9.7 ENERGY DISSIPATION IN A SLIP-LINE FIELD

Consider the plane-strain extrusion in Figure 9.13. There are velocity discontinuities along AB, BC, and CO (Figure 9.13(a)). The hodograph (Figure 9.13(b)) shows that if V ₀=1, . The lengths are and . So the energy dissipation along these lines is . The extrusion pressure was earlier determined as P _ext/2 k=0.762, so P _ext=1.542 k. Thus 1.262/1.542=81% of the energy is expended along these lines of discontinuity. The other 17% is expended in the fan OBC.

Figure 9.13: (a) Slip-line field showing lines of intense shear and (b) hodograph for an extrusion.