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Mathematical examination of the special features of the concentration and dynamic stresses in the vicinity of a brazed joint in resonance conditions

The working conditions of structures in vibration conditions are usually short lasting, but in many cases sufficient to cause extensive cumulation of damage in the material of the structure or its fracture. In most cases, structures contain weak sections with the highest susceptibility to failure in the resonance operating regime. In the case of brazed joints (BJ) these areas include the vicinity of brazed joints which can be interpreted as strain concentrators. Complex mechanical phenomena of local stress concentration, boundary and edge resonance formed during the operation of brazed and bonded–welded components in the vibration field, result in the need for extensive corrections in the generally accepted methods of stress calculation. The aim of the present work was to improve the accuracy of calculation of the spectrum of resonance frequencies for BJ, and the selection of the most economic variant of combination of pairs of parent metals and brazing alloys in butt brazed joints for minimising the influence of dynamic effects, in numerical, analytical examination of the coefficients of stress concentration, determining the parameter of local special features of the stressed state α in the problem zones of the piecewise– heterogeneous right-angled section of a prismatic brazed component. The authors of Refs. 2, 3 and 6 developed methods of examining wave fields in elastic regions of the given geometry, using the asymptotics of general solutions at singular points of the boundaries. The coefficients at a singularity in singular terms of the asymptotics solution, determining the field at these singular points, were investigated in Ref. 2 only for the case of a homogeneous right-angled (in plan) component. In Refs. 3 and 6, on the basis of the modified methods of superimposition, the authors obtained a solution to the problem of harmonic oscillations of a brazed piecewise–heterogeneous component infinite in the direction of the Z axis. The cross-section of the component in the dimensionless coordinates is described by the inequalities