9.4 PLANE-STRAIN INDENTATION

There are two simple fields that meet these requirements. One is a set of straight lines and the other is a centered fan (Figure 9.7). ? ₂ is the same everywhere in the field of straight lines. It is a constant pressure zone. In the centered-fan field, ? ₂ is the same everywhere along a given radius but varies from one radius to another.

Figure 9.7: (a) Net of straight lines and (b) centered fan.

A number of problems can be solved with these two fields. Consider plane-strain indentation. A possible field consisting of two centered fans and a constant pressure zone is shown in Figure 9.8. The ? and ? lines can be identified by realizing that parallel to OC the stress is compressive and the stress normal to it is zero. Or alternatively, that under the indenter the most compressive stress is parallel to P _?

Figure 9.8: A possible slip-line field for plane-strain indentation.

A more detailed illustration of the field is given in Figure 9.9. Along OC, ? _y = ? ₁=0, ? ₂ = ?k, ? _x = ? ₃ = ?2 k. Rotating clockwise along CBAO ? on the ? line through ? = ? ?/2, ? _{2OO ?} = ? _2OC+2 k ? = ?k+2 k( ??/2), P/2 k = P _O/2 k= ?? _2OO/2