A theoretical review of stress relaxation testing

Several theoretical approaches to stress relaxation testing are reviewed with the finding that all are internally consistent. The interesting results are that self-consistency identities prove that a constant dislocation mobility and a constant internal structure stress are commensurate with the assumptions that (∂σ/∂ ln ∈_p)_∈p is constant and (∂σ/∂∈_p) is independent of strain rate. The first of two self-consistency identities leads back to the Gilman - Johnston dislocation mobility analysis. The second identity leads to Feltham's empirical equation for stress relaxation testing, viz. σ₀ - σ = S log₁₀(1 + vt) where σ₀ and σ refer to stresses at time zero and time, t, and S, v are constants related to the slope and curvature of the stress relaxation data. It is shown that this consistent behavior can be easily utilized to interpret dislocation mobility constants at large strains. On the other hand, at small strains where "anomalous" stress relaxation has been observed, experimental data on polycrystalline Fe show an inconsistency with the above approaches. The conclusion is that the mobile dislocation density is not constant at strains near yield.