Application of the Continuous and Discontinuous Fields of Plastic Deformations to the Evaluation of the Initial Thickness of Bent Tubes

The paper presents the derived equations for calculations of the initial wall thickness g₀ of a tube bent to elbow. The expressions for calculating g₀ are presented in a suitable measure of the “great active actual radius R_j” in the bending zone for an exact-generalized solution (continuous fields) and for three formal simplifications (discontinuous fields) of the first-, second-, and third-orders. The expressions to calculate the components of deformation for a generalized solution (continuous fields) are obtained on the basis of kinematically admissible fields of plastic deformations. In any case, a value of initial tube thickness depends on the radius and on the angle of bending α_b on the external diameter of the tube, on the displacement of the neutral axis, and on the allowable (required) elbow thickness according to European, American, or other national technical standard or regulations. The initial thickness also depends on the coordinates of the point where the allowable thickness was determined and on the technological–material coefficient of the bending zone range k (defined during the tests). The obtained calculation results are presented in the form of graphs and in table.