A micromechanical model for heterogeneous nanograined metals with shape effect of inclusions and geometrically necessary dislocation pileups at the domain boundary

Heterogeneous nanostructured materials, including metals, alloys, and composites, have attracted significant scientific interest because of their outstanding performance in overcoming the strength-ductility trade-off, enhancing fatigue strength, and reducing friction and wear damage. In this study, we developed a new micromechanical model to predict the overall mechanical response of heterogeneous nanograined metals that consist of plastically deformable soft and hard domains. This dual-domain heterogeneous structure was modeled as a matrix-inclusion system, and the problem was solved through a secant-moduli approach that considered the existence of geometrically necessary dislocation (GND) pileups at the domain boundaries. We assumed that the inclusions are aligned along one direction according to experimental observations. A significant improvement in this development from previous micro-mechanical models was that the hetero-deformation induced extra strengthening inside the plastically deformable inclusions of different shapes due to the GND pileups was taken into account. In this process, the stress-strain responses of the constituent phases of various grain sizes that spanned over four orders of magnitude are also established by the dislocation density-based model. In accordance with Eshelby's equivalent-inclusion principle, the inclusions are taken to be of spheroidal shape, with an aspect ratio (i.e., length-to-diameter ratio, denoted by β) that could be much larger or smaller than unity. We considered in details the condition that the overall uniaxial tension is applied along the direction of the aligned inclusions, and examined the consequences if the extra strengthening is not considered and if it is considered. It is found that, if extra strengthening was not considered, the inclusion shape had a significant influence on the strain-hardening capability of the heterogeneous metals. The strain-hardening rate increased with increasing β if β≥1, whereas it decreased with increasing β if β<1, which resulted in a maximum strain-hardening rate at β=100 and a minimum one at β=0.5 among all the aspect ratios considered. Interestingly, the strength-ductility trade-off could be overcome by modulating only the shape of the inclusions. In contrast, if extra strengthening was incorporated, the variation of the strain-hardening rate was reversed because larger β (as β≥1) provided less strain partitioning, lower GND density, and reduced back stress, whereas bigger β (as β<1) yielded higher ones. When the overall uniaxial stress was applied normal to the direction of the aligned inclusions, the β dependence of the strain-hardening rate was different. Our findings showed that the tuning of inclusions shape, extra strengthening, grain sizes, and volume fractions of the inclusions circumvented the strength-ductility trade-off and achieved outstanding strength-ductility synergy as demonstrated by the strength-ductility map.