Method For Solving The Problem Of Multi-crack Emanating From A Hole

The types of materials and defects in actual engineering structures are diverse.Defects in crystals and quasicrystals materials have attracted widespread attention from scholars.Among them,cracks emanating from hole are a common type of defects that affect structural integrity.Under different stress conditions,the materials with holes have different types of cracks induced by stress concentration.Therefore,this paper first studies the problem of four asymmetry cracks emanating from a circular hole in an isotropic infinite plate.Secondly,the problem of shear stress on the partial cracks surface emanating from a elliptical hole in the one-dimensional hexagonal quasicrystals is analyzed.Finally,it solves the problem of uniform tensile stress on the partial cracks surface emanating from a elliptical hole in the two-dimensional decagonal quasicrystals.The main work is as follows:The first chapter introduces the research status of the problem of cracks emanating from a hole and fracture mechanics of quasicrystals materials,The first chapter introduces the research background,current situation and significance of the problem of cracks emanating from a hole and fracture mechanics of quasicrystals materials,including the main research methods include the complex variable function method and the truncated conformal mapping approach.The second chapter uses the truncated conformal mapping approach and the complex variable function method to calculate the compound mode stress intensity factor(type I and Type II)and crack surface opening displacement of four asymmetry cracks emanating from a circular hole in an isotropic infinite plate,which is under uniform tensile stress in the unidirectional or bidirectional.The distribution characteristics of stress intensity factor and crack surface opening displacement are analyzed,and the results obtained are compared with the results in related literatures to verify the correctness of thetruncated conformal mapping approach.The third chapter uses the complex variable function method to calculate type III stress intensity factor for phonon field and phase subfield of the two asymmetric cracks emanating from a elliptical hole which part of the crack surface is under shear stress in the one-dimensional hexagonal quasicrystals.The distribution characteristics of type III stress intensity factors are analyzed,and special cases are discussed.The fourth chapter uses the complex variable function method to calculate the field variables for phonon field and phase subfield of the two asymmetric cracks emanating from a elliptical hole which part of the crack surface is under uniform tensile stress in the two-dimensional decagonal quasicrystals.In addition,discussed special situations.