Purely Cohesive Materials (ϕ=0)

Purely Cohesive Materials (ϕ=0)

Materials with no significant frictional strength (cases 4 and 7 in Table 12.1) range from ductile metals to overconsolidated clay. They are the elastic, perfectlyplastic solids (EPS) of classical elasticity and plasticity (at least in compression).

the slip planes are at 45� o to the principal orientation. Equation (12.14c) can be integrated directly to give the normal stress

where K is the constant of integration.

The pair of slip lines at a point are at right angles. Let us consider the slip surface to have the counterclockwise angle α from the x axis so that the normal to it (the other slip line) is at the clockwise angle ρ_z in Figure 12.7. Then from Mohr’s Circle

While mathematically trivial, this solution is physically profound. We know it is correct in regions where τ_zx = const and therefore the orientation of the principal stresses do not change.

A general solution can be obtained by assuming

where a, b, and c are constants.

Thus, for a material with ϕ=0, the failure surface in Cartesian coordinates must be made up of straight lines and/or circles combined in some way to satisfy the stress boundary conditions.