Transverse deflection of a clamped mild-steel plate

The theory of plastic flow by extended slip (Acta Mech 223:655–668, 2012; Philos Mag A 91:3343–3357, 2011; Z Angew Math Mech 84:266–279, 2004; Q J Mech Appl Math 52:645–662, 1999) is applied to a problem of bi-axial strain: the transverse plastic deflection, by means of a flat-ended punch, of a clamped plate of mild-steel. Two new theorems concerned with the Mechanics of Plates are presented. It is shown that, if the static shear yield stress of the plate material remains independent of strain, then the load–deflection relation for the punch, in the case of quasi-static punching of a plate clamped along a closed arbitrary contour, obeys an exactly linear theoretical relation. This prediction is then confirmed by experiments carried out at quasi-static rates of loading with thin plates of hot-rolled mild-steel. It is demonstrated by experiment, in the case of concentric circular punch and clamp contours, that the load–deflection relation for the punch remains linear to within <1 % provided that the maximum principal strain within the free domain of the plate does not exceed the yield-point elongation strain of the mild-steel concerned.