NUMERICAL CONSTRUCTION OF AXISYMMETRICAL SLIP-LINE FIELDS FOR INDENTATION OF THICK BLOCKS BY RIGID CONICAL INDENTERS AND FRICTION AT THE TOOL METAL INTERFACE

A general form of axisymmetric slip-line field solutions using numerical methods is given for cases of axisymmetric smooth and partially rough conical punch indentation of a rigid-perfectly plastic ductile material of semi-infinite thickness, where the cone semi-angle alpha varies from 15-degrees to 90-degrees. The basic problem of indetermination of the field and pressures near the apex of the conical punch experienced earlier by Locket (J. Mech. Phys. Solids 11, 345 (1963), [1]) for small cone angles was overcome by treating small segments of the curvilinear slip lines as arcs of circles of varying radii and assuming a straight boundary to the deformed lip. The numerical method outlined in detail by Chitkara and Butt (Int. J. Mech. Sci. 34, 833 (1992), [2]) allows the construction of axisymmetric slip-line fields for cone indentation, with varying frictional conditions at the tool-metal interface. The computer program developed requires only the cone semi-angle alpha and the frictional conditions at the tool-metal interface as the data set. It includes graphical plotting subroutines to plot the calculated slip-line field on a Hewlett-Packard 7550 plotter. A computographic plot of the associated velocity field for a typical case of conical punch indentation is also included.