Abstract
So-called strength-ductility trade-off is usually an inevitable scenario in precipitation-strengthened alloys. To address this challenge, high-density coherent nanoprecipitates (CNPs) as a microstructure effectively promote ductility though multiple interactions between CNPs and dislocations (i.e., coherency, order, or Orowan mechanism). Although some strain hardening theories have been reported for individual strengthening, how to increase, artificially and quantitatively, the ductility arising from cooperative strengthening due to the multiple interactions has not been realized. Accordingly, a dislocation-based theoretical framework for strain hardening is constructed in terms of irreversible thermodynamics, where nucleation, gliding, and annihilation arising from dislocations have been integrated, so that the cooperative strengthening can be treated through thermodynamic driving force ∆G and the kinetic energy barrier. Further combined with synchrotron high-energy X-ray diffraction, the current model is verified. Following the modeling, the yield stress σy is proved to be correlated with the modified strengthening mechanism, whereas the necking strain εn is shown to depend on the evolving dislocation density and, essentially, the enhanced activation volume. A criterion of high ∆G-high generalized stability is proposed to guarantee the volume fraction of CNPs improving σy and the radius of CNPs accelerating εn. This strategy of breaking the strength-ductility trade-off phenomena by controlling the cooperative strengthening can be generalized to designing metallic structured materials.