obtained from the Cauchy singular integral equations derived by the methods of Fourier integral transform and Green's function. The effects of the imperfections and their inter-couplings on the SIFs are surveyed, yielding three main conclusions: (a) the mechanical imperfection can enhance the SIFs independently; (b) the magnetic or electric imperfection can reduce the SIFs only if it is coupled with the mechanical one; (c) the magneto/electro-mechanical imperfection coupling can help to lower down the SIFs, but the magneto-electric imperfection coupling always has no effect on the SIFs. These conclusions can serves as theoretical references for the optimal design against intra-layer fracture of the multiferroic composites.