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Mechanistic origin and prediction of enhanced ductility in magnesium alloys

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Science  26 Jan 2018:
Vol. 359, Issue 6374, pp. 447-452
DOI: 10.1126/science.aap8716

A framework for more ductile magnesium

Development of ductile magnesium alloys is key to their use in reducing the weight of vehicles and other applications. Wu et al. tackle this issue by determining the underlying mechanisms in unprocessed magnesium alloys. Dilute amounts of solutes enhanced certain ductility-improving mechanisms over ones that cause brittle fracture. From this, the authors developed a theory that may be helpful for screening the large number of potential magnesium alloy compositions.

Science, this issue p. 447

Abstract

Pure magnesium exhibits poor ductility owing to pyramidal Embedded Image dislocation transformations to immobile structures, making this lowest-density structural metal unusable for many applications where it could enhance energy efficiency. We show why magnesium can be made ductile by specific dilute solute additions, which increase the Embedded Image cross-slip and multiplication rates to levels much faster than the deleterious Embedded Image transformation, enabling both favorable texture during processing and continued plastic straining during deformation. A quantitative theory establishes the conditions for ductility as a function of alloy composition in very good agreement with experiments on many existing magnesium alloys, and the solute-enhanced cross-slip mechanism is confirmed by transmission electron microscopy observations in magnesium-yttrium. The mechanistic theory can quickly screen for alloy compositions favoring conditions for high ductility and may help in the development of high-formability magnesium alloys.

Developing high-performance, affordable, lightweight structural metals is an important goal for achieving energy efficiency, safety, and human well-being. Mg is the lightest structural metal (about two-thirds and one-fourth the densities of Al and Fe, respectively), abundant in Earth, recyclable, and biocompatible. These properties make Mg attractive for automotive, aerospace, and biomedical applications. However, Mg has low ductility, making it difficult to process at room temperature and preventing its use in many applications. The poor properties of Mg are connected to its hexagonal close-packed (hcp) crystal structure. Plastic slip in the crystallographic Embedded Image direction is necessary for generalized plasticity, but the required easy-glide pyramidal Embedded Image dislocations undergo a rapid transition to an immobile structure (1) that limits c-axis plastic strain. This is exacerbated by a difference of a factor of ~100 in critical resolved shear stress (CRSS) for the Embedded Image slip as compared with the basal Embedded Image slip. Metallurgical strategies (alloying and thermomechanical processing) aim to increase ductility by engineering grain size, randomizing texture away from the unfavorable strong basal texture in sheet forming, strengthening basal slip, or activating prism slip or twinning (Fig. 1). Rare earth (RE) solutes (Y, Tb, Dy, Ho, Er, Ce, and Gd) (24) at very low concentrations [~0.03 to 1.0 atomic % (at %)] stand out as yielding good room-temperature ductility even at fairly large grain sizes and moderately strong basal texture. However, the mechanistic origins of the enhanced ductility are unknown (5), so the creation of new ductile non-RE Mg alloys is largely empirical.

Fig. 1 Room-temperature tensile failure strain, as a measure of ductility, versus grain size in selected polycrystalline Mg and Mg alloys.

In general, ductility is very low in pure Mg (gray ellipse) and increases moderately (blue ellipse; mainly Mg-Al-Zn and Mg-Al-Zn-Mn) and substantially (green ellipse; mainly Mg-RE) with alloying, while generally increasing with decreasing grain size. The RE alloys (Y, Er, Tb, and Dy) at 3 wt % (~1 at % for Y and 0.3 at % for others), 0.2 wt % Ce, and 0.1 wt % Ca have comparatively high ductility for a given grain size. Labels indicate the weight percentage of each solute. Variations in ductility, especially points outside the ellipses, are attributed to specific or selected loading directions with respect to special crystallographic textures. A much larger and fully referenced data set showing the same trends is provided in fig. S1. All data are from experiments at nominally quasi-static strain rates.

We present a physical mechanism and associated theory for achieving enhanced ductility in Mg alloys. Specifically, appropriate solid-solution alloying can greatly increase the rate of Embedded Image screw dislocation cross-slip. Cross-slip and double cross-slip then naturally lead to multiplication of the easy-glide Embedded Image dislocations at rates much faster than the deleterious transformations of the Embedded Image dislocations (Fig. 2). This reduces the effective Embedded Image CRSS toward that of the easy-glide pyramidal configuration (1) and provides the Embedded Image-axis strain accommodation that satisfies the Von Mises criteria, thus enabling high ductility during deformation. Solute-enhanced Embedded Image cross-slip and slip also contribute to thermomechanical processing of favorable textures by helping to rotate grains into crystallographic orientations that weaken the basal texture normally caused by dominant basal Embedded Image slip and extension twinning (6). In particular, Embedded Image slip tends to result in a DPRD (double-peak basal pole tilted in the rolling direction) texture during rolling and plane-strain compression (6). Enhanced Embedded Image slip can also create three-dimensional dislocation networks that drive recrystallization, refine grains, and help weaken texture. Not withstanding other mechanisms (7, 8), solute-accelerated Embedded Image cross-slip and activity can create favorable conditions for high ductility, with ductility then limited by normal work-hardening mechanisms.

Fig. 2 Competing pyramidal-to-basal transition and pyramidal II–I cross-slip processes during the expansion of an L × L Embedded Image dislocation loop on the pyramidal II plane.

lPB and lXS denote the critical nucleation lengths of the two thermally activated processes. Spheres are atoms colored according to their local atomic environment as identified by the common neighbor analysis (green, face-centered cubic; purple, body-centered cubic; yellow, others); only non-hcp atoms are shown.

A mechanistic, quantitative theory establishes the conditions enabling high ductility as a function of alloy composition. Predictions using density functional theory (DFT)–computed inputs then resolve the puzzle of how RE, Zr, Ca, and Mn solutes can induce ductility at extremely low concentrations (c ~ 0.03 to 0.3 at %) and rationalize the ductility trends across a wide range of existing alloys. Transmission electron microscopy (TEM) studies in Mg and Mg-Y further show explicitly that the alloys have enhanced Embedded Image cross-slip, enhanced Embedded Image activity, and substantially higher ductility relative to pure Mg with a similar texture.

In pure Mg, the pyramidal-to-basal (PB) transition of the edge pyramidal II Embedded Image dislocation has an activation energy barrier ΔEPB of only ~0.5 eV (1). Cross-slip (and double cross-slip) of Embedded Image screw dislocations, leading to new dislocation loops that expand and generate plasticity, can only effectively circumvent this transition if the cross-slip activation energy ΔGXS is much lower than ΔEPB. Pyramidal dislocation cross-slip in hcp Mg requires that the screw dislocations move from the lower-energy pyramidal II slip planes to the higher-energy pyramidal I planes (Fig. 2). While the intrinsic cross-slip activation energy is only ~0.25 eV, an additional energy scaling with cross-slip nucleation length is required owing to the small (but crucial) difference in energy per unit length ΔEI–II between pyramidal I and II screw dislocations (9). In pure Mg, the additional energy Embedded Image greatly increases the total cross-slip activation energy ΔGXS so that it exceeds ΔEPB, making cross-slip ineffective at circumventing the detrimental effects of the PB transition. With appropriate alloying, ΔEI–II can be reduced so that ΔGXS is much lower than ΔEPB, enabling rapid cross-slip, dislocation multiplication, and ultimately greater ductility at similar grain sizes and textures.

To formalize the mechanism, we consider a dislocation loop of L × L (Fig. 2). Enhanced ductility is achieved when the total Embedded Image cross-slip rate RXS, owing to possible nucleation at L/lXS segments along the screw section of length L, is much faster than the total Embedded Image PB transition rate RPB, owing to possible nucleation at L/lPB segments along the edge section of length L. Here, lXS and lPB denote the critical nucleation lengths for these two thermally activated processes. Effective cross-slip for high ductility then requires thatEmbedded Image(1)where lPB ≈ 2 nm (1) and ν0, k, and T are the attempt frequency, Boltzmann constant, and temperature, respectively. To quantify conditions for achieving high ductility, we introduce the “ductility index” χ, where 10χ is the factor by which the cross-slip rate exceeds the PB transition rate. From Eq. 1, for ductility at level χ, the cross-slip barrier should satisfy

ΔGXS = ΔEPBkTln(10χ lXS/lPB)(2)

We consider favorable conditions for ductility as corresponding to χ > 1 (cross-slip 10 times as fast as the PB transition) and poor conditions for ductility as corresponding to χ < 0 (cross-slip slower than the PB transition). The basal-transformed pyramidal II dislocation is so energetically favorable (~0.3 eV/Å) that changing ΔEPB is unlikely (1, 5). So, increasing ductility is achieved by reducing the cross-slip barrier ΔGXS.

The cross-slip process from the low-energy pyramidal II plane to the high-energy pyramidal I plane is driven by the net resolved shear stress Δτ acting to bow out any nucleating cross-slip segment on the pyramidal I plane. We write the cross-slip energy barrier ΔGXS as (9)ΔGXS = ΔGXS,i + ΔEI–IIlXS + ΓΔs – ΔτbA(3)The intrinsic cross-slip barrier ΔGXS,i is associated with the nucleation of dislocation cross-slip jogs of width lnuc ≈ 2.5 nm for Embedded Image cross-slip in pure Mg (9); ΔEI–IIlXS is the extra energy cost to create the pyramidal I segment of length lXS = lnuc + lCXS (fig. S3); Embedded Image is the critical bow-out length, with Γ being the pyramidal I line tension; and the last two terms are the energy to create the additional bowed-out dislocation length Δs on the pyramidal I plane, minus the work done by Δτ over the bowed-out area A. Δs and A are fully determined by lCXS, Γ, b (the magnitude of the Burgers vector), and Δτ (10). The cross-slip barrier ΔGXS can be reduced by reducing ΔEI–II through alloying.

In alloys, ΔEI–II has a contribution that is linear in solute concentration c owing to the difference in solute interactions with the pyramidal I and II stacking faults (SFs) Embedded Image, which is computed using DFT (10). There is also a contribution due to the solute misfit strain interaction with the dislocation stress field, but this term cannot be separated from the SF interaction because there are high stresses in the SF. Fortunately, the total misfit interaction is small compared with Embedded Image in all solutes, except Al. In Al, Embedded Image is small, and the solute misfit energies in the SF are nearly identical to the first-principles values (10), so we use the total misfit energy difference for Al only.

We show the predicted ΔEI–II(c) relative to pure Mg versus c for a wide range of solutes (Fig. 3A). The RE solutes (Ce, Gd, Nd, Y, and Er), as well as Zr and Ca, stand out as especially effective in decreasing the average pyramidal I–II energy difference and so can enhance cross-slip and ductility. Mn has a smaller effect but can still enhance cross-slip. In contrast, Zn and Ag increase ΔEI–II(c) considerably and so are counterproductive to ductility, on average. Overall, the trends in average solute effects on the pyramidal I–II energy difference are qualitatively consistent with the trends in ductility versus solute from experiments (Fig. 1), correctly identifying favorable and unfavorable solutes.

Fig. 3 Activation energy for cross-slip and ductility index χ for binary and higher-order Mg alloys.

(A) Average solute contribution to energy difference ΔEI–II(c) between the pyramidal I and II Embedded Image screw dislocations for various REs, Al, Zn, Zr, Ca, Mn, and Ag, immediately showing which solutes will be effective in enhancing ductility. (B) Predicted pyramidal II–I cross-slip activation energy barrier including solute fluctuations and ductility index χ for binary Mg alloys as a function of solute concentration c for the same solutes. χ > 1 indicates favorable conditions for ductility. RE solutes achieve χ > 1 at very low concentrations; Zr and Ca are also highly effective, and Mn is moderately effective. Zn and Ag (almost identical) have χ < 0 and do not reach favorable conditions for ductility. (C) Mg-Al-X-X′ with varying Al concentrations and (D) Mg-Zn-X-X′ with varying Zn concentrations. In (C), Al-Ca, Al-Mn, and Al-Ca-Mn reach the favorable ductility condition χ > 1 over some ranges of Al concentrations, and binary Mg-Al approaches χ = 0 at 1 to 3 at % Al. In (D), Zn-Ce, Zn-Mn, Zn-Mn-Ce, Zn-Zr, and Zn-Gd reach the favorable ductility condition χ > 1 at low Zn concentrations, and χ decreases as the Zn concentration increases. In (C) and (D), predictions are shown for Al and Zn concentrations above their very dilute limits; 0.1 wt % Ca and 0.2 wt % Ce can be in the very dilute limits. All predictions are consistent with the trends shown in Fig. 1. Attainable solute concentrations are limited by solubility and precipitation, factors not assessed here. The individual labels indicate solute weight percentage to make contact with standard alloy nomenclature.

Solute fluctuations exist naturally in random alloys. Favorable statistical distributions of solutes over the critical length lXS given above reduce the cross-slip barrier. The standard deviation of the statistical distribution of the solute-SF interaction energy difference scales as Embedded Image, which is computed over all unique solute sites within a unit length b (10). The typical favorable (energy-lowering) solute fluctuations within lXS then lead to a solute-modified cross-slip energy barrier Embedded Image(4)

In Eq. 4, the first set of terms is ΔGXS for pure Mg (Eq. 3), the second term is due to the average effects of solutes on the SF energies, and the third term accounts for the spatial fluctuations in the random solute distribution. At very low concentrations c < c* ≈ b/(50lXS), a discrete statistical analysis is required (10). We compute the ductility index χ versus alloy composition by combining Eqs. 2 and 4. Compositions yielding χ > 1 and χ < 0 respectively correspond to favorable and unfavorable conditions for achieving high ductility but do not directly predict measured ductility. Below, we correlate χ with experimental texture and tensile ductility.

We show the effective cross-slip barrier ΔGXS and ductility index χ versus solute concentration at T = 300 K for many binary alloys (Figs. 1 and 3B). We use Embedded Image meV/nm, which is the average of DFT and modified embedded atom method estimates, and Δτ = 10 MPa, which is related to the difference between pyramidal II and I Peierls stresses (10). The model predicts that all RE (Ce, Y, Nd, Gd, and Er) alloys reach χ > 1 at dilute concentrations. For Ce, c ≈ 0.035 at % is sufficient, consistent with the observed very weak texture (11, 12) and high ductility (12, 13). For other REs, results are consistent with measured weak to moderate DPRD texture and high ductility (3, 4, 11), and they rationalize why grain refinement, texture weakening, and ductility are more sensitive to atomic concentration than to RE type (4, 11, 14). Zr and Ca are also predicted to be very effective at levels below the solubility limits [e.g., c ≈ 0.17 at % for Zr (15, 16)]. Ca results are consistent with moderate ductility at 0.036 and 0.3 at % Ca in large-grain-size alloys (200 to 400 μm) (17, 18) and with the observed DPRD texture (19). For Mn, the ductility condition is reached at c ≈ 0.3 at %, in agreement with observed ductility and formability at 0.35 at % and 18-μm grain size (20). For Zn and Ag, χ < 0 at all concentrations, so these solutes are not predicted to create favorable conditions for ductility or for DPRD texture, consistent with experiments (19). Al has weak effects with a minimum χ ≈ –0.3 at 2.0 at % (Fig. 3C), barely lower than the minima for Zn or Ag, whereas experiments show moderate ductility in solution-treated Mg-Al (21) and DPRD texture in as-rolled Mg-Al (19). Precise results are sensitive to Embedded Image and Δτ (10), so conclusions about ductility for cases where χ ~ 0 are less definitive. Nonetheless, the overall predicted trends of the ductility and texture in binary alloys are in broad agreement with the trends in Fig. 1 and fig. S1.

We now show direct physical evidence for the operation of the pyramidal Embedded Image cross-slip mechanism. We show the initial {0001} and Embedded Image pole figures, stress-strain curves, and dislocation microstructures in pure Mg, Mg–1 weight % (wt %) Y (0.28 at % Y), and Mg–3 wt % Y (0.84 at % Y) alloys deformed under uniaxial tensile loading at room temperature (Fig. 4). All samples are process-controlled to yield similar grain sizes and the strong basal texture typical of pure Mg (10), with all TEM observations performed in grains having close-to-basal orientation as confirmed by selected area diffraction, making direct comparisons appropriate. Upon yielding, the alloys have much lower hardening rates that could be due to both the slightly weaker texture (favoring more basal slip) and enhanced Embedded Image slip. We thus examine the deformation microstructures at the same ~3% strain (Fig. 4, B to D). The stress level for pure Mg is much higher than for the two alloys. The alloys exhibit a clear increase in both Embedded Image dislocation cross-slip and overall Embedded Image activity: Connected Embedded Image dislocation segments are increasingly found on both pyramidal I and II planes with increasing Y concentrations, with pyramidal II slip being dominant. This is consistent with earlier observations of slip traces on both pyramidal I and II planes in Mg–3 wt % Y (22). In pure Mg, the Embedded Image dislocations are primarily dissociated on the basal plane, with some indications of limited cross-slip involving either pyramidal II or I slip. These observations indicate that, in the alloys, Embedded Image slip operates and contributes to the lower hardening even at the very early stages of plastic straining, consistent with the theory that posits continued Embedded Image generation and slip at lower stresses. We attribute the presence of some pyramidal I segments in pure Mg to the high tensile stress level in pure Mg (10), which is consistent with single-crystal studies (23) and atomistic simulations (9). The role of easy Embedded Image slip is perhaps more critical at the later stages of deformation (strain > 10% where further extension twinning is limited). In pure Mg polycrystals with grain sizes > 10 μm, excessive basal slip without Embedded Image-axis strain accommodation can quickly build up strain incompatibility and high constraint stresses, leading to damage initiation and limiting ductility (24). In the Mg-Y alloys, the stress-strain curves clearly have a longer range of stable plastic flow at relatively normal hardening rates, indicating that sufficient plastic deformation mechanisms are activated until the onset of macroscopic plastic instability (e.g., the Considère criterion) is reached. These controlled experiments demonstrate that Y solutes do enhance Embedded Image dislocation cross-slip, slip, Embedded Image-axis strain accommodation, and ductility with increasing Y concentration, in excellent agreement with our predictions.

Fig. 4 Experimental results for pure Mg and Mg-Y alloys under tensile deformation at room temperature.

(A) Stress-strain curves and (B to D) initial {0001} and Embedded Image pole figures and bright-field TEM of the corresponding dislocation microstructures after 2.5 to 3% strain for pure Mg (B), Mg–3 wt % Y (C), and Mg–1 wt% Y (D). In (B) to (D), dislocations visible under diffraction vector g = 0002 are Embedded Image dislocations based on two-beam g·b = 0 visibility analysis (b, Burgers vector); the insets show the corresponding crystallographic plane traces identified using diffraction analysis, enabling determination of the crystal planes of the observed Embedded Image dislocations. In (B), Embedded Image dislocation segments are lying on basal and pyramidal II planes; areas where dislocations change from pyramidal II to basal planes are highlighted by turquoise arrows and circles. In (C) and (D), Embedded Image dislocation segments are predominantly on pyramidal II planes, with frequent plane changes to either pyramidal I (highlighted by red arrows and circles) or basal (highlighted by turquoise arrows and circles) planes. In (C), for Mg–3 wt % Y, high-frequency Embedded Image dislocation switching between pyramidal II and I planes (double cross-slip) is evident.

The theory is applicable to dilute solid-solution ternary alloys and other materials. We show the predicted trends for ternary and quaternary alloys involving Al and Zn, respectively, corresponding to many experimental alloys (Figs. 1 and 3, C and D). For Mg-Al-Zn (commercial AZ alloys), the theory predicts χ < –1 at the widely used 1 wt % Zn (e.g., AZ31 alloy with 0.3 at % Zn), indicating poor ductility conditions and thus likely requiring special processing to achieve nonbasal textures. This may account for the very wide range of reported failure strains and formability [Fig. 1 and (25)]. The addition of just 0.4 wt % Mn to create the AZ31B alloy yields χ ~ 0, largely counteracting the deleterious effects of Zn, and this is consistent with the trend of increased ductility for this slightly modified alloy as compared with commercial AZ31 alloy. Mg-Al-Ca at only 0.06 at % Ca with 1 at % Al attains the ductility condition (χ = 1), consistent with the DPRD texture and good ductility in experiments (19), whereas 1 at % Al alone has χ < 0. The Mg–Al–0.4 wt % Mn alloys are predicted to be nearly identical to the Mg–Al–0.1 wt % Ca alloys. Experiments show that extruded and hot-rolled Mg–(3 to 8) Al–0.4 Mn (weight %) alloys have weak texture with DPRD features and high tensile failure strain (25), consistent with enhanced Embedded Image slip owing to Al and Mn solutes. Last, the recently reported Mg-Al-Ca-Mn system at 0.18 at % Ca and 0.17 at % Mn (26, 27) is predicted to have χ > 2 across a wide range of Al concentrations, and indeed these alloys demonstrate good tensile ductility.

For Mg-Zn-X-X′ alloys, high Zn concentrations raise the cross-slip barrier considerably, leading to χ < 0, which is unfavorable for ductility. This is consistent with broad experimental trends where ductility generally decreases or saturates with increasing Zn (19, 2832) (fig. S1). The deleterious effect of Zn also corroborates the texture evolution during rolling, where the DPRD texture, driven by Embedded Image slip in Mg-Ce (33, 34), Mg-Y (35), and Mg-Ca (19, 36), weakens or disappears upon additions of Zn (13, 19, 37). However, alloying with dilute RE solutes can easily yield χ > 1 at low Zn concentrations. We predict that Mg–1.5 Zn–0.2 Ce, Mg–2.3 Zn–0.4 Mn–0.2 Ce, Mg–2 Gd–1 Zn, and Mg–3 Gd–1 Zn (weight %) alloys all satisfy the ductility condition, in agreement with observed weak texture, high ductility, and high formability (13, 34, 38, 39). Mg-Zn-Zr alloys near the limits of Zr solubility are also predicted to reach χ > 2, in agreement with the high ductility seen in solution-treated Mg–0.5 Zn–0.6 Zr (28). Mg-Zn-Mn alloys at 1 wt % Mn show χ > 2 at low Zn, indicating that even dilute Mn may overcome the detrimental effects of Zn. Experiments show a range of ductilities, but they tend to saturate with increasing Zn, in spite of increasing basal strengthening and other mechanisms such as softened prism slip (40). The Mg–1.5 Zn–0.1 Ca (weight %) alloy has χ < 1, below the ductility condition, whereas further increase of Zn leads to less favorable conditions for ductility, consistent with experiments (19).

The theory is generally successful in rationalizing observed ductility across a wide range of existing ternary and higher alloys. This success of the theory, supported by the experimental validation of the physical mechanism, could enable quantitative refinements of a wide range of existing alloys, as well as guide searches for new Mg alloy compositions with high ductility. The theory does not address solubility or precipitation, which limit attainable solid-solution compositions and can impart strength and reduce ductility. Thermomechanical processing for favorable textures also remains a critical aspect of attaining improved ductility. Nonetheless, the theory provides mechanistic insight into which solutes and concentrations could enhance ductility and can contribute to accelerating the development of high-ductility, high-formability Mg alloys.

Supplementary Materials

www.sciencemag.org/content/359/6374/447/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S7

Table S1

References (41150)

References and Notes

  1. Materials and methods are available as supplementary materials.
Acknowledgments: The authors acknowledge financial support of this work through a grant from the Swiss National Science Foundation entitled “Control of atomistic mechanisms of flow in magnesium alloys to achieve high ductility” (project #162350). The authors also acknowledge support from EPFL to the Laboratory for Multiscale Mechanics Modeling that enabled the required high-performance computing provided by Scientific and IT Application Support (SCITAS) at EPFL. All data are reported in the main paper and supplementary materials.
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