Salaheddine Sadi

Abdelkader Hanna

Thierry Baudin

Anne-Laure Helbert

François Brisset

Djamel Bradai

Hiba Azzeddine
email: pr.hibaazzeddine@univ-msila.dz

Evaluation of static recrystallization and grain growth kinetics of hot-rolled AZ31 alloy

Keywords: Activation energy, AZ31 alloy, Grain growth, Kinetics, Static recrystallization, Rolling

The static recrystallization/grain growth kinetics of the AZ31 (Mg-3Al-1Zn, % wt.%) alloy were investigated employing Vickers microhardness and electron backscatter diffraction (EBSD) measurements. The AZ31 alloy was subject to a hot-rolling for 70 % of thickness reduction and then annealed at various temperatures (150, 250, and 350 °C) from 5 min to 24 h. First, the static recrystallization kinetics were analysed by means of the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model. The results showed that the recrystallization occurred under two regimes both involving their own Avrami exponent/activation energy. In regime I, the Avrami exponent was found in the range of 1.5-0.35 depending on the annealing temperature and activation energy of 74.1±5.7 kJ/mol. In regime II, an identical value of Avrami exponent was found (0.1-0.2) and a very low activation energy of 14.8±0.7 kJ/mol was found for all annealing conditions. Non-random nucleation sites such as shear bands were considered as the main factor responsible for the deviation from the JMAK model. Moreover, the grain growth kinetics was well fitted by the general equation where

. Accordingly, Q g = 109± 0.2 kJ/mol which is median between grain boundary diffusion and bulk diffusion values for Mg and its alloys. The derived activation energies were discussed in terms of influencing factors such as solute drag, formation of basal texture, and microstructural heterogeneities like shear bands and twinning.

Introduction

Nowadays, transportation industries are more interested on lightweight design to reach rigorous necessities of fuel productivity and reduce environmental pollution. Lightweight magnesium (Mg) based alloys are promising candidates for these industries owing to their excellent strength-to-weight ratio [START_REF] Kainer | Challenges for Implementation of Magnesium into More Applications[END_REF][START_REF] Song | Latest research advances on magnesium and magnesium alloys worldwide[END_REF]. Nevertheless, at low deformation temperatures, Mgbased alloys endure poor formability because of a lack of deformation mechanisms and the development of sharp basal texture during deformation processing which border their potential structural applications [START_REF] Mordike | Magnesium: Propertiesapplicationspotential[END_REF].

Microstructural changes, which mainly are grain refinement and texture weakening through dynamic recrystallization (DRX) and/or static recrystallization (SRX) during thermomechanical processing are the keys to the development of a new class of Mg-based alloys with required properties [START_REF] Zhang | Effect of annealing on the microstructure and mechanical properties of Mg-2.5Zn-0.5Y alloy[END_REF][START_REF] Amani | Recrystallization and mechanical properties of WE43 magnesium alloy processed via cyclic expansion extrusion[END_REF][START_REF] Guo | The role of recrystallization and grain growth in optimizing the sheet texture of magnesium alloys with calcium addition during annealing[END_REF][START_REF] Samadpour | Processing of AM60 magnesium alloy by hydrostatic cyclic expansion extrusion at elevated temperature as a new severe plastic deformation method[END_REF][START_REF] Zhang | Toward the development of Mg alloys with simultaneously improved strength and ductility by refining grain size via the deformation process[END_REF]. At high temperatures, the formability of Mg-based alloys is increased and improved since further slip systems could be thermally activated and also due to the occurrence of DRX. In fact, DRX is the principal mechanism responsible for grain refinement in Mg-based alloys during deformation processing [START_REF] Beer | Microstructure evolution in hot worked and annealed magnesium alloy AZ31[END_REF][START_REF] Abouhilou | Microstructure and texture evolution of AZ31 Mg alloy after uniaxial compression and annealing[END_REF][START_REF] Hanna | Evaluating the textural and mechanical properties of an Mg-Dy alloy processed by high-pressure torsion[END_REF][START_REF] Guerza-Soualah | The deformation and recrystallization behaviour of an Mg-Dy alloy processed by plane strain compression[END_REF][START_REF] Guerza-Soualah | Microstructural and textural investigation of an Mg-Dy alloy after hot plane strain compression[END_REF][START_REF] Gui | Grain refinement and weaktextured structures based on the dynamic recrystallization of Mg-9.80Gd-3.78Y-1.12Sm-0.48Zr alloy[END_REF][START_REF] Sadi | Characterization of microstructure and texture of binary Mg-Ce alloy processed by equal channel angular pressing[END_REF][START_REF] Kavyani | Microstructure refinement, mechanical and biocorrosion properties of Mg-Zn-Ca-Mn alloy improved by a new severe plastic deformation process[END_REF].

The Hall-Petch relationship indicates that the strength of a material increases through decreasing the grain size and incidentally because to the increase of the number of grain boundaries that prevent the dislocation motion [START_REF] Armstrong | Engineering science aspects of the Hall-Petch relation[END_REF]. However, grain growth generally occurs during the SRX process and causes the loss of thermal stability [START_REF] Su | Recrystallization and grain growth of deformed magnesium alloy[END_REF][START_REF] Chao | Static recrystallization kinetics of a heavily cold drawn AZ31 magnesium alloy under annealing treatment[END_REF][START_REF] Bhattacharyya | Texture enhancement during grain growth of magnesium alloy AZ31B[END_REF][START_REF] Su | Static recrystallization behavior of magnesium AZ31 alloy subjected to high speed rolling[END_REF][START_REF] Roostaei | Microstructural evolution and grain growth kinetics of GZ31 magnesium alloy[END_REF][START_REF] Tighiouaret | Thermal Stability of an Mg-Nd Alloy Processed by High-Pressure Torsion[END_REF]. Consequently, it is crucial to distinguish the static recrystallization/grain growth kinetics of Mg-based alloys.

Usually, any assessment of the static recrystallization/grain growth kinetics is based on two parameters: 1) a phenomenological exponent which characterizes the mechanism responsible for recrystallization and/or the grain growth and 2) the activation energy which determines the magnitude of the resistance to any grain growth. For Mg-based alloys, the calculated activation energies for recrystallization/grain growth are generally compared with grain boundary diffusion activation energy (92 kJ/mol) or with the lattice self-diffusion energy (135 kJ/mol) [START_REF] Frost | Deformation-mechanism maps[END_REF]. However, a deviation from these values due to the presence of inhomogeneous nucleation sites such as twinning and shear bands formed during deformation processing is often reported [START_REF] Beer | Microstructure evolution in hot worked and annealed magnesium alloy AZ31[END_REF][START_REF] Guerza-Soualah | The deformation and recrystallization behaviour of an Mg-Dy alloy processed by plane strain compression[END_REF][START_REF] Su | Recrystallization and grain growth of deformed magnesium alloy[END_REF][START_REF] Chao | Static recrystallization kinetics of a heavily cold drawn AZ31 magnesium alloy under annealing treatment[END_REF][START_REF] Su | Static recrystallization behavior of magnesium AZ31 alloy subjected to high speed rolling[END_REF][START_REF] Murphy | The Recrystallization Behavior of Unalloyed Mg and a Mg-Al Alloy[END_REF][START_REF] Zhao | Kinetics of recrystallization for twin-roll casting AZ31 magnesium alloy during homogenization[END_REF][START_REF] Wang | Unveiling annealing texture formation and static recrystallization kinetics of hot-rolled Mg-Al-Zn-Mn-Ca alloy[END_REF][START_REF] Park | Effect of electric current on recrystallization kinetics in interstitial free steel and AZ31 magnesium alloy[END_REF]. Besides, the static recrystallization/grain growth kinetics of Mg-based alloys are strongly related to their metallurgical and microstructural states and parameters such as alloying elements, grain size, grains orientation, nature and geometry of grain boundaries, and the distribution of particles [START_REF] Higgins | Grain-Boundary Migration and Grain Growth[END_REF][START_REF] Thein | Kinetics of grain growth in nanocrystalline magnesiumbased metal-metal composite synthesized by mechanical alloying[END_REF][START_REF] Silva | Grain growth kinetics and annealed texture characteristics of Mg-Sc binary alloys[END_REF][START_REF] Jin | Drag Effects of Solute and Second Phase Distributions on the Grain Growth Kinetics of Pre-Extruded Mg-6Zn Alloy[END_REF][START_REF] Humphreys | Chapter 7 -Recrystallization of Single-Phase Alloys[END_REF].

In addition to the importance of annealing conditions, i.e., temperature and duration, deformation processing conditions including strain rate, deformation temperature, and thickness reduction in the case of rolling process do greatly affect the static recrystallization/grain growth kinetics. For example, it was expected that the static recrystallization rate might increase with increasing thickness reduction because of the increase of the stored energy at higher thickness reduction [START_REF] Zhao | Kinetics of recrystallization for twin-roll casting AZ31 magnesium alloy during homogenization[END_REF]. However, this is true only when the DRX did not occur during deformation processing [START_REF] Su | Static recrystallization behavior of magnesium AZ31 alloy subjected to high speed rolling[END_REF]. Moreover, the absence of DRX led to the weakening of texture during subsequent annealing [START_REF] Tighiouaret | On the evolution of microstructure, texture and corrosion behavior of a hot-rolled and annealed AZ31 alloy[END_REF][START_REF] Su | Texture Weakening and Grain Refinement by High Speed Rolling and Annealing of an AZ31 Magnesium Alloy[END_REF]. Otherwise, the deformation texture is retained during annealing [START_REF] Bhattacharyya | Texture enhancement during grain growth of magnesium alloy AZ31B[END_REF]. As a new insight, the severe plastic deformation (SPD) resulted in more complicated grain growth kinetics resulting from the large amounts of extrinsic dislocations and the competition of occurrence of SRX during the SPD processing [START_REF] Tighiouaret | Thermal Stability of an Mg-Nd Alloy Processed by High-Pressure Torsion[END_REF][START_REF] Su | Mechanical behaviour and texture of annealed AZ31 Mg alloy deformed by ECAP[END_REF][START_REF] Kim | Activation energies for the grain growth of an AZ31 Mg alloy after equal channel angular pressing[END_REF]. The presence of two ranges of grain growth activation energy depending on the annealing temperature was described in severely deformed Mg-1.43Nd (wt. %) and AZ31 (Mg-3Al-1Zn, wt.%) alloys [START_REF] Tighiouaret | Thermal Stability of an Mg-Nd Alloy Processed by High-Pressure Torsion[END_REF][START_REF] Su | Mechanical behaviour and texture of annealed AZ31 Mg alloy deformed by ECAP[END_REF].

There has been substantial work, particularly in the last 10 years, and with it significant improvements in our understanding of the recrystallization/grain growth behaviour in Mgbased alloys. However, much work is still needed to well understand the static recrystallization/grain growth kinetics and to have valuable data on the deformation and annealing treatments for the optimization and control of the physical and metallurgical properties of forthcoming designed Mg-based alloys.

In this frame, the goal of this work is an investigation of the role of annealing temperature and duration on the static recrystallization/grain growth kinetics of hot-rolled AZ31 alloy.

First, the alloy was hot-rolled at 350 °C to 70% of thickness reduction and then annealed at various temperatures (150, 250, and 350 °C) from 5 min to 24 h. This work is a part of a series of investigations on the AZ31 alloy regarding the effect of rolling conditions and annealing treatments on corrosion behaviour [START_REF] Tighiouaret | On the evolution of microstructure, texture and corrosion behavior of a hot-rolled and annealed AZ31 alloy[END_REF][START_REF] Hanna | Effect of hot rolling on the corrosion behavior of AZ31 magnesium alloy[END_REF]. So far, the results confirmed that small grain size combined with weak texture greatly enhanced the corrosion behavior of the AZ31 alloy [START_REF] Tighiouaret | On the evolution of microstructure, texture and corrosion behavior of a hot-rolled and annealed AZ31 alloy[END_REF][START_REF] Hanna | Effect of hot rolling on the corrosion behavior of AZ31 magnesium alloy[END_REF]. It is believed that the present work will help to provide more data to ameliorate the design of AZ31 alloy.

Experimental procedure

The sheet AZ31 alloy was generously given from MagIC (Magnesium Innovations Center), Germany.

The AZ31 alloy was subject to hot-rolling at 350 °C for 70 % of thickness reduction with 10% of thickness reduction (0.22 mm/pass) in each pass to avoid any sample cracking.

Then, the deformed samples were annealed at 150, 250, and 350 °C for times ranging from 5 min to 24 h. The mean grain size of the different samples was estimated by optical microscopy the line intercept method. For that, the samples were metallographically prepared by mechanical grinding and electropolishing with 5 parts of ethanol and 3 parts of phosphoric acid for 30 min and then etched at room temperature for 3 s in a solution containing 5% HNO 3 , 15% acetic acid, 60% ethanol, and 20% distilled water. At least four fields were exploited for an accurate mean grain size measurement and evaluating the grain growth kinetics.

EBSD measurements were performed using a FEG-SEM SUPRA 55 VP field emission gun scanning electron microscope working at 20 kV in the mid-thickness of the RD-ND plane of the samples (RD and ND mean the rolling and normal directions, respectively). A standard clean-up procedure was used to analyze the orientation imaging microscopy (OIM) data [START_REF] Hanna | Evaluating the textural and mechanical properties of an Mg-Dy alloy processed by high-pressure torsion[END_REF][START_REF] Guerza-Soualah | The deformation and recrystallization behaviour of an Mg-Dy alloy processed by plane strain compression[END_REF][START_REF] Tighiouaret | Thermal Stability of an Mg-Nd Alloy Processed by High-Pressure Torsion[END_REF][START_REF] Mikami | Effect of reference point selection on microscopic stress measurement using EBSD[END_REF]. The scanned areas were 400 × 400 μm 2 with a 1 μm step size for deformed and annealed samples at 250 and 350 °C, respectively and were 200 × 200 μm 2 with a 1 μm step size for annealed samples at 150 °C. In addition, smaller areas of 100 × 100 μm 2 and a step size of 0.5 μm were scanned to examine twins and shear bands. The analysis of the crystallographic texture from EBSD measurements was performed using MTex software [START_REF] Hielscher | A novel pole figure inversion method: specification of the MTEX algorithm[END_REF].

Vickers microhardness of the samples was measured with a load of 100 g (Hv 0.1 ) and a 10 s of a holding time. GOS approach allows quantifying the fraction of recrystallized grains, F rex , by assuming a deviation from the average orientation of the recrystallized grains less than 2° [START_REF] Sadi | Characterization of microstructure and texture of binary Mg-Ce alloy processed by equal channel angular pressing[END_REF][START_REF] Cho | Determination of a mean orientation in electron backscatter diffraction measurements[END_REF]. The F rex is shown on the upper side of the GOS map. The TD-IPF map shows that the microstructure is formed of equiaxed grains with a value of 9.2±1.2 µm in which several twins are present as indicated by arrows. However, the IQ map demonstrates the heterogeneity of the deformed microstructure by the formation of shear bands tilted about 30-36° from RD. In Mg-based alloys, the shear bands are formed due to the activation of twinning [START_REF] Atik | Twinning-induced shear banding and its control in rolling of magnesium[END_REF] or the occurrence of DRX along the grain boundaries [START_REF] Wang | Formation and microstructure of shear bands during hot rolling of a Mg-6Zn-0.5Zr alloy plate with a basal texture[END_REF]. The GOS map shows that only 10 % of grains were dynamically recrystallized during hot-rolling and no evidence of the formation of recrystallized grains on the grain boundaries. While twinning, including: 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), is noticed inside the shear band as zoomed in Figure 1d (yellow box in figure 1b). The present result may suggest that the shear bands were formed due to the activation of twinning. High fraction of LAGBs can be seen inside the shear bands (Fig. 1b) indicating the formation of sub-grains which further will transform to new recrystallized grains during subsequent annealing. Quantitatively, the isothermal static recrystallization kinetics is defined according to the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model [START_REF] Avrami | Kinetics of Phase Change[END_REF]: [START_REF] Kainer | Challenges for Implementation of Magnesium into More Applications[END_REF] where X is the recrystallized fraction, k a temperature-dependent constant, and n the Avrami exponent. According to the JMAK equation, the values of n and k are strongly linked to the nature of grain nucleation and grain growth. Table 1 presents the ideal values of the n exponent [START_REF] Christian | The Theory of Transformations in Metals and Alloys: Advanced Textbook in Physical Metallurgy[END_REF].

Results and discussion

Deformation microstructure

Static recrystallization kinetics

Table 1. Ideal values for Avrami exponent, n depending on the nature of nucleation/ growth of grains [START_REF] Christian | The Theory of Transformations in Metals and Alloys: Advanced Textbook in Physical Metallurgy[END_REF].

Growth geometry site saturation constant nucleation rate Three dimensions 3 4 Two dimensions 2 3 One dimension 1 2

The temperature-dependent constant k, can be stated as:

(

) 2
where k 0 is a constant, Q the activation energy for the recrystallization, R = 8.314 J mol -1 K -1 the gas constant and T the annealing temperature.

To obtain the n and k values, it is required to rescript the equation (1) as:

(

Consequently, n is the slope of the versus ln(t) plot and ln (k) is the yintercept.

The recrystallized fraction, X can be calculated using the microhardness values following the equation:

where Hv def , Hv t and Hv f stand for the microhardness of the deformed, annealed sample at time t and after complete recrystallization, respectively. The H vf value was chosen as for the sample annealed for 24 h at 350 °C since the GOS maps shown in Figure 3 demonstrated that in this condition the alloy exhibits a high recrystallization fraction (93 % with GOS > 2°) compared to those annealed at 150 and 250 °C for the same time (24 h), i.e., 48 and 67 %, respectively. In addition, about 10 % of the deformed microstructure was dynamically recrystallized (Fig. 1), hence the real fraction of static recrystallization can be estimated using the following equation:

(

where X 0 is the fraction of dynamically recrystallized grains.

Figure 4a shows the against ln (t) for the annealed AZ31 alloy. As can be noticed, the experimental data were lie in two straight lines for each temperature indicating the production of two regimes with their own values of n and k. The two regimes coincide with the stage II and III observed in the evolution of microhardness against the annealing time (Fig. 2). Table 2 summarizes the values of n and ln (k) for both regimes in the different samples. In addition, the activation energy of regimes I and II can be calculated by plotting ln (k) against 1000/RT as presented in Figure 4b and their values are also consigned in Table 2. 1, the growth geometry of the recrystallized grains can be presumed to be 1 dimension. The presence of two regimes in the three annealing temperature conditions demonstrated that the static recrystallization kinetics is strongly related to the deformation microstructure. The fitting of the JMAK model into two regimes with two Avrami exponents is rarely reported for Mg-Al alloys [START_REF] Su | Static recrystallization behavior of magnesium AZ31 alloy subjected to high speed rolling[END_REF][START_REF] Murphy | The Recrystallization Behavior of Unalloyed Mg and a Mg-Al Alloy[END_REF] but it has been reported for different deformed metals such as oxygen-free high conducting (OFHC) copper [START_REF] Kalu | A JMAK-microhardness model for quantifying the kinetics of restoration mechanisms in inhomogeneous microstructure[END_REF], low carbon steel [START_REF] Oyarzábal | Effect of stored energy and recovery on the overall recrystallization kinetics of a cold rolled low carbon steel[END_REF] and iron [START_REF] Rollett | Computer simulation of recrystallization in non-uniformly deformed metals[END_REF]. This two-regime behavior was explained by the heterogeneity of nucleation of recrystallized grains [START_REF] Oyarzábal | Effect of stored energy and recovery on the overall recrystallization kinetics of a cold rolled low carbon steel[END_REF]. Apparently, during the first regime, the region with high stored energy will be rapidly expended by the recrystallization nuclei. Subsequently, the remained deformed region with lower stored energy will be progressively recrystallized and this corresponds to the second regime [START_REF] Oyarzábal | Effect of stored energy and recovery on the overall recrystallization kinetics of a cold rolled low carbon steel[END_REF].

Kernel average misorientation (KAM) method allows the quantification of dislocation density (i.e., the stored energy) generated from geometrically necessary dislocations [START_REF] Pantleon | Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction[END_REF][START_REF] Badji | Texture, misorientation and mechanical anisotropy in a deformed dual phase stainless steel weld joint[END_REF]. For example, the Avrami exponent was found in the range of 0.27-3.4 for AZ31 alloy under different deformation and annealing conditions [START_REF] Beer | Microstructure evolution in hot worked and annealed magnesium alloy AZ31[END_REF][START_REF] Su | Recrystallization and grain growth of deformed magnesium alloy[END_REF][START_REF] Chao | Static recrystallization kinetics of a heavily cold drawn AZ31 magnesium alloy under annealing treatment[END_REF][START_REF] Su | Static recrystallization behavior of magnesium AZ31 alloy subjected to high speed rolling[END_REF][START_REF] Zhao | Kinetics of recrystallization for twin-roll casting AZ31 magnesium alloy during homogenization[END_REF][START_REF] Wang | Unveiling annealing texture formation and static recrystallization kinetics of hot-rolled Mg-Al-Zn-Mn-Ca alloy[END_REF][START_REF] Park | Effect of electric current on recrystallization kinetics in interstitial free steel and AZ31 magnesium alloy[END_REF][START_REF] Bourezg | Investigation of recrystallization kinetics in hot-rolled Mg-La alloy using differential scanning calorimetry technique[END_REF]. Moreover, a lower n range (0.6-0.9) was also reported in processed and annealed Mg-RE alloys [START_REF] Guerza-Soualah | The deformation and recrystallization behaviour of an Mg-Dy alloy processed by plane strain compression[END_REF][START_REF] Bourezg | Investigation of recrystallization kinetics in hot-rolled Mg-La alloy using differential scanning calorimetry technique[END_REF].

Two major reasons were anticipated to explain the low n values [START_REF] Humphreys | Chapter 7 -Recrystallization of Single-Phase Alloys[END_REF]. The first reason is the non-random recrystallization sites existing in the processed material. The second reason is being the growth rate of the nuclei which is not constant during the recrystallization process [START_REF] Humphreys | Chapter 7 -Recrystallization of Single-Phase Alloys[END_REF]. As can be seen, the deformed microstructure shown in Figure 1 clearly demonstrated the presence of large zones of shear bands and many twins. It is well known that these deformation features are perfect sites for the formation of new recrystallized grains which will conduct to a non-random distribution of nuclei and result in different growth rates. In addition, Figure 6 clearly shows that the microstructure is heterogeneous even after annealing for 24 h. All samples exhibit a bimodal grain size distribution where the small grains are mostly located in the shear bands as indicated by the delineated areas in Figure 6. It can be observed that the microstructures of the samples annealed for 5 min at 150 °C and 250 °C contain twinning (see arrows). The recrystallization of the samples annealed for 5 min at 150

°C is delayed compared to the samples annealed at 250 and 350 °C at the same time. The creation of recrystallized grains is more visible in samples annealed at 250 and 350 °C for 5 min. This is attributed to the relatively higher temperature that results in a higher rate of nucleation and growth and enhanced kinetics which explain the decrease of Avrami exponent n 1 with increasing annealing temperature. Apparently, the dependence of recrystallization kinetics on the annealing temperature is observed only during the first regime since the Avrami exponent of the second regime n 2 was found similar in the three annealing conditions.

This indicates that most of the recrystallization process occurred during the first regime. The activation energy of regime I is equal to 74.1±5.7 kJ/mol which is lower than the boundary self-diffusion energy (92 kJ/mol) and the lattice self-diffusion energy (135 kJ/mol) [START_REF] Frost | Deformation-mechanism maps[END_REF]. Low activation energy of 85.9 kJ/mol was also reported in heavily cold-drawn and annealed AZ31 alloy [START_REF] Chao | Static recrystallization kinetics of a heavily cold drawn AZ31 magnesium alloy under annealing treatment[END_REF] and in the range of 65-88 kJ/mol depending on the thickness of the twin-roll casting AZ31 alloy [START_REF] Zhao | Kinetics of recrystallization for twin-roll casting AZ31 magnesium alloy during homogenization[END_REF]. The reduced activation energy found in the various AZ31 alloys is mostly attributed to the acceleration of static recrystallization due to the occurrence of heterogeneities such as shear bands. The amount of the activation energy of regime II was found very small ~14.8±0.7 kJ/mol compared to regime I. It can be speculated that at this stage the completion of the recrystallization process did not require high activation energy.

This can be confirmed by the slow decrease of the microhardness value (stage III) shown in Figure 2 indicating that the recrystallized fraction remained almost the same at this stage.

A modified JMAK equation that involves two Avrami exponents was proposed as follow [START_REF] Matsui | Relationship between three-dimensional microstructure and Avrami exponent for recrystallization in pure iron[END_REF]:

(6)
Where A is the fraction of recrystallization in the first regime.

The results of the recrystallized fraction fitted with the modified JMAK equation are presented in Figure 7 and the fitting parameters are shown in Table 3. Table 3. Fitting parameters of the recrystallized fraction X with the modified JMAK equation.

Regime I Regime II

A The fitted curves using the two Avrami exponents equation fit well with the experimental ones, especially for the first regime. It seems that the second regime started when 35-40% (corresponding to A values) of the microstructure have been recrystallized.

Grain growth kinetics

The plot of the mean grain size versus the annealing time of the annealed AZ31 alloy is shown in Figure 8. As expected, the grain size increases with increasing annealing conditions (temperature and duration). The grain size of the as deformed sample (9.2±1. The grain growth kinetics is investigated following the general equation [START_REF] Burke | Recrystallization and grain growth[END_REF]: [START_REF] Samadpour | Processing of AM60 magnesium alloy by hydrostatic cyclic expansion extrusion at elevated temperature as a new severe plastic deformation method[END_REF] Where D is the mean grain size at the annealing time t, D 0 is the initial mean grain size at t = 0 (the deformed state), m is the grain growth exponent and c is a grain growth rate constant and can follow the Arrhenius equation: [START_REF] Zhang | Toward the development of Mg alloys with simultaneously improved strength and ductility by refining grain size via the deformation process[END_REF] where c 0 is a pre-exponential constant and Q g the activation energy of grain growth.

The rate of the grain growth process, dD/dt, can be resulted from equation ( 6):

The slope of the curve ln(dD/dt) against ln(D) allowed the determination of grain growth exponent m. The m assumed that the migrating boundary rate is relative to the driving pressure on that boundary [START_REF] Su | Recrystallization and grain growth of deformed magnesium alloy[END_REF]. Ideally in the case of defect-free metals m = 2. This assumed parabolic growth law and it is expected to hold for both two and three-dimension microstructures [START_REF] Burke | Recrystallization and grain growth[END_REF]. The high m and Q g values may indicate a good thermal stability of the AZ31 alloy under the present deformation and annealing conditions. For comparison, Table 4 presents the grain growth activation energy reported in the literature of some AZ31 alloys and other Mg-based alloys under different deformation conditions [START_REF] Bhattacharyya | Texture enhancement during grain growth of magnesium alloy AZ31B[END_REF][START_REF] Roostaei | Microstructural evolution and grain growth kinetics of GZ31 magnesium alloy[END_REF][START_REF] Tighiouaret | Thermal Stability of an Mg-Nd Alloy Processed by High-Pressure Torsion[END_REF][START_REF] Wang | Unveiling annealing texture formation and static recrystallization kinetics of hot-rolled Mg-Al-Zn-Mn-Ca alloy[END_REF][START_REF] Thein | Kinetics of grain growth in nanocrystalline magnesiumbased metal-metal composite synthesized by mechanical alloying[END_REF][START_REF] Silva | Grain growth kinetics and annealed texture characteristics of Mg-Sc binary alloys[END_REF][START_REF] Su | Mechanical behaviour and texture of annealed AZ31 Mg alloy deformed by ECAP[END_REF][START_REF] Miao | Grain growth kinetics of a fine-grained AZ31 magnesium alloy produced by hot rolling[END_REF][START_REF] Wang | Grain growth kinetics of bulk AZ31 magnesium alloy by hot pressing[END_REF][START_REF] Panda | Texture weakening in pure magnesium during grain growth[END_REF][START_REF] Ma | Mechanical properties and grain growth kinetics in magnesium alloy after accumulative compression bonding[END_REF][START_REF] Zhang | Static recrystallization and grain growth during annealing of an extruded Mg-Zn-Zr-Er magnesium alloy[END_REF]. As shown, the reported investigations have found close range of the grain growth activation energy, except for the AZ31 and Mg-1.43Nd (wt. %) alloys under severe deformation [START_REF] Tighiouaret | Thermal Stability of an Mg-Nd Alloy Processed by High-Pressure Torsion[END_REF][START_REF] Su | Mechanical behaviour and texture of annealed AZ31 Mg alloy deformed by ECAP[END_REF]. However, it must be noted that the m values used in these investigations were a priori fixed (m = 2) and not experimentally calculated. In the present case, the m value increased with increasing annealing temperature. It can supposed that at low annealing temperature the dislocation annihilation controlled the softening process while at high annealing temperature the grain growth is the dominant mechanism [START_REF] Stráská | Microstructure stability of ultra-fine grained magnesium alloy AZ31 processed by extrusion and equal-channel angular pressing (EX-ECAP)[END_REF].

It must be pointed out that the measured m differ from the ideal value (m = 2). Similar to the Avrami exponent, the grain growth exponent m is rarely found in its ideal values in the case of real experimental conditions [START_REF] Su | Recrystallization and grain growth of deformed magnesium alloy[END_REF][START_REF] Bhattacharyya | Texture enhancement during grain growth of magnesium alloy AZ31B[END_REF][START_REF] Thein | Kinetics of grain growth in nanocrystalline magnesiumbased metal-metal composite synthesized by mechanical alloying[END_REF][START_REF] Abdessameud | Grain growth in AZ31 alloy after uniaxial compression[END_REF][START_REF] Cao | Grain growth and kinetics for nanocrystalline magnesium alloy produced by mechanical alloying[END_REF][START_REF] Miao | Grain growth kinetics of a fine-grained AZ31 magnesium alloy produced by hot rolling[END_REF][START_REF] Wang | Grain growth kinetics of bulk AZ31 magnesium alloy by hot pressing[END_REF][START_REF] Abdessameud | Microstructure and Texture Evolution in Hot Rolled and Annealed Magnesium Alloy TRC AZ31[END_REF][START_REF] Azzeddine | On the texture and grain growth in hot-deformed and annealed WE54 alloy[END_REF][START_REF] Panda | Texture weakening in pure magnesium during grain growth[END_REF]. This discrepancy is attributed to two main features: 1) the boundary mobility is very sensitive and changes with the boundary velocity and 2) the existence of a limited grain size value where the grain growth is prevented [START_REF] Humphreys | Chapter 7 -Recrystallization of Single-Phase Alloys[END_REF]. These two features are mostly related to many factors such as dislocation substructure, crystallographic texture, solute drag, and microstructure heterogeneities [START_REF] Higgins | Grain-Boundary Migration and Grain Growth[END_REF][START_REF] Humphreys | Chapter 7 -Recrystallization of Single-Phase Alloys[END_REF].

Among these, it is believed that solute drag, texture, and microstructural heterogeneity are the main factors responsible for the activation energy of the present alloy. The activation energy for grain growth was found higher than for pure Mg (95 kJ/mol) [START_REF] Panda | Texture weakening in pure magnesium during grain growth[END_REF]. In the present case, the segregation of solute atoms and impurities in grain boundaries could cause the decrease of grain boundary motion and hence the delay of grain growth. The effect of increasing the solute element concentration on the retardation of grain growth kinetics was clearly demonstrated in the Mg-xSc (x = 0.2, 0.3, 0.45 (wt.%)) [START_REF] Silva | Grain growth kinetics and annealed texture characteristics of Mg-Sc binary alloys[END_REF] and Mg-5Al-xTi (x = 0, 10.3 (wt.%)) [START_REF] Thein | Kinetics of grain growth in nanocrystalline magnesiumbased metal-metal composite synthesized by mechanical alloying[END_REF] alloys (see Table 4).

In addition, the evolution of the texture shown in Figures 10 and 11 demonstrated that the hot-rolled AZ31 exhibits a typical basal texture where {0002}// RD-TD plane [START_REF] Wang | Texture analysis in hexagonal materials[END_REF]. It was reported earlier that the as-received (before hot-rolling) AZ31 alloy already developed a strong basal texture [START_REF] Tighiouaret | On the evolution of microstructure, texture and corrosion behavior of a hot-rolled and annealed AZ31 alloy[END_REF]. Consequently, the initial texture is retained after hotrolling and then after the different annealing conditions as shown in Figure 10. However, it seems accompanied by a texture weakening as demonstrated by the evolution of texture strength index shown in Figure 12. The texture index was estimated using the MTEX toolbox [START_REF] Bunge | Texture Analysis in Materials Science: Mathematical Methods[END_REF].

The weakening of the annealing texture can be recognized by the low fraction of DRX during hot-rolling (only 10 %) and the recrystallization at shear bands that led to the formation of a variety of orientations as described in several Mg-based alloys [START_REF] Basu | Shear band-related recrystallization and grain growth in two rolled magnesium-rare earth alloys[END_REF][START_REF] Barnett | Deformation microstructures and textures of some cold rolled Mg alloys[END_REF][START_REF] Bohlen | The texture and anisotropy of magnesium-zinc-rare earth alloy sheets[END_REF]. As evidence, neither the hot-rolled nor the annealed samples exhibit a random distribution. The hot-rolled contains about ~ 53% of sub-grain boundaries and low grain boundaries (misorientation less than 5°) resulting from the generation of dislocations due to the deformation process. Annealing at different temperatures causes the decrease of such grain boundaries owing to the development of new grains and a shift towards high misorientation (HAGBs) as noticed from the plots. However, a quite large fraction of subgrain boundaries is still present even after the annealing of 24 h (30 % at 150 °C, 26% at 250 °C, and 9% at 350 °C, respectively). The mobility of very low angle sub-grain boundaries is reported to be governed by bulk diffusion while the grain boundary diffusion in pure metals is responsible for the mobility of high angle boundaries [START_REF] Humphreys | Chapter 8 -Recrystallization of Ordered Materials[END_REF]. This may elucidate the intermediate activation energy found in the present work.

A peak around 30° can be clearly distinguished in the annealed samples corresponding to 30° <0001> grain boundaries which resulted from the development of the basal texture [START_REF] Valle | The distribution of disorientation angles in a rolled AZ31 Mg alloy[END_REF]. Another noticeable peak around 86° is present in the annealed samples especially after annealing at 150 and 250 °C for 5 min. This peak indicates the presence of extension twin in which the <0001> axis of the grains is reoriented by 86.8°. The presence of twins in the annealed samples means that the microstructure is still heterogeneous. To identify the different twin types and their evolution with annealing time, Figure 14 preventing the twins from any growth [START_REF] Cui | Impact of solute elements on detwinning in magnesium and its alloys[END_REF][START_REF] Xin | Annealing hardening in detwinning deformation of Mg-3Al-1Zn alloy[END_REF]. In contrast, the fraction of extension twins 86°<11 0> continuously increases with increasing annealing time.

An interesting finding (Fig. 14e) is shown in the zoomed area of the yellow box in the IQ map of annealed sample for 30 min (Fig. 14b). Inside the grain, a trace of twin (see the black arrows) can be noticed in which the specific twin seems to disappear or become narrower during the annealing. The present phenomenon is analog to the manifestation of the de-twinning process observed under reverse loading or unloading of twinned AZ31 alloy [START_REF] Xin | Annealing hardening in detwinning deformation of Mg-3Al-1Zn alloy[END_REF][START_REF] Keshavarz | In-situ investigation of twinning behaviour in Mg-3Al-1Zn[END_REF]. The KAM map of this zone shows high stored energy (high GND dislocation density) along the twin trace (indicated by arrows). Such observation demonstrated that twins are a source of heterogeneity in the microstructure during annealing treatment. IQ and KAM maps of a zoom of the yellow box, respectively.

Hall-Petch Relationship

The microhardness (Fig. 2) and mean grain size values (Fig. 8) were used to evaluate the static recrystallization/grain growth kinetics. Ultimately, it is interesting to check the validity of the Hall-Petch formula for the present AZ31 samples. Practically, the Hall-Petch formula can be articulated in terms of the Vickers microhardness by setting the flow stress σ equal to Hv/3 and this allows an indirect and very simple verification of the Hall-Petch equation [START_REF] Furukawa | Factors influencing the flow and hardness of materials with ultrafine grain sizes[END_REF].

For this purpose, the microhardness values were replotted versus the grain size values (Figure 15) following the equation [START_REF] Furukawa | Factors influencing the flow and hardness of materials with ultrafine grain sizes[END_REF]: [START_REF] Abouhilou | Microstructure and texture evolution of AZ31 Mg alloy after uniaxial compression and annealing[END_REF] where H v0 is the friction microhardness that characterizes the lattice resistance to the motion of dislocations and K H a parameter that reflects the role of the grain boundaries to the hardening. The H v0 and K H can be estimated from a linear fitting of equation 10. Accordingly,

Figure 1

 1 Figure 1 reveals the OIM in inverse pole figure (TD-IPF, TD is the transverse direction), image quality (IQ) superposed with grain boundaries and grain orientation spread (GOS) maps of the deformed AZ31 alloy, respectively. The grain boundaries were divided as sub-grains boundaries (SGBs) with misorientation θ < 2°, low angle boundaries (LAGBs) with 2°< θ < 5°, medium angle grain boundaries (MAGBs) with 5°< θ < 15°, and high angle boundaries (HAGBs) with θ > 15 °, respectively.

Figure 1 :

 1 Figure 1: (a) TD-IPF, (b) IQ and (c) GOS maps display the microstructure of the deformed AZ31 alloy and (d) IQ map highlighted with different twin types of the zoomed area indicated in Figure 1b (yellow box).

Figure 2

 2 Figure 2 displays the evolutions of microhardness versus the annealing time of the annealed AZ31 alloy at 150, 250 and 350 °C. The microhardness value of the deformed sample is 73.0±1.2 Hv. The microhardness decreases with the increase of annealing time and can be separated into 3 stages: stage I observed only in samples annealing at 150 and 250 °C where the microhardness did not change with annealing time (72.5±1.5 and 70.9±1.1 Hv after 5 min of annealing at 150 and 250 °C, respectively) indicating a recovery process. Stage II where the microhardness decreases continuously with annealing time owing to the recrystallization process. In stage III, the microhardness more-or-less decreases with a further increase of annealing time indicating the completion of the recrystallization process. The microhardness reached values of 63.9±1.4, 62.9±1.3 and 58.8±1.9 Hv after annealing for 24 h at 150, 250 and 350 °C, respectively.

Figure 2 :

 2 Figure 2: Microhardness evolution of annealed AZ31 alloy versus the annealing time at 150, 250 and 350 °C, respectively.

Figure 3 :

 3 Figure 3: GOS maps of annealed AZ31 alloy for 24 h at: (a) 150, (b) 250 and (c) 350 °C. The fraction of recrystallization is shown in the upper of the maps.

Figure 4 :

 4 Figure 4: (a) against ln (t) and (b) ln (k) as a function of 1000/RT for the annealed AZ31 alloy at 150, 250 and 350 °C, respectively.

Figure 5

 5 Figure 5 presents the KAM maps of the deformed and annealed AZ31 at 250 °C, respectively. As shown, the grains formed in the shear bands have the lowest stored energy i.e lower dislocation density (blue color) compared with the other regions which means that the recrystallization took place first at the shear bands and then with progressively increasing annealing time at the rest of the microstructure.

Figure 5 :

 5 Figure 5: KAM maps of the AZ31 alloy : (a) deformed and annealed at 250 °C for (b) 5 min, (c) 30 min and (d) 24 h.

Figure 6 :

 6 Figure 6: TD-IPF maps showing the evolution of microstructure of the AZ31 alloy annealed at 150, 250 and 350 °C for 5 min and 24 h, respectively. A bimodal grain size distribution is evidenced. Arrows show twinning.

Figure 7 :

 7 Figure 7: Fitting of the recrystallized fraction X with the modified JMAK equation.

  2 µm) increases to about 15.1±1.3, 18.2±1.2, and 21.2±1.0 µm after 24h annealing at 150, 250 and 350 °C, respectively. It is noticeable that for all annealing temperature conditions the grain size increases rapidly up to 180 min and then the grain growth rate becomes slow during a longer duration.

Figure 8 :

 8 Figure 8: Mean grain size versus the annealing time of the annealed AZ31 alloy.

Figure 9a presents the

  Figure 9a presents the evolution of ln(dD/dt) against ln(D) for the annealed AZ31 alloy at different annealing temperatures. The grain growth exponent m was equal to 7.9, 9.5, and 10.3 at 150, 250, and 350 °C, respectively. The m value was found in the range of 2-15 in Mg-based alloys under various deformation and recrystallization conditions [18, 20, 30, 57-63].

Figure 9 :

 9 Figure 9: Plot of (a) ln(dD/dt) against lnD and (b) ln(c) as a function of 1000/RT of the annealed AZ31 alloy.

Figure 10 :

 10 Figure 10: ODF sections at φ 2 = 0 and 30° of the AZ31 alloy under deformation and different annealing conditions.

Figure 11 :

 11 Figure 11: Recalculated {0002} pole figures of the AZ31 alloy under deformation and different annealing conditions.

Figure 12 :

 12 Figure 12: Evolution of texture index against annealing time.

Figure 13 :

 13 Figure 13: Grain boundary misorientation distribution of AZ31 samples: (a) hot rolled and annealed for 5 min and 24 h at (b) 150, (c) 250 and (d) 350 °C.

  presents the IQ maps showing the different twins highlighted as extension twins (86°<11 0> in green), contraction twins (56°<11 0> in red) and double twins (38°<11 0> in blue) and 22°<11 0> (in yellow) of the annealed sample at 250 °C for different durations. The fraction of different twins of the hot-rolled and annealed samples is also presented in Figure 14d. As can be noticed, the amount of contraction 56°<11 0> and double 38°<11 0> twins decrease drastically through increasing time while the amount the 22°<11 0> double twin remains stable along with the entire annealing treatment. It has recently been demonstrated that Al and Zn solute elements can segregate during annealing into the twin boundaries leading to a pinning effect and hence

Figure 14 :

 14 Figure 14: IQ maps highlighted with different twin types of the annealed AZ31 alloy at 250 °C for: (a) 5 min, (b) 30 min, (c) 24 h, (d) fraction evolution of different twin types, and (e)

Figure 15

 15 Figure 15 shows that the Hall-Petch relationship more or less holds over the different annealing conditions with the fitting parameters: H v0 = 35.4±2.0 and K H = 113.2 ±7.5 H v µm - 1/2 .

Figure 15 :

 15 Figure 15: Microhardness replotted versus the grain size values.



  The static recrystallization/grain growth kinetics of the hot-deformed AZ31 alloy were evaluated after annealing treatments at 150, 250, and 350 °C from 5 min to 24h, respectively. The static recrystallization was characterized using the JMAK model and seems to occur in two regimes with two Avrami exponents and activation energies. In regime I, the Avrami exponent was found as n = 1.5-0.35 depending on the annealing temperature and recrystallization activation energy of 74.1±5.7 kJ/mol. In regime II, a similar value of Avrami exponent was found near 0.1-0.2 in all annealing conditions and a very low recrystallization activation energy of 14.8±0.7 kJ/mol was estimated. The present experimental data were in complete agreement with the modified JMAK equation:. The grain growth kinetics were well fitted by the classical equation where m = 7.9, 9.5 and 10.3 at the temperature of 150, 250, and 350 °C, respectively and the activation energy of grain growth was found to be 109±0.2 kJ/mol. Solute drag, formation of basal texture, and microstructural heterogeneities like shear bands and twinning are the main factors responsible for the recrystallization/grain growth activation energies and n and m exponent parameters of the present AZ31 alloy. The evolution of microhardness against the mean grain size under different annealing conditions was found to obey the Hall-Petch relationship with the fitting parameters H v0 = 35.4±2.0 and K H = 113.2 ±7.5 H v µm -1/2 . Nevertheless, the dislocation density seems to contribute to the hardening at low annealing temperature (150 °C).

Table 2 .

 2 Values

		Regime I			Regime II
	n	ln (k)	Q I (kJ/mol)	n	ln (k)	Q II (kJ/mol)
	150 °C 1.52 ±0.13 -7.76 ±0.41		0.18 ±0.02 -1.76±0.17
	250 °C 0.62 ±0.03 -2.30±0.11 74.1±5.7	0.10 ±0.01 -1.01±0.08 14.8±0.7
	350 °C 0.35 ±0.02 -1.05 ±0.01		0.12 ±0.01 -0.40±0.08

of Avrami exponent n, and activation energy Q, in different regimes found for the present alloy. The Avrami exponent of regime I decreases with increasing annealing temperature from n 1 = 1.52 at 150 °C to n 1 = 0.62 at 250 °C and then to n 1 = 0.35 at 350 °C indicating a strong dependency of the recrystallization mechanisms on the annealing temperature. While for regime II the n 2 values in the three annealing conditions were very similar around 0.1-0.2 and relatively lower than those for regime I. Based on Table

Table 1 )

 1 , except for the sample annealed at the lowest temperature of 150 °C. Many experimental studies on various metals reported the deviation of Avrami exponent from the

theoretical values

[START_REF] Beer | Microstructure evolution in hot worked and annealed magnesium alloy AZ31[END_REF][START_REF] Guerza-Soualah | The deformation and recrystallization behaviour of an Mg-Dy alloy processed by plane strain compression[END_REF][START_REF] Su | Recrystallization and grain growth of deformed magnesium alloy[END_REF][START_REF] Chao | Static recrystallization kinetics of a heavily cold drawn AZ31 magnesium alloy under annealing treatment[END_REF][START_REF] Su | Static recrystallization behavior of magnesium AZ31 alloy subjected to high speed rolling[END_REF][START_REF] Zhao | Kinetics of recrystallization for twin-roll casting AZ31 magnesium alloy during homogenization[END_REF][START_REF] Wang | Unveiling annealing texture formation and static recrystallization kinetics of hot-rolled Mg-Al-Zn-Mn-Ca alloy[END_REF][START_REF] Park | Effect of electric current on recrystallization kinetics in interstitial free steel and AZ31 magnesium alloy[END_REF][START_REF] Bourezg | Investigation of recrystallization kinetics in hot-rolled Mg-La alloy using differential scanning calorimetry technique[END_REF][START_REF] Zhang | Static recrystallization kinetics and microstructure evolution of 7055 aluminum alloy[END_REF][START_REF] Jägle | The Kinetics of and the Microstructure Induced by the Recrystallization of Copper[END_REF][START_REF] Morozova | Annealing Behavior and Kinetics of Primary Recrystallization of Copper[END_REF]

.

Table 4 .

 4 Grain growth kinetics of some Mg-based alloys collected from the literature.

	Alloy	Initial conditions		Annealing conditions	Grain growth kinetics	Ref.
		Deformation type	D 0 (µm)	T (°C)	t (min)	m	Q g (kJ/mol)
	AZ31	hot-rolling	9.2	150-350	5-1440	7.9-10.3	109.2	Present
								study
	AZ31	hot-rolling	5	250-450	15-120	4	80.8	[59]
	AZ31	hot-pressing	0.04	300-400	30-60	5	110	[60]
	AZ31	Rolling	5.3	260-450	15-10080	5	115	[20]
	AZ31	accumulate compression	<1	350-450	10-240	5	105	[64]
		bonding
	AZ31	equal channel angular	1.9	150-500	30-300	2	29 (<250 °C)	[36]
		pressing					92 (>250 °C)
	Mg-Al-Zn-Mn-Ca	hot-rolling	-	300-400	60-600	1.9-2.2	115.48	[27]
	Mg-1.43Nd	high-pressure torsion	0.6	150-450	60	2	26 (<250 °C)
							147 (>250 °C)

Acknowledgements

Dr-Ing. N. Hort and Dr. D. Letzig from Magnesium Innovations Center (MagIC), Germany, are gratefully acknowledged for providing the AZ31 alloy sheet.


Abla Chaouni Benabdellah

Kamar Zekhnini

Anass Cherrafi

Sustainable and Resilience improvement through the Design for Circular Digital Supply Chain

Keywords: Resilience, Sustainability, Supply Chain Management, Design for X, Circular Economy, Digital technologies

Resilient and sustainable supply chain management (SCM) practices have been established in recent decades to reduce the likelihood and consequences of disruptions and the negative environmental effects along the supply chain. To deal with such issues, it's important to be able to quantify the effectiveness of all supply chain processes in a circular economy model while taking technological revolution into account. Furthermore, Design for X (DFX) approaches show significant potential for improving product and service functionality from a variety of perspectives X. In this respect, the aim of this paper is first to propose a circular digital SCOR model that depicts the impact of digital technology on various circular SCOR processes. Second, using DFX techniques, a conceptual model, called Design for circular digital Supply chain (DFCDSC), has been proposed that includes the key design factors for the development and implementation of the circular digital supply chains. Since it highlights the main lines of research in the area, the proposed framework will provide crucial managerial perspectives for practitioners and managers.

Introduction

In the current global scenario and increasingly complex, digital world, supply chains (SC) are faced various events that interrupt SC operational processes and successful performance. Furthermore, consumers, regulators, and other stakeholders around the world are pushing corporations to conduct their activities responsibly to boost their economic, social and environmental efficiency [START_REF] Jabbour | Digitally-enabled sustainable supply chains in the 21st century: A review and a research agenda[END_REF]. Thus, organizations were forced to adjust their activities and take a constructive position in creating safer and more resilient systems to meet the needs of all stakeholders while improving sustainability outcomes [START_REF] Siegel | Integrated green lean approach and sustainability for SMEs: From literature review to a conceptual framework[END_REF]. In this context, Circular economy (CE) and emerging technologies have emerged as key elements of the sustainability and resilience response to assist organizations in being more successful [START_REF] Sassanelli | Addressing circular economy through design for X approaches: A systematic literature review[END_REF].

Through the achievement of collaboration, transparency, resiliency, responsiveness, and flexibility across all SC processes, DSC can have clear sight in real time [START_REF] Ivanov | Viable supply chain model: integrating agility, resilience and sustainability perspectives-lessons from and thinking beyond the COVID-19 pandemic[END_REF]. Besides, organizations that consider CE gain from material saving, reduced manufacturing and supply costs, improved customer loyalty, and the ability to keep products and parts in use for a longer time [START_REF] Sassanelli | Addressing circular economy through design for X approaches: A systematic literature review[END_REF]. Moreover, when SC is influenced by changes in the operational and environmental conditions, resilience capabilities allow adaptation and recovery [START_REF] Ivanov | Viable supply chain model: integrating agility, resilience and sustainability perspectives-lessons from and thinking beyond the COVID-19 pandemic[END_REF]. Furthermore, a successful transition to sustainability dependent on a variety of social, economic, legal, cultural, and political factors, and it necessitates fundamental changes, not only at the company level but also across the product and service activities [START_REF] Benabdellah | Design for relevance concurrent engineering approach: integration of IATF 16949 requirements and design for X techniques[END_REF]. Methods and tools to enable the systematic integration of all products and services concerns from a digital and circular and perspective, however, are still being developed. From a particular X viewpoint, the Design for X (DFX) approach is used to increase the quality of the product and SC processes [START_REF] Benabdellah | A systematic review of design for X techniques from 1980 to 2018: concepts, applications, and perspectives[END_REF][START_REF] Liverani | Design for Six Sigma (DFSS) for additive manufacturing applied to an innovative multifunctional fan[END_REF].

Many authors explored and explained how to perceive the CE transition through the use of DFX approaches [START_REF] Sassanelli | Addressing circular economy through design for X approaches: A systematic literature review[END_REF][START_REF] Bovea | Identifying design guidelines to meet the circular economy principles: A case study on electric and electronic equipment[END_REF]. Other researchers have created new DFX methods as part of the introduction of Industry 4.0 by DFX techniques [START_REF] Pereira Pessôa | Smart design engineering: a literature review of the impact of the 4th industrial revolution on product design and development[END_REF]. Therefore, no paper dealing specifically with the incorporation of the CE and digitalization to achieve sustainable and resilient concerns in the SC based on the DFX perspective can be found among all the advances made and research contributions. In this respect, the aim of this paper is first to develop a circular-digital SCOR model which serves as a reference model for the enhancement of SCs. Then, by considering the prominent DFX techniques needed in each circular-digital SCOR model, a series of design factors have been enumerated to integrate circular and digital concerns in SC to reach resiliency and sustainability enhancement. The conceptual framework, design for circular digital supply chain (DFCDSC), will provide crucial and managerial implications for both practionners and managers to develop dynamics capabilities theory.

This paper is structured as follows; Sect. 2 presents an analysis of the literature review. Section 3 elaborates the proposed circular digital SCOR model for the integration of circular and digital impacts on the SC. Section 4 proposes the theoretical elements of our integrated model DFCDSC. The key design factors needed to implement DFCDSC fir resilient & sustainable purpose is established. Section 5 presents implications for both practitioners and researchers. The conclusions and future works are drawn in the final section.

Literature review

Considering the high competition atmosphere and technological transition (Industry 4.0), organizations have begun to concentrate on sustainable practices to resolve environmental, social, and economic issues, forming an agenda that aims to promote resilience, digitalization, and circularity along the SC.

Circular Supply Chain

The CE is characterized as an economic model in which resources are used for as long as possible while extracting maximum value. By reducing (or delaying) unintended negative environmental impacts, the principles of CE broaden the boundary of green, resilience and sustainable SCM [START_REF] Sassanelli | Addressing circular economy through design for X approaches: A systematic literature review[END_REF][START_REF] Bag | Examining the role of dynamic remanufacturing capability on supply chain resilience in circular economy. Management Decision[END_REF]. In this regard, as the world moves toward a CE, SCs players are paying more attention to their environmental effects, and opportunities to generate value through minimizing, preserving, and recovering natural resources. "Open-loop SC", "circular SC", and "closed-loop SC", are all terms used to describe SCs in a CE [START_REF] Sassanelli | Addressing circular economy through design for X approaches: A systematic literature review[END_REF][START_REF] Bovea | Identifying design guidelines to meet the circular economy principles: A case study on electric and electronic equipment[END_REF]. More clearly, CSCM includes a vision of a zerowaste economy, restorative and regenerative cycles planned using circular thinking. Motivated by all these benefits, several researchers have contributed significantly to the literature on the CE. Several authors have suggested a complete rethinking of the way products, processes and SC are designed by using DFX Techniques [START_REF] Sassanelli | Addressing circular economy through design for X approaches: A systematic literature review[END_REF]11]. Further ones have studied drivers, barriers and enable for the integration of CE in SCM [START_REF] Farooque | Circular supply chain management: A definition and structured literature review[END_REF][START_REF] Vegter | Supply chains in circular business models: processes and performance objectives[END_REF]. Researchers have also focused on elaborating frameworks for the CSCM [START_REF] Jabbour | Digitally-enabled sustainable supply chains in the 21st century: A review and a research agenda[END_REF][START_REF] Farooque | Circular supply chain management: A definition and structured literature review[END_REF][START_REF] Li | Green product design with competition and fairness concerns in the circular economy era[END_REF] with the integration of green, reverse logistics, industrial ecology with CE concerns. Other ones have included the benefits of using Industry 4.0 technologies such as Additive manufacturing with circular SC [START_REF] Rahito | Additive Manufacturing for Repair and Restoration in Remanufacturing: An Overview from Object Design and Systems Perspectives[END_REF][START_REF] Nascimento | Exploring Industry 4.0 technologies to enable circular economy practices in a manufacturing context: A business model proposal[END_REF].

Digital Supply Chain

Technological and computing advancements have led to a rapidly evolving environment in recent decades [START_REF] Benabdellah | Design for the environment: An ontologybased knowledge management model for green product development[END_REF]. Companies need a digital supply chain (DSC) based on sustainability, visibility, efficiency and flexibility to help them solve the challenges of volatility, resiliency, uncertainty, and transparency [18]. According to [18], DSC can be defined as "an intelligent best-fit technological system that is based on the capability of massive data disposal and excellent cooperation and communication for digital hardware, software, and networks to support and synchronize interaction between organizations by making services more valuable, accessible and affordable with consistent, agile and effective outcomes". This implies a collection of advanced technologies that companies must integrate with human capital to transform their SCs from a traditional to instrumented, integrated and intelligent one [START_REF] Zekhnini | Supply chain management 4.0: a literature review and research framework[END_REF]. Therefore, DSC is about how SCs are handled; how both digital and physical flows help to achieve visibility and quality enhancement as well as real-time feedback at all levels [20]. DSC implementation has gotten high attention from many practionners and academicians. Among the contributions to this research field, few research papers have attempted to implement DSC [START_REF] Jabbour | Digitally-enabled sustainable supply chains in the 21st century: A review and a research agenda[END_REF]18]. Several authors have used systematic reviews to concentrate on advanced technologies effect on SCs, such as "Big Data", "Internet of Things", "Cyber Security" and "Augmented Reality". Other ones have contextualized IT in a SC 4.0 [START_REF] Tao | Digital twin-driven product design, manufacturing and service with big data[END_REF][START_REF] Wu | Toward sustainability: using big data to explore the decisive attributes of supply chain risks and uncertainties[END_REF]. Further, established a structure for understanding DSC based on an overview of key advantages and limitations [18,[START_REF] Zekhnini | Supply chain management 4.0: a literature review and research framework[END_REF].

Circular-Digital SCOR model

The SCOR model is a known structure that divides SC processes into six subprocesses ("plan, source, make, deliver, return, and enable") that serve as the foundation to describe any SC [START_REF] Müller | Contributions of Industry 4.0 to quality management -A SCOR perspective[END_REF]. To achieve sustainability, it is important to assess the actual efficiency of all SC processes in a circular context. To do so, two processes have been added to the standard SCOR model: [START_REF] Jabbour | Digitally-enabled sustainable supply chains in the 21st century: A review and a research agenda[END_REF] Use that represents the end-consumption users of the products as well as maintenance and repair activities to the extent the product lifespan and (2) Recover that represents the remanufacture, reuse, recycle, repair and redesign activities. Furthermore, since the conventional SC is made up of a series of siloed steps, incorporating digital technology may be able to break down these barriers and turn them into a seamless system [18,[START_REF] Zekhnini | Supply chain management 4.0: a literature review and research framework[END_REF]. Fig. 1 represents the circular and digital SCOR (CDSCOR) model that depicts the effect of digital technologies on the various circular proposed processes. For the Make, Deliver, and Return processes, 3D printing aids in the development of product prototypes for evaluation, as well as mass customization [START_REF] Shree | Effect of 3D printing on supply chain management[END_REF]. Cloud Computing encourages collaboration among SC participants, improves connectivity, and adaptability in the Use, Make, and Source processes [START_REF] Novais | A systematic literature review of cloud computing use in supply chain integration[END_REF]. In both Deliver and Return processes, AR increases their efficiency and visibility [START_REF] Merlino | The augmented supply chain[END_REF]. The CPS, which is primarily used in the Make process, through the use of interconnected computers, physical processes and networks assess agility by contributing to production and inventory optimization [START_REF] Silva | Implementation of Industry 4.0 concept in companies: empirical evidences[END_REF]. Besides, RFID allows real-time detection and tracking, which helps to improve data quality [20]. Whereas, Blockchain technology enables the real-time enhancement and monitoring of products and actors, especially for Use and Source processes [START_REF] Tönnissen | Analysing the impact of blockchain-technology for operations and supply chain management: An explanatory model drawn from multiple case studies[END_REF]. In contrast, other techniques such as BD, Cybersecurity, IoT and AI have positive impacts on the entire SC processes. BD gives better forecast, increase SC visibility and strong relationships [20]. IoT help increasing warehouse operations productivity, and unnecessary procedures. In addition to all of these advantages, risk management and control in a DSC would concentrate primarily on cybersecurity, as it is required to identify security incidents, enforce the appropriate safeguarding tools, react to attacks in real-time [START_REF] Zekhnini | Supply chain management 4.0: a literature review and research framework[END_REF]. Furthermore, AI improves the efficiency of SC drivers by developing a great understanding of their interactions [START_REF] Benabdellah | SmartDFRelevance: A Holonic Agent Based System for Engineering Industrial Projects in Concurrent Engineering Context[END_REF]. As a result, by considering CDSCOR model, we connect SC actors to create reliability, transparency, resiliency, and effectiveness in the end-to-end sustainable value chain by including the Use and Recover processes and incorporating Industry 4.0 technologies.

Design for Circular Digital Supply Chain

Given the high level of concurrence, SC must meet new digital and circular features, as well as ensure the integration of resilience and sustainable practices with multiple conventional functionalities. Furthermore, mastering the management of an organization's intellectual resources is critical. As a result, successful SCs have a strong vision and use structures and roadmaps to drive them forward. In this regard, the original structure depicted in Figure 2 presents a roadmap for better understanding the problem of SC sustainability and resilience when taking into account an integrated vision that involves circularity, industry 4.0, and DFX techniques capabilities. More clearly, the framework, called Design for Circular Digital Supply Chain (DFCDSC), defines a set of over 300 design factors that must be considered for each of the proposed CDSCOR processes to achieve sustainability and resilience efficiency outcomes. Therefore, it's important to note that the design factors within each process come from a variety of sources, including applications, guidelines, papers, books, and real design projects and the main DFX techniques used in each process are based on the categorization of [START_REF] Benabdellah | Design for relevance concurrent engineering approach: integration of IATF 16949 requirements and design for X techniques[END_REF]. In the following, a discussion of each process is presented.

• The Plan process purpose is to define SC needs and align them against available assets and resources. Environmental limits, such as the environment's assimilative potential and resource extraction relative to yield, are primarily considered in a CE context. Using Industry 4.0 technologies capabilities, we obtain a synchronized & digital planning with a real-time inventory & disruption prediction. • The Source process aims to organize product deliveries, obtain and validate the product, pass the product, and approve payment to the supplier. Sourcing is linked to all resource principles in the CE model, including sustainable, exhaustible, and renewable resources. Besides, to achieve resilience, back-up suppliers should be incorporated, component replacement and supplier communication portals should be used. Using Industry 4.0 technologies capabilities, we obtain intelligent supply and predictive analysis sourcing. • The Make process aims to organize manufacturing activities, issue materials, manufacture and test, deliver products, and stage products while taking into account waste disposal and packaging limitations. Make covers tasks such as maintenance, recovery, recycling, and material transformation from a circular perspective. Furthermore, flexible manufacturing lines and the application of postponement concepts are regarded as critical drivers of demand resilience and responsiveness. Using Industry 4.0 technologies capabilities, we establish a smart factory and a proactive risk sensing to adjust manufacturing capabilities. • The Deliver process describes the tasks associated with building loads, routing packages, selecting carriers, receiving products, picking, packing, documenting, shipping, installing the product, and fulfilling customer orders. Deliver can also coordinate the supply of replacement parts for repair during usage of the product in a circular context to prolong the product's lifespan. Besides, omnichannel delivery, decentralized logistics, disturbance monitoring, and real-time transportation control are some of the other ways to easily and efficiently use resilience assets. Using Industry 4,0, technologies capabilities we obtain dynamic fulfillment with full inventory transparency and dynamic/predictive routing. • The Use process includes the end-usage user's or use of the product, as well as repair and maintenance to extend the product's lifespan. In a CE, end-users need to return their goods at the end of their useful lives, as these goods are 'after recovery' inputs for the manufacturing process. Besides, using Industry 4.0, we obtain a connected & responsiveness customer. • The Return process to return material from the end-user to the SC return material.

Moreover, resource-related practices which specifically include the return of a faulty or unnecessary product can be linked to the CE's consumer product construct. Recycled products, closed-loop SC tools and constructive procurement dependent plans are all examples of ways to use resilience assets for creating value in the return process. Using Industry 4.0 capabilities, we obtain End to end transparency for customers. • The Recovery process includes the processes of Remanufacturing, recycling, reusing, reducing and redesigning. As a fully circular operation, it takes into account all aspects of assembly, disassembly, remanufacture, and recycling policies, as well as CO2 emissions, hazardous effects, and essential materials. Using the Industry 4.0 technologies capabilities, we obtain intelligent traceability, collaborative value capture and zero landfills. • The Enable process refers to the SCM process, which involves business regulations, facility efficiency, data resources, contracts, enforcement, and risk management, among other things. In a circular perspective, the enablers that were not evident in a linear business model are taken into account. Materials would be sourced not only from manufacturers but also from end-users who are disposing of their obsolete goods. Furthermore, DSC twins and Industry 4.0 technologies enable several vital resilience capabilities, including coordination, visibility and collaboration.

In a summary, by considering the proposed DFCDSC, a specific set of performance objectives such as agility, flexibility, visibility, transparency, security, proactivity, adaptability can be reached. In addition to that, by considering both internal (Errors made by humans, computer malfunctions, and product consistency) and external risks (natural disasters, pandemics, exchange rates, legislations) resiliency can be achieved. There are also several sustainability advantages to be gained. From an economic standpoint, expenses are decreased while sales and profitability are improved. From an ecological standpoint, there is a reduction in carbon footprint, resource depletion, pollution and toxicity. Finally, on a social level, wages, workplace safety and health, social justice, life expectancy, and education are all enhanced, whereas excessive working hours, severe poverty, and child labor are reduced. In this respect, the proposed system can give insights into the consideration of circular, digital, and DFX techniques to have a SC that is both sustainable and resilient.

Managerial and practionners implications

From a managerial and practical perspective, the proposed DFCDSC framework will provide important insights for practionners, decision-makers, and anyone interested in acquiring a more in-depth understanding when incorporating DFX strategies, circularity, and digitalization in SC. More clearly, from a practionners point of view, this paper can help them to facilitate the adaptation to a circular-digital SC while using DFX techniques. Second, in light of significant influential papers in digital [18,[START_REF] Zekhnini | Supply chain management 4.0: a literature review and research framework[END_REF] and circular SC [START_REF] Sassanelli | Addressing circular economy through design for X approaches: A systematic literature review[END_REF], our paper contributes significantly by proposing a SCOR categorization model that incorporates both digitalization and circularity into the SC processes. Besides, a conceptual model for the development and implementation of CDSC has been suggested, which includes the main design factors needed to enhance sustainability and resiliency. This is as far as we know, the first attempt to establish the DFCSSC definition. It is then considered as a significant contribution to theory as it adds a solid structure that combines cutting-edge technologies with DFX techniques to gain a deeper understanding of digital complexities in a CSC. From the Managers point of view, the proposed framework assists them in ensuring that CSC operations are more environmentally aware and offers a roadmap in terms of economic, financial, social, logistical, organizational and operational activities to successfully implement CSC models. Furthermore, the proposed structure emphasizes that in the digital age, managers are continuously forced to strengthen their understanding of cuttingedge technology to promote the adoption, deployment, and dissemination of the key technologies that help SCM sustainability and resiliency. In summary, we conclude that the proposed structure, as well as the CDSCOR model, will serve as a useful guide for DSC project managers, consultants, and practitioners. Furthermore, the DSCC structure can be enhanced in terms of SC participant engagement and appropriate to the needs and skills of a particular organization.

Conclusion and future works

The current competitive environment requires companies to be innovative in their production systems and to rethink the current use of resources and waste management by integrating, CE, digital technologies and DFX techniques into their SCs. However, to resolve all of these problems at once, much of the study has concentrated on the technical side. This means that products should be designed not only with an emphasis on how SC concepts enable products to adapt into a CE or digitalization framework but also with a focus on how products adapt to people's desires, needs and behavioral trends. To achieve sustainability and resiliency, we need strategies to help in the implementation of both digital and circular supply chain architecture, according to this viewpoint. To do so, first, we have proposed a new categorization of the SCOR model that incorporates circular and depicts the impact of emerging technology on each process. We've added the recovery and use processes, as well as the effect of various technologies on SC efficiency, such as BD, Cybersecurity, IoT, and AR. Second, we suggested a set of design factors to DFCDSC to boost resilience and sustain-ability issues while taking into account an integrated view of circular, digital, and DFX techniques in SC. As mentioned in section 5, this framework offers different insights for practitioners and managers.Nonetheless, there are some drawbacks to this article. To evaluate the applicability of these findings, further research is necessary. More precisely, there is a need to delve deeper into not only the direct connection between CSC processes while integrating circular and digital concerns, but to test the design factors in different scenarios. The ability to fully map the interrelationships between various design factors and their impact on the efficiency of the CDSC will be crucial in making realistic suggestions for maximizing return on investment. We propose also to regroup the design factors into homogenous modules to facilitate the implementation of this framework by using classification or clustering algorithms.

Fig. 1 .

 1 Fig. 1. Proposed Circular-Digital SCOR model (CDSCOR)

Fig. 2 .

 2 Fig. 2. Design for Circular Digital Supply Chain (DFCDS)