Quantitative prediction of twinning stress in fcc alloys: Application to Cu-Al

Sandeep A. Kibey, L. L. Wang, J. B. Liu, H. T. Johnson, H. Sehitoglu, and D. D. Johnson

Phys. Rev. B 79, 214202 – Published 4 June 2009

Abstract

Twinning is one of most prevalent deformation mechanisms in materials. Having established a quantitative theory to predict onset twinning stress $τ_{crit}$ in fcc elemental metals from their generalized planar-fault-energy (GPFE) surface, we exemplify its use in alloys where the Suzuki effect (i.e., solute energetically favors residing at and near planar faults) is operative; specifically, we apply it in $Cu- x Al$ ( $x$ is 0, 5, and $8.3 at . %$ ) in comparison with experimental data. We compute the GPFE via density-functional theory, and we predict the solute dependence of the GPFE and $τ_{crit}$ , in agreement with measured values. We show that $τ_{crit}$ correlates monotonically with the unstable twin fault energies (the barriers to twin nucleation) rather than the stable intrinsic stacking-fault energies typically suggested. We correlate the twinning behavior and electronic structure with changes in solute content and proximity to the fault planes through charge-density redistribution at the fault and changes to the layer- and site-resolved density of states, where increased bonding charge correlates with decrease in fault energies and $τ_{crit}$ .

Received 1 January 2009

DOI:https://doi.org/10.1103/PhysRevB.79.214202

Authors & Affiliations

Sandeep A. Kibey¹, L. L. Wang², J. B. Liu², H. T. Johnson¹, H. Sehitoglu¹, and D. D. Johnson^1,2,*

¹Department of Mechanical Science and Engineering, University of Illinois, Urbana-Champaign, 1206 W. Green Street, Urbana, Illinois 61801, USA
²Department of Material Science and Engineering, University of Illinois, Urbana-Champaign, 1304 W. Green Street, Urbana, Illinois 61801, USA

^*duanej@illinois.edu

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Vol. 79, Iss. 21 — 1 June 2009

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Images

Figure 1
(Color online) Planar defect energies (in $mJ / m^{2}$ ) versus displacement along $[11 \bar{2}]$ (in units of $| b_{p} |$ ) of layers above each successive fault plane, i.e., intrinsic SF (isf) at 1, extrinsic SF (esf) at 2, and twin fault (tsf) at 3, with additional layers extending the twin region. Unstable fault energies are at half units. After 5% Al $γ_{ue}$ is smaller than $γ_{ut}$ , which remains independent of concentration in the alloy.Reuse & Permissions
Figure 2
(Color online) Predicted (squares) and experimental (circles) $τ_{crit}$ for Cu-Al versus (a) $γ_{isf}$ and (b) $γ_{ut}$ , with comparison to other fcc metals from Ref. 8. Predicted $τ_{crit}$ is in agreement with experimental data given by reported range of data (low, average, and high). Gray lines are guides for the eyes. In (a), $τ_{crit}$ versus $γ_{isf}$ exhibits nonmonotonic behavior (dotted gray line) contrary to that supposed in simple models. In contrast, in (b) there is a monotonic relation versus $γ_{ut}$ (dashed gray line). In (a), within the Cu-Al, a monotonic relation versus $γ_{isf}$ is apparent (dashed gray line) reflecting %Al-dependent drop of $γ_{isf}$ (see Ref. 8), whereas in (b) there is a distinct change in $τ_{crit}$ above 5% Al (dotted line), reflecting the more rapid drop in $γ_{isf}$ (see text).Reuse & Permissions
Figure 3
(Color online) (a) Local structure and (b) valence-bonding charge density for an intrinsic SF in (i) Cu, (ii) Cu-5%Al, and (iii) Cu-8.3%Al. In (a), Al are shaded red, Cu in $[\bar{1} 10]$ solute plane are gold, and out of plane are gray. (In grayscale, atoms are black, gray, and overlapping light gray, respectively). Dashed line marks the (111) SF plane just above the solute and the $[11 \bar{2}]$ direction. Away from fault arrows mark comparable Cu-Cu bonds and the depletion of charge in Cu-Al (relative to pure Cu) due to substitutional Al. At fault plane, the Al enhances the charge for near-neighbor Cu, decreasing bonding, as shown by accumulation between out-of-plane Cu near Al.Reuse & Permissions
Figure 4
(Color online) For $Cu- x Al$ (a) total DOS per atom and (b) Cu atom DOS in a specific layer for an intrinsic SF. Energy zero is the Fermi energy. In (b), layer-specific Cu site DOS [L0 is below SF, L1 above SF, etc.; see Fig. 3a], with panels displaying Cu (top) and Cu-8.3%Al (middle and bottom). For Cu-8.3%Al results (middle and bottom), Al is in L0 (at the fault) and L3 (not at the fault) permitting determination of solute versus solute-fault effects. The Cu in L1 (L2) is at the fault (not at the fault) and has no intralayer solute. See text for discussion and details.Reuse & Permissions

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