The size effects in hardness of polycrystalline niobium

Strong, Ductile, and Thermally Stable bcc-Mg Nanolaminates

“…The above numbers indicate that both nanocomposites are much stronger (at least 10 times) than that of coarse-grained Mg or Nb or a volume average of their strengths 31 , 32 . While noteworthy, this is an expected trend for nanostructured metals (“smaller is stronger”).…”

Size effects of the strength and elastic properties of individual phases and interphase boundaries of polycrystalline materials

“…At h < 1 µm, when the zone of deformation is less than the characteristic size of individual phases of the inves tigated material, the formation of the indentation can be considered as due to the deformation of material inside the individual phases. As was shown for metallic materials in [12,13], deformation of a few microns to hundreds nanometers inside the zone could be due to dislocation mechanisms. It was shown in [13] that the low values of n (n < 0.5) in the Hall-Petch relation could mean the conditions for the nucleation of geo metrically necessary dislocations are improved as the size of a locally deformed region shrinks (e.g., at the point on the indentation axis on distance z ≈ 0.5r (where r is the radius of curvature of the indenter tip), since the values of stress at this point are higher than the average contact stresses).…”

“…SEs of the Hall-Petch law during indentation have been observed in many works [12,13,18,19]. The most popular explanation of the nature of SEs in the region of micron and submicron indentations is the concept of geometrically necessary dislocations, introduced by J.F.…”

“…As h grows smaller in the region of nanosizes, the role played by dislocation mechanisms of plasticity shrinks and the role of nondislocation mechanisms grows [6,13,17,23]. If the material or its individual phases have a nanocrystalline structure, grains can slide and rotate, but the size dependence on h or the radius of contact upon local loading can be even weaker than the dependence on grain diameter at homogeneous loading.…”

“…In many ways, they are due to changes in the conditions and mechanisms of deformation when the size of zones of plastic deformation are reduced upon indentation. The reasons for SEs in the hardness of coarse crystalline materials upon a change in the size of indentation (especially on the nanoscale) can be fundamentally different from those upon varia tion in grain sizes and other factors [12,13]. However, we must obtain reliable experimental data in order to analyze the nature of SEs in hardness over a wide range of indentation depths h, especially for complex poly crystalline materials.…”