Cluster Hardening Effects on Twinning in Mg-Zn-Ca Alloys

Abstract

Twinning is a critical deformation mode in Mg alloys. Understanding deformation twinning (DT) is essential to improving mechanical properties of Mg alloys. To address the experimentally observed conspicuous hardening effects in Mg-1.8Zn-0.2Ca alloys, interactions between the {10–12} twin boundaries (TBs) and solute clusters in Mg-Zn-Ca alloys were examined via molecular dynamics (MD) simulations. We find that the Zn/Ca-containing clusters show different hindering effects on TBs and an increment in the applied shear stress of 100 MPa is required to accomplish the interaction between the boundary and the cluster with Ca content > 50 at%. The cluster hardening effects on twinning are positively correlated to the Ca content and the size of the clusters in Mg-Zn-Ca alloys.

1. Introduction

Lightweight magnesium (Mg) alloys are in the spotlight for energy efficiency for transportation applications [1,2]. Deformation twinning (DT) on the $\left\{10\overline{1}2\right\}\langle \overline{1}011\rangle$ system is an important plastic deformation mechanism in Mg with a hexagonal crystal structure. Nucleation and growth of twins are responsible for hardening and texture evolution characteristics, and ultimately influence the mechanical properties and formability of Mg and its alloys [3,4].

Once they are nucleated, deformation twins usually propagate quickly by moving the twin boundaries across the matrix grain. This process corresponds to a stage on the stress–strain curve with near-zero strain hardening. Introducing microscopic barriers to hinder the motion of twin boundaries (TBs) is an effective way to strengthen Mg alloys [5,6,7]. Some studies suggested that the segregation of certain solute atoms to the TBs can exert a strong pinning effect on the migration of TBs, resulting in a significant enhancement in hardness and mechanical strength [8,9,10]. The solute/TB interaction can even serve as a new atomic-scale mechanism for dynamic strain aging [11]. Interactions between TBs and precipitates of various shapes (e.g., basal plates, prismatic plates, c-rods) have also been examined by both experimental and computational approaches to elucidate the strengthening effect of those precipitates [12,13,14,15]. On the other hand, little attention has been paid to the interaction between TBs and solute clusters, which are somewhere between single solute atoms and crystallized precipitates.

Clusters are recognized to form in the early stages of precipitation and have a vital influence on mechanical properties of Mg-RE alloys, such as Mg-Y and Mg-Gd alloys [16,17]. Gd-rich clusters are found to segregate onto high-angle grain boundaries, which leads to the grain refinement and texture weakening in Mg-Gd alloys [17]. Clusters of non-RE elements have been less well studied. Recently, Ca-containing Mg alloys have received strong attention because of their excellent mechanical properties and low fabrication cost [18,19,20,21,22]. In particular, Mg-Zn-Ca alloys demonstrate ultra-high ductility and moderate texture [23,24,25,26,27]. Those features are often attributed to the co-segregation of Zn and Ca atoms onto grain boundaries (GBs), which is believed to enhance GB cohesion. On the other hand, how Zn-Ca clusters would affect the deformation mechanisms in the grain interior is not well understood. In the present work, we study the interaction between Zn-Ca clusters and TBs by molecular dynamics (MD) simulations. The result will help us better understand the work hardening behavior of Mg-Zn-Ca alloys.

2. Experimental Methods

2.1. Material Synthesis

A moderate-textured Mg-1.8Zn-0.2Ca (wt.%) alloy (denoted as ZX20) was casted and extruded. The ZX20 alloy was made from pure Mg, pure Zn, and Mg-20 wt.% Ca master alloy in an electric resistance furnace under protective gas consisting of CO₂ (99 vol.%) and SF₆ (1 vol.%). The melt was poured into a cylindrical steel mold preheated to 200 °C and then naturally cooled in air. The actual chemical composition of the cast billets was determined by an inductively coupled plasma atomic emission spectroscopy (ICP-AES) analyzer (Perkin-Elmer, Plasma 400, Norwalk, CT, USA). The cast billets were machined into cylindrical samples 60 mm in diameter and 70 mm in height, followed by homogenization at 400 °C for 12 h. One-step direct extrusion was carried out at 250 °C and 2 mm/s to produce round bars of 14 mm in diameter, which corresponds to an extrusion ratio of ∼18:1.

2.2. Microstructural Characterization and Mechanical Test

Microstructures of the alloy were characterized with electron backscattered diffraction (EBSD) and transmission electron microscopy (TEM). The surface of the sample was mechanically ground using sandpapers and then electro-polished in an ethanol–10% perchloric acid electrolyte for EBSD characterization. TEM was employed to characterize finer microstructures in the alloy using a JEM-ARM200F instrument (JEOL Ltd., Tokyo, Japan). More details of EBSD and TEM analysis can be found in Refs [28,29].

Dog-bone tensile specimens with gauge dimensions of 18.0 mm × (L) × 4.8 mm (W) × 1.4 (T) were machined from the extruded alloys for standard tension tests. Cylindrical specimens with a diameter of 5 mm and a height of 7.5 mm were used for compression tests. The loading axes in tension tests were parallel to the extrusion direction while the compression tests were conducted with loading axes 0, 45, and 90 degrees from the extrusion direction. The tension and compression tests were conducted with crosshead speeds of 0.5 and 0.2 mm/min, respectively, which corresponds to a nominal strain rate of ~5 × 10⁻⁴ s⁻¹ in both tests.

2.3. Experimental Observations

As the solute Ca is dilute in this alloy, precipitates such as Mg₂Ca are not readily formed. A rich profusion of solute clusters in various sizes were found to distribute uniformly in the matrix, as revealed by high-angle annular dark field-scanning transmission electron microscopy (HAADF-STEM) as shown in Figure 1. Since the brightness of individual atomic columns in the HAADF-STEM image is proportional to the square of the averaged atomic number, each bright dot in Figure 1 represents a Zn/Ca-rich column. The presence of solute clusters rather than precipitates in the cast and as-extruded ZX20 alloy is likely the result of low extrusion temperature (250 °C) and high extrusion speed (2 mm/s) which tend to suppress the dynamic precipitation.

For the as-extruded ZX20 alloy, a tension–compression (T-C) asymmetric behavior [30,31,32] is observed. As shown in Figure 2, the stress–strain curve obtained from tensile tests along the extrusion direction (ED) differs strongly from that obtained from compressive tests along the ED. The tensile yield strength (TYS ≈ 150 MPa) was higher than the compressive yield strength (CTS ≈ 100 MPa). Yet, the stress level during the compression test increased rapidly after 2% strain, and the ultimate compressive strength (UCS ≈ 500 MPa) was much higher than the ultimate tensile strength (UTS ≈ 300 MPa).

The T-C asymmetry in the ZX20 alloy is attributed to the more frequent nucleation of deformation twins $\left\{10\overline{1}2\right\}$ in the compression test than that in the tension test. The ZX20 alloy exhibits a moderate extrusion texture (Figure 3). The $\left\{10\overline{1}2\right\}$ twinning would be suppressed under tension along the ED, but be favored under compression along the ED. However, compared to other as-extruded Mg alloys, such as AZ31, MN11, and Mg-5wt.%Y [33,34,35], the ZX20 alloy exhibits a much stronger hardening in the compressive stress–strain curve, which suggests that the growth of twins must have met some resistance. The above experimental observations motivated us to study the interaction between TBs and Zn-Ca solute clusters.

3. Computational Procedures

MD simulations were carried out to investigate the cluster–twin interaction in the ZX20 alloy. The simulations were performed using the open-source code “LAMMPS” [36]. The modified embedded-atom method (MEAM) interatomic potential developed by Jang et al. [37] for the Mg–Zn–Ca ternary system was utilized. The visualization tool Ovito [38] was used for analyzing the simulation data, and atoms were colored by atom type as indicated in the legend of each figure containing an MD snapshot. In particular, with the common neighbor analysis (can) in Ovito, atoms at defect sites such as grain boundaries, dislocations, and faults were distinguished.

The MD sample illustrated in Figure 4 contained 821,530 atoms, having dimensions of 55 nm × 52 nm × 4.5 nm. A pair of $\left\{10\overline{1}2\right\}$ TBs at a separation distance of 32 nm were introduced within the MD supercell under three-dimensional (3D) periodic boundary conditions. The lower TB was fixed by periodically replacing Mg atoms at compression GB sites with Zn atoms such that the interaction with the cluster only involved the upper TB (the TB moving toward the cluster) [8]. To avoid additional size effects in 3D, the shapes of clusters were chosen to be cylindrical with length equal to that of the MD box in the Z direction. The cluster size was measured by the radius R of the circular cross-section. Clusters containing different Zn and Ca contents were produced by randomly replacing Mg atoms by Zn and Ca atoms at a certain Zn/Ca ratio in the cluster domain.

Local strains and stresses were generated due to mismatch in atomic size which was most significant when Ca was introduced. The contents of Ca and Zn in the cluster zone were therefore limited to avoid unexpected defect nucleation, such as dislocations and stacking faults. Thus, only 30% Mg atoms of clusters were set to be replaceable in this study, and the Zn/Ca ratios and radius of clusters were chosen to be x:y $\in$ [0:10, 1:9, 5:5, 9:1, 10:0] and R $\in$ [1.5, 2.5, 4.0] nm, respectively. In this case, the Zn/Ca ratio (indicated as xZnyCa in the following parts, i.e., 10Zn, 1Zn9Ca, 9Zn1Ca, etc.) refers only to the 30% replaceable Mg atoms, irrespective of other Mg atoms.

Energy minimizations were performed on the entire supercell to relax the TB and the cluster. The isothermal–isobaric (NPT) ensemble was then employed to increase the temperature to 300 K at a time interval of 200 ps in zero-pressure conditions and the state was further relaxed at the same temperature by 100 ps with the canonical (NVT) ensemble. Then, simple shear strain was applied in the microcanonical (NVE) ensemble at a strain rate of ${1 \times 10}^8/\mathrm{s}$, which was slow enough to avoid artificial kinetic effects according to previous MD simulations [39,40,41]. The simple shear was applied in the X–Y plane to provide a driving force in accordance with the twinning shear to move the TB in the negative Y direction towards the cluster. A timestep of 0.001 ps was used in the MD simulations and the stress, total energy, and atomic position data were stored every 1 ps. To eliminate thermal noises, all figures were exported after performing conjugate gradient energy minimizations for 5ps to eliminate thermal fluctuation of the atomic structure and atoms at perfect Mg lattice sites were hidden for better observation [42].

4. Results and Discussion

4.1. Effect of the Zn/Ca Ratio

To clarify how cluster-hardening effects depend on the Zn/Ca ratio, a set of clusters with fixed radius R = 2.5 nm were considered. The corresponding stress–strain curves obtained by MD simulations are shown in Figure 5. The cluster-free case is taken as a reference for comparison. Due to the X–Y deformation in current simulations, the shear stress is computed as the sum value of the per-atom ${\tau }_{xy}$ in the MD supercell, while the shear strain is defined as $\Delta L/L0$, where $\Delta L$ is the displacement distance in the X direction from the unstrained orientation and $L0$ is the box length in the Y direction. It is worth noting that since twinning is the only mode of plastic deformation due to the absence of lattice dislocations or other defects, the yield stress defines the critical resolved shear stress (CRSS) for TB migration [43,44].

According to the stress–strain curves, the CRSS of TB migration is found to be ~100 MPa for the cluster-free case, and the subsequent flow stress stays at nearly the same level, indicating that there is hardly any strain hardening effect in the Mg lattice. When clusters are present, the yield points are found to differ significantly. For Zn-rich clusters (i.e., 9Zn1Ca, or 10Zn), the yield stress and the subsequent flow stress are also close to 100 MPa, suggesting a weak cluster pinning effect on TB. On the contrary, the yield stress and the subsequent flow stress apparently decreased with Ca-rich clusters (i.e., 1Zn9Ca or 10Ca), indicating that an attraction force has been imposed on the TB, which is probably caused by lattice distortions due to the large atom size of Ca. A similar attraction force was also observed between precipitates and an approaching TB in a recent study [45]. Then, immediately, a hump-like stress–strain response is observed when the TB migration is temporarily blocked by the Ca-rich cluster after their interaction. This essentially applies a hardening effect, which can be quantified by ${\tau }_{\Delta \mathrm{CRSS}}$ defined as the difference between the peak flow stress in the presence of clusters and the flow stress in the cluster-free case (Figure 5). It is found that the ${\tau }_{\Delta \mathrm{CRSS}}$ value increases from ~10 MPa to nearly 100 MPa as the Ca:Zn ratio rises from 1:9 to 10:0.

According to the stress–strain curves in Figure 5, a work hardening coefficient about 2000 MPa (θ = dσ/dε) was calculated [46,47,48] for the 1Zn9Ca and 10Ca cases, and about 1000 MPa for the 5Zn5Ca case. The ZX20 alloy actually has a θ value of about 750 MPa, which is comparable to the above computational values.

The interactions between a migrating TB and two clusters in different Zn/Ca ratios, 9Zn1Ca and 1Zn9Ca, are depicted in Figure 6a,b. After the onset of plastic yielding, the TB starts migrating towards the cluster by the glide of twinning dislocations, as shown for the T1 step in Figure 6, in agreement with previous MD simulations [45].

Afterwards, two different ways of interaction are observed. The TB can easily cut through the 9Zn1Ca cluster by leaving a basal dislocation behind, while the TB is significantly tangled with the 1Zn9Ca cluster. The different hardening effect by 9Zn1Ca and 1Zn9Ca clusters is likely a result of the misfit strain due to different atomic radii of Mg (150 pm), Zn (135 pm), and Ca (180 pm) [49]. The larger lattice distortion by the 1Zn9Ca cluster due to the higher concentration of Ca forces plenty of Mg atoms out of their original positions. In fact, more non-perfect hcp atoms are found for the 1Zn9Ca cluster, as shown in Figure 6. The misfit strain caused by the lattice distortion makes it difficult for TB to pass through the 1Zn9Ca cluster, leading to more stress.

It is interesting to notice that, after fully departing from the clusters, trailing dislocations connecting the TB and the cluster are observable. These <a> dislocations on basal planes are nucleated from the cluster surface to accommodate the high strain incompatibility between the cluster and twin, leading to a local plastic relaxation once the local stress and misfit strain are sufficiently high [50]. The number of the trailing dislocations increases when Ca dominates the cluster.

From Figure 6, the Ca-rich (1Zn9Ca) cluster has extra resistance against the migration of TBs in Mg-Zn-Ca alloys, indicating a stronger hardening effect than in the Zn-rich (9Zn1Ca) cluster.

4.2. Effect of the Cluster Size and Cluster Concentration

Size is another factor that influences the interactions of clusters with the TB. Stress–strain curves derived from TB interacting with 1Zn9Ca clusters with R = 1.5, 2.5, and 4.0 nm are shown in Figure 7a. It is found that the CRSS of TB migration dramatically reduces to 50 MPa and the ${\tau }_{\Delta \mathrm{CRSS}}$ rises up to nearly 150 MPa when the cluster has R = 4.0 nm. Apparently, the attraction force becomes stronger when increasing the cluster size, and so does the hardening effect.

Moreover, comparing the stress–strain curves for the 9Zn1Ca cluster with R = 2.5 nm (Figure 6a) and the 1Zn9Ca cluster with R = 1.5 nm (Figure 7a) suggests that the latter exhibits a more pronounced hardening effect. Therefore, the element content is regarded to play a more significant role than the cluster size in terms of hardening.

The effect of cluster concentration was studied as well. As mentioned earlier, the cluster considered here consisted of 70% Mg atoms and 30% (Zn + Ca) atoms to avoid unexpected defects resulting from excessive misfit strain before imposing shear strain. For the 9Zn1Ca case, however, the ratio of (Zn + Ca) can reach 50% without causing additional defects, which is due to the smaller atomic radius of Zn. The stress–strain curves in Figure 7b show that increasing the (Zn + Ca) ratio of the cluster from 30% to 50% can significantly enhance the hardening effect.

5. Conclusions

In this work, to understand the pronounced hardening effects observed experimentally, atomistic simulations are performed to systematically investigate the interactions between clusters and moving {10-12} twinning boundaries in Mg-Zn-Ca alloy. Our simulation results indicate that the cluster produced a hindering effect on TB migration, inducing a significant hardening effect in Mg-Zn-Ca alloy. The following conclusions can be reached:

(1)

Increasing the Ca content can aggravate the lattice distortion of clusters and results in a stronger hardening effect. Furthermore, the cluster hardening effect is also in a positive relationship with the size and concentration of the clusters.

(2)

The attractive effect of clusters on the TB is identified. The attractive force increases with the Ca content and size of the clusters.

(3)

Although the twin boundary is eventually able to bypass the clusters, basal dislocations are left behind, which causes a local plastic relaxation.

(4)

The Zn:Ca ratio in the cluster is found to play a more significant role than the cluster size in impeding TB migration.