Transverse deflection of a clamped mild-steel plate

Dynamic Transverse Deflection of a Free Mild-Steel Plate

“…Combining this with the flow-rule associated with the Tresca yield criterion and introducing a hypothetical propagating boundary, an exact description, disregarding the very much smaller elastic deformation, can be made of the geometric form of the plate at any instant during its deformation. This analysis teaches us that, as with clamped and statically punched plates of mild-steel and ARMCO iron [9,12], as well as many cold-rolled sheet metals, the plate thickness measured parallel to the punch axis remains equal to the original thickness of the un-deformed plate.…”

“…In the above analysis, plasticity enters in the form of the solenoidal property of the strain-rate tensor [8][9][10][11][12], which is the mathematical expression of the new physical law regulating plastic deformation in solids that deform by means of the mechanism of extended slip. Combining this with the flow-rule associated with the Tresca yield criterion and introducing a hypothetical propagating boundary, an exact description, disregarding the very much smaller elastic deformation, can be made of the geometric form of the plate at any instant during its deformation.…”

“…Yet the very concept of an equation of state for metals has been criticized by a number of prominent writers. The purpose of the present paper is to set forth the principles necessary to properly analyze the dynamic response of a thin freely supported plate of mild-steel struck at high constant speed by a flat ended rigid punch, assuming the plate to deform by means of the mechanism of extended slip [8][9][10][11][12].…”

“…It will be shown that this boundary-wave travels at one-half of the velocity of elastic waves of rotation in the solid concerned. As in quasistatic deformation by extended slip [8][9][10][11][12], the strain-rate tensor within the plastic domain remains solenoidal.…”

“…Flow by means of extended slip commences, when sufficient cold work has been expended so that these domains have grown suffi-ciently to join, at which stage the yield "curve" of the material exhibits a definite point of yield in loading. The yield curve is generally bi-linear in the case of such solids [8][9][10][11][12] and yield is regulated by the Tresca yield criterion [14] because the surfaces of extended slip are aligned with the surfaces of maximum shear associated with the external constraints and the Tresca criterion requires the maximum shear stress to equal the static shear yield stress of the solid; but we shall amend this criterion so as to encompass the dynamic case directly.…”