Effect of grain size and texture on the slip systems

The well-known Hall-Petch equation describes the relationship between the grain size and yield strength.

Smaller grain size means a higher fraction of grain boundaries that hinder the dislocation migration.

Dislocations accumulate at grain boundaries and produce a backward force to the incoming dislocations [134]. Thus, a higher applied stress is required for the migration and transmission of the dislocations over grain boundaries, resulting in a high yield strength. Figure. 3.1.3 shows the ZN12 sample has a smaller average grain size than the AN12 sample. However, a lower yield strength is found in the ZN12 sample in comparison to the AN12 sample, Figure. 3.1.2. This phenomenon can be derived from the higher fraction of grains with high SF values for basal slip in the ZN12, as shown in Figure. 3.1.5 (c). Another possible reason is the twinning activity as a typical sigmoid-shape feature is observed in the stress-strain curve of the ZN12 sample.

In the quasi in-situ tensile experiments, a higher frequency of slip traces and twins were observed in the ZN12 sample than the AN12 sample. It is not convincing to attribute this phenomenon simply to its weak texture as many factors can influence the deformation modes. The texture of the ZN12 sample consist of RD and TD spread components with a texture intensity of 5 m.r.d., while the AN12 sample has a strong basal texture with a much higher intensity of 14 m.r.d. It is difficult to compare these two textures quantitatively.

To exclude the effect of grain size and texture on the deformation behaviors, some grain subsets according to the grain size and SF value are defined from the EBSD data. The effect of texture on deformation can be estimated with SF value. As shown in Table. 4.1.1, 183 and 314 grains with grain sizes ranging from 10 to 60 μm are extracted from the EBSD data of the initial AN12 and ZN12 samples, respectively. This range is set based on the grain size distribution in Fig. 3.1.3 to consider more representative grains. The reason to exclude the grains smaller than 10 μm from the analysis is that they are too small to have obvious slip traces, although slip systems are activated in the grains. The evaluated grains are termed as small (10-25 μm), middle (25-40 μm) and large grains (40-60 μm). The theoretical SF values for basal slip of the grains are calculated and separated into low (0-0.15), mid (0.15-0.35) and high (0.35-0.5) subsets. Thus, the deformation behaviors in the same subsets of the AN12 and ZN12 can be compared with each other as the effects of grain size and texture are excluded.

The basal slip activities of the AN12 and ZN12 samples are estimated by calculating the number of grains with obvious basal slip traces. It should be mentioned that non-basal slip traces are observed in the grains

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which normally have basal slip traces. More than 70 percent of evaluated grains in the ZN12 sample show obvious basal slip traces in all grain size ranges, as shown in Table. 4.1.1. This is much higher than that of the AN12 sample, especially in the subsets of small grain size. A tendency that basal slip is favored in larger grain can be found in the ZN12 sample. Taking into account the SF value for basal slip, the grains with high SF values naturally have larger probabilities of basal slip traces than those with low SF values in the same grain size range. It is to mention that the ZN12 sample has a higher frequency of slip traces in comparison to its counterpart, independent of the grain size and SF range. This means some underlying factors contribute to the higher basal slip activities in the ZN12 sample which will be discussed later.

The statistical data of the observed slip traces are shown in Table. 3.1.4. Basal slip is the dominant slip mode in both samples, followed by pyramidal and prismatic slip. The occurrence frequency of various slip modes as a function of the grain size and SF values, determined by the observed slip traces at ε = 0.08, is shown in Figure. 4.1.1. The grain size distributions of grains with observed basal slip traces, Figure. 4.1.1 (a) and (b), are very similar to the total grains size distribution in Figure. 3.1.3 (e). The frequency of observed basal slip traces is higher in small grains than large grains in both samples. However, a considerable number of non-basal slip traces were observed in grains larger than 40 μm, Figure. 4.1.1 (c) and (d), despite the very limited number of grains in this range. It seems that non-basal slip occurs easier in large grains than small ones. In finer grain size sample, the local stress concentration is reduced which is important for the activation of basal slip. On the contrary, larger grain size is beneficial to the stress accumulation that promotes non-basal slip.

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Table. 4.1.1 Number of grains with obvious basal slip traces at ε = 0.08 Large (40-60 μm) High SF 3/4 15/37 9/9 28/32 * means 4 out of 27 grains in the subset of small and low SF show obvious basal slip traces. ** means there are 90 grains in this small grain size, among which 27 grains show obvious basal slip traces.

Mid SF 8/13 13/16

Low SF 4/20 6/7

Middle (25-40 μm) High SF 15/17 31/56 47/52 80/103

Mid SF 11/21 24/33

Low SF 5/18 9/18

Small (10-25 μm) High SF 12/24 27/90** 69/75 132/179

Mid SF 11/39 39/60

Low SF 4/27* 24/44

Sample AN12 ZN12

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Figure. 4.1.1 Distribution of: (a) and (b) the grain size in the AN12 and ZN12 sample, (c) and (d) the corresponding SF value of grains with observed slip traces at ε = 0.08, respectively.

Due to the strong anisotropy of Mg alloys, the initial texture plays an important role in the deformation behaviors. In the AN12 sample, the c-axis of most grains are parallel to ND. This orientation results in a nearly zero basal slip SF so that basal slip can hardly occur. On the contrary, the ZN12 sample with a weakened texture has a higher potential for basal slip. The SF for basal slip varies from 0 to 0.5 while the SF for the prismatic and pyramidal slip are higher than 0.35 in most grains, as shown in Figure. 3.1.5. It should be mentioned that only the max SF value of slip systems are shown in the figure, though there are 3, 3 and 6 equivalent variants for basal, prismatic and pyramidal slip systems, respectively. The measured SF of different slip systems based on the observed slip traces are shown in Figure. 4.1.1 (c) and (d). There is an obvious trend that the number frequency of grains showing basal slip traces increases with increasing the SF range for basal slip. The average SF value for basal slip of grains with observed basal slip traces are 0.29 and 0.32 for the AN12 and ZN12, relatively. This minor difference in the SF value cannot explain the much higher frequency of the observed basal slip traces in the ZN12 than the AN12, as shown in Table. 4.1.1.

The distributions of non-basal slip SF of grains with observed slip traces are distinct from the max SF in both samples. Some of the grains with observed prismatic and pyramidal slip traces show a lower SF than

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0.15, Figure. 4.1.1 (c) and (d), which are much lower than the calculated SF value for non-basal in Figure.

3.1.5 (e) and (f). This phenomenon is called non-Schmid factor behavior that low SF slip systems or twin variants occur instead of those with high SF. The non-Schmid behavior of non-basal slip is attributed to the local stress that can be quite different from the applied stress. The non-basal slip usually occurs at large strain due to high CRSS. As a result, the SF value calculated based on the applied stress state is inapplicable to the non-basal slip.

One reason for the significant difference in the basal slip activities between the AN12 and ZN12 samples is the inhomogeneity of deformation. This inhomogeneous deformation in the AN12 sample causes a localized strain in a few grains while other grains are less (or not) deformed. These less deformed grains have a low dislocation density to show obvious slip traces. Strain compatibility is important to understand the strain localization. Continuous incoming basal dislocations will pile up at the grain boundaries and exert stress on the adjacent grain such that dislocation slip is activated. In this case, the geometrical compatibility factor m‘, determining the possibility of basal to basal slip transmission between the adjacent grains, is investigated.

The details of the geometrical compatibility factor are described in the experiment chapter 2.5.

The geometrical compatibility factor between the neighboring grains is shown in Figure. 4.1.2. The majority of the grain boundaries in the AN12 sample, colored in yellow and orange, have a high compatibility factor.

This means that basal slip is easy to transfer across the grain boundaries, and homogeneous deformation is expected. On the contrary, the ZN12 sample shows the low geometrical compatibility factors, Figure. 4.1.2 (b), which hinder the basal slip transfer. The average geometrical compatibility factors are 0.71 and 0.45 for the AN12 and ZN12, shown in Figure. 4.1.2 (c). It is no surprise to get these results when recalling the initial textures of the two samples. In the AN12 sample with a strong basal texture, basal planes of the adjacent grain pairs align almost parallel, and the basal slip transfer is facilitated. On the contrary, the basal slip in the ZN12 sample is difficult to cross the grain boundary because of the large misorientation of basal planes in adjacent grain pairs. However, the experimental results of the slip trace analysis opposite, i.e., higher frequency of basal slip traces in the ZN12 than the AN12 sample. Again, a conclusion can be drawn that the geometrical compatibility is not the main reason for the high activity of basal slip in the ZN12 sample.

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Figure. 4.1.2 Geometrical compatibility factor of basal slip transmission: (a) the AN12 sample, (b) the ZN12 sample, (c) distribution of geometrical compatibility factor.

The mechanism possible to explain the distinct basal slip activities between the AN12 and ZN12 samples is the CRSS value for basal slip. That is, the ZN12 sample seems to have a lower CRSS for basal slip than the AN12 sample, even though the CRSS values estimated with the stress-strain curve are comparable in both samples. Owing to the stronger affinity of Al to Nd, large and stable precipitates are more easily formed in the AN12 sample than the ZN12 sample. This is also presented in Figure. 3.2.6 that the AN12 sample has much more coarse precipitates than the ZN12 sample. The large precipitates act as obstacles against the dislocation motion, which significantly hinder basal slip. On the contrary, the alloying elements in the ZN12 sample exist in a solid solution condition. The strengthening from solute atoms is weaker compared to non-shearable precipitates, leading to a higher strength in the AN12 than the ZN12 sample. Besides, the solutes in the matrix, e.g., Zn and Nd, also influence the stacking fault energy and eventually change the CRSS [135, 136].

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The slip trace data in Table.3.1.4 shows that the ZN12 sample has a higher frequency of non-basal slip traces than the AN12 sample at ε = 0.02. Interestingly, the total number of pyramidal slip trace is twice as high as that of prismatic slip trace after ε = 0.08 in both samples. In general, pyramidal slip is believed to be more difficult than prismatic slip due to a higher CRSS. The result suggests that strengthening by alloying elements is smaller on pyramidal slip than prismatic slip in both AN12 and ZN12 samples.