9.9 INDENTATION OF THICK SLABS

The plane-strain indentation of a thick slab by two opposing indenters is shown Figure 9.15. The simple slip-line field in Figure 9.16 is appropriate for special case where the slab thickness H equals the indenter width L. Along AO, ? _x=0 so ? ₂= ?k. The stress is the same everywhere in triangle O ?OA so along OO ?,

Figure 9.15: Plane-strain indentation of a thick slab by two opposing indenters.

Figure 9.16: Special case of plane-strain indentation where the slab thickness H, equals the indenter width L.

A different field must be used for larger values of H/L. Figure 9.17 shows the field for H/L=5.43. This is a field determined by two centered fans. In triangle O ?OA ? _y = ?P _? , ? _2(OA)= ? _y +k= ?P _? +k. Moving along an a line to (0, 1) and moving back along a ? line to (1,1), ? _2(1,1) = ?? _2(OA) + . At 1,1, and at every point (n, n) along the centerline . Since ,

where is the absolute value of the rotations.

Figure 9.17: Slip-line field for mutual indentation with H/L=5.43.

Because there is no x-direction constraint,

Substituting equation 9.15, or

Figure 9.18 gives the values of ? as a function of y for nodal points on a 15 net. There is a...