Peculiarities of the local stresses field near the crack tip which goes out from the angular point of the broken interface
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 79, Issue 3
Abstract
The homogeneous problem of the elasticity theory about the stress-strain state of piece-homogeneous body near the tip of the semi-infinity crack of arbitrary orientation under the plane strain is considered. The crack tip coincides with the corner point of the broken interface of two different isotropic elastic media. The ideal joint on the interface is supposed. Using the Wieghardt - Williams formulas of the expansion of the stresses near the tip of homogeneous wedge in terms of its own functions, the formulated static boundary problem of the elastic theory is reduced to the system of algebraic equations for unknown coefficients of the expansion. A characteristic equation of the problem, the roots of which determine the degrees of distance to the tip in the expansion of the asymptotic field of stresses and displacements near the crack tip, is derived from the condition of non-triviality of the desired solution. The analytical expressions for the calculation of the expansion coefficients are found. The numerical analysis of the roots of the characteristic equation of the problem for some elastic parameters of the joined materials, the crack orientation and the interfacial angles reveal the presence of values with negative real part among them – the singularity index, which stipulates the stress concentration at approaching to the crack tip. It is discovered that the singular behaviour of stresses near the crack tip differs from the root. Physically incorrect spatial oscillations stipulated by the presence of imaginary part in the index of singularity superimpose on the power singularity of stresses in some interval of interfacial angles depended on the elastic parameters of the joined materials and the crack orientation. It is supposed that the formation of the contact area of crack lips corresponds to this situation. The expression for the crack opening near the tip was found and the possible contact zone sizes were estimated. On the basis of this expression the condition of correctness of the found problem solution was formulated. The received results can be used for the estimation of the fracture toughness of piece-homogeneous body with an arbitrary orientation crack, which goes out from the corner point of the broken interface.
Authors and Affiliations
Mykhailo Volodymyrovych Dudyk, Volodymyr Fen'kiv
Keywords
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