The concept of a yield surface is central to the mathematical formulation of classical plasticity theories. However, at elevated temperatures, material response can be highly rate-dependent, which is beyond the realm of classical plasticity. Viscoplastic theories have been developed for just these conditions. In viscoplastic theories, the flow law is given in terms of inelastic strain rate rather than the inelastic strain increment used in rate-independent plasticity and in unified viscoplastic theories no yield criterion is used. Thus, surfaces of constant inelastic strain rate or flow surfaces, which describe hardening behavior, are considered to be more useful than yield surfaces.
Experimental procedures to determine yield surfaces in axial-torsional stress space are well established. The use of small-offset definitions of yield minimizes the change of material state and allows multiple loadings to be applied to a single specimen. Flow surfaces are determined using the same procedures with the exception that inelastic strain rates are used rather than total inelastic strains. The key to these experiments is precise, decoupled measurement of axial and torsional strain. With this requirement in mind, the performance of a high-temperature multiaxial extensometer was evaluated through comparison with strain gage results at room temperature. Yield surfaces (both initial and subsequent) were found to be nearly identical when determined for Type 316 stainless steel using the extensometer and strain gages. The extensometer was then used successfully to determine flow surfaces for Type 316 stainless steel at 650°C.