New interfacial crack models for plane fracture problems in magnetoelectroelastic bimaterials

Abstract

Magnetoelectroelastic (MEE) materials are a class of new multifunctional composites. They have been promising candidates for the core components of adaptive systems, for example, sensors, actuators, transducers, and microwave devices, owing to their special coupling effects among elastic, electric and magnetic fields. In engineering practice, layered structures are very common. In such structures, interface delamination will result in interfacial cracks, which is the main reason behind structural failure. In the past couple of decades, although many researchers have studied the interfacial crack problems of MEE materials, most of their work is on the basis of Griffith crack model, in which the stresses in the vicinity of the crack tips have oscillating singularity. This is not realistic in practice. Therefore, this thesis is devoted to developing more rational interfacial crack models for investigation of the fracture behaviors of MEE bimaterials.

First, in order to eliminate the oscillating behaviour of stresses near the crack tip, an electrically conductive interface crack model with a frictionless contact zone in an MEE bimaterial is developed. A combined Dirichlet-Riemann and Hilbert boundary value problem is formulated and solved analytically. Second, the crack models with pre-fracture zones are developed between two MEE materials, which are adhered by means of a thin interlayer, and the extended stresses are assumed to be finite within the pre-fracture zones. By utilizing the corresponding boundary conditions, the aforementioned problems are finally formulated mathematically as a system of equations. The fracture parameters, such as lengths of contact zone and pre-fracture zones, field intensity factors and the extended displacement jumps at the initial crack tips, related to these two sorts of models are provided. Numerical results are presented to study the influence of various factors on the fracture parameters.

Third, as an alternative to Green’s function, the integral identities are derived for a semi-infinite interfacial crack problem in an anisotropic MEE bimaterial subjected to an asymmetric load on the crack surface. This crack problem is formulated in terms of singular integral equations, which establish the relationship between the applied external load and the extended displacement jumps across the crack faces. Illustrative examples demonstrate that the proposed method is very convenient for the fracture analysis of MEE solids.

Finally, a static fracture analysis of interfacial crack problems in MEE bimaterials is presented with the extended finite element method (X-FEM). In order to capture the oscillating singularity of the stresses near the crack tip, suitable crack tip enrichment functions for MEE bimaterials are newly derived and applied to perform X-FEM analysis. By comparing yielded results with the analytical and numerical solutions of the corresponding interfacial crack problems, the validity of the proposed formulation is verified.

All the aforementioned work can significantly enrich and improve the theory of fracture mechanics of MEE solids and they can also serve as the benchmark for the future endeavors of fracture analysis. Moreover, results presented in this thesis will provide the theoretical reference and techniqucal support for the design and application of multilayered MEE structures and devices.