A novel general theory for bending and plastic hinge line phenomena in indentation and flattening processes

摘要

This article presents a novel general theory to estimate total absorbed energy (TAE) by two main absorber mechanisms: bending and plastic line. Furthermore, as case studies, some theoretical formulas are derived for predicting TAE of circular metal tubes during lateral flattening and indentation processes, based on three different material models of Rigid-perfectly plastic, Rigid-linear work hardening and Power hardening. Furthermore, some indentation and flattening tests are carried out on circular brazen and aluminum tubes to investigate correctness and accuracy of the derived theories. In the theoretical part, theoretical equations are derived for both thick-walled and thin-walled structures; and a multi criteria equation is derived to estimate TAE of two main energy absorbing mechanisms involving bending and plastic hinge line; and, then, based on the derived general formulas, some theoretical relations are calculated to predict TAE of indentation and flattening processes, as case studies. In the indentation process, circular tubes are considered between a slab rigid indenter and a rigid platen; and in the flattening process, circular tubes are laterally compressed between two rigid platens. To verify the derived equations, various experiments are performed on some circular brazen and aluminum specimens that are laterally indented and flattened in the quasi-static condition. In the indentation tests, different tubular samples with various wall thicknesses and radii of cross-section and material types are loaded under different slab rigid indenters with different widths. Then theoretical estimations of TAE by circular tubes during the indentation and flattening processes are compared with the corresponding experimental results. Also, effects of tube wall thickness and indenter width are investigated on TAE of tubes, experimentally and theoretically. Performed investigations illustrate that by increasing the wall thickness and indenter width, TAE of indented tubes increases. Also, the present research work affirms that TAE by circular tubes through the flattening process is higher than the corresponding value of their indentation process, theoretically; and upper limit of TAE of circular tubes through the indentation process occurs when, width of slab indenter reaches to half of tube initial perimeter.