Design of Thin-Walled Single-Curvature Parts for Use in Lightweight Structures

Abstract

The aim of the study - the purpose of the study was to find the minimum (critical) curvature of sheet material, to which it can be bent without fracture (formation of longitudinal cracks) and which is determined by the combined «play» of two deformational parameters: thinning, responsible for cross-section weakening, and strain hardening of the material, characterized by the intensity of deformations. The existing sheet bending pattern is analyzed with regard to the kinematics of deformational changes in the initial radii of the part due to the continuity of compressive (radial) and tensile (tangential) deformations. Assuming the Bernoulli’s hypothesis in sheet bending conditions, a mathematical model has been developed for estimating the deformational and geometric (thinning) parameters during the formation of a torus surface of various curvatures. The level of radial stresses has been identified taking into account strain hardening and thinning of the bent material, which lead to the exhaustion of its load-bearing capacity (fracture), where the plasticity criterion is the mechanical properties of a particular material obtained in tensile tests (yield and strength limits, relative elongation), approximated by a power law. The obtained results can be applied in the design of lightweight power structures; in modeling the stressstrain state of metal when developing technological processes of sheet stamping (bending) for calculating the magnitude of thinning, assessing the level of radial stresses in metal bending along the end edge of a pressing punch, as well as when designing bending equipment.

Keywords

• sheet bending
• radius of curvature
• thinning
• radial stress
• plastic buckling
• material failure