The strength-differential effect in disordered solids

In the plasticity of disordered solids the critical shear resistance fc at yield in eompression and that in tension tt are substantially different, with the ratio tq/tt being referred to as the strength-differential-effect (S-D) ratio. In comparison with the critical shear resistanee is in simple shear, the S-D effect results in the ordering of resistances as tt Ts ic. The phenomenon is well known in glassy polymers (see e.g. Argon et al. (1968)) and in amorphous metals (see e.g., Donovan (1989) and references therein). The discussion of the S-D effect in the yielding of noncrystalline solids has been extensive and dates back to the well-known unsymmet-rical yield criteria of Coulomb (1773) and Mohr (1900) for soils and granular media (for an overview of these see Anand and Gu (2000)). 

In the yielding of polyerystalline ductile metals that obey symmetrical 3D yield criteria of von Mises or Tresca type (McClintock and Argon 1966) the plastic shear resistance is nearly independent of pressure and the S-D effect is negligible. In comparison it is very substantial in disordered solids, with the ratio rc/ T being in the range 1.2-1.3. 

The S-D effect has been viewed in two different ways and is associated with two different yield conditions. 

since tension and compression differ fundamentally by the presence of a positive or negative mean normal stress 7m, the S-D effect has been attributed in one case to the effect of on the governing mechanism of nucleation of STs, as we have done in Section 7.6.6. If deformation does not localize into shear bands and remains homogeneous at a mesoscale, this results in unsymmetrical von Mises- or Tresca-type yield criteria such that the critical shear resistance Zg is pressure-dependent (Ward 1983) as discussed in Chapter 3. 

Alternatively, where plastie flow is strongly localized into intense dilatant shear bands, as in the cases of cohesionless granular media (Coulomb 1773 Mohr 1900), the S-D effect has been viewed as the effect of a normal stress On acting across the shear plane and thereby increasing or decreasing the shear resistance of such bands through a friction effect on the shearing material. This alternative explanation results in a Coulomb Mohr-type unsymmetrical yield condition similar to the behavior of cohesionless sand or soils, where, however, the linear dependence of the shear resistance is on is continuous around zero in the form of 

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