On buckling and fracture of thin elastic-plastic foils

摘要

The interaction of simultaneous fracture and buckling constitutes problems at manufacturing and handling of thin foils. Buckling occurs as an additional event that complicates the prediction of the critical load that may lead to fracture. For most sufficiently thin foils the plastic slip occurs through the foil thickness which leads to reduction of the cross section width until the foil fails. The process leads to a necking type of deformation which confines itself to a narrow region that extends ahead of the crack tip. The width of the region is close to the foil thickness. At failure the width of the necking region is twice the foil thickness. In the present investigation the crack is assumed to be small compared to the foil geometry and the foil is assumed to be small compared with the crack length. Because of the latter the necking type of plastic region is modelled as a cohesive zone. Since the fracture toughness is not involved in the failure the only two relevant length parameters are crack length and foil thickness. The material model is defined by the elastic modulus, Poisson's ratio and yield stress. The remote load at buckling and at failure is determined and given on dimensionless form, which leaves Poisson's ratio and the ratio of buckling stress versus failure stress as the only free parameters. Two scales of yielding, the load at the ASTM-limit for linear fracture mechanics and twice that load, including the purely elastic result are investigated. Poisson's ratio is varied in the interval from -0.9 to 0.5 for the elastic case and from -0.6 to 0.5 for the plastic cases. The lower theoretical limit -1 for Poisson's ratio was not obtained because of numerical difficulties. The results rules out the possibility of failure before buckling for any reasonable construction material.