An Overview of the Effect of Grain Size on Mechanical Properties of Magnesium and Its Alloys

Amanda P. Carvalho; Roberto B. Figueiredo

doi:10.2320/matertrans.MT-MF2022005

Abstract

Recent studies show significant advances in improving the mechanical properties of magnesium and its alloys. While many papers deal with different alloy compositions, it is apparent that grain size plays a key role in the mechanical behavior of these materials. The ability to produce samples with very fine grain sizes leads to observations of high strength and/or high elongations. There are recent reports of exceptional elongations of over 100% in pure magnesium and a few alloys. These recent findings are critically reviewed in the present study. The experimental data from over 300 papers are collected, and trends between flow stress, elongation, strain rate sensitivity, and grain size are identified. The role of alloy content is examined. The data clearly shows a transition in the flow stress vs. grain size relationship which is attributed to a change in deformation mechanism from twinning controlled in coarse grained to slip controlled in fine and ultrafine grained samples. The slip controlled deformation agrees with the model of grain boundary sliding, which has shown good agreement with multiple metallic materials. It is shown that the elongations display a maximum in the grain size range in which there is a transition in the deformation mechanism. Three strategies are described for achieving high strength, high ductility, and good strength-ductility combination.

1. Introduction

Over the years, great research efforts have been made to understand and improve the mechanical properties of magnesium and its alloys. This interest can be explained by the great potential for the application of these materials in transportation and biological industries, among others. It is known that the grain size plays a major role in the properties of metallic materials and recent papers have shown that it might play a more prominent role in magnesium and its alloys. Other parameters affecting magnesium’s mechanical properties include alloying content, thermal treatment, and texture. Many papers in the literature discuss these topics, including the effect of alloying elements,¹^–³⁾ precipitation hardening,⁴⁾ and texture.⁵^,⁶⁾ Thus, the present overview focuses on the general effect of grain size on the strength and ductility of magnesium and its alloys.

There has been a great advance in understanding the effect of grain refinement in metallic materials through the advent of severe plastic deformation techniques,⁷^,⁸⁾ which enables the introduction of ultrafine grains in bulk samples. However, magnesium is usually considered a material with low formability at low temperatures. Metalworking operations used to shape components are then carried out at high temperatures, then the grain size achieved in products is usually larger than a few microns. Processing magnesium by some severe plastic deformation techniques such as Equal-Channel Angular Pressing (ECAP) and Accumulative Roll Bonding (ARB) also needs to be carried out at high temperatures, compromising the grain refinement ability. For instance, early processing of magnesium by ECAP failed to achieve significant grain refinement.⁹⁾ Advances were made which enabled the decrease in ECAP temperature and grain size of processed magnesium. These advances include the understanding of stress and damage distribution during ECAP¹⁰⁾ and the grain refinement evolution,¹¹^–¹³⁾ and the development of processing routes such as the Extrusion-ECAP.¹⁴⁾ A great advance in grain refinement of magnesium was made possible by the use of High-Pressure Torsion (HPT). This severe plastic deformation technique introduces large shear strains under high hydrostatic stresses¹⁵^,¹⁶⁾ and prevents the development of cracks. As a consequence, it provides the opportunity to process magnesium¹⁷⁾ and its alloys¹⁸^,¹⁹⁾ at low temperatures and to produce ultrafine grains. An overview of the use of HPT to process magnesium alloys is available elsewhere.²⁰⁾

There are now multiple reports of pure magnesium and magnesium alloys with ultrafine grains in the literature. Studies have shown that grain refinement affects significantly the properties of magnesium. For instance, it might affect the corrosion behavior.²¹⁾ It was suggested that the grain refinement produced by severe plastic deformation could change the corrosion mechanism from localized to a more uniform type and increase corrosion resistance.²²⁾ Furthermore, many advances were reported in mechanical properties. Grain refinement has been associated with improved strength, as expected from the Hall-Petch trends. However, there are now many reports showing that the Hall-Petch slope changes in fine grained magnesium. In fact, the inverse Hall-Petch effect has been reported in pure magnesium²³^,²⁴⁾ and in Mg alloys.²⁵^,²⁶⁾ Also, exceptional ductility has been reported in fine grained pure magnesium²³^,²⁷^,²⁸⁾ and magnesium alloys,²⁹^–³³⁾ including a report of superplastic elongation at room temperature.³⁴⁾ It is thus apparent that grain refinement plays an important role in the mechanical properties of magnesium and its alloys. In order to provide a comprehensive evaluation of the effect of grain size on the mechanical properties of magnesium, data from over 300 papers were collected and critically examined in the present study. It is shown that grain refinement greatly influences the improvement of both strength and ductility and thus, overcoming the paradox of strength-ductility. The mechanism of deformation is also examined.

2. A General Evaluation of the Different Alloys

Multiple alloying elements are used in magnesium both commercially and in research. The number of alloying elements and their amount varies significantly in the literature. So, in order to facilitate the visualization, the collected data were initially divided into groups defined by the main alloying element, which was defined as the element with a larger amount for each sample. Thus, Fig. 1 shows plots of (a) flow stress (σ) vs. grain size (d), (b) elongation vs. grain size, and (c) flow stress vs. elongation for groups of pure magnesium⁹^,²³^,²⁴^,²⁷^,³⁵^–⁵³⁾ and Mg–Al,⁹^,¹⁹^,²⁶^,³⁹^,⁴²^,⁴³^,⁵⁴^–¹⁸²⁾ Mg–Zn,²⁵^,³⁹^,⁴⁰^,⁵¹^,¹⁴⁰^,¹⁷⁶^,¹⁸³^–²⁶²⁾ Mg–Li,³⁴^,³⁹^,⁵⁴^,⁶⁹^,⁸³^,²⁶³^–²⁸⁵⁾ Mg–Y,³⁷^,³⁹^,⁴⁰^,⁴⁶^,²⁸⁶^–³⁰³⁾ Mg–Mn,²⁹^,³⁹^,¹⁴⁶^,³⁰⁴^–³¹³⁾ Mg–R.E. (Rare Earth) – Mg–Ce,⁴⁴^,¹¹⁵^,³¹⁰^,³¹³⁾ Mg–Dy,³¹⁴⁾ Mg–Er,³¹⁵⁾ Mg–Gd,⁴⁶^,⁹²^,¹⁷⁷^,²⁹⁴^,³⁰²^,³¹⁶^–³³⁴⁾ Mg–La,³³⁵⁾ Mg–Nd,¹⁹⁸^,³³⁶^–³⁴⁴⁾ Mg–Sm,³⁴⁵⁾ Mg–Yb⁴⁵⁾ - and other Mg alloys – Mg–Ag,³⁹^,³⁴⁶⁾ Mg–Bi,³⁰⁸^,³⁴⁷^,³⁴⁸⁾ Mg–Ca,⁵²^,¹⁴¹^,²³³^,³⁴⁹^–³⁵²⁾ Mg–Sn,³⁵^,³⁹^,⁴⁷^,⁸⁸^,⁹⁵^,¹⁶⁴^,³⁵²^–³⁶⁹⁾ Mg–Sr,³¹¹^,³⁷⁰^–³⁷²⁾ Mg–Zr.³⁰⁸^,³⁷⁰^,³⁷³^,³⁷⁴⁾ The majority of the data was collected from tensile tests, but some points are related to hardness (H) and a relationship of σ = H/3³⁷⁵^,³⁷⁶⁾ was adopted in these cases. There are ∼1,600 data points in Fig. 1(a), and they show a trend of increasing σ with decreasing d. as expected from the trend of grain refinement hardening in metallic materials at room temperature.

Fig. 1

Experimental data of (a) flow stress vs. grain size, (b) elongation vs. grain size, and (c) flow stress vs. elongation of magnesium with different major alloying elements.

Figure 1(a) raises some important points though. First, there is an overlap between the different alloying groups such that there is no clear distinction between them, except for pure magnesium, which tends to display lower strength compared to Mg alloys. This suggests there is no clear strength advantage between the alloying groups. Second, there seems to be an almost linear trend between flow stress and grain size for grain sizes larger than ∼1 µm, but there is a change in slope in the ultrafine (d < 1 µm) range. This means that grain refinement hardening is more effective down to grain sizes of ∼1 µm, and there is a “plateau” for grain refinement hardening in the ultrafine range. Finally, some points show grain refinement softening in the ultrafine range.

Figure 1(b) also raises some important points. First, it seems that elongations tend to be larger in the grain size range between 2 µm and 10 µm. It is clear that the elongations decrease at larger grain sizes. Most points show a decrease in elongation at d < 2 µm but some points show exceptional elongations with decreasing grain size. There is an overlap between the great majority of data points, with elongations less than ∼40%, from the different groups. However, the points that show exceptional elongations over 100% are from pure magnesium and Mg–Li, Mg–Mn, and other magnesium alloys. It is worth noting that an increase in ductility with decreasing the grain size from 125 µm to 5.5 µm was reported in pure magnesium and attributed to the activation of non-basal dislocations in the finer grain structure.³⁷⁷⁾ Non-basal slip activity was also considered a source of high ductility of an AZ31 alloy with a grain size of 6.5 µm.¹²⁴⁾ This agrees with the trend depicted in Fig. 1(b) of increasing elongation with decreasing the grain size from the coarse grained range down to a few microns.

Figure 1(c) shows the strength vs. ductility plot which tends to illustrate the paradox of strength-ductility. This means that the materials tend to display either high strength or high ductility and the data agree fairly well with this assumption. It is important to note that the data was collected from research papers, meaning that the results were obtained from non-standard and miniature tensile specimens. This means that the elongations can be overestimated. Still, the high strength data, in which σ is larger than 400 MPa, display limited elongation of less than 20%, while the high elongations of over 100% display low strength with σ less than ∼120 MPa. Most data from the different groups overlap in agreement with the observed in Figs. 1(a) and 1(b). This shows no clear edge from any family group.

3. Evaluation of the Effect of the Amount of Alloying Element

As the previous examination did not reveal a clear difference between the alloy groups, the data were then divided into 5 groups based on the total amount of alloying elements (pure Mg, up to 1%, between 1% and 3%, between 3% and 5% and over 5% of alloying elements). Figure 2 shows plots of (a) σ vs. d, (b) elongation vs. d, and (c) σ vs. elongation in which different symbols and different brightness are used to separate the groups. Thus, brighter symbols are used for pure Mg and low alloying content, and darker symbols are used for higher alloying content. It is then possible to visualize a distinction between the groups. Figure 2(a) shows that pure Mg and alloys with up to 1% of alloying content tend to display lower strength and increasing the amount of alloying content tends to increase the overall strength. Careful inspection of the data suggests that samples with alloying content between 1% and 3% almost overlap the data from samples with higher alloying content. There is no clear edge between samples with alloying content between 3% and 5% and samples with over 5% of alloying content.

Fig. 2

Experimental data of (a) flow stress vs. grain size, (b) elongation vs. grain size and (c) flow stress vs. elongation of magnesium with different alloying content.

An analysis of the plot of elongation vs. grain size in Fig. 2(b) shows that the data for the samples with different alloying content tend to overlap for grain sizes larger than a few microns, but there is a distinction in the ultrafine range between pure Mg and dilute Mg alloys (up to 1% alloy content) on one side and Mg alloys with high alloying content on the other side. Pure Mg and some dilute alloys tend to display an increase in elongation with decreasing grain size, while Mg alloys with high alloying content tend to display a decrease in elongation. There are three points, not following this trend, of elongations over 100% in samples with high alloy content (>5%) which are related to an Mg–8% Li alloy³⁴^,²⁷⁵⁾ without other alloying elements. Different trends are observed in the σ vs. elongation plot in Fig. 2(c). Pure magnesium and dilute alloys (<1% alloy content) display limited strength but can display high ductility. In contrast, alloys with high alloying content have limited ductility but can display high strength. The Mg–8% Li alloy is also an exception in this plot.

4. Effect of Grain Refinement on Strength and Ductility

The previous analysis showed that the alloying content affects strength and ductility. Low alloy content tends to increase ductility, while high alloy content tends to increase strength. However, both high strength and high ductility are only observed in fine grained samples. This is shown in Fig. 3(a), where the data points are arranged into groups based on the grain size range. It is seen that decreasing the grain size tends to increase the strength, and most points with flow stress over 300 MPa were reported in samples with grain size smaller than 2 µm. The high strength of 575 MPa was reported in a sample with a relatively large grain size of 13 µm, but the structure contained several nano-spaced stacking faults.³³²⁾ It is important to note that the highest strength in an Mg alloy was reported in an Mg–17% Ni–17% Pd processed by ultra-severe plastic deformation. A hardness of over 3 GPa,³⁷⁸⁾ which corresponds to flow stress of over 1 GPa, and a grain size of only 10 nm³⁷⁹⁾ were reported in this alloy which displays b.c.c. structure. This value is not shown in the plots due to the less conventional alloy composition and crystalline structure. Other highly alloyed systems that display high strength after SPD processing include Mg–Ni–Sn,³⁷⁸⁾ Mg–Zr,³⁸⁰⁾ Mg–Al,³⁸¹⁾ and Mg–Zn.³⁸²^,³⁸³⁾

Fig. 3

Flow stress vs. elongation of magnesium with different grain size ranges.

Figure 3(a) also shows that grain refinement tends to increase ductility. The great majority of the elongations larger than 40% were reported in samples with grain size smaller than 10 µm, and the elongations larger than 100% were reported in samples with grain size smaller than 2 µm. In order to ease the observation of the increase in strength and ductility of magnesium due to grain refinement, the data from intermediate grain sizes are removed in Fig. 3(b), which only shows data for grain sizes larger than 20 µm and smaller than 2 µm. The ranges for the majority of the data are delineated by different shades. An exception is given by one point, which shows an elongation of ∼64% in a coarse grained magnesium alloy and is associated with an Mg–11.4% Li–5% Al–2% Zn–0.5%Y alloy which displays b.c.c. structure,⁸³⁾ therefore, does not follow the same trend as h.c.p. magnesium alloys. It is clearly observed that grain refinement increases the range of data to higher strength and higher ductility. It is worth noting that an increase in both strength and ductility due to grain refinement was reported in an Mg–Zn–Zr–Ca alloy.³⁸⁴⁾ An early review paper also pointed out that grain refinement improves both strength and ductility in magnesium³⁸⁵⁾ which agrees with the trend depicted in Fig. 3.

5. The Occurrence of Extended Ductility at Room Temperature in Pure Magnesium and Dilute Alloys

An early paper pointed out pure magnesium’s increased room temperature elongation with decreasing grain size.³⁸⁶⁾ The advent of processing routes able to refine the grain structure of pure magnesium down the ultrafine range confirmed this trend. For instance, pure magnesium processed by HPT, in which the average grain size was only ∼0.32 µm, displayed elongations larger than 100% at strain rates of 10⁻³ s⁻¹ and lower, including an elongation of 360% at 10⁻⁵ s⁻¹.²⁷⁾ The trend of increasing elongation with decreasing grain size is clearly revealed in Fig. 4, which shows experimental data of elongations observed in pure Mg with different grain sizes.

Fig. 4

Elongation plotted as a function of the grain size for pure magnesium.

The increase in elongation of fine grained pure magnesium is attributed to an increase in strain rate sensitivity, m, with decreasing grain size. Early papers²³^,²⁷⁾ showed that pure magnesium can display strain rate sensitivity of ∼0.2 in the fine and ultrafine grain range. This level is much higher than the observed in commercial magnesium alloys. Figure 5 shows the values of strain rate sensitivity reported for commercial alloys,²⁵^,²⁶^,⁷¹^,³⁸⁷⁾ pure Mg,²⁴^,²⁷^,³⁸⁸⁾ Mg–Mn,²⁹^,³⁹⁾ and Mg–Li alloys³⁴^,³⁹⁾ plotted as a function of the grain size. The commercial alloys, which include data from the AZ31, AZ91, and ZK60 alloys, show an increase in m with decreasing grain size but the values are limited to m < 0.10 for grain sizes as small as ∼100 nm. On the other hand, pure magnesium shows a significant increase in m to values larger than 0.10 at grain sizes of ∼1 µm and less. Later it was reported that the strain rate sensitivity of an Mg–8% Li alloy also increases significantly in the ultrafine grained range, and a maximum value of 0.37 was reported for a sample with a grain size of only 240 nm.³⁴⁾ Remarkable values of strain rate sensitivity, even larger than those of pure Mg, were reported in Mg–Mn alloys.²⁹^,³⁹⁾ It was recently reported that fine grained Mg–Bi dilute alloy also display high strain rate sensitivity and great formability even at high strain rates.³³⁾

Fig. 5

Strain rate sensitivity, m, plotted as a function of the grain size for different magnesium alloys.

The increased strain rate sensitivity in fine grained magnesium is usually attributed to the contribution of grain boundary sliding to deformation. In fact, grain boundary offsets, typical of grain boundary sliding, have been reported during room temperature deformation of pure magnesium.²³^,²⁴^,²⁷⁾ The significant contribution of grain boundary sliding to the room temperature deformation was also reported in an AZ31 alloy.¹²⁴⁾ A study on the room temperature deformation of fine grained dilute Mg alloys showed that alloying elements present along grain boundaries may enhance or decrease the contribution of grain boundary sliding.³⁹⁾ Thus, some alloy groups such as Mg–Li, Mg–Mn, and Mg–Bi can display high room temperature ductility provided the grain size is fine enough. In contrast, most commercial alloys, with multiple alloying elements, usually display low ductility with decreasing the grain size below 1 µm.

The segregation of alloying elements at grain boundaries has been extensively reported in ultrafine grained magnesium.³⁰⁴^,³⁸⁹^,³⁹⁰⁾ The transition in strain rate sensitivity was observed experimentally during the mixing of pure magnesium and pure zinc through high pressure torsion (HPT). An Mg–20% Zn hybrid material displays a high strain rate sensitivity of ∼0.20 in the early stage of processing (10 turns), which is typical of ultrafine grained pure Mg. Still, the value of m becomes negligible with increasing the number of turns to 20 and increasing the mixing of elements.³⁸³⁾ Significant segregation of Zn along Mg grain boundaries was observed at the final mixing stages. This is depicted in Fig. 6, which shows scanning transmission electron microscopy images of the Mg–20% Zn hybrid subjected to 20 turns of HPT. An EDS mapping of a selected region is shown in Fig. 6(a), and the segregation of Zn at Mg grain boundaries is apparent. Figure 6(b) shows an area in which the grain boundaries are brighter due to the high segregation of Zn and an MgZn₂ precipitate is identified at a triple junction in Fig. 6(c). The decrease in strain rate sensitivity with increasing the mixing of pure elements was then attributed to the formation of precipitates at segregations along grain boundaries which prevents grain boundary sliding.³⁸³⁾

Fig. 6

HAADF images of an Mg–20%Zn hybrid produced by mechanical mixing of pure elements, (a) EDS mapping, (b) segregations of Zn along grain boundaries, and (c) precipitate at triple junction (adapted from Ref. 383)).

6. The Strength of Magnesium Alloys with Ultrafine Grains

The relationship between strength and grain size in magnesium is not straightforward. Many metals display a linear relationship between flow stress and the inverse of the square root of the grain size, which is known as “Hall-Petch” behavior. As a consequence, the flow stress can be estimated by eq. (1):

\begin{equation} \sigma = \sigma_{0} + K/\sqrt{d} \end{equation}

(1)

Where σ₀ is the flow stress of a single crystal and K is the Hall-Petch slope. Yet, it is now known that pure magnesium does not follow this trend at all grain sizes. Break in the “Hall-Petch” relationship, defined as the change in slope in σ vs. d^−1/2 plots, and inverse “Hall-Petch” behavior, defined as grain refinement softening, have been reported in fine grained pure magnesium.²³^,²⁴⁾ The occurrence of grain refinement softening in pure magnesium is observed in Fig. 2(a). The occurrence of grain coarsening hardening, similar to grain refinement softening, in pure magnesium was also reported in pure magnesium processed by HPT and subjected to room temperature annealing.³⁹¹⁾ Deviation in flow stress vs. grain size trends has also been reported in fine and ultrafine grained magnesium alloys.²⁵^,²⁶⁾ However, these deviations seem to occur at smaller grain sizes in magnesium alloys than in pure magnesium.

In order to evaluate the trends, the data of flow stress for magnesium alloys is plotted as a function of the grain size in Fig. 7. A trend, considering a constant Hall-Petch behavior, is estimated from the data related to grain sizes larger than 5 µm and plotted as a dashed line. The trend line displays a high Hall-Petch slope of K ≈ 400 MPa µm^1/2 which is within the upper range reported for magnesium alloys.³⁹²⁾ A fair agreement is observed between the dashed line and the experimental data for grain sizes larger than a few microns despite the great dispersion in the flow stress values in the coarse grained range. However, the Hall-Petch trend line clearly overestimates the flow stress for grain sizes smaller than a few microns. There is a change in the trend for magnesium in the ultrafine grain range.

Fig. 7

Flow stress of magnesium alloys plotted as a function of the grain size. An empirical prediction of the Hall-Petch relationship and the prediction from the grain boundary sliding model are also shown for comparison.

Recently, a model for grain boundary sliding was adapted to account for the higher stresses of low temperature deformation compared to the high temperature range.³⁹³⁾ The model predicts the flow stress as a function of the threshold stress, temperature, strain rate, and fundamental properties of the materials. The flow stress is given by eq. (2):

\begin{equation} \sigma = \sigma_{0} + \sqrt{\frac{3GkT}{2d_{s}b^{2}}\textit{ln}\left(\frac{\dot{\varepsilon}d_{s}{}^{3}}{10\delta D_{gb}} + 1 \right)} \end{equation}

(2)

Where G is the shear modulus, k is the Boltzmann’s constant, T is the absolute temperature, d_s is the spatial grain size, b is the Burgers vector, $\dot{\varepsilon }$ is the strain rate, δ is the grain boundary width (considered δ = 2b) and D_gb is the grain boundary diffusion coefficient. The model displays excellent agreement with experimental data for different materials, grain sizes, strain rates, and temperatures. It was shown that the model can predict the relationship between flow stress and grain size for multiple materials in agreement with experimental data.³⁹³^,³⁹⁴⁾ Later it was shown that the predictions from the model agreed with experimental data from over 30 pure metals³⁹⁵⁾ and a multicomponent alloy.³⁹⁶⁾ The model also showed good agreement with experimental data of flow stress of magnesium alloys AZ31,³⁸⁷⁾ AZ91,³⁹³⁾ and ZK60²⁵⁾ in the ultrafine grain range. The prediction from the model, considering the threshold stress of σ₀ = 180 MPa is shown in Fig. 7 using a continuous line. The values of the parameters in the model were considered as G = 16.6 GPa, b = 0.321 nm, D_gb = 5.8 × 10⁻¹⁹ m²/s.³⁹⁷⁾ A temperature of 298 K and a quasi-static strain rate of 10⁻³ s⁻¹ were considered in the calculations. The model predicts a lower slope in the flow stress vs. grain size plot in agreement with the experimental data of magnesium alloys in the ultrafine range.

The transition between the different slopes is attributed to a change in the deformation mechanism as twinning is expected to play a significant role in the deformation of coarse grained magnesium and slip controlled deformation takes place at the fine and ultrafine range. This transition occurs at larger grain sizes with increasing temperature.¹⁷⁵⁾ Also, experiments show increased non-basal slip activity with decreasing grain size in pure magnesium³⁷⁷⁾ and magnesium alloy.¹²⁴⁾ It is important to note that the grain boundary sliding model is based on the assumption of dislocation slip as the carrier of deformation and on experimental data from multiple materials that deform by dislocation slip.³⁹³^,³⁹⁴⁾ Thus, the agreement between the model of grain boundary sliding and the experimental data for magnesium alloys in the fine and ultrafine grain range is supporting evidence that deformation is controlled by dislocation slip in this range. Moreover, the value of threshold stress (σ₀ = 180 MPa) considered in the model of grain boundary sliding is in reasonable agreement with the expected value of stress needed to activate non-basal slip in magnesium alloys³⁹⁸^,³⁹⁹⁾ considering σ₀ = Mτ_crss where M is the Taylor factor and τ_crss is the critical resolved shear stress for non-basal slip. Hence, the present analysis shows that twinning controlled deformation displays lower threshold stress but a larger slope in σ vs. d plots. There is a transition at fine and ultrafine grain sizes to dislocation slip controlled deformation, which display larger threshold stress but reduced slope. It is important to note that the reduced slope in the ultrafine grained range limits the maximum strength achieved in magnesium alloys through grain refinement. For comparison, high flow stresses in the range of ∼900 MPa were reported in Al alloys with a grain size of ∼100 nm,⁴⁰⁰⁾ while the maximum strength in ultrafine grained magnesium alloys, with h.c.p. structure, is less than 500 MPa.

It is interesting to note that the transition between the different slopes in the σ vs. d plot takes place at grain sizes of a few microns. This is the same range at which the elongations in magnesium alloys display a maximum. This is illustrated in Fig. 8, which shows the flow stress and the elongations of magnesium alloys plotted as a function of the grain size. The transition between the twinning-controlled and slip-controlled deformation is highlighted by a different shade. It is apparent that there is a trend of decreasing elongations with increasing grain size in the twinning-controlled range, and the opposite trend is observed in the slip-controlled range. The exceptional elongations observed in some dilute alloys in the ultrafine grained range are exceptions to the overall trend observed in commercial alloys. As a consequence, the maximum values of elongations are reported within the grain size range between 2∼8 µm. Thus, good combinations of high strength and high ductility are observed in magnesium with grain size in this range. Further grain refinement down to the ultrafine grained range can increase the strength, but tends to decrease the ductility, in most magnesium alloys. Pure magnesium and some specific alloys (Mg–Li, Mg–Mn, Mg–Bi) display an increase in ductility and decrease in strength with grain refinement down to the ultrafine range.

Fig. 8

Overview of the effect of grain size on flow stress and elongation of magnesium alloys and the different deformation regimes.

7. Summary and Conclusions

A large set of data was collected from the literature to evaluate the general relationship between grain size, flow stress, elongation and strain rate sensitivity in pure magnesium and Mg alloys. The following observations are drawn:

(1) There is no clear edge in strength and ductility between the different Mg alloy groups. Yet, there is a noticeable difference in both strength and ductility depending on the amount of alloying elements. Pure Mg and dilute alloys display lower strength and may display increased elongation with decreasing grain size.
(2) Grain refinement plays a key role in the strength-ductility relationship. It is shown that decreasing the grain size can increase both the flow stress and the elongation and there is a clear expansion in the flow stress vs. elongation plots of fine grained magnesium compared to coarse grained counterparts.
(3) Exceptional elongations of over 100% are observed in fine grained pure magnesium and some alloys such as Mg–Li and dilute Mg–Mn and Mg–Bi. These high elongations are attributed to enhanced strain rate sensitivity in these materials, which can reach values over 0.20 at room temperature.
(4) Grain refinement increases the strength of magnesium alloys, and two different trends are observed. Twinning controlled deformation occurs at grain sizes larger than ∼4 µm, and the relationship between the flow stress and grain size follows a Hall-Petch type with a high slope. A transition to slip controlled deformation takes place at grain sizes smaller than ∼4 µm and the data follows the prediction from the model of grain boundary sliding³⁹³⁾ in this range.
(5) There is an optimum range of grain sizes (2 µm < d < 8 µm) in which there is a peak in elongations of most magnesium alloys. This range coincides with the transition between twinning-controlled and slip-controlled deformation.
(6) Three strategies, based on grain size range, for attaining optimum mechanical properties are identified. 1-Maximum strength is attained with significant grain refinement in Mg alloys with over 3% alloying content. 2-Maximum ductility is achieved with significant grain refinement in pure Mg and some dilute Mg alloys. 3-Optimum combinations of strength and ductility are attained in Mg alloys with grain sizes in the range between ∼2 µm and ∼8 µm.

Acknowledgements

The authors acknowledge support from CAPES, CNPq, and FAPEMIG.

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