Three-Dimensional Analysis On Mode-? Elliptical/Penny-Shaped Crack Problems Of Multi-Ferroic Composite Media

Multi-ferroic(or magneto-electro-elastic)composite media are a kind of advanced smart materials,which consist of ferro-electric and ferro-magnetic phase components.These composite materials possess not only pizeo-electric and pizeo-magnetic effects,but also significant magnetoelectric effect,and could realize efficient signal conversion among multiple physical fields.Due to these characteristics,multi-ferroic composite materials could serve as sensors,actuators,transducers,electronic storage device,etc.They have enormous application potential in many modern high-tech fields,such as aerospace,nuclear power facilities,information,biology and medicine.However,multiferroic composite materials are usually brittle,and their fracture toughness is weak.Defects such as cracks are liable to appear in the manufacture process of the materials or devices.The defects may affect the stability of the corresponding devices,or even disable them.Therefore,studies on crack or other defect problems,which investigates the influence of defects on the mechanics behavior of multi-ferroic composites,are of great engineering value.Scholars have done a lot of research works on crack problems of multi-ferroic composites.However,there are still some weak links in the research system.For example,compared with the two-dimensional crack problems,three-dimensional crack problems are more realistic from a engineering point of view,but the researches on three-dimensional crack problems are relatively inadequate.Moreover,in many researches,the electrically and magnetically permeable/impermeable crack models are adopted,but these are idealized models,which may not accurately reflect the real physical situations.In addition,it is very common in engineering that materials or structures are weakened by multiple cracks.However,multi-crack problems are relatively complicated,and thus investigations on multi-crack problems of multi-ferroic composites are relatively rare.In view of the above weak links,this dissertation studies on the following issues:(1)In the framework of magneto-electro-elasticity,the mode-I problem of an elliptical(or penny-shaped)crack embedded in a three-dimensional infinite multi-ferroic composite body is studied,on the basis of the more realistic Maxwell stress crack model.The differential-integral boundary equations are established by applying Fabrikant's potential theory method and the general solution for static mechanics problems of multiferroic composite media.The three-dimensional physical fields in the infinite body are analytical solved.Through numerical examples,the influences of Maxwell stress on some important parameters in fracture mechanics are investigated.By comparing Maxwell stress crack model with other crack models,the applicabilities of other crack models are discussed.(2)In the framework of magneto-electro-thermo-elasticity,the mode-I problem of an infinite multi-ferroic composite body containing an elliptical crack under mixed mechanical,electric,magnetic and temperature loadings is researched.The idealized electrically and magnetically permeable/impermeable crack models are adopted,and the four combinations of electric and magnetic crack boundary conditions are considered.For each case,the potential functions and differential-integral boundary equations are established.The differential-integral boundary equations are solved with the potential theory method,and a three-dimensional full-field solution and expressions for some important quantities in fracture mechanics are proposed based on the general solution for multi-ferroic composite materials.The distributions of elastic,electric,magnetic and thermal field physical quantities in the vicinity of the crack are numerically presented.The influence of electric and magnetic permeabilities of a crack on the fracture behaviors of multi-ferroic composite media is investigated through numerical examples.(3)In the framework of magneto-electro-elasticity,the mode-I problem of an infinite multi-ferroic composite body weakened by multiple arbitrarily distributed coplanar penny-shaped cracks is studied.In order to solve this problem,Kachanov's method is extended to magneto-electro-elasticity,and thus the multi-crack problem is converted into the superposition of a group subproblems each concerning only one crack.The subproblems are solved with the potential theory method,and eventually an approximate three-dimensional solution for the original multi-crack problem is obtained by the superposition theorem.Through numerical examples,crack interaction is investigated.The influences of the factors,such as distances among different cracks,sizes of cracks,on the stress intensity factors at crack tips and other important physical quantities are numerically characterized.Some simplified method for the analysis of coplanar multi-crack problems are proposed.