Nonadditive strengthening functions for cold-worked cubic metals: Experiments and constitutive modeling

Abstract Strong metals are greatly desired for lightweight and energy-efficient industrial design. The strengthening of metals is traditionally accomplished by the additive contributions of various obstacle families (e.g., solid solutions, particles, and grain boundaries) and dislocation self-interactions that impede dislocation motion. In the present work, unlike a traditional additive understanding, a distinctive nonadditive strengthening mixture rule for obstacles and dislocations were validated based on experimental and modeling analyses in numerous cold-worked steels and aluminum alloys. Concretely, numerous well-annealed body-centered cubic steels and face-centered cubic aluminum alloys were prepared, in which the hierarchical strength levels of solid solutions, grain boundaries, and/or particles were estimated. The above specimens were then cold rolled to various strain levels. Dislocation densities were quantified by utilizing X-ray diffraction line-profile-analysis, and the dislocation density was found to increase faster with an increasing strain level when a high strength was presented in well-annealed specimens. When plotting the yield stresses as a function of the square roots of the dislocation densities in massive distorted samples based on the Taylor hardening law, it is interesting to note that an approximate single linearity was obtained. Individual dislocation strengthening was found to respond to the total strength in the deformed specimens, which indicated that the full nonadditive strengthening mixture rule was employed between the obstacle families and the dislocation contributions. The mechanisms of the observed nonadditive strengthening were also discussed by implementing additional experiments and transmission electron microscopy observations. Then, the modified constitutive models based on both one and two internal parameters’ Knocks-Mecking models were developed respectively, which excellently captured the effects of the various obstacle families on dislocation storage processes. The developed models also rationalized the observed nonadditive strengthening mixture rule.