Analysis of the twin spacing and grain size effects on mechanical properties in hierarchically nanotwinned face-centered cubic metals based on a mechanism-based plasticity model

• A dislocation density-based plastic model is developed for hierarchically nanotwinned fcc metals.
• The flow stress and failure strain are dependent on twin spacings and grain size.
• Two softening stages are observed with variation of twin spacing in simulations.
• Transition twin spacing for softening is sensitive to the grain size and twin spacings.
• The up- and low-bonds of critical twin spacing are obtained for generating the subordinate twins.

Hierarchical twin lamellae in polycrystalline face-centered cubic (fcc) metals possess a possibility to achieve higher strength with keeping an acceptable elongation. The present work is concerned with the analysis of twin spacing and grain size-dependent plastic performance in hierarchically nanotwinned fcc metals using a generalized strain-gradient plasticity model. The dislocation density-based physical model for constitutive description of nanotwinned fcc metals is expanded for the hierarchical structures of nanotwins. The strengthening mechanism and the failure behavior in these hierarchical nanostructures are studied to evaluate the strength and ductility. Moreover, the transition twin spacing between the strengthening and softening is obtained in different order of twin lamellae. A dislocation-based model on nucleating deformation twins is presented to predict the critical twin spacing in the lowest twin lamellae for generating the subordinate twin lamellae. Our simulation results demonstrate that the existence of the hierarchical nanotwins gives rise to a significant enhancement in the strength, and the resulting global flow stresses are sensitive to the twin spacings of the hierarchical twin lamellae and the grain size. Two softening stages are observed with variation of twin spacing, and the relevant transition twin spacing depends on the microstructural size in hierarchically nanotwinned metals. We further find that the predicted failure strain decreases with decreasing the twin spacing, which is quite different from the case of the individually nanotwinned fcc metals. The critical twin spacing for generating subordinate twins also depends on the twin spacing of superordinate twin lamellae and the grain size. These findings suggest that the high yield strength and good ductility can be achieved by optimizing the grain size and the twin spacings in the hierarchical twins.