1.2 Deformation mechanisms of Mg alloys
1.2.2 Slip systems in Mg alloys
In materials science, plastic deformation is usually achieved by the motion of dislocations, namely slip. Slip systems describe the set of slip planes and slip directions for which dislocation motion easily occurs. The Burgers vector, denoted as b, represents the direction and magnitude of lattice distortion caused by a dislocation. Dislocations usually slide on the close-packed planes and in close-packed directions because of a small magnitude of Burgers vector. The smaller magnitude of Burgers vector indicates a smaller energy barrier for atoms to move from one position to the next position. In Mg alloys, (0001) plane and <112�0>
direction are the close-packed plane and direction, also called basal plane and <a> direction. Apart from that, slip can occur on the {101�0} prismatic planes which are perpendicular to the basal planes, or the inclined pyramidal {112�1} and {112�2} planes. The <c+a> Burgers vector of pyramidal slip can accommodate strains along [0001] axis, c-axis, which is the very important deformation mode at high temperature. Slip systems in Mg alloys are normally classified into three categories, basal <a>, prismatic
<a> and, pyramidal slip <c+a> slip. The schematics of different slip systems are shown in Figure. 1.2.2.
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Table. 1.2.1 Three main slip systems in Mg alloys.
Slip systems Slip planes Slip directions Burgers vector Magnitude
Number of independent
slip system
Basal (0001) <112�0> 𝑎𝑎⃑ |𝑎𝑎| 2
prismatic {101�0} <112�0> 𝑎𝑎⃑ |𝑎𝑎| 2
{101�1} <112�0> 𝑎𝑎⃑ |𝑎𝑎| 4
pyramidal {112�1}
<112�3> 𝑐𝑐⃑+𝑎𝑎⃑ �|𝑎𝑎|2+ |𝑐𝑐|2 5 {112�2}
Figure. 1.2.2 Slip systems in Mg alloys: (a) <a> slip on basal, prismatic and pyramidal planes, (b) <c+a>
slip on pyramidal planes. Slip planes and slip directions are marked as transparent frames and thick black arrows, respectively.
Basal slip is the most common slip system at room temperature due to the lowest CRSS compared with other slip systems. This slip system has a Burgers of <112�0> vectors and glides on (0001) basal planes, which are the close-packed direction and planes in pure Mg. There are three <a> Burgers vector on the basal plane, however, only two of them are independent. According to the Von Mises Criterion, five independent slip systems are required for uniform polycrystalline deformation. This is why basal slip is usually discussed with other deformation modes like prismatic slip and twinning.
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At room temperature, it is believed that prismatic slip can hardly occur in Mg alloys because its CRSS was 50-100 times higher than basal slip [23]. However, a considerable amount of prismatic slip traces were observed at room temperature deformation by Hauser [22]. The Burgers vector of prismatic slip is <112�0>
vector which is the same with basal slip. It provides another two independent slip systems. However, both basal slip and prismatic slip with <a> Burgers vectors cannot accommodate the strain along c-axis.
Pyramidal slip has a Burgers vector of <c+a> either on 1st order {101�1} or 2nd order {112�2} planes. It is believed to play a minor role in the deformation process due to its large Burgers vector. In fact, pyramidal slip was present in all Mg alloys with various deformation temperature [24]. Pyramidal slip tends to dissociate into partial dislocations to reduce the high energy. Pyramidal slip is the only slip system that can accommodate the strain along c-axis, and thus is important for the homogeneous deformation [25].
Temperature is one of the key factors that affect the activation of deformation modes. In the crystal lattice, the defects like precipitates and solute atoms hinder the dislocation motion by producing short-range stress.
When the temperature is increased, the dislocations within the material have sufficient energy to overcome these short-range stresses, in other words the CRSS is reduced. Compared with other deformation modes, basal slip is less sensitive to the temperature. The difference of CRSS between basal slip and other deformation modes rapidly dropped with increasing temperature, as is shown in Figure. 1.2.3 [26]. This phenomenon can be explained with cross slip from basal to non-basal planes and will be discussed later.
The improved ductility of Mg alloys derives from the cooperation of various deformation modes at elevated temperature.
Figure. 1.2.3 The relationship between CRSS values of different deformation modes and temperature in literature [26].
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The activation of slip systems is influenced by many factors such as solid solution, precipitations and texture.
The solution atoms introduce mismatch and stress field into the lattice because of the difference in atomic radius. This mismatch will hinder the movement of dislocations. A high level of stress is necessary for dislocations to overcome this obstacle, so called solid solution strengthening mechanism. The experimental work shows that rare earth elements improve the creep resistance by strengthening the basal slip [27]. The solution softening of prismatic slip was firstly reported by Dorn [22]. They associated the improved ductility by Li addition with the enhanced activity of prismatic slip. The reduced c/a ratio [28] and cross slip [29]
mechanisms are the most likely reasons for the phenomenon.
The geometric relationship between precipitate and basal plane plays an important role in the aging hardening behaviors. Nie [30] proposed that the plate shape precipitates on basal planes, which are the most common precipitates like Mg17Al12 in Mg alloys, are the least effective precipitate geometry for pinning basal dislocations. The precipitates in Mg-RE alloys, such as WE54 and WE43, are plate shape and located on prismatic planes. These precipitates are the most effective to impede basal slip. As prismatic and pyramidal slip are considered as complement deformation modes to basal slip, it is difficult to exclude the effect of precipitates on non-basal slip from basal slip.
The empirical Hall-Petch relationship, smaller grain size better mechanical properties, has been developed for Mg and its alloys [31]. Decreasing the grain size will decrease the dislocation concentration at the grain boundaries, and increase the applied stress necessary to move a dislocation across a grain boundary. There are controversial views on the grain size effect on slip systems. One is that smaller grains suppress basal slip more than prismatic and pyramidal slip [32]. Prismatic slip was mostly observed within some micrometers to the grain boundaries due to the highly localized stress in boundary region. Giving a certain dimension of a material, the one with a smaller grain size microstructure has a higher volume fraction of preferred sites for prismatic and pyramidal slip. In another world, the activity of prismatic and pyramidal slip will be increased. However, the study by Jain [33] showed a similar level of basal vs non-basal slip activity in different grain size samples.
Due to the relatively low basal stacking fault energy, the basal dislocation tends to dissociate into partial dislocations. Thus, the basal to non-basal planes cross slip, which requires the constriction of partial dislocations is less likely to occur in Mg alloys. Nevertheless, the activation of cross slip was reported to play an important role in the deformation behaviors [34]. Yoshinaga [35] proposed the jog-pair mechanism to explain the cross slip in Mg alloys, as is shown in Figure. 1.2.4. Screw <a> dislocations on primary basal plane firstly constricted in some atomic length scale. It can cross slip onto prismatic plane and dissociate in another basal plane.
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Figure. 1.2.4 Schematic illustrations of jog-pair mechanism: (a) dissociate basal screw slip constrict and cross glide onto prismatic plane, (b) the non-basal part of the glide dislocation cross slip onto basal planes
again, (c) the basal screw dislocation entirely climb to the neighboring basal plane [35].