Unified Hall-Petch description of nano-grain nickel hardness, flow stress and strain rate sensitivity measurements

Abstract

It is shown that: (i) nano-grain nickel flow stress and hardness data at ambient temperature follow a Hall-Petch (H-P) relation over a wide range of grain size; and (ii) accompanying flow stress and strain rate sensitivity measurements follow an analogous H-P relationship for the reciprocal “activation volume”, (1/v*) = (1/A*b) where A* is activation area. Higher temperature flow stress measurements show a greater than expected reduction both in the H-P kε and in v*. The results are connected with smaller nano-grain size (< ∼20 nm) measurements exhibiting grain size weakening behavior that extends to larger grain size when tested at very low imposed strain rates.

Enhanced grain refinement and microhardness by hybrid processing using hydrostatic extrusion and high-pressure torsion

“…where f is the fraction of HAGBs, M is the Taylor factor, α, k and σ 0 are material constants, G is the shear modulus, θ LAGB is the average misorientation angle of the LAGBs and b is the Burgers vector. It was shown that the values calculated using this approach are in good agreement with experimental results [11,30,43,[46][47][48]. Furthermore, the applicability of this model is also confirmed in the present work because the datum points corresponding to samples processed only by HPT with a small numbers of turns tend to lie below the trend line in Fig.…”

Crystal Engineering for Mechanical Strength at Nano-Scale Dimensions

“…Calculated values of v* from Equation (6) showed an agreement with the additional increase in order of magnitude measurements [50]. These higher nano-scale dimensions seem reasonable with respect to individual atomic displacements being associated with grain boundary shearing deformations.…”

“…Whereas, the (1/v*) values are shown to increase by an order of magnitude between conventional and nano-scale grain sizes, there is an additional order-of-magnitude increase to atomic-scale dimensions for the grain size weakening behavior that itself is strain rate dependent, as demonstrated in Figure 4 for connection of the lower (1/v*) value for the 40 nm grain size material tested at (dε/dt) = 1.04 s −1 as compared with the higher value at a creep-connected strain rate 10 −5 times slower [49]. Calculated values of v* from Equation (6) showed an agreement with the additional increase in order of magnitude measurements [50]. These higher nano-scale dimensions seem reasonable with respect to individual atomic displacements being associated with grain boundary shearing deformations.…”

“…On such basis, an apparent H-P type dependence for the reciprocal value of v* is obtained from both Equation (2) H-P σ 0ε and k ε terms as Figure 4 shows a compilation of (1/v*) measurements for conventional and nano-scale nickel materials [46][47][48][49]. The measurements follow an H-P type dependence because of the constant value of τ Cε v C *, at least at small strains [50]. Additional grain size weakening measurements have been added to the figure.…”

Influence of Accumulative Roll Bonding on the Texture and Tensile Properties of an AZ31 Magnesium Alloy Sheets

“…Material strengthening due to grain size refinement may be expressed by the Hall-Petch relationship: where σ ε is the true stress at true strain ε, σ 0ε is friction stress, k ε is microstructural stress intensity, and d is average grain diameter. The value of ε may be the initial yield strain or proof strain that is determined for yielding or the subsequent strain for a plastic flow stress that is finally terminated in fracturing [ 30 ]. In the dislocation pile-up model, k ε is related to the concentration stress, τ C , as k ε = m T (π m S G b τ C /2 α) 1/2 In Equation (3), m T and m S are Taylor and Sachs orientation factors, G shear modulus, b magnitude of the Burgers vector, and α, a numerical factor following from the mutual dislocation interactions.…”