Analysis Of The Strength For Heterogeneous Material Notch By Boundary Element Method

Due to the change of the structure shape or material property,there are many V-notches in the engineering structures.The serious stress singularity will occur at the tip of the heterogeneous material V-notch,which will affect the strength and safe of the structure.The research of the singularity characteristic and singular stress field at the tip of the heterogeneous material V-notch has an important significance for the safety of the engineering structure.The singular stress field,stress intensity factor and stress intensity coefficient for the heterogeneous material V-notch,interfacial crack and rigid linear inclusion are respectively studied by the boundary element method.The main research contents are listed as follows:First of all,the singularities for the plane and anti-plane heterogeneous V-notch are studied.The singularity characteristic equation for the heterogeneous V-notch is built after the singularity asymptotic expansion is introduced into the governing equation of the elasticity.The numerical method is introduced to solve the singularity characteristic equation.The singularity orders for the V-notches,whose elastic modulus are changed as exponent function,power function and reciprocal function,are respectively evaluated.Secondly,the singular stress field at the tip of the heterogeneous V-notch and crack are respectively calculated by the boundary element method.Basing on the singularity order obtained by the singularity characteristic analysis,the stress intensity factors for the heterogeneous V-notch are determined by the post processing method.The rules between the stress intensity factors of the heterogeneous V-notch and the elasticity modulus ratio,depth of the V-notch and opening angle of the V-notch are respectively studied.Then,the stress intensity coefficients for the semi-circle heterogeneous notch are studied by the boundary element method.The similarities of the singularities between the notches in different radii are analyzed.The variation rule for the singularity of heterogeneous semi-circle notch with the radius is got.The stress intensity factors for the crack at the tip of semi-circle notch are calculated by the boundary element method and the results agree well with the predicted ones from the theoretical solutions.The variation rule of the stress intensity factor for the crack at the tip of the semi-circle notch with respect to the crack length is studied.Finally,the stress intensity factor for the rigid linear inclusion in heterogeneous material plate is studied by the boundary element method,where the uniaxial and bi-axial conditions are respectively considered.The stress intensity factors for the linear inclusions located at the center and edge of the heterogeneous plate are respectively studied.The variation rules between the stress intensity factor of the rigid linear inclusion and the length of the line and the shear modulus are yielded.