Influence of dislocation–solute atom interactions and stacking fault energy on grain size of single-phase alloys after severe plastic deformation using high-pressure torsion
Introduction
Severe plastic deformation (SPD) processes such as high-pressure torsion (HPT) and equal-channel angular pressing (ECAP) are effective for producing ultrafine-grained (UFG) materials [1], [2], [3], [4]. For all SPD methods, the grain size decreases with increasing strain at an early stage of straining but enters into a steady state at large strains, where the grain size remains unchanged with further straining. The steady-state grain sizes are characteristics of single-phase materials and they remain the same irrespective of the strain, pressure and initial microstructure [5]. Several theoretical models (e.g. [6], [7], [8], [9], [10], [11], [12], [13]) and experimental works (e.g. [14], [15]) have been developed to investigate the steady-state grain sizes, dS. Most of these reports deal with pure metals, whereas little is understood to date regarding the correlations between dS and the physical parameters of alloys after processing by SPD.
This study is thus initiated with two main objectives: one is to investigate variations of dS with respect to physical parameters such as melting temperature, diffusivity, valence electrons and stacking fault energy, as attempted earlier in Refs. [14], [15] for pure metals; and the other is to examine the effect of dislocation–solute atom interactions on grain size and hardness.
Section snippets
Theoretical background
Among the models developed to predict dS, a dislocation model developed by Mohamed has received much attention [10], [11]. The model can be represented as:where b is the Burgers vector, A is a constant, β ≈ 0.04, Q is the activation energy for self-diffusion, R is the gas constant, T is the absolute temperature, DPO is the frequency factor for pipe diffusion, G is the shear modulus, ν0 is the initial dislocation velocity, k is Boltzmann’s constant, γSFE
Experimental materials and procedures
Samples of several pure metals (Mg, Al, Fe, Co, Ni, Cu, Zn, Pd, Ag) and several single-phase fcc alloys (Al–Mg, Al–Ag, Al–Cu, Cu–Al, Cu–Zn, Pd–Ag, Ni–Fe, Ni–Co) were used in this study. Table 2 gives a list of materials and their physical parameters taken from Refs. [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57]
Results
Fig. 1 plots the microhardness vs. shear strain for pure Al and for four selected Al–Mg alloys. Fig. 1 demonstrates that all hardness data for each material follow a unique function of shear strain and reach steady-state levels at large shear strains. The steady-state hardness appears to increase with an increase in the fraction of solute Mg atoms. It should be noted that the hardness–strain behaviors for all selected alloys in this study were similar to the ones represented in Fig. 1, as shown
Discussion
The current findings show that solute atoms influence SPD-processed materials not only through enhanced solid-solution hardening but also through a more enhanced grain refinement when compared to pure metals. The relation between dS and the stress required for dislocation motion in the presence of solute atoms having larger mismatch with matrix atoms provides a practical means to reduce the grain size to the nanometer scale (dS < 100 nm) through manipulation of the chemical composition. It should
Conclusions
Several pure metals and single-phase Al–Mg, Al–Ag, Al–Cu, Cu–Al, Cu–Zn, Pd–Ag and Ni–Fe alloys were processed by HPT and the following conclusions were obtained:
- 1.
The dominant factor for extra grain refinement by alloying is the effect of atomic-size and modulus mismatch on the mobility of edge dislocations. The solute atoms increase the localized stress needed for dislocation motion (Δτ in Eq. (3), Eq. (5) and Fig. 4), and thus diminish the dislocation recovery, recrystallization and grain
Acknowledgements
One of the authors (K.E.) thanks the Japan Society for Promotion of Science (JSPS) for a Grant-in-Aid for Research Activity (No. 25889043). We would like to thank Furukawa-Sky Aluminum Corporation (now UACJ Corporation) for providing the Al–8.8% Mg alloy. This work was supported in part by the Light Metals Educational Foundation of Japan and in part by a Grant-in-Aid for Scientific Research from the MEXT, Japan, in Innovative Areas “Bulk Nanostructured Metals” (Grant No. 22102004).
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