NECKING IN PLANE-STRAIN UNDER BENDING WITH CONSTANT TENSION

AS PART OF A study of failure of plates at built-in supports, modes of plane strain failure under increasing bending with constant tension are calculated for an elastic, power-law plastic material with kinematic hardening. Under increasing bending, the moment reaches a maximum when the bending curvature (normalized by the initial plate thickness) is approximately twice the strain-hardening exponent. At the maximum moment, different boundary conditions result in different failures. Under applied bending moment, rotational instability occurs. Under applied bending angle, stable localized kinking occurs. Kinking leads to high curvatures and then tensile necking. Large further applied bending curvature gives tensile necking. For example, with a strain-hardening exponent of n = 0.1 and a constant tensile force of 90% of that for necking under pure tension, a bending curvature of 0.865 (normalized by the initial plate thickness) is required for tensile instability. For most practical cases (that is, for the radius of curvature greater than the order of thickness), bending decreases the tensile necking force by 7-17% for a strain-hardening exponent of n = 0.2-0.05. Reversal before reaching the maximum moment requires almost the same curvature change to reach a maximum moment as for monotonic loading.