The mechanisms of grain growth of Mg alloys: A review

Qinghu Chen ,Ruinn Chen ,Jin Su ,Qingsong He ,Bin Tn ,Cho Xu ,Xu Hung,Qingwei Di,*,Jin Lu

a School of Metallurgy and Materials Engineering,Chongqing University of Science and Technology,Chongqing 401331,China

b Department of Mechanical Engineering,City University of Hong Kong,Hong Kong,China

Abstract Grain growth directly influences the plasticity and strength of Mg alloys.As the grain size decreases from the microscale to the nanoscale,the plasticity of Mg alloys continually increases,whereas the strength first increases and later decreases.These trends are observed because the plastic deformation mechanism changes from dislocation–twinning dominance to grain boundary dominance.In this study,the factors influencing grain growth,such as the temperature of plastic deformation/annealing,second-phase particles and solute atoms,are examined to aid effective control of the grain size.Additionally,the mechanisms of grain growth,typically induced by strain and thermal activation,are clarified.Strain-induced grain boundary migration is attributable to the difference in the strain energy stored in adjacent grains with high-density dislocations.Heat-induced grain boundary migration is driven by the difference in the energy of the grain boundary/subgrain boundary and boundary curvature.Abnormal grain growth can be induced by anisotropy of the strain energy,anisotropy of the grain boundary mobility,depinning of the second phase and high misorientation gradient.

Keywords: Mg alloys;Grain growth;Mechanical properties;Microstructure.

1.Introduction

Magnesium (Mg) alloys have attracted considerable attention in the transportation,electronics and military domains because of their low density and excellent specific strength.Mg alloys are generally processed by hot forming and subsequently annealed at elevated temperatures,and grain growth(GG) inevitably occurs during these processes.GG represents a microstructural evolution phenomenon that determines the final microstructures and physical properties of the materials,such as the strength [1–4] and plasticity [5,6].The grain size is closely related to the material properties.For example,the strength is negatively proportional to the grain size,according to the classic Hall–Petch relationship based on the dislocation accumulation theory [7].Notably,when the grain size is at the nanometer level,the dislocation accumulation theory no longer holds: the plastic deformation mechanism dominated by the grain boundary (GB) emerges,and the reverse Hall–Petch effect is observed [8–11].Thus,the relationship between the grain size and strength is attributable to the plastic deformation mechanism.Additionally,the grain size influences the plasticity,which is typically evaluated in terms of the elongation.Mg and Mg alloys exhibit high plasticity when the grain size is a few microns or nanometers,attributable to the deformation mechanism dominated by GB sliding,non-basal plane dislocation slip and deformation twinning [5,12,13].When the grain size is more than a few microns,the deformation mechanism is transformed to dislocation slip and twinning.Thus,the dominant deformation mechanisms at different grain sizes must be determined.However,when the grain size of pure Mg is decreased to 5 μm,the plasticity becomes lower than the original value because the deformation mechanism transforms from non-basal plane slip to basal plane slip [14].This singularity also needs to be clarified.

GG is a complex process,and the associated microstructural evolution depends on various factors such as the temperature,second phase,solute and orientation.The GG mechanisms also vary owing to these factors.Several GG mechanisms for Mg alloys have been identified,such as the mobility of high-angle grain boundaries (HAGBs),misorientation distribution,average subgrain misorientation,the initial texture and/or the texture evolution,and coarsening and interaction of the second phase [15–17].Although the microstructural evolution has been extensively studied,the GG mechanisms of Mg and Mg alloys at the atomic level remain to be clarified.In this context,the GG mechanisms under different combinations of the above-mentioned impact factors must be studied.

Enhanced understanding of GG can help improve the mechanical properties of Mg alloys.In this paper,the relationship between grain size and mechanical properties is explained from the perspective of plastic deformation mechanisms.Moreover,by clarifying the impact factors and mechanisms of GG,processing strategies to control the grain size can be optimized.Finally,some key scientific issues in the field of Mg alloys research are proposed.

2.Influence of the grain size on the plasticity and strength

To enhance the plasticity and strength of Mg and Mg alloys,their grain sizes and textures are typically controlled by inducing severe plastic deformation(e.g.,by rolling/extrusion)and subsequent annealing.According to the classic Hall–Petch relationship based on the dislocation accumulation theory,the strength increases with decreasing grain size[8,18,19].The strength enhancement required for the propagation of slip with the help of pile-ups of dislocations blocked at GBs into the surrounding grains.Grain size at a certain micron scale,dislocation-based or twinning-based deformation mechanism dominate the plastic behavior.In pure Mg and AZ31 Mg alloys as shown in Fig.1,their yield stress depends on grain size.The Hall-Petch plots exhibit different trends relate to the deformation mechanism.As the grain size decreases from 87 to 3 μm,a plastic deformation transition from twinning-dominated to dislocation slipping-dominated occurs in Mg alloy [20,21].Twins can hinder the dislocation propagation and dislocation pile-up at the twin boundaries.It is well known twin is sensitive to the grain size.The formation of twin is mainly induced by stress concentration from the anisotropy of dislocation slip,whereas the compatibility stress from the increased fraction of GB may reduce the levels of stress concentration in the grain interiors,finally the density of twinning reducing.Thus,the twinning propensity reduces with decreasing grain size.When the grain size decreases from the microscale to the submicron or nanoscale,the reverse Hall–Petch effect emerges.The forward and reverse transitions in pure Mg and AZ31 Mg alloys occur at a critical grain size,and critical values for Cu and Ni have also been identified [9,22–24].At this scale,the traditional Frank–Read dislocation source no longer controls the deformation because of the increase in the GB atomic proportions.GB sliding dominates the plastic deformation,leading to the softening of the GBs [9,10].Consequently,with the decrease in the grain size from the microscale to the nanoscale,the deformation mechanism changes from dislocation/twinningdominant to GB-dominant.

Grain refinement can enhance the plasticity of Mg alloys for several reasons: i) The microstructure becomes more uniform,and uniform plastic deformation can occur;ii)the stress concentration is reduced;iii) sufficient strain hardening ability is regained,attributable to twinning and the activation of basal and non-basal slip[25];and iv)a layered bimodal structure is favorable for plastic deformation [25,26].In particular,the enhancement in the plasticity is attributable to the deformation mechanism.With the decrease of grain size,the deformation modes such as prismatic and pyramidal dislocation slip or other modes of twinning,can be activated readily,which are sufficient to accommodate homogeneous plastic deformation.As the basal slip of Mg alloys transforms to a non-basal slip,the plasticity initially increases with decreasing grain size from 125 to 5.5 μm [13,27].However,owing to a strong basal texture generated after rolling/extrusion deformation,the plasticity decreases with a significant decrease in the grain size from 36 to 5 μm [14,28].The plasticity decreases because the deformation mode transits from non-basal slip to basal slip.Moreover,a strong basal texture makes the available basal dislocation slip even more difficult to activate and operate,leading to low plasticity.Interestingly,when the grain size decreases to the submicron level,the plasticity of Mg alloys with a strong basal texture is enhanced.The main deformation mechanism now is the relative sliding of grain groups with similar orientations rather than GB sliding between individual grains,associated with crystal grain rotation as the coordination mechanism [5].These findings highlight that the grain size,plasticity and deformation mechanisms are interrelated.Considerable research has been performed to clarify these correlations.Certain researchers noted that as the grain size of AZ31 Mg alloys decreases from 13.5 to 2.4 μm,the elongation increases from 19.6% to 23.9% because the non-basal slip and activation of twins promote the plastic deformation [29].Therefore,the increased plasticity is attributable to favorable deformation modes.Grain size of over 1 μm in pure Mg,dislocation slip is the main deformation mechanism.At grain sizes less than 100 nm,GB sliding promotes plastic deformation,and the twins are inhibited[30].Overall,the continuous transitions of the deformation mechanism and plasticity for grain sizes ranging from the nanoscale to microscale have not been systematically clarified yet.

Fig.1.Variation in 0.2% yield stress with grain size-1/2 for (a,b) pure Mg [6,30,37–43];(c,d) Mg alloys [44–50–51].

The research findings on these continuous transitions at the nanoscale to microscale can be summarized as follows.When the grain size of Mg and Mg alloys decreases to the nanoscale,the traditional dislocation slip is replaced by GB sliding and grain rotation as the main deformation mechanism [9–12,31].The proposed mechanism is dependent upon the grain size,since GB sliding and grain rotation becomes easier to activate and operate for smaller grain sizes.When grain size is reduced to be comparable to the GB width,such slide planes are relatively smooth and the stress required for GB sliding decreases.Thus,the portion of GB sliding contributing to total deformation will increase with decreasing grain size.After deformation,grains initially with hard orientation,rotated to a softer orientation.Such grain rotation allowed more grains to gain an improved capability of plastic deformation.Specifically,as the grain size decreases from 59.7 to 650 nm,the elongation of pure Mg increases from 10% to 65%,and the grain size of 1.57 μm represents the transition point of the deformation mechanism from dislocation slip/deformation twinning to GB sliding [32].This transition occurs because the grain size is too small to accumulate dislocations at the GBs,and deformation twinning is inhibited in ultrafine and nanocrystalline configurations.However,according to more recent studies,the grain size at which the deformation mechanism transitions is as large as 10 nm for pure Mg [33],similar to those for Ti and Cu [34–36].In the case of other nanocrystalline metals,the elongation decreases with the decrease in the grain size,as shown in Fig.2(a).The elongation decreases because work hardening becomes more difficult with the decrease in the grain size after yielding,resulting in plastic instability in the early tensile stage.In addition,owing to the immaturity of processing strategies,defects are induced in samples with a small grain size,leading to the brittle fracturing of nanocrystals.The GB resistance to dislocation source initiation increases after grain refinement,leading to a decrease in the number of movable dislocations and limited plastic deformation.

The deformation mechanism for Mg and Mg alloys with grain sizes at the micron scale is GB-dislocation interaction.The elongation increases with decreasing grain size,as shown in Fig.2(b),and dislocation slip or GB sliding is the main deformation mode.Grain size of～1 μm to～110 μm,the micrometer region,where the elongation of AZ31 Mg alloy negatively positive to the grain size.In the regime,as demonstrated in Hall–Petch strengthening behavior,plasticity depends on the lattice dislocation interactions with GBs and/or twin boundaries.The plasticity of Mg alloy can be improved by suppressing twin formation by the grain refinement.For instance,when the grain size of pure Mg decreases from 125 to 5.5 μm,the elongation increases from 6.3% to 23% [13].Non-basal plane dislocations are activated and twin formation are suppressed to promote plastic deformation.Moreover,when the grain size of pure Mg decreases from 12 to 1.2 μm,the elongation increases to 100% [5].Such good plasticity of pure Mg is because the deformation is dominated by the relative sliding of the crystal grain groups,and grain rotation and dislocation slip are coordinated mechanisms.The occurrence of local stress concentration is delayed by deformation,which enhances the plasticity of pure Mg at 25 °C [5,6].As described,when the grain size of pure Mg is less than 1.57 μm,the deformation mechanism transforms from dislocation slip/deformation twinning to GB sliding [32].As the grain size decreases,the activity of deformation twins is inhibited [6,32].Consequently,when the grain size is less than a critical value,twinning is less facile than slip phenomena.

Fig.2.Elongation plotted as a function of the average grain size.(a) Pd,Cu,Ni and Al alloys,nanocrystalline [52–57];(b) AZ31 Mg alloy,microcrystalline[25–27,58–64].

The findings of research on the yield strength and plasticity of Mg and Mg alloys with grain sizes ranging from the nanoscale to the microscale can be summarized as follows.The yield strength and plasticity of Mg and Mg alloys are consistent with the Hall–Petch effect when the grain size is at the microscale.At the submicron and nanoscale,as the grain size decreases,the yield strength decreases and the plasticity increases.These changes occur owing to the transformation of the deformation mechanisms from dislocation/twinningdominated to GB-dominated.At the submicron level,a new deformation mechanism appears,that is,the relative sliding of grain groups.

3.Factors influencing GG

GG can be considered to be a process of thermal activation and GB migration driven by energy.According to the Arrhenius formula,the GG rateKcan be expressed as

whereAis a constant,Qis the activation energy of GG(kJ·mol-1),Ris the gas constant andTis the annealing temperature (K).Alternatively,according to the GG kinetics,Kcan be expressed as [65]

whereDis the grain size (μm) after annealing for timet(s),nis the GG exponent andD0is the initial grain size before annealing(μm).Theoretically,the value ofnis 2 for pure metals[66];however,the actual value ofntends to be larger because of the pinning and drag effects of the second-phase particles or solute atoms on the GBs [67,68].The studies reported in the literature exhibit a wide variation in the activation energyQfor GG (12.3–110 kJ mol-1),as concluded in Table 1.The abnormally lownandQvalue may be attributable to the dislocation and twinning [69,70].Thus,understanding the distribution of the second-phase particles and solute atoms in the GBs and the interaction of dislocation slip and twinning are important for extensively examining the GG process.

Table 1 Parameters of GG kinetics of reviewed Mg alloys.

3.1.Temperature

The temperature is a key factor influencing the microstructural evolution of Mg alloys.During thermomechanical processes and annealing,GG or recrystallization occurs,which can increase or decrease the average grain size of Mg alloys.Therefore,according to the Hall–Petch effect,the thermomechanical processes and annealing can be optimized to adjust the mechanical properties of materials by changing the grain size.

Mg and its alloys have poor formability at room temperature due to their limited slip system.Therefore,Mg alloys usually require processing at higher temperatures.The grain size in Mg alloys after the deformation process is smaller than that of the initial specimen,indicating that dynamic recrystallization occurred during the deformation process [77].For instance,the cast Mg-4Al-1Ca with average grains size of 200 μm,after severe plastic deformation at 250 °C the grains are refined to average size of 2.4 μm due to the dynamic recrystallization [78].When the deformation temperature increases from 350 to 450 °C,the corresponding microstructures of AZ31 Mg alloy reveals a recrystallized structure with the growing average grain size from 2.7 to 6.0 μm,indicating the GG occurs at higher extruding temperature [79,80].During deformation at 450 °C,AZ31 Mg alloy experiences the dynamic GG,which affects grain-boundary-sliding creep,and plastic anisotropy [81].The driving force for the GG is provided from the different stored energies or dislocation densities at both sides of the moving boundary.

For some applications,thermomechanical processing is followed by various annealing schedule,during which GG is inevitable.Annealing is a commonly used and effective heattreatment strategy to obtain fine or large grains to enhance the mechanical properties of alloys.In industrial thermomechanical processes,the GG can be controlled by the annealing temperature and time.At temperatures greater than the recrystallization temperature,the grains exhibit a continuous growth with the increase in the temperature.As shown in Fig.3(a),the mobility of GBs increases when the temperature is higher than 400 °C,leading to GG in Mg-Gd-Y-Zr alloys[3].Notably,GG is restricted to a temperature of 350 °C and controlled by lattice self-diffusion.As shown in Fig.3(c),in the temperature range of 150–400 °C,the grain size of pure Mg increases with the increase in the annealing temperature and time.The activation energyQis 95 kJ·mol-1,similar to that for GB diffusion in Mg (Q=92 kJ·mol-1),which indicates that GG is mainly controlled by the mobility of HAGBs[82].After annealing for 1440 min,owing to the continuous change in the GB mobility,the correlated misorientation distributions around small and large grains become similar[17,83].In strain-free and twin-free conditions,grains grow to different degrees after a hot-rolled sheet AZ31 is annealed at 350 °C,and the grain size exhibits a bimodal distribution [84].This observation suggests that smaller grains are consumed by larger grains owing to the surface-driven phenomenon and Ostwald ripening.The rate of non-basal GG is higher owing to the consumption of basal grains[26].Mg and Mg alloys annealed at temperatures up to 300 °C exhibit abnormal GG (AGG) owing to the anisotropy of the GB energy.When a friction-stir-processed Mg-Y-RE Mg alloy sample is annealed at 300 °C for 6 min,several large grains with specific orientations grow to consume the surrounding smaller grains,and this process is an example of AGG [15].AGG is also observed in shape memory alloys.For example,Yang et al.[85] demonstrated that cast Cu-Al-Mn-V alloy exhibits AGG when annealed at 900 °C,and a super-elasticity of as high as 7% can be achieved.Such high super-elasticity is attributable to the grain size and special orientation of abnormal grain.This phenomenon has not been reported for Mg and Mg alloys yet.Therefore,the annealing process must be modified to promote such AGG emerged in Mg and Mg alloys to achieve super-elasticity.

High temperatures typically destabilize the GBs,leading to significant GG.However,the rate of GB migration can be reduced by the pinning effects of thermal grooving,the film-thickness effect and the drag effect of solute atoms.After an AZ31 Mg alloy sample is annealed at 180 °C and 250 °C for 30 min,the second-phase particles exhibit a homogeneous distribution and exert a pinning pressure on the GBs,thereby restricting the GG.However,GG is not observed when other pure metals (Cu/Ni) are annealed at high temperatures (slightly lower than their melting point).The lack of GG can be explained by the fact that the plastic deformation of most grains is dominated by local dislocation,which causes the GBs to spontaneously exhibit a low-energy state[86–88].

3.2.Second-phase particles

Grains can be refined by the pinning effect of secondphase particles,leading to enhanced material properties.The distribution of second-phase particles at the GBs can decrease the GB migration rate [89,90].The extent of this effect can be approximated as [65]

wherevis the GB migration rate,pis the driving pressure,mis the intrinsic mobility of the boundary,γis the GB energy,?is a small geometric constant,pzis the pinning pressure andrandfvare the radius and volume fraction of the dispersed second-phase particles,respectively.When the driving force gradually decreases to that associated with the pinning pressure,the GG stagnates at a limiting valueDglimas

Fig.3.Variation in the average grain size and activation energy with annealing time at different temperatures: (a,b) Mg-Gd-Y-Zr alloys [3];(c,d) pure Mg[82].

The effects of the volume fraction and size of second-phase particles on the GG process have been extensively studied.The critical particle size and volume fraction exert different pinning effects on the GBs [91],as shown in Fig.4(a).When the matrix contains second-phase particles,the critical value of the second-phase particle size is smaller than the critical particle size.A larger particle size corresponds to a greater pinning effect on the GG.When the second-phase particle size is greater than the critical value,a larger particle size corresponds to a smaller pinning effect on the GG.Therefore,a quantitative relationship can be identified between the driving force of the GG and pinning resistance of the second phase,as shown in Fig.4(c).The pinning effect is almost nonexistent when the volume fraction of the particles is small[90,92].Furthermore,several researchers have examined the influence of second-phase particles with various shapes (such as spherical,disk-shaped or rod-shaped) on the GG.When the particle area fraction is more than 8%,the pinning effect of rod-shaped second-phase particles is greater than that of round-shaped second-phase particles [93].

The evolution of the second-phase particles may induce AGG.As shown in Fig.4(b),the GBs are initially pinned in the presence of second-phase particles.When the grains meet the second-phase particles in the growth process,the GBs are pinned by the second-phase particles,with all the particles located at the GBs.As GG occurs,the pinning of the GBs is weakened.The GBs gradually straighten with the grain evolution,and the associated driving force to eliminate the pinning effect of the second-phase particles weakens.Thus,most of the second-phase particles at the GBs remain in the straightened parts of the GBs in the resulting microstructure.As the GBs between the grains tend to straighten,GG is terminated.At high temperatures,the pinning effect of the second-phase particles is a possible mechanism for the increase in the activation energy of GG,which can lead to AGG [94].The confinement of the second-phase particles at the GBs hinders the normal GG.Additionally,some of the second-phase particles dissolve at high temperatures,and the absence of such precipitates at GBs promotes further GG.

Many scholars have recommended the introduction of trace elements such as Gd [95],Sm [96] and Al [97] in Mg alloys for grain refinement through the corresponding second-phase particles.The presence of these particles can enhance the mechanical properties owing to the activation of non-basal slip.With the increase in the number of second-phase particles,the grain size decreases.Furthermore,the stacking fault energies of the basal and non-basal planes decrease,which increase the potential of slip and enhance the plasticity of Mg alloys[98,99].

Fig.4.Relationship between second phase particle and grain growth (GG).(a) Relationship between the particle size and stable grain size [91];(b) variation in the driving pressure for recrystallization,driving pressure for GG and Zener pinning pressure with the annealing time [100];(c) evolution of a polycrystalline system containing second-phase particles [101].

3.3.Solutes

According to thermodynamic principles,solute segregation decreases the interfacial energy,thereby increasing the GB stability.According to kinetic principles,solute segregation has a pinning or dragging effect on GB migration,which inhibits GG,as shown in Fig.5.The segregation of Gd or Zn atoms at the GBs results in sluggish GB migration because the solute drag mechanism hinders the recrystallization and GG [76,102].Specifically,the distribution of Gd at dislocations and GBs can hinder the dislocation motion and GB migration.Additionally,the influence of co-segregation of multiple solute atoms is greater than that of single solute atoms.The minimization of the total energy and elastic strain energy can promote the ordered segregation of solute atoms(e.g.Gd,Nd,Ag and Zn atoms) in twin boundaries [102–104].In general,the solute atoms smaller and larger than Mg atoms tend to segregate at the compression and elongation sites,respectively.Thus,co-segregation significantly decreases the GB energy.Gd/Bi atoms,which are larger than Mg atoms,tend to segregate at the elongation sites [105,106].This separation is dominated by chemical bonds(coordination and solute electron configuration),rather than elastic strain minimization.Ordered atomic segregation occurs at the twin boundaries of Mg alloys,which induces a pinning effect on the twin boundaries.In this case,the driving force of twin boundary migration is the minimization of the total energy and elastic strain energy in the system [107].The ordered distribution of solute atoms exerts a stronger pinning effect on the migration of the twin boundaries than that associated with a single solute atom,resulting in enhanced strengthening of the material.Two factors facilitate the segregation of Gd/Y at the GBs in NC Mg-Gd-Y-Zr alloys: the difference in the atomic radii of Mg and Gd/Y,and enhanced solute diffusivity in NC alloys.Notably,GBs can function as preferred sites for the absorption of solute atoms.As shown in Fig.5(b),the nanograins in Mg-Gd-Y-Zr alloy do not grow significantly during aging treatment.Thus,the age softening observed at high temperatures of 200 °C and 225 °C is attributable to the decrease in the solute concentration in the grain interior.

Fig.5.Relationship between the solute parameters and GG.(a) Results of GG simulation considering the solute drag and pinning effects at 1200 °C [108];(b) schematic of the solute partitioning (⊥denotes dislocations gliding into,located at and emitted from the grain boundaries.) [109].

Grain refinement can enhance the plastic behavior[110,111].The segregation of solute atoms limits the GG,and grain refinement can be achieved.The solute atoms segregated at the GBs can pin the GB dislocations and suppress their emission from the GBs.This suppression can increase the critical stress associated with the dislocation emission from GBs,therefore strengthening the alloy.

Similarly,as two different modes of atomic movement,dislocation slip and twinning have an effect on GG.Generally,non-equilibrium GBs containing a large number of extrinsic dislocations,show higher atomic mobility.The emergence of a screw dislocation creates a ledge site where the attachment of atoms can easily occur without any energy barrier,thus promoting GG [112,113].While the uneven distribution of dislocations between grains may induce AGG [114].Additionally,the narrow twins with an average thickness of 1.8 μm would be consumed by matrix after annealing,for the narrow twins exhibits a higher curvature and higher thermal mobility [115].However,the increase of dislocation density can increase the active stress of twin-growth,thus reducing the mobility of twin boundary.

According to the above analysis of the factors influencing the GG,the second-phase and solute atoms in the alloys may be pinned,dragged or segregated at the GBs,thereby limiting the GG.In addition,the deformation/heat-treatment temperature influences the evolution of the microstructure,because plastic deformation/annealing can induce solute atom segregation at the twin boundaries/GBs of Mg alloys.Considering these aspects and the relationship among the plasticity,strength and grain size described in the previous Section 2,the plastic deformation/annealing process must be optimized obtain Mg alloys with fine and uniform grains.Furthermore,the elements and their contents must be considered in the alloy design.By introducing second-phase particles or solute atoms in an alloy,the GG can be inhibited during deformation/annealing.Thus,these factors can be appropriately adjusted to enhance the final properties of Mg alloys.

4.GG mechanisms

Understanding and controlling the GG behavior can help enhance the mechanical properties of Mg alloys.Therefore,the GG mechanism of Mg alloys have been extensively studied.When polycrystalline materials are annealed at sufficiently high temperatures or an external stress is applied,the GBs migrate,and the atoms rearrange.Thus,the average grain size increases,and the GB area per unit volume decreases.Many GG mechanisms have been proposed,and each mechanism is valid in certain regimes,as indicated in Table 2.The well-known driving forces for GG include non-equilibrium GBs,uniformly distributed residual stress,and differences in the strain energy associated with dislocation density accumulation,which commonly occur in ultrafine crystals and nanocrystalline materials.In a crystal with large grains,the GG is attributable to the surface tension caused by the boundary curvature,storage energy,sub-GB energy and continuous gradient misorientation.Several GG mechanisms for Mg and Mg alloys have been suggested,such as i) thermal activation;ii) continuous dynamic recrystallization;and iii) dislocation slip or twinning.Moreover,the (0002) grain family exhibits anisotropic GG behavior because the grains store considerable energy during the initial severe plastic deformation[116].Ultimately,GG mechanisms are induced by GB migration.Therefore,to understand the GG behavior of Mg and Mg alloys,the GG mechanisms are typically divided into strain-induced GB migration (SIBM) and heat-induced GB migration (HIBM).

Table 2 Summary of GG mechanisms.

Fig.6.Progress of GG.(a) Schematics of deformation mechanism of nanomaterial grain rotation leading to GG [133];(b) quasi in situ EBSD results showing HAGB migration during annealing of Mg alloys,including inverse pole figure (IPF) maps,boundary maps and grain orientation spread (GOS) maps [131].

4.1.Strain-induced GG

SIBM is defined as the motion of an existing GB portion that leaves behind reduced dislocation content [128].In the case of plastic deformation induced by nano-indentation,compression and tension,high cycle fatigue,and cyclic loading,among other processes,the plastic anisotropy of grains results in the heterogeneous accumulation of the stored deformation energy among grains.Driven by the stored deformation energy,the SIBM decreases the deformation energy stored in the polycrystalline.SIBM is typically observed in ultrafine crystalline and nanocrystalline forms.For example,Yao et al.[129] observed that the substantial GG in Al alloys with average grain sizes of 21–63 nm is attributable to SIBM.Furthermore,grain rotation can be achieved by decreasing the GB angle or eliminating the GBs after deformation,which leads to the coalescence of adjacent grains in nanocrystalline Ni[122],as indicated in Fig.6(a).Larger grains grow by consuming smaller grains;however,the deformation is replaced by GB sliding,which is coupled with GB migration and rotation and results in GG.

In Mg and Mg alloys,SIBM typically occurs during the growth of micron-scale grains.The GG driven by SIBM considerably changes the microstructure of fine-grained AZ31 Mg alloy with an average grain size of 30.2 μm,subjected to precompression and subsequent annealing,owing to the high internal strain energy of the alloy [130].The internal strain energy depends on the density of the dislocations formed by the compressive deformation before annealing.A similar result can be observed in the case shown in Fig.6(b): the average grain size of AZ31 alloy after precompression and subsequent annealing at 250 °C is 19.2–38.5 μm [131].Because the SIBM occurs from the residual matrix region with a smaller amount of stored strain energy to the twinned region with a higher strain energy,the residual matrix region exhibits pronounced growth behavior.This behavior is attributable to the lower stored strain energy in the residual matrix.Because basal slip is dominantly activated during room-temperature deformation,the strain energy accumulates in the residual matrix region.Additionally,the grain size increases with the increase in the deformation degree (0–15% strain) [132],and this phenomenon has also been observed in Mg alloys with 0–20% strain [119],as shown in Fig.7(a) and 7(b).In this case,the maximum strain is 4%,and GG occurs through GB migration.The driving force is the dislocation density gradient induced by the dislocation slip between grains during precompression,and not the surface tension caused by the boundary curvature.Thus,the differences in the strain energy stored in the grain lead to SIBM and subsequent GG.Under the influence of the temperature and strain rate,recrystallization grains appear,leading to grain refinement in the Mg alloy [119].It remains uncertain whether the GG is induced by stress or thermal activation.However,the strain and grain size are correlated,and thus,the strain range that promotes GG during deformation and enables the control of the grain size must be identified.A typical mechanism is strain-induced synergistic heat-induced GG: selective GG occurs owing to the activation of SIBM,stimulated by the large amount of stored strain in equal channel angular pressing (ECAP)-processed sheets.The dissolution of Mg17Al12particles during annealing can also be considered a potential factor leading to the onset of rapid GG [16].

Fig.7.(a) Microstructure and texture of AZ31 Mg alloy subjected to precompression followed by annealing [132];(b) Average grain size of the alloy as a function of strain for different strain rates [119].

4.2.Heat-induced GG

When pure Mg or Mg alloys are annealed to a certain temperature,GG occurs because of the instability of the GBs and decline in the GG energy,corresponding to the HIBM process [134].Driven by the GG activation energy,atoms are rearranged,and twin boundary/GB migration occurs.A classic example is the effect of thickness of the twin boundaries/GBs,induced by HIBM [115],as shown in Fig.8.In a grain with narrow twins,an average thickness of 1.8 μm,the HAGB of a narrow twin exhibits a higher curvature and higher thermal mobility,resulting in the detachment of the twins from the GBs.The HAGB migration of the narrow twin during annealing is preferable,which leads to the disappearance of the narrow twin.Moreover,the stored energy difference on either side of the boundary leads to twin boundary/GB migration[115].

Fig.8.Schematic showing the influence of the HAGB curvature for a narrow twin or narrow matrix on the thermally activated GB migration of the twins[115].

Mg and Mg alloys may exhibit AGG after being annealed at high temperatures.Currently,the mechanisms of AGG are being widely investigated,and the following mechanisms have been proposed: (i) evolution of initial textures/textures;(ii)coarsening and interaction of the second phase [17];(iii) formation of HAGBs;and iv) evolution of the average subgrain misorientation [15].The probable causes of AGG in pure Mg are the large GG exponentnand anisotropic GB mobility[82].For AZ31 Mg alloy,the GG during annealing is related to the mobility and excess energy of its GBs,which depend solely on the misorientation angle.As shown in Fig.9,the detwinning observed during annealing is driven by the relaxation of the stored strain around the twin tips in contact with the GBs.As the second-phase particles dissolve into the matrix during annealing,the pinning pressure decreases.Consequently,a few grains may overcome the restraint imposed by the local pinning pressure,leading to AGG [16].

Fig.9.IPF maps showing the microstructure: (a,e) after ECAP,(b,f) after 15 min of annealing at 250 °C.KAM maps determined using the 4th neighbor in the microstructure: (c,g) after ECAP,(d,h) after annealing [16].

The refinement of grains to the nanoscale may decrease the structural stability,leading to significant GG.However,recent studies have indicated that the crystal structure may become more stable when the grain size decreases to the nanoscale.Moreover,the mechanism of GG inhibition has been explained.Luke et al.highlighted that in pure Cu/Ni with a gradient nanograined structure,the nanocrystals on the surface layer remain stable regardless of subsequent mechanical loading or annealing,owing to the autonomous GB evolution to low-energy states and plastic deformation dominated by twinning [88].In addition,a metastable structure is observed when the grain size is reduced to a few nanometers by surface mechanical grinding.The metastable structure does not allow GG even when the annealing temperature is close to the melting point of pure Cu,owing to the GB relaxation [86].Recently,Zhou et al.[87] reported that the intensive boundary relaxation of pure Cu nanograins with grain sizes in the submicrometer regime may be triggered by rapid heating,owing to the generation of high-density nanotwins.Nevertheless,the activation mechanism of twinning when the grain size is at the nanoscale regime remains unclear.It is known that annealing twins were observed after a severe heat treatment of extruded AZ61 and AZ31 Mg alloy sheets[135,136].Thus,according to the characteristics of Mg and Mg alloys,by extending the abovementioned techniques and concepts to Mg and Mg alloys,the stability of nanocrystalline structure can likely be maintained even after high-temperature annealing.

5.Prospects

The correlation between the grain size,plasticity,strength and deformation mechanisms has been demonstrated.In addition,the factors influencing GG and GG mechanisms in Mg alloy have been studied.Future work can be aimed at examining the following aspects,which have not been extensively investigated yet.

As the grain size decreases from the microscale to nanoscale,the plasticity of Mg and Mg alloys increases,and the strength first increases and then decreases.For certain shape memory alloys with macroscopic grains,the plasticity disappears and super-elasticity appears.It remains to be verified whether the same phenomenon occurs in Mg alloys,especially in terms of the plastic deformation mechanism of large grains.In addition,twins typically do not form easily in nanocrystals.However,several researchers have reported that twins with stacking faults exist in nanocrystals,the formation mechanisms of which are still unclear.The clarification of these deformation mechanisms will be valuable for industrial production.The mechanical properties of metallic materials with small grains are very important for the design and fabrication of reliable nanodevices and nanostructures,while superalloy turbine blades and silicon photovoltaic systems require materials with large grains [35,85].

Furthermore,annealing in industrial production can promote or inhibit the GG,depending on the annealing temperature and time.When the annealing temperature is similar to the recrystallization temperature,recrystallization occurs,and fine grains are obtained.As the temperature increases,the second-phase particles and solute atoms dissolve and thus do not impede the GG.The pinning of the second phase and segregation of solute atoms inhibit the GG.The annealing process can be optimized to control the roles of the second phase and solute atoms in the microstructure.In this context,the synergistic effect of the second phase and solute atoms on the GG must be clarified.

Understanding the factors influencing the GG can help clarify the GG mechanisms.However,the GG mechanisms are complex owing to the driving and inhibiting forces.The mechanisms of GG and twinning in Mg and Mg alloys at the nanometer scale must be further investigated.The clarification of GG mechanisms can process strategies to control the grain size.

Overall,the existing studies have mainly focused on GG from the perspectives of dynamics,and the in-depth mechanism remain to be clarified.The investigation and clarification of these mechanisms can enhance the understanding of GG.Therefore,future research must be performed from the perspectives of GG kinetics.

6.Conclusion

This paper presents a review of the influence of the grain size on the plasticity and strength of pure Mg and Mg alloys,factors influencing GG and mechanisms of GG.The following conclusions are derived:

1.As the grain size of pure Mg and Mg alloys decreases from the microscale to the nanoscale,the plasticity increases,and the strength first increases and then decreases.These trends are observed because the plastic deformation mechanism changes from dislocationtwinning to a GB-dominant mechanism.

2.The GG process is influenced by the temperature of plastic deformation/annealing and presence of secondphase particles and solutes.The pinning of the second phase and segregation of solute atoms inhibit the GG.The process of plastic deformation/annealing can be optimized to control the roles of the second phase and solute atoms in the microstructure to obtain small and uniform grains.

3.GG mechanisms can be divided into SIBM and HIBM.SIBM occurs owing to the difference in the strain energy stored in adjacent grains with high-density dislocations.HIBM is driven by the difference in the energy of GBs/sub-GBs and boundary curvatures.AGG can be induced by the anisotropy of strain energy,anisotropic GB mobility,depinning of the second phase and high misorientation gradient.

4.Clarification of GG mechanisms can facilitate better control of the properties of Mg and Mg alloys and other metals.The internal mechanisms of GG at the atomic scale must be further explored.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

The work is supported by Innovation Research Group of Universities in Chongqing (CXQT21030),Chongqing Talents: Exceptional Young Talents Project (CQYC201905100),Chongqing Youth Expert Studio,Hong Kong Scholars Program.The contribution of Qinghua Chen and Ruinan Chen is equal.