TABLE OF CONTENTS Slip-line fields can be used to solve problems with sticking friction or a constant friction interface. One example is the compression between rough platens. This approximates conditions during hot forging. With sticking friction the slip lines are parallel and perpendicular to the platens. There is a dead metal zone where they do not meet the platens. Figure 9.26 shows the appropriate slip-line field. The appropriate boundary condition is ? x= ? 1=0 along the left-hand side of the field. Values of P ?= ?? x along the centerline can be found by rotating on ?- and ?-lines. Then P ?ave can be found by numerical integration. How much of this field should be used depends on H/L. Results of calculations for various values of H/L are shown in Figure 9.27. The slab solution of P ?/2k=1+(1/4) H/L is shown for comparison.
If there shear stress at the tool interface, ?=mk, the ?- and ?-lines meet the interface at an angle ?=(1/2)(arc cos m) and ? ?=90 ? ?. A general Mohr s stress circle plot for this condition is shown in Figure 9.28.
