Mechanically Activated Transition from Linear Viscoelasticity to Yielding: Correlation-Based Unification

The mechanically activated transition (MAT) from linear viscoelasticity to yielding is considered an essential part of the operational behavior of ductile materials. The MAT region is restricted by proportional limit at σ₀ and ε₀ and the yield point at σ_y and ε_y, or, in terms of this paper, $E_0={\sigma }_0/{\epsilon }_0$ and ε₀ and $E_y={\sigma }_y/{\epsilon }_y$ and ε_y, respectively. This stage precedes yielding and controls the parameters of the yield point. For bulk plastic (co)polymers and cellular polymeric foams, the quantitative correlations between $E_0$, ε₀, $E_y,$ and ε_y were determined. The ratios ${\displaystyle \raisebox{1ex}{$E_0$}\!\left/ \!\raisebox{-1ex}{$E_y$}\right.}=1.55\pm 0.15$ and ${\displaystyle \raisebox{1ex}{${\epsilon }_y$}\!\left/ \!\raisebox{-1ex}{${\epsilon }_0$}\right.}=2.1\pm 0.2$ were specified as yielding criteria. For all the samples studied, their mechanical response within the MAT region was unified in terms of master curve constructed via re-calculation of the experimental “stress–strain” diagrams in the reduced coordinates ${\displaystyle \frac{\lg \mathrm{E}-\lg {\mathrm{E}}_0}{\lg {\mathrm{E}}_0-\lg {\mathrm{E}}_y}}=f\left({\displaystyle \frac{\mathit{lg}\epsilon -\mathit{lg}{\epsilon }_0}{\mathit{lg}{\epsilon }_y-\mathit{lg}{\epsilon }_0}}\right),$ where $E=\sigma /\epsilon$ and ε are the current modulus and strain, respectively. To generalize these regularities found for bulk plastics and foams, our earlier experimental results concerning the rheology of soil-based pastes and data from the literature concerning the computer simulation of plastic deformation were invoked. Master curves for (1) dispersed pastes, (2) bulk plastics, (3) polymeric foams, and (4) various virtual models were shown to be in satisfactory coincidence. For the materials analyzed, this result was considered as the unification of their mechanical response within the MAT region. An algorithm for the express analysis of the mechanical response of plastic systems within the MAT region is proposed. The limitations and advances of the proposed methodological approach based on correlation studies followed by construction of master curves are outlined.