domain: spi chim

text:
Hiba Azzeddine
email: azzeddine@univ-msila.dz

Fairouze Guerza-Soualah

Abdelkader Hanna

Anne-Laure Helbert

Francois Brisset

Thierry Baudin

Djamel Bradai

Investigation of the deformation and recrystallization kinetics in an Mg-Dy alloy processed by plane strain compression

In the present study, the deformation and recrystallization kinetics of Mg-0.41Dy (wt. %) alloy processed by plane strain compression (PSC) at 200 °C under strain rate of 10 -2 s - 1 were investigated using electron backscatter diffraction (EBSD) and microhardness measurements. The deformation microstructure was characterized by the presence of high amount of extension, contraction and double twins. A basal <0001> and prismatic <10 ̅ 0> fibers were developed during PSC test. The recrystallization and grain growth kinetics were investigated after subsequent annealing at 450 °C for time periods ranging from 30 min to 7 days. A homogenous microstructure with equiaxed grain was developed during annealing. The average grain size increased with increasing annealing time and reaches a value of 95.93.2 m after 7 days. While, the microhardness decreased from 43.30.14 (deformed state) to 37.90.3 HV after annealing for 7 days.

Introduction

During the last decades, Mg-based alloys containing rare-earth elements (RE) have extensively been investigated due to their excellent mechanical properties and good formability at low and high temperature compared to conventional Mg-based alloys with aluminum as alloying element like AZ31 (Mg-3Al-1Zn, wt.%) one [START_REF] Imandoust | A review on the effect of rare-earth elements on texture evolution during processing of magnesium alloys[END_REF]. It has been stated that the proposed RE elements can change the stacking fault energy of Mg matrix and this renders the activation of non-basal slip systems such as pyramidal <c+a> easier [START_REF] Sandlöbes | On the role of non-basal deformation mechanisms for the ductility of Mg and Mg-Y alloys[END_REF] and also plays a strong role on the enhancement of a solute drag and dislocation annihilation [START_REF] Jung | Role of RE in the deformation and recrystallization of Mg alloy and a new alloy design concept for Mg-RE alloys[END_REF][START_REF] Barrett | The effect of rare earth element segregation on grain boundary energy and mobility in magnesium and ensuing texture weakening[END_REF]. Moreover, the presence of Mg-RE second particles strongly affects the evolution of the microstructure and texture by activation of Particle-Stimulated Nucleation (PSN) mechanism [START_REF] Al-Samman | Modification of texture and microstructure of magnesium alloy extrusions by particle-stimulated recrystallization[END_REF]. However, the effect of RE elements on the evolution of deformation, recrystallization, and grain growth processes is not yet fully understood. Hence, the present study aims to investigate the deformation and recrystallization behaviours of the binary Mg-0.41Dy (wt.%) alloy after plane strain compression (PSC) at 200 °C up to a true strain of 1.2 and subsequent annealing at 450 °C for time periods ranging from 30 minutes to 7 days.

Experimental material and procedures

The Mg-0.41Dy alloy has been provided in an as-cast condition by the Institute für Metallkunde und Metallphysik (IMM-RWTH) in Aachen, Germany. The as-cast microstructure exhibited coarse grains (800 μm) with random texture and the presence of Mg 24 Dy 5 second phase [START_REF] Guerza-Soualah | The deformation and recrystallization behaviour of an Mg-Dy alloy processed by plane strain compression Materials Today[END_REF]. Samples with dimensions of 14 mm (longitudinal direction, LD) × 10 mm (transverse direction, TD) × 6 mm (compression direction, CD) were deformed by PSC test at 200°C under strain rates of 10 -2 s -1 to a final true strain ε = 1.2. After that, the samples were annealed at 450 °C for 30 min to 7 days. The microstructure of the samples was investigated in the LD-TD plane using optical microscopy and EBSD measurements. The EBSD data (scan area was 823 × 786 μm 2 with a step size of 1 μm) acquisition and analysis were undertaken using the TSL Orientation Imaging Microscopy, OIM TM software. The grain size data was obtained using a grain tolerance angle of 5°, and minimum grain size of 5 pixels. The confidence index (CI), which quantified the reliability of the indexed Kikuchi, was taken higher than 0.05 to exclude poor-quality pixels during the clean-up procedure. Average Vickers microhardness was measured using at least five indentations under a load of 100 g and a dwell time of 10 s (SHIMADZU type HMV-2 tester).

Results and discussions

Deformation microstructure

Figure 1 shows a scanning electron microscopy (SEM) micrograph of the Mg-0.41Dy alloy after the PSC test in the backscattering mode with different magnification. The deformation microstructure exhibits large amounts of deformation features such as twins and shear bands (as indicated by arrows). The high magnification of the yellow box shows (Figure 1b) the presence of linearly extended second phase particles inclined at 40° relatively to the loading direction and this feature indicates a possible dynamic precipitation during PSC test. Their small size did not allow their definitive identification but they possibly are those identified in the as-cast condition (Mg 24 Dy 5 ) [START_REF] Guerza-Soualah | The deformation and recrystallization behaviour of an Mg-Dy alloy processed by plane strain compression Materials Today[END_REF]. Moreover, a massive dynamic precipitation has been evidenced in the Mg-0.41Dy alloy after PSC test at higher temperature (400 °C) and under lower strain rate (10 -4 s -1 ) [START_REF] Guerza-Soualah | The deformation and recrystallization behaviour of an Mg-Dy alloy processed by plane strain compression Materials Today[END_REF]. Figures 2a and2b show the microstructure of a deformed Mg-0.41Dy alloy in terms of orientation imaging micrographs in an inverse pole figure (CD-IPF) mode and grain orientation spread (GOS) maps. The white and black lines in the ND-IPF map were ascribed to low-angle grain boundaries (LAGBs, 5-15°) and the high-angle grain boundaries (HAGBs, >15°), respectively. The GOS parameter is defined as the average deviation between the orientation of each point in the grain and the average orientation of the grain which allows a net separation between the recrystallized grains and the deformed ones [START_REF] Cho | Determination of a mean orientation in electron backscatter diffraction measurements[END_REF]. Usually, the grains are considered as recrystallized in Mg-based alloys if the GOS parameter varies between 1 and 2° [START_REF] Tighiouaret | Thermal Stability of an Mg-Nd Alloy Processed by[END_REF][START_REF] Drouven | Twinning effects in deformed and annealed magnesium-neodymium alloys[END_REF]. The black zones shown in CD-IPF map indicate the highly deformed areas of the sample. In addition, massive twins in form of steps were observed in the CD-IPF map (see arrows). Similar observation was reported in the same alloy after PSC at 200 °C under lower strain rate (10 -4 s -1 ) [START_REF] Guerza-Soualah | The deformation and recrystallization behaviour of an Mg-Dy alloy processed by plane strain compression Materials Today[END_REF]. However, the twin fraction was more obvious under processing at higher strain rate (10 -2 s -1 ). The corresponding {0002} pole figure shows that during PSC test, basal fiber <0001> // CD and prismatic fiber <10 ̅ 0> // CD were formed. It has previously been demonstrated that the 86°<11 ̅ 0> extension twin caused the tilt of the c-axe about 86° from the basal plane of the parent grain, which led to the formation of prismatic <10 ̅ 0> // CD fiber. While, the contraction 56°<11 ̅ 0> and double twins (38°<11 ̅ 0> and 22°<11 ̅ 0>) caused the spread of the basal plane toward TD [START_REF] Guerza-Soualah | The deformation and recrystallization behaviour of an Mg-Dy alloy processed by plane strain compression Materials Today[END_REF]. The GOS map (Figure 2b) demonstrated that dynamic recrystallization (DRX) did manifestly not occur at 200 °C contrarily to what already was reported for hot-deformed Mg-based alloys [START_REF] Barrett | The effect of rare earth element segregation on grain boundary energy and mobility in magnesium and ensuing texture weakening[END_REF][START_REF] Abdessameud | Grain growth in AZ31 alloy after uniaxial compression[END_REF]. The pinning effect of RE elements and their capacity to reduce the stacking fault energy were the main raisons for the softening of the Mg-RE alloys [START_REF] Jung | Role of RE in the deformation and recrystallization of Mg alloy and a new alloy design concept for Mg-RE alloys[END_REF][START_REF] Barrett | The effect of rare earth element segregation on grain boundary energy and mobility in magnesium and ensuing texture weakening[END_REF]. Meanwhile, some zones on the microstructure with GOS values between 2 and 4° dynamically recovered. An example of recovered zone is limited by a black square in Figure 2b. Figure 2c demonstrated that this specific zone contains several twin types as highlighted. They are: extension twins (86°<11 ̅ 0> in green), contraction twins (56°<11 ̅ 0> in red), double twins (38°<11 ̅ 0> in blue) and 22°<11 ̅ 0> (in yellow). It is well known that twins are the preferable site for DRX and even for static recrystallization during annealing [START_REF] Guerza-Soualah | Microstructural and textural investigation of an Mg-Dy alloy after hot plane strain compression[END_REF][START_REF] Guan | Twin recrystallization mechanisms and exceptional contribution to texture evolution during annealing in a magnesium alloy[END_REF]. It can be observed that double twin dominates due to the rapid transformation of the contraction twin into the double twin during deformation processing [START_REF] Niknejad | The role of double twinning on transgranular fracture in magnesium AZ61 in a localized stress field[END_REF].

Recrystallization and grain growth kinetics

Figure 3 shows the evolution of the microstructure of the processed Mg-0.41Dy after annealing at 450 °C between 30 min to 7 days. The alloy exhibits a typical recrystallized microstructure with equiaxed grains. The evolution of the mean grain size as a function of annealing time is shown in Figure 4a. Obviously, the mean grain size increased rapidly with increasing annealing time from 48.12 μm after 30 min to 95.93.2 μm after 7 days. The evolution of microhardness of the Mg-0.41Dy alloy as a function of annealing time is shown in Figure 4a. After a pseudo-plateau, the microhardness decreased rapidly from 43.30.5Hv in asdeformed state to 38.6 0.6Hv after 3h of annealing and then a steady state is reached (37.9  0.3 Hv after 7 days of annealing). The achieved value after 2 hours annealing leveled up more or less. The overall evolution is certainly indicative of a recrystallization and grain growth processes. Subsequently, the recrystallization kinetics of the alloy were investigated using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model [START_REF] Vandermeer | Microstructural modeling of recrystallization in deformed iron single crystals[END_REF]:

(1) where X is the recrystallized fraction, k a pre-exponential constant, and n the Avrami exponent. The X can be estimated by microhardness values as followed:

(

) 2
where Hv t is the microhardness of the annealed sample at time t, Hv 0 is the microhardness of the deformed sample annealed, and Hv f is the microhardness after annealing for 7 days. The Avrami (n) exponent was obtained by a linear relationship from equation (1) as presented in Figure 4b. The n value was lower than to the unity (n = 0.5). Usually n = 1 indicates that the static recrystallization is governed by one-dimensional grain growth due to the migration of high misorientation grain boundaries [START_REF] Fenghui | Recrystallization Kinetics of Fe-3%Si after Deformation at High Strain Rate and High Temperature[END_REF]. A lowering of n value to less than unity may be explained by the non-random recrystallization sites present in the deformed alloy [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF]. It may be stated that the recrystallization preferentially occurred within the twins and shear bands as shown in Figure 1 and2.

It was previously found that the n value decreased with increasing deformation temperature owing to the change of the deformation features present in each deformation condition such as presence of twins and the occurrence of DRX [START_REF] Guerza-Soualah | The deformation and recrystallization behaviour of an Mg-Dy alloy processed by plane strain compression Materials Today[END_REF][START_REF] Guerza-Soualah | Microstructural and textural investigation of an Mg-Dy alloy after hot plane strain compression[END_REF]. In addition, similar n value (~ 0.5) was obtained for Mg-0.41Dy processed by PSC at 200 °C under lower strain rate (10 -4 s -1 ) [START_REF] Guerza-Soualah | The deformation and recrystallization behaviour of an Mg-Dy alloy processed by plane strain compression Materials Today[END_REF] indicating that the strain rate does not strongly affect the recrystallization and grain growth kinetics.

Conclusion

 The deformation microstructure of Mg-0.41Dy alloy after PSC test at 200 °C under strain rate of 10 -2 s -1 was characterized by the presence of high amount of extension, contraction and double twins. The deformation texture was characterized by the formation of basal {0001} and prismatic {10 ̅ 0} fibres.  The recrystallization microstructure of the processed alloy after annealing at 450 °C up to 7 days was characterized by a homogenous normal grain growth. The Avrami exponent of recrystallization (~ 0.5) indicated that the recrystallization preferentially occurred within the deformation features, mainly the twins in their different sorts.

Figure 1 :

 1 Figure 1: SEM micrographs with different magnification of the Mg-0.41Dy alloy after the PSC test.

Figure 2 :

 2 Figure 2: (a) CD-IPF map, (b) GOS map, (c) corresponding {0002} pole figure of the CD-IPF map and (d) the selective zone showing the presence of different twins in the PSC processed Mg-0.41Dy alloy.

Figure 3 :

 3 Figure 3: Evolution of the microstructure of the PSC processed Mg-0.41Dy alloy after annealing at 450 °C for: (a) 30 min, (b) 10 h, (c) 3 days and (d) 7days.

Figure 4 :

 4 Figure 4: (a) Evolution of mean grain size and microhardness as a function of annealing time and (b) evolution of ( ) as a function of ln(t) for the processed Mg-0.41Dy alloy.

Acknowledgements

Dr. Talal Al-Samman and his staff from the Institüt für Metallkunde und Metallphysik, RWTH Aachen, are heartily acknowledged for providing the samples and their assistance. This work was supported by the PRFU national project under Grant Agreement No. B00L02UN280120180005.