Fracture mechanics for a mode III crack in a magnetoelectroelastic solid

Abstract

In this paper, we developed a Stroh-type formalism for anti-plane deformation and then investigated the fracture mechanics for an elliptical cavity in a magnetoelectroelastic solid under remotely uniform in-plane electromagnetic and/or anti-plane mechanical loading, which allowed us to take the electromagnetic field inside the cavity into account. Reducing the cavity into a crack, we had explicit solutions in closed forms for a mode III crack, which included the extreme cases for an impermeable crack and a permeable crack. The results were illustrated with plots, showing that in the absence of mechanical loads, an applied electric or magnetic field, positive or negative, always tended to close the crack. On the other hand, in the presence of a mechanical load, a negative electric or magnetic field retarded crack growth, while a positive field could either enhance or retard crack propagation, depending on the strengths of the applied electric/magnetic fields and the level of the mechanical load as well. In other words, the effect of electric/magnetic fields on the fracture behavior is mechanical load-dependent.

General solutions of mechanical‐electric‐magnetic fields in magneto‐electro‐elastic solid containing a moving anti‐plane crack and a screw dislocation

“…Since the defects may exist or appear with external loads during the service life and result in destroying the structures, the analysis of structural strength becomes important for the design of magneto-electro-elastic systems. Then as one of the most important fields for the strength analysis, fracture characteristics of magneto-electro-elastic materials have become a topic with increasing interests [5][6][7][8][9].…”

Antiplane Shear Crack Normal to and Terminating at the Interface of Two Bonded Piezo-Electro-Magneto-Elastic Materials

“…Gao et al [4] derived the exact solution for a permeable interface crack between two dissimilar Magnetoelectroelastic solids under general applied loads. Gao et al [5] derived also the static solution related to antiplane crack problem. The antiplane shear cracks are a class of simple problems.…”

Transient response of the crack-tip field in a magnetoelectroelastic half-space with a functionally graded coating under impacts

“…Along this line, crack problems in magnetoelectroelastic materials have received considerable attention. Many efforts have been made to give static analyses of magnetoelectroelastic materials with crack (e.g., [2][3][4][5][6][7]). When the materials or structures are subjected to dynamic loading, Li [8] investigated the transient response of the magnetoelectroelastic field of a cracked magnetoelectroelastic solid under sudden X.-L. Peng · X.-F. Li (B) IMST, School of Civil Engineering and Architecture, Central South University, 410083 Changsha, China E-mail: xfli@mail.csu.edu.cn impact loading.…”