Numerical Analysis Method Of Fatigue And Fracture For Cracks In Bimaterial

Bimaterial(the combination of different metals,metal and nonmetal such as ceramic,and coatings)are widely used to manufacture the mechanical parts and components in the bad and special environment of the mechanical manufacturing,automotive,aeronautics and astronautics,as well as electronic information industry,due to its special and excellent properties of light weight,high hardness,high wear resistance and high temperature resistance.The performance and life of these parts and components may be improved greatly taking advantage of such properties of the bimaterial.The bimaterial may induce greater stresses than a single material under the same load considering the mismatch of the two materials.Therefore it is more likely to result in the crack initiation and propagation even the failure of the material,especially in the interface of the two materials due to its weakness,since the cracks initiate there likely under a higher stress,thus leading to the fracture and delamination.So it is significant to study the mechanism of the fracture and fatigue of the bimaterial and provide the foundation for the design and life extension of the engineering structures and components.A hybrid boundary element method for the analysis of the linear elastic fracture and crack propagation for the 2D and 3D crack system in the bimaterial is established based on the first kind singular integral equations and the second kind hyper singular integral equations.The detailed studies on the discretization of boundary integral equations,all kinds of boundary elements(especially mode ?-? coupled oscillation singular element for the interfacial cracks),the determination of the stress intensity factor,the calculation of the singular integrals and super singular integrals are carried out.The proposed method is verified by comparing with the relevant research efforts and experimental study.1.A method for solving the hyper-singular integral equations(the second kind integral equations)of 2D and 3D crack problems in bimaterial is established based on the elasticity theory.The unit force basic solution(the first basic solution)and unit displacement discontinuous basic solution(the second basic solution)of the bimaterial system are derived.For the 2D and 3D interfacial crack problems,a concept about relative displacement basic function between the upper and lower surface of the crack is proposed.The basic function is(?)·ris singular(mode I-II coupled oscillation singularity)and(?)singular(mode III non-oscillation singularity)at the crack tip.Then a kind of interfacial crack element considering mode I-II coupled oscillation singularity and mode III singularity is established,and the numerical solution technique is deduced and analyzed in detail.The numerical results show that the proposed method is high accurate.2.A hybrid boundary element method for solving the bimaterial crack problems is established by combining the above second kind integral equations and the usual first kind integral equations.The numerical solving technique relating to the discretization of the boundary integral equations,the division of various elements,the establishment of interpolation functions,and the treatment of singular and hyper singular integrals are analyzed in detail.The proposed method is applied to the fatigue propagation analysis of surface cracks.3.In analyzing the fatigue propagation of surface crack,the stress intensity factor at each crack propagating step must be calculated,and accordingly the large non-symmetric coefficient matrix should be computed repeatedly.A method is proposed that the master matrix is calculated only once in the initial crack state,while a very small-scale matrix is calculated during the subsequent fatigue crack propagating.The elements on the crack surface are remeshed according to the mapping relationship.Therefore the proposed method is high efficient(small-scale matrix calculation)and accurate(precise calculation of stress intensity factor at each crack propagation step)in analyzing the fatigue propagation of surface crack.Finally the accuracy and reliability of the proposed method are verified by the corresponding experiments.