Unified Model for Size-Dependent to Size-Independent Transition in Yield Strength of Crystalline Metallic Materials

Size-dependent yield strength is a common feature observed in miniaturized crystalline metallic samples, and plenty of studies have been conducted in experiments and numerical simulations to explore the underlying mechanism. However, the transition in yield strength from bulklike to size-affected behavior has received less attention. Here a unified theoretical model is proposed to probe the yield strength of crystalline metallic materials with sample size from nanoscale to macroscale. We show that the transition in yield strength versus size can be fully explained by the competition between the stresses required for dislocation source activation and dislocation motion, which is regulated by dislocation density, irradiation defect, grain boundary, and so on. Based on various grain boundary densities, the extended Hall–Petch relation, incorporated into the unified model, captures the reverse size effect for polycrystalline samples. The proposed model predictions agree well with reported experimental measurements of various specimens, including the prestrained nickel, irradiated copper, ultrafine grain tungsten, and so on.

Figure 1

Schematic of yield strength ${\sigma }_y$ as a function of the sample size $D$.

Figure 2

CRSS ${\tau }_c$/Yield strength ${\sigma }_y$ as a function of pillar diameter for (a) Ni single crystal at different prestrains and (b) irradiated and unirradiated Cu single crystals. Symbols represent experimental data from Refs. [9] and [27].

Figure 3

Normalized GB density $S_V/S_V^{\mathrm{bulk}}$ as a function of $D/d$. Embedded graph shows a simplified illustration of polycrystalline materials.

Figure 4

Size dependence of normalized yield stress ${\sigma }_y/{\sigma }_y^{\mathrm{bulk}}$ for (a) Cu [29] and (b) austenitic stainless steel [30] polycrystal samples. The material constant $k$ is taken as $0.06\mathrm{MPa}·\sqrt{\text{m}}$ and $0.2\mathrm{MPa}·\sqrt{\text{m}}$ for Cu and austenitic stainless steel, respectively.

Figure 5

Size-dependent yield stresses ${\sigma }_y$ for the single crystal and ultrafine grain W. Symbols represent experimental data from Ref. [11].