The Half-inverse Method Research On The Problem Of Fracture Of Quasicrystals And Piezoelectric Material

As the developing of modern production, high strength steel structure、large-scale forging and soldering structure are extensive applied in newproduct, yet fragile accidents are frequently happen in process of new productfixing、testing and running, which bring more trouble and puzzle in peopledaily life and production, a lot of scholar and expert’s attention focus on that,then a rising branch of learning is took shape in the seventies of the20thcentury. Finally people find that existing all kind of macroscopic ormicrocosmic defects and cracks in new product are causing accident maincause through deep and vast research, macroscopic or microcosmic of defectsand cracks appear because of material itself relatively fragile or outsideworking environment、 machining and assembling factors and so on.Obviously fragile material have crystal and piezoelectric material in ourknown material, crystal have coupling phonon and phase fields andpiezoelectric material have unique mechanical electric coupling function,many parts and equipments are made using unique structure and function ofcrystal and piezoelectric material, which are widely applied in fields such asour daily life, modern electronic products, medical treatment and war. In orderto avoid many fragile accidents happen, many scholar and expert carry out thefracture mechanics research of quasi-crystals and piezoelectric material. The method of least calculation is the half-inverse in the most methodsof solving fracture mechanics problem, it only need solving one linearequation group, the analysis solution of stress field is immediately obtained,this is the maximal advantage of the half-inverse method. The solving processis very simple, it choose different displacement potential aiming at differentdefect problem, then ensure undetermined coefficient according to boundarycondition, and then the analytical solution of each stress components aredrawn. Yang Weiyang、Li Junlin etc research the problem about crack inorthotropic composite material and anisotropic composite material using thehalf-inverse method, gaining a lot of significant achievements. This paperspread half-inverse method into one-dimensional orthorhombicquasi-crystals,which control equation is more complicated, the problem aboutone-dimensional orthorhombic quasi-crystals with crack and collinearperiodic cracks are investigated, the analytical solutions of the stress fieldintensity factor for the problem of crack and collinear periodic cracks can beobtained, the stress field intensity factor for the problem of collinear periodiccracks restore the stress field intensity factor for the problem of Griffith crackunder the limiting conditions. The maximal advantage of the half-inverse islittle calculation, meanwhile it exist difficulty that is choosing suitabledisplacement potential function, it is the key of successful half-inverse at thesame time. Then, using half-inverse method and choosing suitabledisplacement potential function, the problem about one-dimensional orthorhombic quasi-crystals with elliptical hole is considered, the analyticalsolutions of the stress field intensity factor for the problem of elliptical hole isobtained, moreover the stress field intensity factor for the problem of ellipticalhole restore the stress field intensity factor for the problem of Griffith crackunder the limiting conditions.Further, the half-inverse method spread into piezoelectric material, theproblem about piezoelectric material with collinear periodic cracks andelliptical hole are investigated, corresponding the problem of the analyticalsolutions of stress, the stress field intensity factor, electric displacementintensity factor and mechanical stain energy release rate are given explicitlywith the assumption that the surface of the crack is electrically impermeable.The problem of collinear periodic cracks and elliptical hole degenerate into asingle crack under the limiting conditions, corresponding the problem of theanalytical solutions of stress field and field intensity factor are obtained.Numerical examples are given to discuss the influences of geometricparameter and the electromechanical loads on the mechanical stain energyrelease rate, some useful conclusions can be drawn.