Critical radius of pipe bending caused by the material destruction

The authors investigate the possibility of intensification of pipe bending by creating a minimum curvature considering the thin-wall profile, which is on the limit of exhausting the material’s bearing capacity (destruction). They consider an annular shell (pipe) under the action of pure bending moment, assuming the hypothesis of planar cross-sections and regarding the effect of T. Karman. The deformation changes of geometrical parameters (profile ovalization, wall thinning) are found. The compressive (radial) and tensile (tangential) deformations are calculated with account of their continuity based on the condition of volume constancy. In accordance with the accepted assumptions of mathematical modeling, the dependence of the radial stress on the edge of the bending segment, known from the theory of sheet stamping, is taken, where the most convenient criterion for plasticity is the hypothesis of the energy of shape change of the Mohr’s theory, characterized by the intensity of deformations in the bent section of the pipe, which determines the destruction of the material. The criterion of plasticity, specific mechanical properties of the material obtained in tensile tests (yield and strength limits, relative elongation) and approximated by a step dependence are used for making a combined estimation of the influence of geometric parameters (thinness, ovalization of the profile, deformation thinning of the wall) on the realization of bending of minimum curvature, characterized by loss of wall stability with subsequent failure due to exhaustion of the bearing capacity of the material possessing specific plasticity. Summarizing the results of the minimum (corrugation) and critical (destruction) bending radii, makes it possible to establish the ultimate degree of bending intensification.