The Analysis Of The Theory And Application For V-shaped Notch In Bimaterial

Under the subsidy of academic step and characteristic study in Lanzhou university of technology, for the application of crack technology on machining of mechanism, the theory of plane V-shaped notches in bimaterial is investigated in detail. The aim is at offering a high-efficient and convenient method forming artificial notch in crack technology.Based on the existing achievements of the theory of plane V-shaped notches in homogeneous material and the theory of a crack perpendicular to bimaterial interface, as well as the basic equations of the plane problems and stress functions provided by Zak and Williams, stress singularity eigenequation for V-shaped notches in bimaterial models is deduced. This equation can be considered as a generalization to those obtained by Williams for a V-shaped notch in a homogeneous material and by Zak and Williams for a crack perpendicular to bimaterial interface. A new definition that is different from Cook and Erdogan's definition for the stress intensity factor of a crack perpendicular to bimaterial interface is provided, and then is extended to the problem of bi-material V-shaped notch. Thereout, a generalized expression of the stress intensity factor is obtained for a crack in single material, a V-shaped notch in single material and a crack perpendicular to bimaterial interface. Some finite element methods used to solve for the stress intensity factor are discussed, and through taking double edge cracks in finite plate loaded by uniaxial uniform tension and three-point bending specimen as objects investigated, the span of extrapolation nodes and the crack tip element size is studied in detail, and then availability of stress extrapolation method applied in bimaterial models is verified. Under the same boundary condition, a comparative analysis of the stress intensity factor in single material and bimaterial is done, the results verify feasibility of V-shaped notch in bimaterial as artificial notch. The influences of notch depth and notch angle and material's Poisson ratio on singular stress fields near the V-shaped notch tip are analysed systematically, some useful conclusions are acquired, consequently, these results provide necessarily theoretical foundations for the application of V-shaped formed by dissimilar material in stress blanking.