Discussion: “A Critical Reexamination of Classical Metal Plasticity” (Wilson, C.D., 2002, ASME J. Appl. Mech., 69, pp. 63–68)

Abstract

The author correctly identifies the backbone of metal plasticity as the Mises yield criterion, the Prandtl-Reuss flow law, and isotropic/kinematic hardening. However, there has always been the qualification that these simplifications of plasticity work well for “most metals” or “some metals.” It is noteworthy that while the author has devoted a section of his paper to Richmond’s work refuting the widespread use of the assumption of pressure-independent flow in metals, he did not reference the keystone work of Spitzig and Richmond 1, where they provide additional results for 1100 aluminum. This would have further reinforced his point. Spitzig and Richmond found 1100 aluminum to exhibit pressure-dependence but not a strength-differential. Here the term strength-differential means a tension-compression asymmetry (e.g., compressive yield strength larger than tensile yield strength), which is different from a Bauschinger effect. The yield function that Spitzig and Richmond used can be written in the forms f=aI1+3J2−cf=αI1+3J2c−1where I1 and J2 are the usual stress invariants and α=a/c,a is the pressure coefficient, and c is the strength coefficient. The strength-differential depends only on the parameter a, but pressure-dependence is affected by both a and c. While a and c were shown to be strain-dependent, α was not (1). In fact, α=a/c for aluminum was approximately three times that of iron-based materials. Based on the tensile and compressive yield strengths reported by Wilson for 2024-T351 aluminum, presumably using the 0.2% offset strain definition; the yield function parameters can be calculated and compared with results from Spitzig and Richmond in Table 1. The pressure-dependence of 1100 and 2024-T351 is similar, but 2024-T351 exhibits a strength-differential 2a of 5.9%, while 1100 does not exhibit an appreciable strength-differential. While Wilson did not measure volume change, Spitzig and Richmond did, and found there to be no significant dilation; indicating that an associated flow rule will not correctly predict plastic strain. This is also the case for frictional materials, where it is common to employ a nonassociated flow rule. We have observed strength-differential in laboratory experiments using aged Inconel 718 (a precipitation strengthened nickel-base alloy) (23), 6061-T6 aluminum and 6092/SiC/17.5-T6 (a particulate reinforced aluminum alloy) (4). The Mises yield criterion does not apply well to these materials either. Our work on Inconel 718 (3) indicates that a J2-J3 yield function, which we called a threshold function because we were working in the realm of viscoplasticity, along the lines of that proposed by Drucker 5 for an aluminum alloy was most suitable. Finally, while it is fairly obvious, it is worth pointing out that the Drucker-Prager yield criterion predicts more flow for the same tensile stress than the Mises yield criterion simply due to the presence of the positive I1 term. Thus, the finite element results of Wilson for Mises and Drucker-Prager yield criteria are self-consistent. It would be interesting to know the range of I1 for a particular notch geometry.