Bend of izotropic plate with two indentical co-axial open cracks at plastic zones meeting between them taking into account the contact of crack banks
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 80, Issue 4
Abstract
A problem of biaxial bending under distributed on infinity moments of isotropic plate with the co-axial cracks of identical length is stated and solved. The vectors of the applied to the plate moments are perpendicular and parallel to the cracks. Under the action of the external loading the crack banks are expected to contact smoothly in the areas of fixed width. Plastic zones appeared in their tips, where the terms of Trasck’s plasticity are satisfied as a surface layer or plastic to the hinge. For the internal crack tips the plastic zones are considered to meet. Due to the contact of crack banks the problem is presented as superposition of two problems: plane problem of elasticity and bending problem taking advantage of classic theory. The problem is solved with such boundary conditions: , , ; , , , ; , , , where , and , components of stress tensor and components of displacement vector on the axis and of the plane problem; and unknown quantities, normal stress and bending moment in plastic zones; contact force ; deflection plate; і bending moment and cutting force according to Kirchhoff; area, where cracks are placed, area, where plastic zone is placed; ; "+" and " " are marked limit value of the appropriate value at ; ; , , , plate height, the width of the contact area the interfaces cracks. Using the complex potentials of plane problem and classic theory of plate bending the solving of problem is reduced to the problem of linear coupling, on the basis of which the analytical solution of the problem is built in the class of functions limited in the plastic zones tips. Using the conditions of plasticity it was found analytically: unknown normal tension and bending moment in the plastic zones accordingly in a plane problem and problem of bending; divergence of crack banks and length of plastic zones in their external tips. The numerical analysis of the problem was conducted, loading at which meet in the internal tips. Graphic dependences of the plastic zone length and divergence of the crack banks in their external tips on the change of the external loading and distance between the internal crack tips are presented.
Authors and Affiliations
Victor Opanasovich, Mykola Slobodyan
Keywords
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