Revealing extra strengthening and strain hardening in heterogeneous two-phase nanostructures

Heterogeneous metals and alloys are a new class of materials that emerged recently with outstanding mechanical performances such as excellent strength-ductility synergy, significant friction and wear reduction and high fatigue limits. Experiments demonstrated that back stress plays an important role in enhancing the strength-ductility balance. However, how does the back stress play the role remains fully unsolved. Here for a two-phase heterogeneous nanostructured Cu we proposed that the strong strain partitioning between the phases with high mechanical contrast due to the large variation of their grain sizes produces significant strain gradient and geometrically necessary dislocations (GNDs). The piling up of the GNDs at the phase interface generates high back stress towards the dislocation source in order to emit new dislocations. The above physical picture is incorporated into a newly developed theoretical model, in which the mechanical responses of the constituent phases with various grain sizes are described by a dislocation density based model, while the overall response is obtained by a secant method for an inclusion-matrix composite. The results show that the soft phase is considerably strengthened. The strain hardening capability of the heterogeneous composite is also enhanced to a large extent, even much higher than that the coarse-grained Cu. The strong strain hardening capability makes the heterogeneous Cu overcome the strength-ductility tradeoff that is usually the case of the homogeneous counterparts. The predicted stress-strain response agrees well with the existing experimental data. A strength-ductility map is also given for designing strong and ductile heterogeneous Cu by selecting smaller grain size in the hard phase, larger grain size in the soft phase and less soft materials. The developed model can be easily extended to investigate the strengthening and strain hardening behavior of other heterogeneous nanostructures such as gradient, laminate, nanotube strengthened and metallic glass/metallic substrate structures.