An Energy Method Analysis in Three Dimensions of the Compression of a Square Sectioned Block Between Rigid Flat Tools

This paper deals with distortion of square sectioned rigid-perfectly plastic blocks compressed between two rigid flat tools. Deformation is analysed utilising a velocity field, described by trigonometric series. The velocity field is made admissable by the relation between coefficients in the series, which describes velocities in three orthogonal directions. An approximate velocity field is obtained by minimising the energy function. The shapes resulting from non uniform deformation, due to tool/workpiece friction, strain distribution and working loads can be obtained by numerical calculation. It is discovered that, due to friction, the edges of the workpiece/tool contact surface can become either concave or convex, according to the width to height ratio of the workpiece. The type of velocity field described here should be applicable to a wide range of metalforming processes.