Analysis of Ⅲ crack in a finite plate of functionally graded piezoelectric/piezomagnetic materials using boundary collocation method

摘要

In this paper, a fracture problem in a rectangular plate of functionally graded piezoelectric/piezomagnetic material is investigated. The physical parameters of FGM are assumed to continuously vary along the axis-x. Two magneto-electric types of crack surface are considered, permeable type and impermeable type. A semi-inverse method is used to reduce the problem to power-series equations with the boundary collocation method employed, as numerical method, to calculate these equations in the finite region. The effects on fracture behavior of the gradient parameter, combing magneto-electric loads and two types of crack surface, are investigated. An increase in the gradient parameter is accompanied by a decrease in the ability of FGM to fracture. Increasing the magnetic load, as opposed to the electric load, promotes crack initiation and growth. Under the magneto-electrically permeable assumption, the electric and magnetic loads have no impact on the potentials field in terms of the crack singularity. On the other hand, when impermeable type is involved, the electric and magnetic loads make a critical contribution to the crack tip singularity.