9.10 PLANE-STRAIN DRAWING

This type of field with two centered fans is useful in analyzing plane-strain drawing or extrusion operations with larger H/L values than are described by equation 9.11 (i.e., r<2 sin ?/(1+2 sin ?). Figure 9.20 shows the field in Figure 9.17, tilted by the die angle ? and bounded by ? and ? lines that meet the centerline at 45 . The appropriate boundary condition for finding ? _d is F _x = ? ? _x dy+ ?? _xy dx along a cut from A to n, n+1. Everywhere along the cut A, (0,1), ( n, n+1), ? _x = ? ₁ , and ? _xy=0, so F _x = ? _x dy. The x and y values of the nodes in Figure 9.18 are now designated as x ? and y ?. They may be transformed into the coordinates x and y in Figure 9.20 by

Figure 9.20: (a) Slip-line field for drawing with r<2 (sin ?) (1+2 sin a), (b) Coordinate system for analysis along the cut A, (0, 1), (n, n+1) where ? _x= ? ₁.

The stress state at any node point, ( n, n+1), can then be found in terms of P _?. In triangle AOB, and along the line AO, P _AB =P _? ?k. Rotating on an ? line through

?