Optimizing mechanical properties of magnesium alloys by philosophy of thermo-kinetic synergy:Review and outlook

Tinle Wng ,Feng Liu,b,

a State Key Laboratory of Solidification Processing,Northwestern Polytechnical University,Xi’an,Shaanxi 710072,China

bAnalytical &Testing Center,Northwestern Polytechnical University,Xi’an,Shaanxi 710072,China

Abstract Although several strategies (including grain refinement texture adjustment,precipitation hardening,etc.) have been verified to effectively improve the mechanical properties of lightweight magnesium (Mg) alloys,considerable efforts are still needed to be made to comprehensively understand the potential mechanisms controlling complex microstructures and deformation behaviors exhibited by the hexagonal close-packed host lattice of Mg,thus assisting the rational design of materials at a more physical level.As the cornerstone of this review,a universal rule,the so-called synergy of thermodynamics and kinetics (i.e.,thermo-kinetic diversity,correlation and connectivity),including a recently proposed theory of generalized stability(GS),is introduced to deepen our understanding on common behaviors in Mg alloys(i.e.,deformations(slip and twining modes),phase transformations (especially for precipitations) and interactions in between) at a new perspective.Guided by the GS theory,typical cases for Mg alloys design are qualitatively evaluated to reemphasize the traditional strengthening and toughening strategies mentioned above and to illuminate their exquisite coordination for breaking through the trade-off relationship between strength and ductility,corresponding to a typical thermo-kinetic pair (i.e.,high driving force (ΔG) -high GS).To produce the Mg alloys with superior strength-ductility balances,the potential capacity of this GS theory for guiding processing path design is discussed,finally.

Keywords: Magnesium alloys;Synergy of thermodynamics and kinetics;Generalized stability;Superior strength-ductility balance.

1.Introduction

In the past decades,magnesium (Mg) and its alloys,as a kind of lightweight structural metallic materials with excellent physical and chemical properties (e.g.,low density,high specific strength and stiffness,good biocompatibility,large hydrogen storage capacity,etc.) [1-4],have becoming more and more promising in automotive,aircraft,aerospace,and 3C(computer,communication and consumer electronic product)industries,etc.Unfortunately,their relatively low strength and ductility inevitably caused major barriers against their wider structural applications.Undoubtedly,the mechanical properties of Mg alloys should be directly related to the potential behaviors of well-known deformation modes in hexagonal closepacked (hcp) host lattice,i.e.,slip systems (basal 〈a〉 (two independent),prismatic 〈a〉 (four independent),pyramidal I 〈a〉(four independent) and pyramidal Ⅰor Ⅱ〈c+a〉 (five independent) dislocations) and deformation twinning (contraction twinning (six {101}〈102〉 variants) and extension twinning(six {102}〈101〉 variants)) [4-6].Following the Von Mises criterion [7],at least five independent deformation modes are required to accommodate uniform arbitrary strain of polycrystals,thus upon deformation,the coordination and mutual interactions of these operative dislocations and twinning with different activation barriers or critical resolved shear stresses(CRSS),must lead to a complex evolution of microscopic defects,while reflecting a specific macroscopic anisotropic mechanical property [8].How to improve the strength-ductility combination and reduce the plastic anisotropy depends essentially on how to optimize the activation and exhaustion of different deformation modes in Mg alloys.

Generally,alloying and thermal-processing are performed to induce phase transformations (PTs) and plastic deformations (PDs) in original as-cast Mg alloys,which are prominent methods for improving mechanical property via altering microstructures influencing deformation modes,e.g.,grain refinement texture weakening and precipitations [9,10].A traditional procedure can be summarized as follows:multifarious technologies corresponding to different kinetic processes will be employed to modify the microstructures of the processed materials,until a targeted thermodynamic state that can resist deformation at a specific strength-ductility level is achieved,where the relative strength of CRSSs among different deformation modes could be changed.Since much unknown behaviors of PTs and PDs in Mg alloys are required to be explored,how to use the above procedure to develop advanced Mg alloys mostly depends on experimentally trialand-error approaches.Conventionally,PTs and PDs with their respective thermodynamics and kinetics are treated independently,but intrinsically,both of which are kinetic atomic displacement processes of microstructural variation triggered by thermodynamic driving forces (ΔG).

Following previous works in authors’ group,there exists a synergetic effect of thermodynamics and kinetics,i.e.,the correlation between thermodynamics and kinetics reflected by a trade-off relationship between ΔGand kinetic energy barriers(Q),for the usual material behaviors at atomic level,e.g.,PTs dominated by diffusion [11] or shearing [12,13],grain boundary (GB) migration [14] and dislocation movement [15],etc.On this basis,generalized stability (GS),as a universal theory describing the thermodynamic stability and the kinetic transient transition of a specific state along the reaction coordinate of an atomic displacement process,was proposed to uniformly treat PTs and PDs with a thermo-kinetic connection in between,by which PTs can be directly correlated to mechanical properties [15].Following the conception of GS,many cases of metallic material design (e.g.,for steels and aluminum alloys) with optimized strength-ductility have been verified to satisfy a rule that,the original trade-off relationship between strength and ductility must be inherited from the trade-off between ΔGandQof PTs and/or PDs arising from materials processing.Most importantly,a thermokinetic triplet (i.e.,high ΔG-highQ-high GS) of PTs and/or PDs (which should be simplified as high ΔG-high GS,as explained in Section 2.1.2) by forming the microstructure corresponds to the excellent mechanical properties by deforming the microstructure.

Obviously,the GS coupling with the thermo-kinetic synergy,known as a universal theory,should also provide an effective guidance for improving mechanical properties of Mg alloys.This review summarizes the main progresses of structural Mg alloys in recent years at a newly perspective of thermo-kinetic synergy,including correspondences between the macroscopic mechanical properties and the microscopic activity of deformation modes (i.e.,thermodynamics and kinetics of dislocations and twinning under the load)[16],forming mechanisms of the structural factors controlling operative deformation modes (i.e.,thermodynamics and kinetics of PTs and PDs in processing) [17],and interactions between the microstructures and the deformation modes (i.e.,the effect of processing on thermodynamics and kinetics of dislocations and twinning) [18].This will be beneficial for building a unified theory or framework that is indispensable for understanding common behaviors of different Mg alloys and corresponding universal thermo-kinetic mechanisms of PTs and PDs to rationally design Mg alloys.

This review consists of four sections Section 1.just gives the introduction Section 2.briefly introduces the theoretical cornerstone of this review,i.e.,thermo-kinetic synergy and the GS theory,and the status of understanding the deformation mechanisms of Mg alloys.In Section 3,typical cases of synchronously improved strength and ductility in different Mg alloys and corresponding alloying and thermal-processing methods are analyzed in the concept of thermo-kinetic synergy,qualitatively verifying the thermo-kinetic criterion,i.e.,the thermo-kinetic pair of high ΔG-high GS.Finally,a summary is provided,and accordingly,the potential guiding capability of the theory of GS for improving strengthening and toughening strategies in rational design of Mg alloys is discussed in Section 4.

2.Theoretical background for property optimization

The mechanical properties of structural materials are generally correlated with the microscopic crystalline defects(e.g.,dislocations,twins and grain boundaries,etc.),whose interactions,for Mg alloys as examples,can induce effective strengthening mechanisms,as verified by experimental observations [19,20],numerical simulations [21,22] and theoretical models [23,24].A basic strategy can be described as,immobile crystalline defects (e.g.,precipitates [25],forest dislocations [26],and GBs [27],etc.) collectively serve as local sites inhibiting the motion of glissile dislocations or deformation twinning.Accordingly,theoretical backgrounds for breaking through the strength-ductility trade-off paradox,including the concept of thermo-kinetic synergy (Section 2.1),the deformation mechanisms (Section 2.2),and the structural factors for altering deformation mechanisms (Section 2.3),are provided in this Section 2 to deepen the understanding on strengthening and toughening mechanisms.

2.1.Material behaviors by philosophy of thermo-kinetic synergy

Different material behaviors including PTs and PDs could be induced during manufacturing materials via a specific technology for attaining the mechanical properties satisfying their service requirements.Although thermodynamics and kinetics of these material behaviors have been treated independently for a long time,it is noteworthy that the usual PTs or PDs should be controlled by the synergetic effect of thermokinetics.For example,as the kernel controlling factor in grain refinement strengthening,the stability of GB is simultaneously dominated by the thermodynamic effect (i.e.,the reduced GB energy via solute additions) and the kinetic effect(i.e.,the drag force exerted by added solute atoms) [28-30].Furthermore,as for precipitation hardening,the formation sequence among several potential precipitates is originated from the thermo-kinetic competition at a specific circumstance,i.e.,the kinetically favorable precipitates with smallerQof nucleation may preferentially forms,as the metastable phases,relative to the thermodynamically favorable precipitates with larger ΔG,which are the final stable phases [31].Especially,as for the solidification process of any as-cast alloys,the increased undercooling decreases the critical nucleation barriers but increases the activation energies of atomic diffusion,leading to the contradictory effects of the former thermodynamic one and the latter kinetic one on the nucleation rate [32].Consequently,only when both thermodynamics and kinetics of PTs and PDs are considered concurrently,a realistic material behavior can be truly understood and predicted.The manifestation (i.e.,thermo-kinetic diversity),intrinsically characteristics (i.e.,thermo-kinetic correlation) and application (i.e.,thermo-kinetic connection) of thermo-kinetic synergy are illustrated as follows.

2.1.1.Thermo-kinetic synergy in phase transformations and plastic deformations

Thermo-kinetic diversity and correlation:Depending on the interior factors(i.e.,the initially atomic status and interactions of defects,etc.) and the exterior factors (i.e.,the temperature,magnetic,electric and mechanical fields) for a specific alloy system,different modes of PTs or PDs proceed with different combinations of thermodynamics and kinetics,both of which determine the initiation and development of a typical structural changing process,thus reflecting the thermal or mechanical stability of the initial state and the competitive capacity of this process relative to the other potential processes.As for PTs,different product phases could be transformed from the parent phases in a specific sequence influence by above factors,and form by different ways,e.g.,spinodal decomposition [33],nucleation via different modes [34,35] (i.e.,continuous,site saturation and Avrami nucleation,etc.),and growth mainly controlled by interface or diffusion [36],etc.As for PDs,analogously,different deformation modes,i.e.,slip systems and twinning,could be initiated under different loading conditions.It is just due to the various thermo-kinetic combination,i.e.,the thermo-kinetic diversity,that results in these complex and abundant evolving phenomena.

Fig.1.Schematic representation of the thermo-kinetic synergy in material.(a)Thermo-kinetic correlation;(b)generalized stability;(c)the trade-off relationship between strength and ductility and between thermodynamic driving force and kinetic energy barrier;(d) the thermo-kinetic framework for property improvement (For interpretation of the references to color in this figure the reader is referred to the web version of this article).

Actually,a codependent relationship between thermodynamics and kinetics can be deduced from the above thermokinetic diversity,so that a trade-off relationship between thermodynamic ΔGand kineticQ(i.e.,an increasing/decreasingΔGand a decreasing/increasingQalways synchronize) has been found in all studied PTs of metallic materials in authors’group,which is define as the thermo-kinetic correlation and can be uniformly schematically shown in Fig.1(a).For instance,the minimum energy paths of shear dominated martensitic transformations in steels,obtained via density functional theory (DFT) calculations [37,38],have revealed the temperature dependent [12] and composition dependent [13] thermokinetic correlations.Analogously,the temperature dependent,the structure-dependent and the composition-dependent thermo-kinetic correlation have been verified in diffusion dominated precipitations of steels [11,39] and aluminum alloys [40],in austenite-to-ferrite transformation [41] via theoretical modeling,and in GB migration via molecular dynamics(MD)simulations[14,42].Additionally,the thermo-kinetic correlation has also been inherently included in many traditional theoretical models for PTs descriptions,e.g.,the classical model of GB migration for thermally activated growth[14],the dendrite growth model for solidification [43] derived from the thermodynamic extremal principles [44],the classical Kaufman-Cohen [45] and Olsen-Cohen [46] models for martensitic nucleation,etc.As for dislocation slip upon deformation,which is also the elementary step for martensitic nucleation [46],the trade-off relationship of thermodynamic ΔGand kineticQcan inherently hold [15,47].

Thermo-kinetic connectivity:Since the thermo-kinetic correlation is considered as a universal intrinsic characteristic of thermo-kinetic combination of PTs and PDs,then generally,the PTs of high ΔG-lowQcan produce the microstructures of high strength but low ductility,and vice versa.For example,with increasing the cooling rate,i.e.,increasing the ΔG,austenite can transform to pearlite,bainite and martensite successively in steels,accompanied by the transformation from diffusion controlled to interface controlled growth,i.e.,decreasing theQ,corresponding to the increased strength but decreased plasticity in the resultant microstructure [48].Similar phenomenon can be observed upon highly undercooled solidification [49].More importantly,it is inherently reflected in the classical dislocation theory [15,50]:σε=withσ=andε=ρmbl/M,whereσis the yield strength or the flow stress,εthe strain or the plasticity,αthe empirical constant,Mthe Taylor factor,Kthe shear modulus,bthe Burgers vector,ρthe total dislocation density,ρmthe mobile dislocation density andlthe mean free path of dislocations,i.e.,the mean spacing between forest dislocations acting as obstacles for a moving dislocation.Accordingly,the increased strength orσ,i.e.,the increased ΔG,is originated from the increasedρ,which further leads to the decreasedρmdue to the larger exhaustion rate than generation rate of mobile dislocations at a larger slip velocity caused by the decreasedQ[50],thus resulting in the decreased ductility orε,and vice versa.

This implies that the trade-off relationship between ΔGandQcould be correlated with the trade-off relationship between strength and ductility.How to modulate the balance of material properties in trade-off paradox can be logically and vividly described using a so-called "seesaw" (Fig.1c),where,the thermodynamic ΔGand the strength stay together on the one end,and the kineticQand the ductility on the other end.As such,the directly unmeasurable correspondence between the high/low ΔGand the low/highQarising from forming the microstructure (i.e.,PTs and/or PDs) can be intrinsically reflected by the well-known directly measurable correspondence between the high/low strength and the low/high ductility arising from deforming the microstructure.This philosophy,as reflected via this "seesaw",can be define as the thermokinetic connectivity.Noted that,the length of the prop rod of this "seesaw" should not be fixed (Fig.1(c)),so that the exact values for the thermodynamic ΔGand the strength or the kineticQand the ductility are decided by the absolute height of the two ends that are directly determined by the length of the prop rod connected threaded with the pedestal.As the prop rod is rotated relative to the pedestal,the exposed length of the prop rod can be lengthened,and the height of the two ends of the "seesaw" can be simultaneously elevated,i.e.,the ΔG-Qand strength-ductility can be simultaneously improved.Therefore,how to fine and rotate the prop rod of this"seesaw"is the main mission for materials design.

Based on the second law of thermodynamics,the evolution of systems should follow a path dissipating the energy as fast as possible [44],and part of the energy could be stored or released by forming or alleviating defects,e.g.,the martensitic transformation and the tempering in steels,which separately correspond to two extreme cases that,the process of high ΔG-lowQdeviating the equilibrium and the process of low ΔG-highQtending to the equilibrium,with the resulted high strength-low ductility and low strength-high ductility.Accordingly,the structural changing process (i.e.,PTs or PDs) of high ΔG-highQshould mean,the one type of defects inducing the process proceeding and the other type of defects inducing the process termination,have been produced in the microstructures to effectively suppress the subsequent structural change (i.e.,high strength),and additionally,the transformation rate from the former type of defects to the latter type should also be low enough to ensure a long service time of the former type to change the material structure as much as possible (i.e.,high ductility).Nearly all strategies for simultaneously improving strength-ductility of structural materials follow this rule in literatures,e.g.,dual-phase bimodal nanostructure [15],nanoscale second-phase precipitates dispersed in nanostructured grains [51],nanoscale twin boundary (TB)[52],transformation-induced-plasticity and twinning-inducedplasticity effects [53],etc.This alloy design ideology of high ΔG-highQis just the method for rotating the prop rod of the “seesaw” in Fig.1(c).

2.1.2.Generalized stability for unifying material behaviors

Physical description for material behaviors:Upon manufacturing and service of a structural material,the microstructures are changed continually by multistage (referred asnstages) processing,during which PDs and PTs can proceed alternately or simultaneously,and the applied materials are the factory products of preceding (n-1)-stage processing,with their properties reflected by the PDs during their service at the finalnth stage of processing.Accordingly,thermo-kinetic connectivity is naturally hold between the continuous PTs and/or PDs in the processing,i.e.,the thermo-kinetic combination of any one ofn-stage is established based on the accumulative result of all the previously stages of processing,which is directly correlated with the thermo-kinetics of the adjoining stage before this one.

Following the basic philosophy reflected in Fig.1(c),it is time to ask,how to select and control the PTs and PDs in the preceding (n-1)-stage processing to artificially attain the objective thermo-kinetics of PDs at thenth stage of processing during the service.Regarding it,recently,the GS criterion is proposed in authors’group[15],which,considering both thermodynamics and kinetics,seems essentially different from the usual thermal or mechanical stability only considering thermodynamics,and thus,not only measures the stability of a static state,but also measures the ability of holding at a transient state,i.e.,holding off the subsequent structural change,during the dynamic behaviors of PTs or PDs.

Potential design by generalized stability:A detailed construction of the GS is available in Ref [15].,so only a concise expression is provided here:

whereQ,Q,ΔG,andΔGstand for different meaning for different material behaviors:commonly,as for grain growth,they are,respectively,the activation energy for GB migration,the activation energy for GB migration of pure solvent,the GB energy of the alloys,and the GB energy of pure solvent;as for PTs,they are,respectively,the activation energy for phase boundary migration,activation energy for phase boundary migration at the beginning of PT,effectiveΔG,andΔGchemfor PTs mainly controlled by diffusion or shear;as for PDs,they are,respectively,the effective activation energy for dislocation slip upon uniform deformation,the activation energy for dislocation slip at yielding,the effectiveΔGupon uniform deformation,and theΔGat yielding.

Basically,Eq.(1) shows that,the combinations of high ΔG-lowQ,corresponding to the combination of high strength-low ductility,should result in relatively low GS.Therefore,in order to increase the ductility and induce PTs or PDs of high ΔG-highQ,one could improve theQwithout sacrificing the strength,and the corresponding GS will be increased.As such,the ideology of high ΔG-highQfor rotating the prop rod of the “seesaw” in Fig.1(c) transforms to the thermo-kinetic triplet of high ΔG-highQ-high GS,which could be further simplified as the thermo-kinetic pair of high ΔG-high GS,due to the increasedQmust lead to the increased GS while maintaining the ΔGin Eq.(1).The GS can be schematically explained as shown in Fig.1(a) and (b),where,the initial and the final states,are separately indexed as the green and orange points on the energy change curves of the whole mesoscopic process in Fig.1(a);while in Fig.1(b),they,as the transient states,correspond to the green and orange energy change curves of microscopic subprocesses.This clearly implies that the whole mesoscopic process in Fig.1(a)should be composed of multiple microscopic subprocesses in Fig.1(b),i.e.,the curves of Fig.1(b) stand for every transformation event connecting green,purple and orange points of Fig.1(a).Whereupon,the GS can be used to evaluate the sustainability of the transformation from the green to the orange states with the purple dotted curves as intermediate states (Fig.1(b)).

Using the GS,a thermo-kinetic framework for optimizing the strength-ductility of materials can be naturally constructed.As shown in Fig.1(d),the relationship between the thermo-kinetic synergy (the blue region) and the GS (the red region) seems analogous to the relationship between Yin and Yang in this Chinese Taiji diagram;Yin acts as part of Yang,and Yang acts as part of Yin,both of which evolve continuously and control the material properties.Starting from the left site of the circle (Fig.1(d)),modulating the thermokinetics of PTs in the preceding (n-1)-stage processing to obtain the microstructures corresponding to high ΔG-high GS,and thereafter;the deformation inherits this thermo-kinetic combination due to the thermo-kinetic connection,thus a material with synchronously improved strength and ductility can be obtained;then using the thermo-kinetic correlation,the obtained material should follow a new strength-ductility tradeoff balance.Hence,the continuous rotation of this Taiji diagram corresponds to the simultaneously elevated two ends of the “seesaw” in Fig.1(c) caused by the continuous rotation of the prop rod.This thermo-kinetic Taiji concept will be considered as the background for analyzing how to improve mechanical properties of Mg alloys in this review.

2.2.Deformation mechanisms of magnesium alloys

The commonly activated deformation modes in Mg alloys,responsible for both the formability during manufacturing and strength-ductility in service,are concisely introduced here,including basic behaviors and influencing factors of intra-granular slip (Fig.2(a)) and twinning (Fig.2(b)),as well as their interactions.In addition,inter-granular deformation modes,e.g.,GB sliding (Fig.2(c)),occurring by virtue of GB diffusion in conjunction with intragranular dislocation motion in the vicinity of GB,also contribute to the strain accommodation when the grain size approaches 1 μm or less in polycrystalline Mg and its alloys [4,54,55].

Fig.2.Schematic illustration of deformation modes in Mg Alloys [4]:(a)basal,prismatic and pyramidal slip systems;(b) extension and contraction deformation twinning systems;(c) grain boundary sliding.(d) The critical resolved shear stress values for deformation modes and their variation with temperature in Mg single crystals [4].

For a given applied stressσ,only if the resolved shear stressτalong the slip or twinning direction on the slip or twin plane (define asτ=σcosαcosβwith cosαcosβas Schmid factor,αthe angle between the applied stress axis and the slip or twinning direction,βthe angle between the applied stress axis and the slip or twinning plane normal) becomes larger than a critical value,i.e.,the CRSS,the corresponding deformation mode could be activated.The CRSSs of different deformation modes could be experimentally estimated by testing single crystals in different crystallographic directions[56],fittin mechanical behaviors of polycrystals with varying textures under different loading conditions [57],and nanomechanical testing methods,e.g.,instrumented nanoindentation[58].

As plotted in Fig.2(d),the basal 〈a〉 slip and {102} extension twinning are readily activated at ambient temperature due to their prominently lower CRSS compared to other non-basal slip and twinning modes [8].These dissimilarities in the CRSS values,accounting for macroscopic plasticity anisotropy and poor cold workability of polycrystalline Mg,will decrease with increasing the temperature.In order to improve the mechanical properties,it seems very significant to select the dominant deformation modes through controlling the sets of CRSSs via alloying effects and thermal-mechanical processing.

Fig.3.(a) Atomic structures of intrinsic stacking faults I1 (top) and I2 (bottom) in Mg [59].(b) GSFE curves for basal (top) and prismatic (bottom)slip systems in Mg from DFT calculations and MD simulations using Kim[79] and MEAM potential [67],and for the basal plane (top),only the curves for shifting along the leading partial dislocation Burgers vector are drawn,which are identical to the trailing partial ones.The differential displacement plot and contors of the Nye tensor showing structures of edge and screw 〈a〉dislocation cores on (c) basal and (d) prismatic plane [69].

2.2.1.Slip modes pertaining to〈a〉dislocations

Fundamental characteristics:The deformation behavior of metals,i.e.,the CRSSs associated with the competing deformation modes,is directly tied to the stacking faults(SF),which are common two-dimensional defects usually surrounded by partial dislocations [59].There exist four types of basal SFs for perfect stacking sequence …BABABABA… in the hcp lattice of Mg [60,61].As shown in Fig.3(a) [59],two are intrinsic SFsI1bounded bypartial dislocations(i.e.,…BABACACA…,formed by removal of a basal plane followed by slip of(1/3)〈100〉in the crystal)andI2bounded by(orp) partial dislocations (i.e.,…BABACBCB…,formed by direct slip of(1/3)〈100〉 in the perfect crystal),whereas,the other two are,respectively,the external SF (i.e.,…BABACBABA…,formed by inserting an extra plane) and the twin-like fault (i.e.,…BABACABA… in mirror symmetry about the fault plane) [60].The corresponding stacking fault energy (SFE),which significantly determines the properties of dislocations and twinning,could be obtained in experiments and especially via theoretical methods (e.g.,DFT calculations),following[62].The stable or unstable SFEs are actually the local extrema of the generalized stacking fault energy (GSFE) surfaces (or gamma surfaces in 2D) introduced by Vítek in 1968 [63],which is an energy profile manifested by interactions among the atoms near the SF [64,65].It is noteworthy that the probable slip path,the dislocation dissociations,the dislocation core width,the dislocation mobility and the SF width are all closely correlated with the GSFE surfaces [66].Furthermore,the GSFE can be used to obtain the maximum restoring forces (i.e.,the theoretical minimum forces to deform materials),and serve as the input of the Peierls-Nabarro model to calculate the core structures and Peierls stresses (i.e.,the critical stress to move a single dislocation in absence of other defects).The GSFE curves for basal and prismatic slip systems in Mg are shown in Fig.3(b) [67],assisting the understanding for the subsequently introduced characteristics of 〈a〉 dislocations.

Since the detailed studies for the plastic properties of Mg single crystals during the 1950s and 60s [68],the thermally activated slip of dislocations with(1/3)〈110〉 (or＜a＞) type Burgers vectors on basal(0001)plane has been deemed as the primary deformation modes in Mg.However,only the basal slip modes of 〈a〉 dislocations are not enough for homogeneous deformation accommodation,thus the activity of nonbasal prismatic and pyramidal slips of 〈a〉 dislocations,with much higher CRSSs relative to the basal slip especially at the ambient temperature,also deserves carefully investigations,which could supplement the number of the total independent slip modes to four from the original two of basal slip.The nucleation of the prismatic 〈a〉 dislocations might stem from cross-slips of basal 〈a〉 dislocations,which changes the slip plane from one basal plane to another with a prismatic plane connected in between [64].Due to the infeasiblein situmeasurements for the atomic-scale motion of dislocations,lots of reliable theoretical atomic-scale works [69-71] have been done to investigate the nature of dislocations in Mg,e.g.,the core structure,the dissociation behaviors and the mobility,etc.

The edge and screw 〈a〉 dislocation core structures on the basal and prismatic planes obtained via DFT calculations and MD simulations in Ref [69].are shown in Fig.3(c) and (d),using the differential displacement plot and contors of the Nye tensor.Both edge and screw 〈a〉 dislocations can dissociate into two Shockley partials with a metastable SF on the basal planes,but maintain the compact core on the prismatic planes because of no existence of metastable SF on the prismatic planes or symmetrical extreme on the corresponding GSFE curves[64,69,72],as shown in Fig.3(b).Moreover,for the〈a〉dislocations on the pyramidal planes,the edge type will keep perfect,but the screw type will dissociate.The differences in the core structures can further lead to the anisotropy of the dislocation mobility,quantifie by the Peierls stress,which is demonstrated to be strongly correlated with the number of core atoms moving collectively [71].The Peierls stress of the basal 〈a〉 dislocations are two orders of magnitude lower than the prismatic 〈a〉 dislocations,so that the dislocation velocity on the prismatic plane is always slower than that on the basal plane.Additionally,the anisotropy of dislocation velocity,controlling the plastic flow,is also related to the dislocation character,i.e.,edge or screw,and the former one usually moves faster than the latter one on the same slip plane.

Thermo-kinetic synergistic analysis:Strengthening the basal slip of 〈a〉 dislocations could improve the ductility due to the reduced basal to non-basal CRSS ratio and the enhanced isotropy [73].Furthermore,the improved ductility has also been demonstrated to be correlated with the increased thermally activated cross-slip probability of 〈a〉 dislocations from the easy basal plane onto the hard prismatic plane [73-75],caused by the increasedI2SFE [76].This cross-slip phenomenon can be facilitated by large stresses or high temperatures,and proceed via double-kink (i.e.,so-called jog-pair)nucleation mechanism above the room temperatures (where a screw dislocation has cross-slipped two planes and been bound by two edge type jogs) [73-75],or Friedel-Escaig mechanism [77] below the room temperatures (where a screw dislocation has been constricted and bowed).The thermally activatedQb?prifor the process of double-kink nucleation follows [74]:

where τb?priis the cross-slip stress,the prismatic Peierls stress andthe formation energy of a single kink. Accordingly, the plastic strain ratefor the prismatic shear could be written as:

wherekBis the Boltzmann constant,Tthe temperature andυb?prithe attempt frequency for double-kink nucleation.As can be seen in Eq.(2),the cross-slip should intrinsically reflect the thermo-kinetic correlation,i.e.,the decreasedτb?pri,or the ΔG,is always accompanied by the increasedQb?pri,based on Eq.(3),which will further lead to the decreasedεpri,i.e.,the prolonged duration for dislocation activity corresponding to the improved ductility.This thermo-kinetic correlation has also been revealed in the atomic study work of Itakura et al [75].,and could be implemented via additions of alloying elements,e.g.,Li [78],to lower theτb?prirequired for the cross-slip of 〈a〉 dislocations.

2.2.2.Slip modes pertaining to〈c+a〉dislocations

Fundamental characteristics:The slip modes pertaining to 〈a〉 dislocations cannot accommodate the c-axis strain,thus restricting the ductility enhancement of Mg.The nonbasal slips of 〈c+a〉 dislocations on the pyramidal I plane{101} and Ⅱplane {122},as the only sustainable deformation mechanism for accommodating c-axis deformation and greatly dominating the plasticity of Mg alloys,have received abundant attentions since its firs confirmation in experiments during the early 1970s [80,81].Due to the lower symmetry of the non-closest-packed pyramidal slip planes and the larger Burgers vector compared with basal 〈a〉 dislocations,the propensity and nature of 〈c+a〉 dislocations are so complex that the fundamental aspects of their formation,dissociation and core structures are still poorly understood,and there still exist considerable debates in literatures in regard to their predominant slip planes,i.e.,the relative importance of pyramidal I and Ⅱplane,usually supported as type I plane[82-85],type Ⅱplane [80,81] or both of them [86-90].As shown in Fig.4(a),there are two types of atoms stacking on the rugged pyramidal I plane but one type of atoms stacking on the planar pyramidal Ⅱplane [91].Due to the higher atomic packing density of the type I plane than that of the type Ⅱplane,the Peierls stress for the type I plane should be smaller than the type Ⅱplane,as revealed by MD simulations in Ref [85].and GSFE curves for shear along the Burgers vector of 〈c+a〉 dislocations on pyramidal I andⅡplanes [67],as shown in Fig.4(b) and (h),suggesting the more readily formation of〈c+a〉dislocations on the pyramidal I plane relative to that on the pyramidal Ⅱplane [92].The temperature dependent mobility of the 〈c+a〉 dislocations,i.e.,the favorable slip on the pyramidal I plane at low temperatures while on both the pyramidal I and Ⅱplanes at elevated temperatures,was reported in Ref [88]..Furthermore,it was found that edge 〈c+a〉 dislocations have lower mobility than screw ones in experiments [81,93].

Fig.4.(a) Schematic diagram of pyramidal I (101) plane and Ⅱ(212)plane [91].(b) and (h) are GSFE curves for pyramidal I and Ⅱ planes in Mg from FP calculations and MD simulations using Kim [79] and MEAM potential [67].(c) and (d) are edge and screw 〈c+ a〉 dislocation cores on pyramidal Ⅱplanes obtained from DFT [94];(i) and (j) are edge and screw〈c+ a〉 dislocation cores on pyramidal I planes obtained from MD simulations using a MEAM potential [67];all these core structures are manifested via the superimposed differential displacement plot and contors of the Nye tensor.(e) -(g) are schematic diagrams of edge and screw 〈c+ a〉 dislocations dissociated on pyramidal Ⅱand basal planes,and (k) -(m) correspond to mixed and screw 〈c+ a〉 dislocations dissociated on pyramidal I and basal planes [101].

The core structures of edge and screw 〈c+a〉 dislocations on the pyramidal Ⅱplanes obtained from DFT in Ref [94].and that on the pyramidal I planes obtained from MD simulations using a modified embedded-atom method (MEAM)potential in Ref [67].are shown in Fig.4(c),(d),(i) and (j),respectively.As can be seen,no matter edge or screw 〈c+a〉dislocations on the pyramidal I or Ⅱplanes,all of them can dissociate into two pure edge or screw 1/2＜c+a＞partials separated by a specific distance,which is determined by the balance between the elastic repulsion of the two partials and the attraction on account of SFE [95].Moreover,the differences of the core structures between two dissociated partials,corresponding to the differences in the GSFE curves along the〈c+a〉 direction (Fig.4(b) and (h)),will further lead to the asymmetrical Peierls stresses.A high anisotropy of Peierls stresses for glissile core structures of pyramidal I 〈c+a〉dislocations has also been revealed via MD simulations [93].Since the core energy of the screw pyramidal Ⅱ〈c+a〉 dislocation is lower than that of the screw pyramidal I 〈c+a〉dislocation in contrast with the opposite rule followed by the edge dislocations,and the core energy of the screw 〈c+a〉dislocations is lower than that of the edge ones,then the slip was suggested to be preferentially on the pyramidal Ⅱplane in Ref [67].

An elaborate ab-initio investigation for the alloying effect on the variation of GSFE curves of pyramidal I and Ⅱplanes,influencin the formation of 〈c+a〉 dislocations via the synergistic effects of the formation energy barriers of leading and trailing partial dislocations,was made in Ref [96].It was found that,as for the rugged pyramidal I plane (Fig.4(a)),solely substituting the alloying atoms at one of two types of sites will lead to different variations of the corresponding GSFE curves,i.e.,controlling the emergence of the stable SF;As for the rugged pyramidal Ⅱplane (Fig.4(a)),due to the existence of a fla potential-energy surface around the position of the stable SF,the resulted SF cooperative movement will lead to the corresponding symmetrical GSFE curves (i.e.,two dissociated equivalent partial dislocations),accompanied by the decreased global unstable SFE facilitating the formation of trailing partial dislocations [92].As such,in the light of the GSFE curves of pyramidal planes,different alloying elements were deduced to presumably facilitate (e.g.,Ca,Sn,Li and Re,etc.) or restrain (e.g.,Zn,Al and Ag,etc.) the formation of 〈c+a〉 dislocations on the pyramidal I or Ⅱplanes,which could also be reflected by the energy change of the basal SFsI1andI2.The facilitated activation of〈c+a〉dislocations was deemed to be related to the reduced SFE ofI1(which might act as the heterogeneous nucleation source for 〈c+a〉 dislocations) [97,98],and the increased SFE ofI2(which should be attributed to the promoted cross-slip between the basal and non-basal planes) [96].Nevertheless,a quantitative comparison between the effects of Y,observed to yield high 〈c+a〉 dislocations activity,and Al and Zn,observed to yield low 〈c+a〉 dislocations activity even at much higher concentrations,on the SFE of Mg stated that the reduction of theI1SFE is unlikely the key factor for the promoted activation of 〈c+a〉 dislocations [95].Therefore,a thorough investigation for the connection between SFE and the 〈c+a〉 dislocations is still required to explain this contradiction and to capture the true key design parameters for improving ductility of Mg.

For alloys with high SFE,perfect 〈c+a〉 dislocations could nucleate at GBs or TBs [99];For alloys with low SFE,〈c+a〉 dislocations are generated via the combination of the firs nucleated leading partial dislocation with a strip of SF and the subsequent nucleated trailing partial dislocation.Apart from the nucleation source provided byI1SFs [97],it was reported that a 〈c+a〉 dislocation could be formed by virtue of the cross-slip of an attractive junction formed by the glissile〈a〉 and sessile 〈c〉 dislocations on a prismatic plane into the pyramidal plane [100].Furthermore,a nucleation mechanism of 〈c+a〉 dislocations on pyramidal Ⅱplanes was proposed to follow a process that,twopartial dislocations,obtained from the reaction of the sessile 〈0001〉 partial and the glissilepartial,react to produce the sessiledislocations on the basal plane,and then move onto the pyramidal Ⅱplane to become glissile [62].Additionally,pyramidal Ⅱ〈c+a〉 dislocations might also be transformed from the preferentially formed pyramidal I 〈c+a〉 dislocations,as revealed by the MD simulations [86].

Thermo-kinetic synergistic analysis:The highly complicated and spatially extended dissociated configuration of the edge and screw〈c+a〉dislocations on the pyramidal Ⅱplane are,respectively,shown in Fig.4(e)-(g),and those on the pyramidal I plane are,respectively,shown in Fig.4(k)-(m)[101].The normal coplanar dissociations referred above,as shown in Fig.4(e),(g),(k) and (l),could be understood via the GSFE curves of the pyramidal I and Ⅱplanes,i.e.,the position of stable SFE may be the indication of the dissociation.Furthermore,the non-planar and non-conservative thermally activated dissociations of the glissile pyramidal Ⅱedge and pyramidal I mixed〈c+a〉dislocations on the basal plane,i.e.,the so-called pyramidal-to-basal (PB) transition,as shown in Fig.4(f)and(l),have attracted much more attentions in recent years,due to the significant deleterious effect of the sessile basal-dissociated structures on the ductility of Mg alloys.As for the climb-like dissociation of the pyramidal Ⅱdislocations,there exist three possible stress-dependent basal-dissociated configuration revealed by MD simulations [102],including(1)dissociation into two,i.e.,＜p+1/2＜c＞＞,Frank partials bounding anI1SF;(2) dissociation into onedislocation with the other non-nucleated counterpart;(3) dissociation into 〈c〉 and 〈a〉 dislocations,which,respectively,correspond to the situations under the zero,moderate and high compressive stresses normal to the pyramidal Ⅱplane.The dissociation case (1) has been clearly demonstrated to be an energetically favorable process relative to the coplanar dissociation based on the continuum elasticity dislocation theory[97],and the dissociation case(3)could be supported by multiple aspects,e.g.,transmission electron microscopy (TEM)observations[101,103],MD simulations[102]and anisotropic elastic energy considerations [104],etc.It should be noted that,although received rare attentions,〈c〉 dislocations,usually as the dissociated product in case (3),can also contribute in part to the ductility and affect the activity of 〈c+a〉 dislocations [105].As for the dissociation of the pyramidal I＜c+a＞dislocations,it was found that the corresponding PB transition could occur much faster than it on the pyramidal Ⅱplane,thus the pyramidal I dislocations are less stable than the pyramidal Ⅱdislocations [106].

Fig.5.(a) Competing PB transition and pyramidal Ⅱ-I cross-slip during the expansion of an L×L〈c+a〉dislocation loop[108].(b)The relationship of the mean PB transition time and QPB with the stress normal to the pyramidalⅡplane obtained via MD simulations [102].(c) Schematic illustration of the pyramidal Ⅱ-I cross-slip of 〈c+ a〉 screw dislocation [108].(d) The relationship between QXS and l under different [107];.(e) The relationship between QXS and τ under different stress normal to the pyramidal Ⅱplane[107].

The energy difference between the screw pyramidal I andⅡ〈c+a〉 dislocations is so small that the cross-slip in between should occur very easily [101].The cross-slip from the pyramidal Ⅱto pyramidal I planes was revealed via MD simulations to undergo three distinct stages,i.e.,nucleation,propagation and annihilation[107].In contradiction with the effect of the PB transition on the property,the facilitated 〈c+a〉screw dislocation cross-slip could enhance the non-basal slip of 〈c+a〉 dislocations,thus increase the c-axis strain capacity and improve the ductility.As such,this paradox of property effect might also follow the rule controlled by the"seesaw" in Fig.1(c),with the "strength" end controlled by the PB transition,which increases the immobile dislocation density,and the "ductility" end controlled by the 〈c+a〉dislocation cross-slip,which increases the mobile dislocation density.The competitive relationship between the PB transition of the edge-segment of a 〈c+a〉 dislocation loop and the cross-slip of the screw-segment of a 〈c+a〉 dislocation loop is schematically shown in Fig.5(a) [108].For Mg alloys usually with low formability,sustaining the activity of〈c+a〉 dislocations,i.e.,increasing the corresponding GS,is indispensable for improving the ductility,thus a primary material design concept will naturally emerge,i.e.,making the occurrence of the 〈c+a〉 dislocation cross-slip fast and frequent enough to circumvent the deleterious dislocation locking effects of PB transitions,and the corresponding potential thermo-kinetic mechanisms could be further discussed.

On the basis of the forgoing idea,the enhanced ductility of Mg alloys should meet the requirement [108,109]:

whereν0is attempt frequency,Lthe edge length of the square dislocation loop shown in Fig.5(a),lXSandQXSthe critical nucleation length and the energy barrier for the 〈c+a〉 dislocation pyramidal Ⅱ-I cross-slip,lPBandQPBthe critical nucleation length and the energy barrier for the PB transition.Accordingly,no matter increasingQPBor decreasingQXS,Eq.(4) can be achievable to improve the ductility.Based on the cross-slip process shown in Fig.5(a) and (c),QXScan be derived as [109]:

whereQXS,iis the intrinsic cross-slip barrier,lthe bow-out length of the pyramidal I dislocation,l+lnucthe initial length of the cross-slipped pyramidal I segment before bowing-out,Γthe screw dislocation line tension,Athe area swept out during bowing-out,τthe resolved shear stress,ΔEII-Ithe energy difference per unit dislocation length between the pyramidal I and Ⅱdislocations,andΔsthe increased length of the pyramidal I caused by bowing-out.Obviously,the thermo-kinetic correlation is intrinsically established in Eq.(5),i.e.,increasingτ,or driving force ΔG,could lead to the decreasedQXS,thus the cross-slip is enhanced.The DFT investigations using the nudged elastic band method in Ref [107].has also revealed this thermo-kinetic trade-off relationship in Eq.(5).The relationship betweenQXSandlunder differentτis shown in Fig.5(d),which indicates that,whenτ,i.e.,ΔG,increases,theQXSwill decrease.The relationship betweenQXSandτunder different stress normal to the pyramidal Ⅱplane is shown in Fig.5(e),which indicates that the more tensile normal stress,corresponding to the more ΔGfor cross-slip,will lead to the lowerQXS.The relationship of the mean PB transition time andQPBwith the stress normal to the pyramidalⅡplane,obtained via MD simulations in Ref [102].,is shown in Fig.5(b).As can be seen,the more compressive normal stress,corresponding to the more ΔGfor PB transition,will lead to the lowerQPBand shorter transition time.It could be found that,although Fig.5(b) and (e) are published in different works,the stress normal to the pyramidal Ⅱplane exactly has the opposite effect on theQPBandQXS,seemingly revealing the trade-off relationship in thermo-kinetics,in activity of PB transition and cross-slip and in strength-ductility.

2.2.3.Twinning modes accommodating the c-axis strain

Fundamental characteristics:Mechanical twinning,as a competitor of the foregoing non-basal slip modes,contributes to the plastic strain in a directionally dependent polar manner,e.g.,the predominantly activated and largely researchedextension twinning with low CRSS could only accommodate the c-axis tension while the relatively less concernedcontraction twinning with high CRSS could only accommodate the c-axis compression [8,68].Accordingly,the prominent detrimental aspects for ductility,i.e.,the normally observed tension-compression asymmetry and texture formation,are closely tied to the twinning behavior especially under deformation conditions of high strain rates and low temperatures [62,110].As for cast Mg alloys with random texture,the extension or contraction twinning could be activated under loading of arbitrary orientation,whereas,as for wrought Mg alloys with strong basal texture,the extension twinning could be activated when applying a uniaxial compression to the extrusion along the extrusion direction or to the sheet along any direction in the rolling plane,and analogously,a uniaxial tension corresponds to an activated contraction twinning [111,112].

Fig.6.(a) Crystallography of twinning [113].(b) GPFE curves for Ti,Zn and Mg in hcp lattice,where γut is the unstable twinning energy barrier,γtsf is the stable twin stacking fault and b is the Burgers vector of the twinning disconnection [124].(c) Schematic representation of twin nucleation,propagation and growth in a grain [121].(d) The free energy change with image number (i.e.,the reaction coordinate) under the c-axis tensile stress and (e) the tensile stress vs.activation energy and critical nucleus size during heterogeneous {1012} twin migration [133].

As shown in Fig.6(a) [113],the twinning could suddenly re-orient the crystal in the twinned region,whose volume is directly proportional to the amount of the accommodated strain [68],and the reorientation degrees corresponding to{1012},{1011} and {1013} twinning are,respectively,86°,56° and 64° along the 〈1210〉 axis [62].Whereupon,crystallography “soft’’ orientations could be created via twinning,which favor subsequent dislocation slip,such as the facilitated basal slip on account of the {1011}-{1012} double twinning(i.e.,twins within a twin),thus leading to apparent work softening [112,114].Inversely,the twining-detwinning process,usually commencing under the cyclic loading of tension and compression,also plays a great role in stress-strain response,during which considerably profuse dislocations are accumulated to cause hardening [115,116].Moreover,the TBs could divide the parent grains,thus leading to a Hall-Petch effect[117-119].As such,although much uncertainties and obstructions remain now,both experimental and theoretical efforts still deserve being devoted to unravel the microscopic mechanisms of deformation twinning,thus assisting in reducing the accompanied property anisotropy.

Deformation twinning,traditionally viewed as a threedimensional ellipsoid domain [120],will,in turn,undergo nucleation,propagation until being impinged by the obstacle or exhausting the driving stress,and thickening,as shown in Fig.6(c) [121].All these formation stages are dominated by the accompanying stress redistribution,comprising of the stress concentration at the twin tip and the stress relaxation in the twin and the adjacent surrounding regions,as revealed via the finite element simulation [122,123].Under the condition of high stress,the required stresses for the twin nucleation are suggested to be much higher than those for the twin growth,both of which,however,are of the same order of magnitude under the condition of low stress [121].Furthermore,due to no nucleation stage involved in detwinning,the required stresses for detwinning should be lower than those for twinning.Analogous to the GSFE curves describing the dislocation slip in a specific plane,the so-called generalized planar fault energy (GPFE) curves could provide the energy barrier for twin nucleation and migration of the TB during a twinning process involving multiple planes [59],indicating the twinning tendency.However,due to the complexities of twinning in Mg,few attempts have been made to obtain the corresponding GPFE curves,and the only recently reported GPFE curves for the {1012} extension twinning in several hcp metals,as a typical example,are shown in Fig.6(b) [124].Obviously,the nucleation and growth stages,respectively,correspond to two segments in the GPFE curves,therein,a periodic region for TB migration exist.Additionally,the significantly lower migration energyγ TBM(define as(γut-2γtsf)withγutas the unstable twinning barrier andγtsfas the stable twin stacking fault) thanγutimplies the more energy cost for the nucleation than that for the growth,in consistent with the experimentally observed rapid migration of TB during the post-nucleation stage [124].

Generally,high stress concentration and distributed defect structures required for twin nucleation can be satisfied at the low angle GBs [55].As a stochastic event,the initiation of twin nucleation and the selection of twin variant will continuously change with the twinning progress,i.e.,the ahead formed twins could influence the subsequent twin formation in the same or surrounding grains.Regarding the twin nucleation in a single grain,the produced twin pattern will be determined by three modalities of twin-twin interactions,including parallel alignment of single twin variant,cross alignment of single twin variant and cross alignment of multiple twin variants [125],during which the initially formed twins could be more sensitive to the Schmid factor.Twin thickening was found to be correlated with the Schmid factor,thus obeying the CRSS law [55,126].However,other nucleation cases that do not follow the CRSS law also exist.For example,the breakdown of CRSS law has been reported,where,the formed twins may not be the potential ones with high Schmid factor but those meeting the requirement of the strain compatibility,the so-called slip/twin-assisted nucleation [127],i.e.,the resulted shear can be accommodated by the soft slip modes or another twin in the neighboring grain [5,128].Furthermore,in order to explain the observed non-stress driven twinning[129],energy-based criteria have also been proposed to evaluate the twin nucleation and variant selection based on the principle that the twinning is driven by minimizing the local stored energy [130-132].Considering the complexities in the twinning determined by the local microstructural conditions,predicting the twinning events,although challengeable,could rely on the statistical analysis approach,such as machine learning for mining the correlation between twinning and lots of underlying physical variables [5,129].

Thermo-kinetic synergistic analysis:In expectation,the deformation twinning process obeys the rule of thermo-kinetic correlation,as revealed by the phase-field models [133],DFT calculations [134] and MD simulations [135] in literatures.The variation of free energy,activation energy and critical nucleus size under different c-axis tensile stress during heterogeneous {1012} twin migration are shown in Fig.6(d) and(e).Apparently,the increased tensile stress,i.e.,the increased driving force ΔG,is always accompanied by the decreased energy barrierQfor twinning,thus naturally enlightening the possibility of modulating the twinning behavior in Mg via the thermo-kinetic synergy rule,provided the abundant underlying internal (e.g.,the grain size,the grain shape and the texture,etc.) or external factors (e.g.,the temperature,the loading direction and the strain rate,etc.) [5] influencing twinning are all considered for constructing the thermo-kinetic “seesaw” in Fig.1(c).

The twin nucleation of Mg has been envisioned to follow homogeneous [136] or heterogeneous mechanisms with the latter dominate in literatures [133,137-139],due to the required high stresses for the former one.The typical heterogeneous model for {1012} twinning,i.e.,the so-called pole mechanism proposed by Thompson and Millard [140],insists the nucleation is resulted from the non-planar dissociation of 〈c〉 dislocations.Indeed,several other dislocation-assisted formation mechanisms were also established based on the interrelationship between the lattice dislocations and twinning,such as the{1012}extension twinning embryo stemming from the reaction between one 〈c+a〉 and one basal 〈a〉 dislocation [141] or the dissociation of edge 〈c〉 and mixed 〈c+a〉dislocations [137,142],and the {1011} contraction twinning stemming from the dissociation of pyramidal I 〈a〉 dislocation [143].

There are several influencing factors for the twin growth about the properties of twinning dislocations and the structures of TB,which are responsible for the more readily occurrence of{1012}twinning than{1011}twinning.For one thing,the{1012}twinning dislocations with wider core width,lower Peierls barrier and lower dislocation energy could be more easily gliding than the {1011} twinning dislocations [55,144].For another,the {1012} TB with higher energy should be less stable than the{1011}TB[145].It is well known that the twin growth in hcp metals should be a shear (displacive/military)and shuffle (diffusive/civilian)mixed controlled process[146],where,the shuffle component dominates the earlier stage(which should be more temperature and strain-rate sensitive in light of the smaller activation volume) and the shear component dominates the later stage [134].In this regard,the TB migration,especially for {1012} twin,was suggested to be driven by propagation of the special facets or disconnections present at the TB consisting of coherent twin boundary(CTB),basal-prismatic and prismatic-basal(BP/PB)interfaces[147-149],during which the predominant atomic shuffling occurs in several layers of the parent lattice immediately adjacent to the TB [150].On the one hand,the twin propagation might be hindered inside the grains depending on the accommodation of plastic stress ahead of the twin via the relaxation mechanism of emissary slip [141].On the other hand,when the twin propagates to the GB,three interaction phenomena of twin and GB are summarized in Ref [125].,i.e.,“parallel”,“refracting” and “fusing” passing through behaviors occurring,respectively,at the low,medium and large misorientation angles.

2.2.4.Integrated effect of deformation modes

Dislocation-dislocationinteraction: Regarding the dislocation-dislocation interactions corresponding to different combinations of relative orientations of the dislocation lines and Burgers vectors between the interaction pair,four possible phenomena can be described as follows:annihilation (for two dislocations with opposite Burgers vectors in the collinear slip systems),junction formation via zipping/unzipping mechanism (for cases with minimized strain energy),and two states of elastic interaction without combination of dislocations,i.e.,repulsive state and crossed state[16,151,152].Accordingly,the dislocation-dislocation interactions in Mg are categorized as＜a＞/＜a＞interactions (including basal/basal (Fig.7(a)),prismatic/prismatic (Fig.7(b)),collinear basal-prismatic (Fig.7(c)) and non-collinear basalprismatic cases (Fig.7(d))),＜a＞/＜c+a＞interactions(including semi-collinear basal/pyramidal (Fig.7(e)),semicollinear prismatic/pyramidal (Fig.7(f)),basal/pyramidal(Fig.7(g)) and prismatic/pyramidal cases (Fig.7(h))),and＜c+a＞/＜c+a＞interactions (including semi-collinear pyramidal/pyramidal (Fig.7(i)),＜c+ai＞/＜c+ak＞(Fig.7(j))and＜c+ai＞/＜c-ak＞(Fig.7(k))cases),as shown in Fig.7(ak) [6],where blue and green vectors represent the Burgers vectors of the interaction pair and red vectors represent that of the interaction product with solid and dash lines express different possible cases.Effects of these interactions are interpreted as latent hardening,which represents the resistant effect of dislocations and junctions on a specific slip system to slips on the other systems [16,152,153].The latent hardening coefficient pertaining to different dislocation-dislocation interactions are of great significanc for the mechanical responses modeling [16,154,155],yet cannot be trivially obtained by experimental measurement and numerical calculation [151].Beside,the latent storage of dislocations,i.e.,the transformation between glissile and stored dislocation density,is tied to these dislocation-dislocation interactions by virtue of the dislocation junction formations [155],therein,the sessile junction,or lock,from the basal/pyramidal＜a＞/＜c+a＞interaction,was suggested to be a very stable one to act as the obstacle for dislocation motion,thus significantly contributing to the strain hardening [16,151].

Fig.7.Schematic representations of (a-k) dislocation-dislocation interactions in Mg and its alloys, where blue and green vectors represent the Burgers vectors of the interaction pair and red vector represent that of the interaction product with solid and dash lines express different possible cases [16].Twin-twin interactions of (l) Ti →Ti±3, (m) Ti →Ti±1, and (n) Ti →Ti±2 [158].(o) The interaction between the basal a dislocations and the three-dimension extension twin, where the red and blue dashed lines represent the dislocation line and are parallel to the z-axis and the c-axis, respectively, with the black arrows denote their motion directions [167].(p) Two a60 dislocations are successively incorporated and transmuted at the CTB to form a unit c+as dislocation [168] (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

Twin-twin interaction:Since the seminal work of Reed-Hill and Buchanan in 1960s [156], twin-twin interactions have been largely investigated, especially the extension twinning cases for Mg, yet corresponding knowledge storage seems still scarce [157].Assuming the six variants of {10ˉ12} twins as Tiwith the subscript i changing from one to six accompanied by the counterclockwise rotation around the c-axis, as shown in Fig.7(l-n),the twin-twin interactions of Ti→Tjbetween the incoming Tiand the encountering Tjcould be classified into two types from the crystallography [125,158–160]:the cozone interactions of Ti→Ti±3(Fig.7(l)), for which two twins share the same <110> zone axis, and the noncozone interactions, which can be further categorized as two types regarding the misorientation of the different zone axis,i.e., the interactions of Ti→Ti±1(Fig.7(m)) and Ti→Ti±2(Fig.7(n)).Correspondingly, three characteristic morphologies can be developed via twin-twin interactions, as observed in experiments, including the quilted-looking, the "apparent crossing" and the double twin structures [158,160].

More importantly, typical microstructures, such as twin-twin junctions and twin-twin boundaries (TTBs) [157–159,161–163] that play a great role in subsequent twinning process, can be produced, as shown in Fig.7(l-n).Different mechanisms, such as impinging, zipping and dissociating,were proposed to elucidate the formation of TTBs based on the twinning-dislocation reactions [158].Based on the angle between two twinning planes, the TTBs can be further categorized as the TTBO(i.e., the TTB at the obtuse side),the TTBA(i.e., the TTB at the acute side), and the TTBI(i.e., the TTB parallel to the receiving twinning plane {10ˉ12})[158,159,161].For the low angle tilt TTBs from the interactions of Ti→Ti±3(Fig.7(l)), the TTBOand the TTBAalign with the prismatic {10ˉ10} and the basal {0002} planes, respectively;as for the TTBs from the interactions of Ti→Ti±1(Fig.7(m)) and Ti→Ti±2(Fig.7(n)),the TTBOand the TTBAalign with high index crystallographic planes.Moreover,a new type of TTB for non-cozone interactions,i.e.,TTBBP,was found in Ref [159].via MD simulations,stemming from the interaction between BP/PB interfaces and the CTB.In view of these exclusive structural characteristics of TTBs,multiple roles they could play on defects formation.It was reported that twins,dislocations and microcracks can nucleate at the twin-twin junctions[164].The detwinning can be retarded by the twin-twin junctions on account of the unfavorable dissociation of TTB dislocations [160].Furthermore,the variation of the kinetics and morphology of twinning,e.g.,the inhibition of direct twin transmission and the facilitation of secondary twins,are correlated with the TTBs [159,161].Additionally,the twin-twin interactions will increase the stress for the twin propagation more than that for the nucleation,thus facilitating the profuse nucleation and contributing to strain hardening due to the twin-induced refinement [157].

Dislocation-twin interaction:When a dislocation impinges on the TBs,which do not merely serve as the simple barriers for slips,several other consequences might occur,such as dislocation absorption,transmission and transmutation [125,157,165-169],depending on the dislocation type,the twinning mode,the atomic structure of the TB,the grain size,the local stress,the temperature,as well as the loading condition.Thereupon,unraveling the kinetic process of these dislocation-twin interactions are of great interest in previous experimental [99,168-170] or computer simulation [166,167]works,due to their influence on local structure of the TB,the mobility of the TB,the strain accommodation nearby the TB and the hardening effect.Compared with the interaction between dislocations and {1011} or {1013} contraction TBs,the interaction between dislocations and{1012}extension TBs has attracted much more attentions,while mostly focused on the interaction between the basal 〈a〉 dislocation and extension CTB since both of them can be activated concurrently and the mutual interaction is unavoidable [165,169,171-174].As shown in Fig.7(o) [167],where thex,yandzaxis,respectively,denote the twin shear direction[1011],twin normal[078],and the lateral direction [110],the boundaries of a 3D extension twin include the normal-TB (consisting of the CTBs and the coherent BP/PB steps),the forward-TB (consisting of the BP/PB facets),and the lateral-TB (consisting of twist pyramidal{1101}-pyramidal{1011} (T-PP1) boundaries) and prismatic{110}-prismatic{2110} boundaries.Accordingly,profuse interactions corresponding to the different combinations of matrix dislocations with different Burgers vectors or line directions and the different components or sides of TBs should exist actually.However,the knowledge about the dislocation-twin interactions is largely missing,especially that for the combinations of non-basal dislocations and different sides of 3D twins.

The basal〈a〉dislocations may possess three types of Burgers vectors,i.e.,〈a1〉([110]),〈a2〉([2110]),and〈a3〉([110])shown in Fig.7(o),in which mixed 〈a2〉 and 〈a3〉 are usually denoted as 〈a60〉 in literatures having Burgers vector inclined at 60° to the dislocation line,thus having the same interaction with the TBs,and the screw 〈a1〉 is denoted as 〈as〉 in literatures [176].Regarding the interaction between the 〈as〉dislocation(red dashed line in Fig.7(o))and the CTB,the〈as〉dislocation could directly transmit across the TB and transform the slip plane from {0001} in the matrix to {1010} in the twin [167,168].As for the interaction between the basal〈a60〉 dislocation (red dashed line in Fig.7(o)) and the CTB,it was found that two scenarios might occur:(Ⅰ)one 〈a60〉 dislocation will dissociate into twinning dislocations on the twin plane and produce the BP/PB steps on the TB with the slip transformation accomplished via the gliding of 1/2＜c+as＞on the prismatic plane of the twin [167];(Ⅱ) when two 〈a60〉dislocations are successively incorporated and transmuted at the CTB,as shown in Fig.7(p),a unit 〈c+as〉 dislocation could form on the prismatic plane of the twin,which is most likely sessile and could serve as the forest hardening mechanism [168].Indeed,this dislocation transmutation of 〈a〉 to〈c+a〉is of great significance for plasticity due to the role of〈c〉 containing dislocations for accommodating c-axis strain,which has been confirmed by multiple experiments,such as the TEM analysis for a textured AZ31 Mg alloys [168] and for a pure Mg single crystal,where abundant non-basal 〈c〉and 〈c+a〉 dislocation substructures andI1SF are found in the vicinity of the advancing TB [119].The interaction between the basal 〈a〉 dislocation (blue dashed line in Fig.7(o))and the lateral side of TB is similar,depending on the orientation of the Burgers vector relative to the zone axis of the twin,as discussed in Ref [167].As for the interactions between 〈c+a〉 dislocation and extension CTB,it was reported that,no matter what character the 〈c+a〉 dislocation prevails on the pyramidal Ⅰplane,it will always be absorbed by TB without dislocation transmutation based on the MD simulations [165].

Nevertheless,the controversy about the hardening effect of the dislocation-extension twin interactions was prevalent in previous literatures.Kadiri et al.claimed that,the {1012}TBs,serve as the effective sinks for dislocations,could propagate through a forest basal dislocation without the mobility reduction and the coherency loss [174].More singularly,the basal-dissociated sessile 〈c+a〉 dislocation,which is detrimental to ductility as discussed in Section 2.2.2,could be removed by {1012} TBs,accompanied by the formation of steps at TBs,which could further emit glissle〈a60〉dislocation under the normal stress,thus this dislocation-twin interaction has excellent implications for ductility improvement[175].Su et al.thought the dislocation-twin interaction could inspire a new technique for improving the ductility of Mg,based on their contention that the BP/PB interfaces resulted from the interaction between the {1012} TB and an array of basal 〈a60〉dislocations could facilitate the TB motion via emitting twinning dislocations [176].Hence,these researchers and other not mentioned here have a consensus for the negligible effect of dislocation-extension twin interaction on the work hardening of Mg alloys [174-176].

The interaction between the dislocation and the contraction twin was less concerned previously.The basal〈as〉dislocation can be absorbed by {1011} TB and dissociate into twinning dislocations [177].Furthermore, the pyramidal SF was found inside the twin during this interaction [178].Recently, an intriguing MD simulation result about the interaction between the prismatic a dislocation and the{101}twin was reported by Chen et al [166]., which told that the successively incoming prismatic a dislocation could transform to the {111}twin in the {1011} twin, and this transformed twin could further propagate to reach the opposite side of {101} TB, then transform back to the prismatic a dislocation in the matrix.The difference in the interaction behaviors of dislocations with extension and contraction twins should be ascribed to the difference in TB structures, for which {1012} TBs are usually incoherent and highly deviates from the twinning plane, but{1011} TBs are coherent [166].

Deformation modes coupled by thermo-kinetic synergy:Following the discussion in Section 2.1.1, the plastic flow for a given deformation mode α (where α represents basal or non-basal dislocation sliding and twin)is governed by the relative density of mobile dislocations for this modeand the total forest immobile dislocations, and the corresponding contribution to the total plastic strain rate ˙εpof this deformation modecould be written as [102]:

where bαis the Burgers vector of the dislocations for the deformation mode α, Rescis the thermally activated escape rate of the α dislocations past the immobile defects, νescis the attempt frequency of escape, Q0is the energy barrier for thermally escape in zero-stress condition, ταis the applied resolved shear stress on the α dislocations,is the CRSS for surmounting the Q without thermal activation, p and q are constants related to activation energy surface,is the interaction matrix parameters between deformation modes α and.

Obviously, an intrinsically thermo-kinetic correlation is reflected in Eq.(7): for a constant Rescand τα, the increased, i.e., the driving forceG, will always correspond to the decreased Q0, in accordance with the "seesaw" in Fig.1(c).In order to elevate the "seesaw" to break through the trade-off relationship of thermo-kinetics or strength-ductility, Rescandmay provide some clues and enlightenments.With reference to Eq.(8), iforare changed via modulating interactions from the dislocation-dislocation, the twin-twin and the dislocation-twin couples to increase,ταcould be proportionally increased while maintain any other parameters in Eq.(7) unchanged, so that, theG and the strength of material are correspondingly improved.For the sake of increasing the ductility simultaneously,should keep a positive value to be as enduring as possible, that requires theof every deformation mode α to fulfill the duty of themselves with no effort spared in a "rational" manner and follow a "organized"service period, i.e., making the best use of every deformation modes to balanceandas one falls another rises.Furthermore, when the material withstands higher exterior ταin an improved strength level of, Q0should be increased to keep the smooth of Resc, thus the longer service time, i.e., the higher GS arising from a typical deformation mode α is obtained.This is the philosophy of thermo-kinetic modulation of deformation modes to elevate the "seesaw" in Fig.1(c),which will be further elucidated with the Taiji diagram in Fig.1(d).

2.3.Altered deformation mechanisms by structural factors

Inspired by the previous consideration for the lifetime of a structural material suffering from n-stage processing in Section 2.1.2.1, the Mg alloys design could be vividly analogous to a microscale military defense campaign, namely, constructing the“bastion”(i.e.,generating the structural factors including alloying elements, GBs, textures, and precipitations, etc.)at an appropriate “geographic position” (i.e., the specific location in a perfect Mg single lattice) during the preceding (n-1)-stage processing used for defending the “invasion” at the nth stage (i.e., the deformation during service).The outcome of this microscale military defense campaign should depend on the type, the moment, and the location of the employed structural factors, which connect the “seesaw” of PTs and/or PDs occurring at any adjacent two stages of n-stage processing via thermo-kinetic connection, ensuring the continuously evolving G-GS pairs with the whole structural evolution accompanied by the energy storage and release at different time and space scales.However, several unsatisfied effects arising from these structural factors have prevailed in Mg alloys, e.g.,poor formability,low ductility at high strength,edge cracking,yield asymmetry, and basal/fiber texture for rolling/extrusion[55], thus necessitating the rational application of these structural factors with the knowledge of their characteristics reflected in their connection roles of thermo-kinetic history.

2.3.1.Element effect

Element effects on deformation mechanisms include direct and indirect aspects, therein, the former refers to the effect caused by the changed material intrinsic parameters via alloying, e.g., the SFE and the axial ratio c/a, which is briefly introduced in this Section, and the latter refers to the altered deformation mechanisms caused by the produced structural factors determined by the composition, which is introduced in Sections 2.3.2 and 2.3.3.Effects of different alloying elements, chosen and added in the alloys with a specific proportion during the first metallurgical fabrication stage, on the mechanical properties of Mg alloys have already been summarized in literatures [179].Hence, more attention is herein paid on the rare earth (RE) elements (La, Ce, Pr, Nd, Gd, Tb,Dy,Ho,etc.),which is the research hotspot nowadays due to their role on simultaneously improved strength and ductility of Mg alloys.

The direct element effects are usually correlated with the relative added quantities of the different solute atoms,which have distinct influence on the CRSS (reflected as the ΔGin Eq.(1)) and activities (reflected as the GS in Eq.(1)) of different slip or twinning modes in solid solutions,thus certainly change the resultant microstructures and properties.The varied axial ratioc/acaused by solute atoms is related to the twinning shear,and the lower the numerical value of twinning shear becomes,the more frequent the twinning should be[55],e.g.,the Li addition could decrease the axial ratioc/aand alter the deformation modes due to the changed Peierls stress of the dislocations (or ΔG) accompanied by the changed interplanar spacing.The element effect on the pyramidal 〈c+a〉slip,which has attracted much attention,was studied via DFT calculations in Ref[96].As shown in Fig.8(a),the varied formation energy of 〈c+a〉 dislocations ΔεIand ΔεⅡon pyramidal I and Ⅱ planes by alloying,obtained from the GSFE curves,has reflected the promotion or impediment effect of different solute atoms on the 〈c+a〉 slip,i.e.,apart from Zn,Al,and Ag,all other considered elements could promote the 〈c+a〉 dislocation formation on pyramidal Ⅱplanes (RE and Li) or both pyramidal I and Ⅱ planes (Sn and Ca),thus being beneficial to the ductility due to the prolonged nonbasal slip,i.e.,the increased GS.Furthermore,the energy barrierQXSfor the pyramidal Ⅱ-I cross-slip of 〈c+a〉 dislocation in different Mg binary alloys with different solute concentration has been computed via Eq.(5),as shown in Fig.8(b) [109],where the ductility indexχwas used to measure the ductile effect due to the facilitated pyramidal Ⅱ-I cross-slip or the restrained PB transitions based on the criterion of Eq.(4),i.e.,the largerχis,the largerQPBfor PB transitions should be,thus,the larger GS and the prolonged activity of 〈c+a〉 dislocation for improving ductility is obtained.The element effects in Fig.8(b) are partially not in accordance with those in Fig.8(a),especially for Li and Sn,highlighting the necessity of concurrently considering the formation and the transformation of 〈c+a〉 dislocations to estimate the element effect on property.In addition,electron work function charactering the electron behavior in metals was used to evaluate the element effect with the indication that the solutes with lower electron work function than that of Mg (e.g.,Cs,Ca,Y,Gd,and Nd,etc.) can improve both strength and ductility,and conversely,only strength can be improved with sacrifice ductility (e.g.,Mn,Ag,Al,Zn,and Sn,etc.)[180].Nevertheless,all these investigations for direct element effects only take account of the solid solution,thus some contradictions exist.Indirect element effects stemming from the grain size and orientation influencing the distribution of solute atoms,and from the precipitations competing for solute atoms with the solid solution should be considered together for precisely evaluating the element effects on the“seesaw” in Fig.1(c).

2.3.2.Grain size and orientation effect

Refining the coarse grained (＞100 μm) structures to fine grained (1-10 μm),ultrafine grained (＜1 μm),and even nano-crystalline (＜100 nm) structures has remarkable influ ence on the mechanical properties of Mg alloys [20],usually by virtue of severe plastic deformation methods [181],such as equal channel angular pressing (ECAP) [10],high-pressure torsion (HPT) [182],multi-axial forging (MAF) [183],alternate biaxial reverse corrugation (ABRC) [184],accumulative back extrusion (ABE) [185],and accumulative rolling bond(ARB) [186],etc.,during which recrystallization and texture could occur to dominate the final grain size and orientation.Depending on the strain rate,the temperature,the occurrence of twinning,the initial grain size,and the texture,multiple types of microstructures could be produced,including uniform fine-grained and bimodal or multimodal structures[55].It was reported that when the grain size of pure Mg decreases,the strength and ductility could be simultaneously increased,due to the altered deformation mechanisms,as reflected by variation of the CRSSs of different slip,twinning and GB shear modes with the grain size (Fig.8(c)) [20].Obviously,there exist two critical grain sizedc1anddc2,indicating the transition of dominant deformation modes with the decrease of grain size:whend ＞dc1,the extension twinning and the basal slip dominate the PD;whendc1＞d ＞dc2,the twinning is gradually restrained and more non-basal slips could be activated [182];whend ＜dc2,the deformation will be mainly mediated by the GB sliding (Fig.2(c)),considered as the GB shear,improving the ductility drastically.

The existence ofdc1should be attributed to the different Hall-Petch effects corresponding to the twinning and slip,i.e.,the twinning displays a stronger grain size sensitivity than the dislocation slip [187],due to the dominant role that GBs play on the twin nucleation[55,188].However,uncovering the Hall-Petch effect in Mg alloys is cumbersome,especially for twinning,on account of the complexities in the Hall-Petch parameter determined by the texture,the loading direction,the grain size,and the GB parameters (e.g.,GB structure,GB energy,GB mobility,GB network topologies and spatial distribution of orientation) [189],which should all be taken into account to accurately characterize the GB obstacle effect [190].Resulted from the competition between strengthening and weakening,respectively,induced by the TB and twin growth [187],beside thedc1in Fig.8(c),other critical grain sizes of the twinning to slip transition during different processing have also been reported,e.g.,1 μm [191],2.7 μm[192],and 8 μm [193],the magnitude of which are nearly two orders larger than those of other metals [20,194].Additionally,the twinning to slip transition could also take place with decreasing the strain rate and increasing the temperature,not just with the grain size refinement [190].Giving credit for the restrained twinning and the facilitated non-basal slip with decreasing the grain size,the tension-compression yield asymmetry is eliminated [4] and the texture is weakened [55],thus usually leading to the simultaneously increased strength and ductility [186,195],i.e.,the high ΔG-highGSpair,due to the enhanced GB strengthening and dislocation activity.Furthermore,some contradictions about the existence of the twinning to slip transition also exist in literatures [196,197].For example,the twinning can be activated in the nano-crystalline Mg-Ti alloys,which may be ascribed to the changed GPFE curves by Ti addition [198].

Fig.8.(a) The formation energy of 〈c+ a〉 dislocations ΔεI and ΔεⅡon pyramidal I and Ⅱ planes in different Mg binary alloys,where the positive and negative values mean the promotion and impediment effects of solute atoms,respectively [96].(b) Variation of the energy barrier for pyramidal Ⅱ-I cross-slip of 〈c+ a〉 dislocation and the ductility index χ with solute concentrations in different Mg binary alloys [109].(c) The variation of CRSS of different slip,twinning and GB shear modes with grain size of pure Mg,where two critical size dc1 and dc2 exist [20].(d) Textures in Mg alloys sheets (SB and WB)and extrusions (BF,PyF and PrF) [4].(e) The variation of the CRSS increment ratio of twin growth and prismatic slip with the precipitate size,affected by precipitates in shapes of basal plates,c-axis rods and spheres [220].(f) The Orowan strengthening effect of the normally formed precipitates in Mg alloys on different slip modes,evaluated based on the variation of the normalized CRSS with the volume fraction of precipitates,where q represents the aspect ratio of precipitates [24].

The mechanical asymmetry,i.e.,the difference in compression and tension strength,is resulted from the textures formed in wrought process,during which the basal plane rotates to be parallel to the plane of plastic flow [55].The commonly observed textures in Mg alloys are shown in Fig.8(d),where the strong basal (SB) and the weak basal(WB) textures belong to the sheet textures;the basal fibe(BF),the pyramidal fiber (PyF) and the prismatic fiber (PrF)textures belong to the extrusion textures;the rolling direction(RD),the normal direction (ND),the transverse direction(TD),and the extrusion direction (ED) are labeled relative to the crystallographic orientation of the Mg lattice [4].The SB-1 and BF-1,also called the deformation texture,mainly present in the severely deformed sheets and extrusions,respectively;the SB-2 and BF-2,also called the recrystallization texture,occurs after the full-recrystallization of sheets and extrusions without Ca and RE addition,respectively;the WB-1 and PyF are the weakened textures in Mg sheets and extrusions by adding RE,respectively;the WB-2 texture usually presents when Zn is added together with RE or Ca in Mg sheet;the PrF texture in extrusions only occur in a few cases,e.g.,Mg-Mn-RE and Mg-RE-Ag [4].Strong texture stemming from the severely plastic deformation with high ΔGcan induce significant strengthening effect at the expense of ductility [199],and the weakened texture by RE addition means the materials with grains in a larger spread of orientations,so that more basal slips can be activated by the strain in an arbitrary direction with the increased GS to decrease the anisotropy and improve the ductility [200].The formation mechanism of RE textures is closely related to the retardation of recrystallization due to the solute drag caused by solute segregation at GB [55,185],i.e.,the increased thermal stability of the GB,and conversely,recrystallization is affected by the texture due to the altered deformation modes determined by the relative orientation between the loading direction and the c-axis of the grains [201].

Recrystallization,as the critical mechanism for texture randomization and grain refinement can be normally classified as two types,i.e.,dynamic recrystallization (DRX) during hot deformation and static recrystallization (SRX) during postdeformation annealing [200].The recrystallization could occur at the local regions of precipitations (i.e.,particle stimulated nucleation),TBs (i.e.,twin induced nucleation),and GBs (i.e.,GB bulging nucleation),in which the firs two will render the new recrystallized grains different orientations from the parent grains,while the last one will keep the orientational connection in between [55].Depending on the prominent deformation modes,the initial texture,the solutes,the second phase particles and the strain rate,etc.,several nucleation mechanisms of DRX,including continuous DRX,discontinuous DRX and twinning related DRX,could operate simultaneously,with different contributions to the whole nucleation process [4,55].Normally,the higher ΔGfor DRX from the stored energy in system will lead to higher nucleation frequency,resulting in fine grains with improved strength,and meanwhile,the ductility could be increased due to the largely activated slip modes and increased GS in the weakened texture.As for the twin induced nucleation of DRX,since significantly more stored energy can be introduced by contraction twins than extension twins,the former one may be more in favor of DRX than the latter one [202],which is intrinsically dominated by thermo-kinetic connection,i.e.,the lower ΔG(or the smaller CRSS) for the formation of extension twins is inherited to the lower ΔGof the DRX relative to the case of the contraction twins.

2.3.3.Precipitation effect

Precipitates,as the effective structural factor for strengthening,can form after solution treatment and aging(or dynamically form during deformation) of the Mg alloys,which consist of alloying elements decreasing significantly with decreasing temperature [203,204],e.g.,RE,Al,Zn,Sn,etc.Manipulated by the collective effect of chemical free energy,strain energy from the misfi between the matrix and the precipitate,and interface energy [11],the precipitation can be considered as a very complicated phenomenon leading to sophisticated microstructure composed of diversified types,shape,lattice structure,orientation,size,volume fraction,number density,and distribution of precipitates[205,206].Although the underlying precipitation mechanisms are still far from being well known,in order to make best use of precipitation effect,extensive efforts have been devoted to characterize the thermodynamics,kinetics,and crystallography of precipitations in Mg alloys [17,204].The basic precipitation behaviors of the commonly observed precipitates in most Mg alloy systems were thoroughly reviewed in Ref [206].,and the previous microscale investigations for the structural stability,thermodynamics properties,electronic structures and interface structures of precipitates in Mg alloys via DFT calculations were summarized in Refs [205,207,208].Furthermore,the morphological evolution of precipitates has been largely modeled by phase-field methods [209-214],providing a fundamental understanding for precipitation mechanisms.The interactions of precipitates with different slip and twinning modes are focused here for analyzing the precipitation effect on mechanical properties.

Depending on the operative slip modes and the shape,the habit plane,the modulus and the coherency of precipitates,the precipitate-dislocation interactions in Mg alloys,i.e.,the manner used by the particle to inhibit the dislocation motion,are commonly described as follows:(Ⅰ) a dislocation loop is produced by the passed dislocation around the “hard”particle remaining undeformed,and the corresponding CRSS increment can be qualitatively ascertained via the Orowan equation [22,23,215];(Ⅱ) the “soft” particle is plastically deformed by the passed dislocation,and the corresponding strengthening effect is dominated by the anti-phase domain boundary energy [216],the produced interface dislocations,and the local bond energies across the slip plane [217].For instance,theβ1andare usually,respectively,regarded as non-shearable and shearable precipitates to the basal slip in Mg-RE alloys [218].In addition,discriminated from the traditional Orowan bowing mechanism in case (Ⅰ),the interfacial gliding mechanism was confirmed by thein-situTEM experiment for the interaction between a single dislocation andβ1precipitates [18].Furthermore,when multiple dislocations interact with a specificβ1distributed region,the effect of dislocation pile-up at the precipitate interface could make the non-shearableβ1become penetrable [218],due to the local accumulated stress,i.e.,the increased ΔG.It should be noted that the case (Ⅱ) usually points to the coherent precipitates with high ΔG-lowQformed at the initial stage of the precipitation as the small difference in the Burgers vector at the two sides of interfaces [217],and with the PT proceeding,the solute content required for precipitate formation in the matrix is lowered with the decreased ΔG,the incoherent precipitates with low ΔG-highQwill form to behave as the case (Ⅰ),indicating the changing precipitate-dislocation interactions with the thermo-kinetic “seesaw”.The Orowan strengthening effect of the normally formed precipitates in Mg alloys (including {100} plate,{120} plate,(0001) plate,and [0001] rod) on various slip modes (including pyramidal I＜c+a＞,pyramidal Ⅱ〈c+a〉,pyramidal I 〈a〉,prismatic〈a〉 and basal 〈a〉 slips) are evaluated in terms of the variation of the normalized CRSS with the volume fraction of precipitates in Fig.8(f) [24].In accordance with the viewpoints in the works of Nie [23] and Robson [219,220] et al.based on Orowan equations,non-spherical precipitates inhibit the dislocation slip more significantly than spherical ones,especially for the prismatic{100}and{120}plate-shaped precipitates,which produce more CRSS increment than the basal(0001) plate and c-axis [0001] rod,reflectin their excellent strengthening effects.Moreover,except for (0001) plate,all other precipitates can strengthen basal slips more effectively than non-basal slips,indicating the potential role of precipitates for improving the strength without sacrificing the ductility due to the increased GS corresponding to more activations of non-basal dislocations.

Depending on the relative size of the precipitate and the twin,the precipitate-twin interactions in Mg alloys,which are unfortunately less understood than the case for dislocations,can be classified as three cases [220,221]:(Ⅰ) the incident growing twin can be arrested by the big precipitate and continue to shear the matrix with a new twin nucleating in the matrix far away from the incident side of the precipitate [219,222];(Ⅱ) the incident growing twin can fully engulf and shear the small precipitate [223-226];(Ⅲ) the incident growing twin can fully engulf and elastically rotate but not shear the small precipitate[21,227-229].There was a consensus that precipitates mainly suppress the twin growth but not nucleation in literatures [55,141,230]:therein,the former corresponds to the increased stress required for TB migration,which cannot be accurately evaluated by Orowan equations due to the dominant role of back stress produced during embedding the precipitate into the twinned matrix[215,220,221];and the latter is related to the changed structures and compositions of the GBs by nearby precipitates [125].Therefore,large quantity of twins could form with little size as the result of the nucleation of high ΔGbut growth of highQstemming from the precipitate-twin interactions,providing the great strengthening effect [227].Additionally,it was reported that the precipitate-twin interactions could be circumvented by a highly adaptive migration behavior of TBs,thus leading to weak precipitation hardening [231].

Due to the anisotropy in the strengthening effect of precipitates on different deformation modes as aforementioned,for the optimized microstructure containing the combination of different precipitates in a proper quantity proportion,the corresponding anisotropy and tension-compression asymmetry should decrease.As shown in Fig.8(e),through the CRSS increment ratio of {102} twin growth and prismatic slip affected by precipitates in shapes of basal plates,c-axis rods and spheres,the asymmetry for a strengthening effect can be evaluated by a critical value,below which the asymmetry should decrease,and vice versa.The most effective role of basal plates for reducing the asymmetry is displayed,thus benefittin the ductility [220],although less effective for improving strength than the prismatic plate (Fig.8(f)),indicating the “seesaw” rule of precipitate effect.Element effects could modulate the formation of the precipitates in Mg alloys,e.g.,Nd (or RE) addition usually leads to the formation of prismatic plate-shaped coherentβ1precipitates generated by an invariant plane strain transformation of high ΔG[218],further resulting in the prominently increased ΔG(or CRSS)of deformation modes and improved strength,which is dominated by the thermo-kinetic connection between PTs and PDs.

3.Developing magnesium alloys in the philosophy of thermo-kinetic synergy

For the commonly prevalent cast or wrought Mg alloys(e.g.,Mg-Al,Mg-Zn,Mg-Sn,Mg-Li and Mg-RE alloys,etc.),the final mechanical properties at thenth stage,i.e.,the behaviors of dislocations and twins(Section 2.2),should actually be determined by the integrated effects of the common structural factors (Section 2.3) with different contributions of grain size,textures and precipitates,the thermo-kinetics of whose formation by PTs and PDs during the preceding (n-1)-stage processing will change stage by stage due to the thermo-kinetic accumulation arising from the thermo-kinetic connection,following the "seesaw" rule,i.e.,the thermo-kinetic correlation(Section 2.1).As mentioned before,the structural evolution by high ΔGand high GS should,respectively,correspond to excellent strength and excellent ductility,thus naturally,the Mg alloys design lies on manipulating the evolution of thermokinetic pair ΔG-GS via the combination of PTs and PDs at different processing stages.Guided by the Taiji diagram in Fig.1(d),two prevalent evolution paths ultimately reaching high ΔG-low GS (i.e.,improving strength via sacrificing ductility) (Section 3.1) and high ΔG-high GS (i.e.,simultaneously improving strength and ductility) (Section 3.2) in Mg alloys are analyzed,so that the feasibility of the thermokinetic synergy rule and the GS theory will be highlighted,for assisting the development of excellent strength-ductility synergy of advanced Mg alloys.

3.1.Improved strength via intense thermodynamic driving force

In order to achieve the deformation with high ΔGat thenth stage of processing,i.e.,during service of Mg alloys,the ΔGof the PT or PD at the (n-1)-th stage,which is directly connected to the final stage,should be high enough to produce an excellent combination of structural factors,serving as the effective carrier for transmitting thermo-kinetic property,by virtue of accumulating ΔGin a specific sequence of PDs and PTs at the preceding stages.Indeed,this thermokinetic accumulation effect has already been reflected in the viewpoint of Ref [48].,in which three possible sequences for combining PTs and PDs were summarized:(Ⅰ) the PD prior to PT;(Ⅱ) the PD after PT;(Ⅲ) the repetition of PD and PT.For the case (Ⅰ),the PD with high ΔGperformed for the parent phase usually increases the storage energy of the system,thus accelerating the subsequent PT,i.e.,decreasingQ,via providing more nucleation sites for the newly formed phases and more atomic diffusion channels,and manifesting the PT with high ΔG.For the case (Ⅱ),the PT with high ΔGproduces the initial structure for the subsequent PD,for which the DRX during PD can be accelerated and the strain required for refining the grain to a specific size is decreased,due to the inherited high ΔGfrom the PT.For the case (Ⅲ),both repetition of PT or PD and repetition of combined PT and PD (i.e.,case (Ⅰ) and (Ⅱ)) can accumulate the storage energy of the system,eventually producing the ultrafine structure with excellent strength.As for Mg alloys,several typical thermo-kinetic accumulation paths for inducing PD with high ΔGat thenth stage of processing,i.e.,modulating the "seesaw" rule (or thermo-kinetic correlation) of slip or twinning(Section 2.2) by different effective structural factor groups,will be reviewed here.

3.1.1.Introducing intense thermodynamic driving force by altering precipitation behaviors

The mechanical properties of the whole system after aging should be controlled by combination of the precipitates and the matrix material,therein,the former formed by absorbing solute atoms in the matrix can significantly increase the CRSSs (or ΔGin Eq.(1)) of different deformation modes(Section 2.3.3),and the latter might become less ductile with decreasing solute concentrations due to the inactive dislocation activity [109],i.e.,the decreased GS resulted from the suppressive cross-slip of the 〈c+a〉 dislocations (Section 2.2.2);thus the structural factor groups containing precipitates for transmitting high ΔGprevail in literatures,especially for Mg-RE alloys of ultra-high strength.With different intentions of modulating the orientation,shape,number density or size of the precipitates,the thermo-kinetic accumulation paths for achieving the structural factor groups can be further categorized as two types:(Ⅰ) aiming at producing prismatic precipitates with triangular arrangement in the matrix,which can provide the most effective barrier (or high ΔG) to the slip and twinning (Section 2.3.3);(Ⅱ) aiming at enhancing the number density and decreasing the size of the precipitates with high ΔGof nucleation relative to growth.Certainly,these two types of paths may overlap each other in some cases.

Regarding the type (Ⅰ) path,several processing routes have been employed to induce the high ΔGfor the formation of prismatic precipitates with large aspect ratio,which are highly desired in Mg alloys [203].Changing the habit planes of precipitates to be the prismatic plane can be realized by microalloying.For instance,Mg-0.3Ca-1.0In (at.%) alloys with In addition have pronouncedly intense age-hardening response relative to Mg-0.3Ca (at.%) alloys ("homogenization for 2 h at 500 °C"+"solution treatment for 1 h at 520 °C"+"aging at 200 °C"),due to the production of a high number density of fully coherent prismatic precipitates enriched with Ca and In [232].Owing to the large negative mixing enthalpy between Ca and In,the favored Ca-In clusters will result in large strain,which thus alters the habit plane of precipitates from the basal to prismatic planes.Following the Taiji diagram,the In addition conveys the additional ΔGin the form of strain energy to the nucleation of prismatic precipitates(i.e.,as compared to the nucleation of basal precipitates with low ΔGfor Mg-0.3Ca (at.%) alloys),thus accumulating a high ΔGfor nucleation of coherent precipitates in Mg-0.3Ca-1.0In (at.%) alloys,which is subsequently transmitted to the PD corresponding to the improved strength.Furthermore,Mg-6Zn-3Al-1Mn (wt.%) alloys with Al addition ("extrusion at 350°C"+"homogenization for 12 h at 400°C"+"pre-aging for 48 h at 70 °C"+"aging at 150 °C") show more excellent age-hardening response than Mg-6Zn-1Mn (wt.%) alloys,due to the production of prismatic cuboidal precipitates [233].The added Al atoms can decrease the SFE of the basal plane to facilitate the decomposition of dislocations into partial ones(i.e.,1/3＜110＞→ 1/3＜1010＞+1/3＜0110＞),which will serve as the nucleation sites for the prismatic precipitates distributing along＜1010＞directions.This typically accelerated heterogeneous nucleation by dislocations equivalently corresponds to the homogeneous nucleation with increasedΔG.Following the Taiji diagram,the Al addition conveys the additional ΔGto the formation of prismatic precipitates with low ΔGin Mg-6Zn-1Mn (wt.%) alloys while decreasing theQfor heterogeneous nucleation at pre-existing dislocations due to the thermo-kinetic "seesaw",and thereafter,the accumulated high ΔGis transmitted to the PD corresponding to improved strength of Mg-6Zn-3Al-1Mn(wt.%).

Recently,a technology by coupling twinning,aging and detwinning (namely TAD) processes has been employed to regulate the orientation of plate-shaped precipitates from basal planes to prismatic planes[230,234,235].As for AZ80 Mg alloys("solution treatment for 24 h at 420°C"+"in-plane compression"+"aging for 30 h at 185 °C"+"through-thickness compression"+"annealing for 2 h at 185 °C"),the original Mg17Al12without TAD is basal precipitates but with little strengthening effects [230].Following the Taiji diagram,the second stage produces twins to change the lattice orientation and transmit large ΔGto the subsequent nucleation of vast amount of basal Mg17Al12precipitates at the third stage;and then,the fourth stage further conveys the additional ΔGto the system,reflected as the changed orientation of the precipitates by detwinning to the prismatic planes based on the principle of the precipitate-twin interactions (Section 2.3.3);thus finally,the net multi-stage thermo-kinetic accumulation effect is reflected as the precipitation of dense prismatic Mg17Al12,which transmit high ΔGto the PD to improve strength of AZ80 Mg alloys.

Provided precipitates can concurrently form on basal and prismatic planes,the corresponding strengthening effect should be further enhanced,as compared to the monotonous precipitation on the prismatic planes.This should be attributed to the many near-isolated regions,effectively hindering slip and twinning,produced by dividing grains via the nearcontinuous network of the prismatic and basal precipitates[1,24,206].There may exist a precipitation competition between the prismatic and the basal precipitates,i.e.,the amount of any one increases,the other one may decrease,indicating the "seesaw" of strength and ductility balanced by the relative amount of prismatic and basal precipitate,wherein,the former one is advantageous for strength and the latter one is for ductility(Section 2.3.3).Therefore,when adding the elements(e.g.,Ag and Zn),which provide ΔGfor formation of basal precipitates,into Mg-RE alloys (for which the main strengthening phases are prismatic precipitates),the corresponding RE concentration should be increased to circumvent the decrease of ΔGfor formation of prismatic precipitates caused by basal precipitations via modulating the "seesaw".Additionally,Ag addition can provide higher ΔGfor nucleation ofγ’’ basal precipitates than Zn,thus,the high ΔGof prior precipitation ofγ’’ at the early stage of aging could transmit to the subsequent precipitation of prismaticβ’ at the peak-aged stage,eventually,leading to denser relative perpendicular distribution ofγ’’ andβ’ in Mg-15.6Gd-1.8Ag-0.4Zr (wt.%) alloys with Ag addition than that in Mg-Gd-Y-Zn-Zr alloys with Zn addition [236],which is dominated by the thermo-kinetic connection between two continuous PTs.

Regarding the type (Ⅱ) path,pre-aging [233,237,238] and pre-deformation [239-241] are usually used to facilitate the subsequent precipitation of the main strengthening phases during aging.As for the pre-aging (or double aging) processing,the additional ΔGfor the precipitation during the second aging should stem from the nucleation conditions provided by the prior formed precipitates.For instance,the aging hardening response of Mg-2.2Sn-0.5Zn (at.%) alloys can be enhanced by double aging ("homogenization for 48 h at 525 °C"+"solution treatment for 0.5 h at 525 °C"+" preaging for 24 h at 70°C"+"aging at 200°C"),as compared to alloys processed by single aging[237].Following the Taiji diagram,the precipitation of MgZn2during the pre-aging stage will reject the Sn atoms into the surrounding matrix to elevate the Sn concentration at the tip of MgZn2,thus conveying the additional ΔGto accumulate high ΔGand decreasingQvia providing heterogeneous nucleation sites for nucleation of strengthening phase MgSn2during the second aging stage.Accordingly,the fine sizes and dense distributions of MgSn2further transmit the high ΔGto the PD corresponding to improved strength of Mg-2.2Sn-0.5 Zn (at.%) alloys.

3.1.2.Intense driving force transmitted by cooperation of precipitates and other structural factors

Although precipitates dominate in the forgoing cases,the accumulated high ΔGfor PTs or PDs should always be transmitted by the cooperation of precipitates and other structural factors (e.g.,solid solution,solute segregation,texture and GB,etc.),especially for aging hardenable Mg alloys undergoing pre-deformation processing (partly referred above).This is the reason why the wrought Mg alloys with more thermo-kinetic transmitters usually display more excellent mechanical properties than cast Mg alloys.Four representative cases in literatures for accumulating high ΔGduring processing (“pre-deformation”+“aging”) of Mg-Gd-based alloys[199,240,242,243],which are regarded as one of the ideal candidates for developing high strength Mg alloys nowadays,are chosen and analyzed here for illustrating the fundamental aspects of the thermo-kinetic accumulation effect.These four cases are mainly differentiated by the pre-deformation techniques (e.g.,the amount of deformation stages,deformation degree,and processing temperature during the predeformation,etc.) and the components of the structural factor groups for transmitting the ΔG.

Regarding the case (Ⅰ),the pre-deformation is composed of two successive deformation processing,both of which result in large PDs at high temperatures,and the corresponding ΔGis transmitted to thenth stage by the cooperation of precipitates and GBs.For instance,the strength of Mg-12Gd-3Y-0.6Zr (wt.%) alloys ("homogenization for 10 h at 525 °C"+"hot extrusion at 460 °C with the extrusion ratio of 16:1〞 +" hot extrusion at 430 °C with the extrusion ratio of 16:1 " +"aging for 10 h at 225 °C") can be monotonically enhanced stage by stage with the accumulated ΔGand the decreased ductility,exhibiting the “seesaw” rule [242].Following the Taiji diagram1:(1) the firs extrusion provides the additional ΔG1to the subsequent structural changing process,which is temporarily stored and transmitted in the form of basal fiber textures (BF-1 in Fig.8(d)),GBs (for which the grain size is refine from 60 μm after homogenization to averaged 35 μm),and second phase particles Mg3Y3Gd2;(2) the second extrusion further provides the additional ΔG2to the system,so that the system have to further refin the grain size by fully DRX from 35 μm at last stage to 3 μm to increases the GBs,during which the dynamic precipitation of Mg5(GdY) and Mg3Y3Gd2occur with the facilitated DRX nucleation and the inhibited DRX grain growth,accompanied by the weakened texture due to RE effect (Section 2.3.2);(3)the aging makes full use of the accumulated ΔG1and ΔG2in the defects for the nucleation of prismaticβ’ with high ΔG,during which the grain size nearly keeps unchanged;(4)eventually,the cooperation of fine grains,denseβ’ formed by aging,Mg5(GdY) and Mg3Y3Gd2formed by dynamic precipitation during extrusion,can transmit the total intense ΔGto the PD dominated by the contraction twinning,prismatic and basal 〈a〉 slips,corresponding to improved tensile yield strength (TYS) of 350 MPa.

Regarding the case (Ⅱ),the pre-deformation is also composed of two successive deformation processing,for which the former one corresponds to the large PD at high temperatures but the latter one corresponds to the large PD with dynamically variation of loading directions at low temperature,and the corresponding ΔGis also transmitted by the cooperation of precipitates and GBs.For instance,recently,the ultrahigh strength bulk nanocrystalline Mg-8Gd-3Y-0.4Zr(wt.%) alloys ("homogenization for 15 h at 540 °C"+"hot extrusion at 450°C"+"four passes of rotary swaging at room temperature"+"aging for 72 h at 175 °C") have been fabricated without severe PD methods (Section 2.3.2),which are generally used for refining the structure but have modest effect,i.e.,the resulted grain sizes are rarely below 1 μm[243].Following the Taiji diagram:(1)the hot extrusion provides the additional ΔG1to the system via refining the equiaxed grain size to 8 μm by DRX;(2)and then,due to the high frequency period variations of loading directions during rotary swaging at room temperature and the RE effect (Section 2.2.2),more non-basal 〈c+a〉 dislocations can be activated at the moment that multiple non-basal planes are oriented to have high Schmid factors,and more twins and SFs can form,thus,the additional ΔG2at this stage is accumulated by further refining the grain size to nanocrystalline region of 80 nm via twinning,slipping and SFs;additionally,many Gd-rich clusters have formed and more prominent GB segregation have occurred in this nanocrystalline alloy than its coarse counterpart,which further accumulates ΔG2by stabilizing the GBs to slow down the dislocation nucleation at GBs and inhibit the GB-mediated deformations with the decreased ductility(Section 2.3.2);(3) the subsequent aging produces prismaticβ’without changing grain size to provide additional ΔG3;(4)finally,the high ΔGaccumulated by ΔG1,ΔG2,and ΔG3is mainly transmitted by the nano-grains andβ’ precipitates to the PD corresponding to improved TYS of 650 MPa.

Although the dynamically precipitated Mg5(GdY) and Mg3Y3Gd2also contribute to the improved strength in the case (Ⅰ),the dynamic precipitation during pre-deformation is inhibited in the case (Ⅱ) due to the low temperature condition,where,the higher solute concentration can be maintained,leading to more significant precipitation of prismaticβ’.Furthermore,the grain size is refine by DRX in the case(Ⅰ),for which the refining effectiveness should be limited by the high temperature,but the grain size is refine by deformation at room temperature in the case (Ⅱ),during which the DRX is inhibited and nano-grains can be produced.Therefore,it seems that the suppressive DRX may be conducive to the cooperation of precipitates and GBs to transmit the high ΔG,as reflected by the obtained better strength in the case(Ⅱ) than that in the case (Ⅰ) with the alloys in similar compositions.This can be further discussed in the case (Ⅲ) and (Ⅳ).

Regarding the case (Ⅲ),the pre-deformation seems like the case (Ⅱ),except for the second deformation processing corresponding to the large PD under the directional loading at low temperature,where,the corresponding ΔGis transmitted by the cooperation of precipitates and textures.For instance,the strength of Mg-14Gd-0.5Zr (wt.%) alloys ("homogenization for 24 h at 505 °C"+"hot extrusion with extrusion ratio of 28:1 at 505 °C"+"cold rolling with total thickness reductions of 10%,19%and 27%"+"aging at 200°C")can monotonically increase with the increment of cold rolling degree,seemingly exhibiting the scaling relation between the amount of the additional ΔGthat the material could obtain and the mechanical work that the external field have done [240].Following the Taiji diagram:(1) the hot extrusion provides the additional ΔG1to the system via refining the equiaxed grain size to 20 μm by the DRX with random texture due to the RE effect (Section 2.3.2);(2) the cold rolling provides the additional ΔG2in the form of the strengthened basal texture,for which the RE effect on texture weakening is circumvented due to the inhibited DRX at low temperature;in addition,the more cold rolling degree can induce higher dislocation densities,thus more ΔG2being transmitted to the subsequent aging;(3) the aging provides the additional ΔG3by precipitation of prismaticβ’ without changing grain sizes;(4) fi nally,the high ΔGaccumulated by ΔG1,ΔG2,and ΔG3is mainly transmitted by the strong basal texture andβ’ precipitates to PD corresponding to improved TYS of 445 MPa.It can be seen that the DRX during the second PD processing is also inhibited relative to the case (Ⅰ),and the grain size cannot be sufficiently refine by the deformation of limited non-basal slips and twinning due to the directional loading of cold rolling relative to the dynamically variation of loading directions of rotary swaging in the case (Ⅱ),thus the main ΔGtransmitter transforms from ultra-fin grains to textures.

Regarding the case(Ⅳ),the pre-deformation only points to one stage of processing corresponding to the relatively small PD at high temperature,and the corresponding ΔGis also transmitted by the cooperation of precipitates and textures.For instance,merely through the extrusion with a relatively small PD and the subsequent aging (as compared with the above cases),the strength of Mg-13Gd (wt.%) alloys ("homogenization for 24 h at 510 °C"+"hot extrusion with extrusion ratio of 4:1 at 320 °C"+"aging at 200 °C") can be enhanced to be high enough to be comparable with the alloys with similar compositions but processed by severe PD[199].Following the Taiji diagram:(1) due to the weak DRX resulted from the hot extrusion with relatively small PD,the as-extruded microstructures are mainly composed of strong basal textures formed by large un-DRXed grains with the high proportion of 85%,and the fine DRXed grains only occupy a low proportion of 15%;furthermore,some dynamical precipitates are distributed along the GBs of DRXed grains,and dynamical precipitation of prismaticβ’ can occur within the un-DRXed grains;the hot extrusion provides the additional ΔG1to the system in the form of this texture dominated morphology;(2) the aging provides the additional ΔG2by producing profuse nanoscaleβ’ only within the un-DRXed region where high density of dislocations exist for stimulating the precipitate nucleation;(3) finally,the high ΔGaccumulated by ΔG1and ΔG2is mainly transmitted by the strong basal texture andβ’ precipitates to PD corresponding to improved TYS of 470 MPa.Compared with the above three cases,the DRX is inhibited during the hot extrusion due to the relatively small PD and low extrusion temperature.

The scaling relation between the amount of the PD exerted to the material and the ΔGor strength enhanced by the external mechanical field is exhibited in the case (Ⅲ).However,the unexcepted high strength can be obtained by the single stage of relatively small PD processing in the case (Ⅳ),even exceeding the strength improved by two successive large PD processing in case (Ⅰ).Is there something wrong about the thermo-kinetic accumulation effect? Please keep in mind that the amount of work that the external fields have done cannot directly equal the net ΔGthat the material could accumulate,which should depend on the combat between the material and the external fields For a material suffering the PD caused by the external fields at the initial stage,large part of the mechanical work can be transformed to the stored energy in the form of imperfections in the material;when the amount of PD increases to a threshold value,i.e.,the limit capability of the material to accommodate the imperfections at the current state,the material might redistribute these imperfections by DRX to improve the capability of itself to accommodate more imperfections during the subsequent PD,i.e.,refinin the grain size with increasing the GBs,and this DRX process should decrease the energy of the system following the second law of thermodynamics.Accordingly,the net stored energy during the PDs in the current processing stage,providing the additional ΔGfor the PDs or PTs in the next processing stage,is determined by the relative intensity between the PD increasing the energy and the DRX decreasing the energy,which is affected by the strain rate,the strain amount and the temperature,etc.As for the case (Ⅲ),the cold rolling has inhibited the DRX,thus the scaling relation has emerged.As for the case (Ⅰ),although large PD has been exerted on the material,the DRX has also been enhanced at the high temperature,thus the corresponding net stored energy might be lower than that in the case (Ⅳ) with relatively small but sufficient PD and weak DRX.Last but not least,it is reflected in these four cases that,as long as the ΔGcould be accumulated during the preceding (n-1)-stage processing to be high enough via altering the thermo-kinetic “seesaw”,the excellent strength at thenth stage processing could be obtained,no matter the ΔGtransmitters being fine grains,textures or precipitates.

3.2.Improved strength-ductility balance based on thermo-kinetic pairs

In order to simultaneously improve strength and ductility of Mg alloys following the Taiji diagram,not only high ΔGbut also high GS or highQshould be imparted to the system via the thermo-kinetic accumulation effect in the processing stage,which acts as the so-called thermo-kinetic criterion(i.e.,high ΔG-high GS) for simultaneously elevating the two ends of the “seesaw” (Section 2.1.2).Noted that this criterion should not be contradictory with the thermo-kinetic correlation,i.e.,the increase of ΔGmust lead to the decrease ofQ.As the thermodynamic precondition for alloy design,the“high ΔG” means accumulating ΔGas more as possible,whereas,the “highQ” or “high GS” means,although theQor GS should be deceased responding to the increased ΔG(Eq.(1)),the decreasing part should be as small as possible to maintain a relatively highQor GS over a long period of time,thus forming a kinetic sustainable structural changing process.Taking Mg alloys as examples,the integrated effect of the ultrafine grains and the densely distributed precipitates,arising from the high ΔGfor nucleation of recrystallization and precipitation and the high GS for growth of the recrystallized grains and the nucleated precipitates,must correspond to the deformation mechanisms of high ΔG-high GS,i.e.,the enhanced dislocations multiplication with the hindered dislocations motion,thus leading to improved strengthductility balance,as discussed in Section 2.2.4.4.Analogous philosophy can be reflected by the metal flow during PDs described via the constitutive relationship of σflow=where the uniform elongationεuniformcan be obtained via the Considère criterion for predicting the onset of plastic instabilitydσflow/dε=σflow,withσflowas the flow stress,Sthe strength coefficientthe strain rate,jthe strain hardening exponent,andgthe strain rate sensitivity[244,245].Variation of the ΔG-GS pairs during the PD at thenth stage,dominated by the multiple defect interactions,can be macroscopically reflected as the elongation measuring the strain limit and the work hardening measuring the ability for resisting necking during the uniaxial tension [246],which is usually correlated with the activity of non-basal slips,especially the〈c+a〉dislocations[247-249].Since the high ΔGaccumulation process has already been largely analyzed in Section 3.1,serving as the precondition for satisfying the thermo-kinetic criterion,the structural factors design for maintaining the high GS during accumulating high ΔGare mainly focused here.

3.2.1.Thermo-kinetic criterion by grain boundaries

As discussed in Section 2.3.2,decreasing the grain size could lead to the simultaneously improved strength and ductility for Mg alloys,thus being favorable for satisfying the thermo-kinetic criterion.The beneficial effect of grain refine ment for maintaining high GS could stem from the avoided PB transition of the 〈c+a〉 dislocations (Section 2.2.2),due to the easier traverse of〈c+a〉dislocations in smaller grains,thus being favorable for satisfying the ductilization condition of Eq.(4) [108].Nonetheless,upon refining the grain size of Mg alloys to the nano-crystalline (＜100 nm) region,the strain hardening capability will decrease and the strength will increase with the expense of ductility [185],since the shrinking space for dislocation accumulation and multiplication and large GBs act as the sinks for dislocations [243],thus leading to the decreased GS.As for nanoscale Mg single lattice,however,it was experimentally demonstrated that,the corresponding extremely high strength and short dislocation length is conducive to activate alternate deformation mechanisms to promote latent hardening and dislocation storage,thus leading to more uniform deformation,i.e.,the higher GS [250].Accordingly,the GBs play significant roles for adjusting the strength-ductility balance in polycrystalline Mg alloys,and the sufficiently high ΔGcan be accumulated while the high GS could be maintained,via modulating the average grain size,the grain size distribution,and the GB stability.

Regarding the grain refinement the high ΔG-high GS of full recrystallization is required to be further transmitted to the final PD stage,during which the twinning to non-basal slip transition could occur to enhance the work hardening rate(Section 2.3.2) [251].For instance,the accumulated ΔGin the Mg-3Gd (wt.%) alloys was manipulated by the annealing at different temperatures at the (n-1)-th stage of processing in Ref [186].,and subsequently,the different ΔGcan be further transmitted by the corresponding grains with different sizes to the final PD.The results indicated that,with increasing ΔGby decreasing the annealing temperature,the grain size is decreased,the strength is improved due to the Hall-Petch effect,and the ductility is improved due to more activation of＜c+a＞dislocations,which arises basically from the higher GS corresponding to the growth kinetics of the smaller grains transmitted to the final PD,thus leading to the more significantly improved strength-ductility balance.In virtue of predeformation of cold forging,lots of twins can be introduced in the Mg-3Al-Zn (wt.%) alloys [252],which can lead to the high ΔGof DRX nucleation by providing preferential sites(i.e.,twin induced nucleation in Section 2.3.2)during the subsequent extrusion,and the corresponding high GS orQfor the growth of recrystallized grains can also be maintained due to the low processing temperature.This pair of high ΔG-high GS can be further transmitted to the final PD corresponding to improved strength through grain refinement and improved ductility by suppressing the double twins,which can accelerate cracking by dislocations pile-up at twin-matrix interface.Analogously,the low temperature electropulsing treatment has been used to produce the high ΔGof SRX nucleation and high GS of recrystallized grain growth for the samples of the Mg-6Al-Zn (wt.%) alloys after two-step ECAP processing,and the resulted ultrafine grains have overcome the trade-off relationship of strength and ductility,compared with the same alloys processed by other methods [253].

Regarding the modulation of grain size,the bimodal grain structures are particularly beneficial to satisfy the thermokinetic criterion of high ΔG-high GS.This should be attributed to the wonderful cooperation of small recrystallized grains and large non-recrystallized grains,for which the former ones provide excellent GB strengthening effect (contributing to the strength),and the latter ones endow large dislocation storage rate and work hardening (contributing to the ductility) [4,254].The bimodal structures can be formed by twin induced DRX,due to the incomplete DRX resulted from the relatively low temperature at which twins could be activated [4].Furthermore,the formation of bimodal structures could also be related to the restrained recrystallized grain growth of high GS by precipitates [254-256],see discussion in Section 3.2.3.Regarding the modulation of GB stability,the solute segregation could decrease the GB energy,so that,on the one hand,the increased thermal stability of GBs tends to generate the pile-ups of more dislocations to increase the ΔGfor dislocation across GBs,thus improving the strength;and on the other hand,the decreased GB mobility,i.e.,the increased GS,tends to keep more small grain,thus activating more non-basal slips to improve the ductility [189].Additionally,the GB sliding could significantly stabilize the PD via increasing the strain rate sensitivity to improve the ductility [257].The critical grain sizedc2for GB sliding could also vary with the GB properties (Section 2.3.2),thus providing another strategy for maintaining the high GS based on the GB-mediated deformation [20],which is deemed as the principal mechanism governing the superplastic behavior[258,259].

3.2.2.Thermo-kinetic criterion by precipitates

Lots of works in literatures have been devoted to understand the strengthening effects of precipitates,actually,the ductile effects of precipitates should not be overlooked.It was reported that,for Mg-Al-Ca-Mn alloys,both strength and ductility of the peak-aged state could be improved relative to that of the solution state.The high GS of Mg-Al-Ca-Mn alloys can be attributed to the facilitated cross-slip of dislocations due to the decreased Al concentrations in the matrix,which can change SFE,after the precipitation of G.P.zones [260].Although the uniform elongation will decrease after aging,the strain rate sensitivity,serving as a key parameter for sustaining a high strain to failure,will increase due to the precipitation of G.P.zones,thus the post-uniform strain will increase to compensate the decrease of the uniform elongation and make the increment of the total elongation,i.e.,maintaining a high GS with the high ΔGin peak-aged condition [244].

The prismatic precipitates have also been reported to be conducive to the ductility in some cases where the high ΔGhigh GS criterion is satisfied For instance,it was reported that,for Mg-5Sn (wt.%) alloys,when the habit plane of the precipitated lath-shaped Mg2Sn is transformed from basal plane to prismatic plane by TAD processes,during which the high ΔGis gradually accumulated (Section 3.1.1),the ductility could also be improved,as compared to the same alloys with basal Mg2Sn lath [235].This should be ascribed to the maintained high GS by prismatic Mg2Sn,which impedes basal slips more effectively than prismatic slips to decrease the CRSS ratio of prismatic slips to basal slips(Section 2.3.3),thus facilitating the non-basal slips to mediate more PDs.The distributions of precipitates influence their ability of maintaining high GS of the system.For instance,the original nonuniform distribution of Mg17Al12phases in Mg-8.1Al-0.7Zn-0.18Mn (wt.%) alloys could be improved in virtue of the pretwinning deformation,which could provide profuse nucleation sites for the fine continuous Mg17Al12formed by precipitation of high ΔG-high GS,but completely inhibit the coarse discontinuous Mg17Al12formed by precipitation of high ΔGlow GS,so that the strength and ductility have been simultaneously improved,as compared to the same alloys without the pre-twinning deformation [261].

Precipitates can be used to induce alternate deformation modes to sustain the PD,thus maintaining a high GS when play the precipitation hardening role of themselves.For instance,by carefully alloy chemistry design,the high ΔG-high GS of precipitation can produce dense distribution of nonshearable but deformable Al2Ca in Mg-6Al-Ca (wt.%) alloys[246],which display an excellent strength-ductility balance.During the PD,the geometrically necessary dislocations could form around Al2Ca to increase the total dislocation density to facilitate the strain hardening,while the Al2Ca can internally deform to relieve the stress concentration at the Mg/ Al2Ca interface.Upon deformation,after yielding of the material,the basal slip will firstly be activated in the matrix Mg followed by the deformation of Al2Ca via the dislocation slips and SFs in itself,and then,the 〈c+a〉 dislocations will be activated at the GBs due to the segregation of Ca,simultaneously with the enhanced cross-slip of 〈c+a〉 dislocations between pyramidal I and Ⅱ planes by Al and Ca (Section 2.2.2).In a word,the resulted high ductility has reflected the high GS transmitted with high ΔGfrom forming Al2Ca to this PD stage.

3.2.3.Thermo-kinetic criterion by cooperation of grain boundaries and precipitates

Similar to the philosophy in Section 3.1.2,the superposition effects of the structural factors could generally produce more controllable conditions for attaining the thermo-kinetic criterion.On the basis of the high ΔGthat could be transmitted by the coordination of GBs and precipitates,two cases about how the high GS could be concurrently maintained are analyzed here,including the uniform or bimodal grains cooperated by precipitates.

Compared with the pre-deformation for inducing high ΔGof precipitation,the aging prior to extrusion for the Mg-7.63Al-0.38Zn-0.15Mn (wt.%) alloys could improve their strength and ductility simultaneously relative to the same alloys extruded without pre-aging [262].The aging could produce profuse fine Mg17Al12,which could result in high ΔGhigh GS of DRX during the subsequent extrusion by providing nucleation sites and pinning GB migration.Meanwhile,due to the lowered Al concentration in the matrix caused by the pre-aging,the dynamic precipitation of large banded Mg17Al12during the extrusion is inhibited,thus relieving the large stress concentration nearby,and decreasing the probability for the mobile dislocations being temporarily arrested by the Al atoms at forest dislocations.Accordingly,the high ΔGcould be transmitted by the fine DRXed grains and small Mg17Al12with the high GS maintained,eventually reflected as the PD of high ΔG-high GS.Contrarily,the promoted dynamic precipitation is utilized to cause the DRX of high ΔG-high GS during multi-directional forging of Mg-8.8Al-0.47Zn-0.21Mn-0.17Ag (wt.%) alloys [183],and abundant〈c+a〉 dislocations could be activated due to the changing loading directions,thus the texture produced could be weakened with the refine grains,leading to the PD of high ΔG-high GS finally.Furthermore,the drop of the strain hardening rate can be suppressed to delay the plastic instability with the prolonged uniform deformation by ultrafine grains in Mg-6.2%Zn-0.5%Zr-0.2%Ca (wt.%) alloys [263],which are produced via fully recrystallization with inhibited grain growth by finel dynamical precipitates during the HPT,and the high ΔG-high GS of the PTs forming this coordination of ultrafine grains and precipitates is transmitted to the final PD again.

As discussed in Section 3.1.1,the co-precipitation on basal and prismatic planes could accumulate the considerably high ΔG,and if combined with the ultrafine grains,the high GS may be concurrently maintained.For instance,the high ΔGof Mg-10.6Gd-2Ag (wt.%) alloys,undergoing ECAP and aging,can be transmitted by the basalγ’’ plates,the prismaticβ’plates and the fully recrystallized fine grains;and the high GS can be maintained by homogeneous fine grains and the approximately random texture,with the corresponding strengthductility balance jumping out the “banana curve” region of Mg-RE wrought alloys [10].Adding Yb into the Mg-3.5Sm-0.6Zn-0.5Zr (wt.%) casting alloys could establish a more excellent strength-ductility balance than the conventional Mg-RE casting alloys[264].The co-precipitation of fine prismaticβ’’ and basalγ’’ could occur during the aging for transmitting the high ΔGto the final PD,during which the activity of 〈c+a〉 dislocations can be enhanced due to the decreased SFE by Yb,thus more strain hardening can be caused by the dislocation-dislocation interactions to improve the ductility,thus reflecting the high GS being maintained by fine grains.

In view of the superiority of bimodal grains(Section 3.2.1),the coordination of bimodal grains and precipitates for attaining high ΔG-high GS have been largely reported.For instance,the Mg-4.35Y-3RE-0.36Zr (wt.%) alloys can benefit from the non-uniform dynamic precipitation ofβduring ABE processing,which thus causes the inhomogeneous growth of DRXed grains,and further leads to the bimodal grain distribution for maintaining the high GS with the weakened texture,while the high ΔGis transmitted by the fine grains and precipitates [185].For Mg-0.4Al (wt.%) alloys undergoing extrusion,a better strength-ductility balance could be established with minor Mn addition [265].The high ΔGis transmitted by the extruded texture in un-DRXed large grain region and the dynamically precipitation ofα-Mn and Al8Mn5,and the high GS is maintained by the DRXed region where the random orientation of fine grains is conducive to the activation of non-basal dislocations and the inhibition of twinning.

3.2.4.Thermo-kinetic criterion by other microstructural configurations

Apart from the forgoing structural factors in traditional alloy design,some other innovative microstructural configurations have been confirmed to make unprecedented contributions on improving strength-ductility balance with the satisfied thermo-kinetic criterion,which are briefly introduced here.It was reported that the low angle GBs play a significant role in controlling the dislocation activity in Mg-Ca-Al-0.2Zn-0.1Mn(wt.%) alloys (“homogenization”+“extrusion”) [266].The relatively higher extrusion temperature and leaner solute additions could preserve fewer residual dislocations in grains,thus the probability transforming the activated mobile dislocations to the immobile ones is decreased.Moreover,more produced low angle GBs could serve as the source for emitting new dislocations to enhance the dislocation multiplication,so that,more mobile dislocations could be produced and sustained a long period to facilitate the alternate deformation modes,reflected as the high GS.Meanwhile,the high ΔGcan be transmitted by GBs and nano-precipitates,eventually overcoming the strength-ductility trade-off.The nano SFs in Mg have the similar effect on strengthening and ductilization [182],where,on the one hand,theI1SFs provide significantly effective barrier on 〈c+a〉 dislocations,and the corresponding improved yield strength was reported to be inversely proportional to the average spacing of SFs [267],and on the other hand,theI1SFs could serve as the source for 〈c+a〉 dislocations.This paradox effect of nano SFs on the non-basal slips just reflect the thermo-kinetic pair of high ΔG-high GS corresponding to the high multiplication rate and the high hindered effect for dislocations.

Beside the bimodal structures mentioned above,the heterogeneous structures have been largely reported to bestow the materials a superior strength-ductility synergy,also including gradient structures [268],harmonic structures [269] and nanotwined grains [270],etc.,which are composed of multiple domains with different strength,geometries and sizes[271].Accordingly,there should exist large strain gradients at the domain interfaces,forcing the production of profuse geometrically necessary dislocations for accommodating the corresponding strain incompatibility [272,273].The pile-up of geometrically necessary dislocations will further induce large back stress,which contributes not only to the improved yield strength (i.e.,the accumulated high ΔG) but also to the improved ductility (i.e.,the maintained high GS) with the enhanced strain hardening for stabilizing tensile deformation [268].For instance,a heterogeneous laminate Mg-Y alloy has been fabricated by sandwiching a hard layer Mg-11Y (wt.%) and two soft layers Mg-5Y (wt.%) via HPT,the strength-ductility balance of the whole system has been significantly optimized,due to the satisfied thermo-kinetic criterion [274].

The hierarchical nanotwins with high thermal and mechanical stability are beneficial for attaining the thermo-kinetic criterion.Although the twinning is suggested to be inhibited in most previous cases due to the ease of dislocation pile-ups and lack of plastic relaxation at TBs,the highly dense nanotwin boundaries could prevent the void formation and block crack propagation [275].It has been demonstrated that,during the PD of a multiscale twin architecture,the sequential deformation mechanisms could be activated at different stages,thus sustaining a steady hardening source with improved strength and delaying the necking with improved ductility [270],i.e.,the inherent philosophy of high ΔG-high GS.For instance,both the densely hierarchical {101}-{101} double contraction nanotwins produced in Mg-8Li (wt.%) alloys [276] and the contraction nanotwins-SFs structures produced in Mg-12Li(wt.%)alloys[277]by ultrahigh pressure treatment,have exhibited excellent strength-ductility balance arising from the coherent TBs,which can not only block but also transmit the incoming dislocations and provide huge space for dislocation storage,contributing to the strength and the ductility,respectively [270].Indeed,all these microstructures containing nanotwins are formed by a structural changing process of high ΔG-high GS,therein,the high ΔGis provided by the exterior ultrahigh pressure,and the high GS corresponds to the enduring reduplication of twinning,detwinning and retwinning with strain hardening for forming the multiscale hierarchical nanotwin structures.Thereupon,this thermo-kinetic pair is transmitted by nanotwins to the PD at thenth stage of processing.

4.Summary and outlook

4.1.Summary

A newly fundamental understanding on designing Mg alloys with excellent mechanical properties has been provided in this review following the rule of thermo-kinetic synergy:

(1) By reviewing the activity of deformation modes,the formation of structural factors,and the interaction between imperfections in Mg alloys,the ubiquitous paradox phenomenon represented by the thermo-kinetic and strengthductility “seesaw” has been revealed,serving as the critical medium for guiding alloy design with the thermo-kinetic synergy.

(2) Following the Taiji diagram,the structural changing processes,i.e.,PTs and PDs,at different stages of the thermomechanical processing of Mg alloys could be interrelated by the rule of thermo-kinetic connection,thus,the rational design for the thermo-kinetic processing path of Mg alloys has become feasible.Equipped with the thermo-kinetic criterion of high ΔG-high GS,the Taiji diagram has provided a universal strategy for improving the strength-ductility balance of Mg alloys.

(3) Developing Mg alloys by philosophy of thermo-kinetic synergy mainly contains a fundamental idea,which should be applicable for any mechanical materials,i.e.,making full use of the coordination of different structural factors.Accordingly,the structural factors can be adopted to transmit the high ΔG-high GS from thermo-kinetic accumulation effect during processing to the final PD with the improved yield strength,and to manipulate the corresponding tensile or compression elongation,during which the sequential and sustainable deformation modes could be activated to contribute to the prolonged uniform or post-uniform elongation with the improved ultimate strength and ductility.

(4) Several effective structural factors in Mg alloys should be paid more attention:(Ⅰ) the alloying elements (especially for RE elements),which can influence the characteristics of dislocations (or twinning) by changing GSFE (or GPFE),influence the properties of GBs or TBs by solute segregation,influence the thermo-kinetics of precipitations,and so on;(Ⅱ)the grain size,therein,the ultrafine grained or nano-crystalline structures (where more non-basal slips could be activated and twinning could be inhibited) and the bimodal structures (usually caused by incomplete recrystallization)should be focused on;(Ⅲ) the textures,which provide an effective strengthening strategy but reinforce mechanical anisotropy,and could be substituted by grain refinement of DRX;(Ⅳ) the precipitates,therein,the concurrently precipitations on basal and prismatic planes deserve further investigations;(Ⅴ) the nano SFs and nanotwins.All these structural factors can be adjusted and combined to affect the deformation modes in a paradox way(e.g.,facilitating and inhibiting the activity of 〈c+a〉 dislocations,etc.),following the philosophy of Chinese Taiji,i.e.,balancing the coordination between dynamics and statics or rigid and soft.

4.2.Outlook

The Taiji diagram proposed herein has been qualitatively verified by analyzing the existing typical cases for Mg alloys design in literature.Although the quantitative evidences are required for thoroughly explaining this thermo-kinetic strategy for developing Mg alloys,as the seminal work herein,we aim at stressing its fascinating application potential in the future.To completely realize this rational design process,the relevant works in this immature but intriguing realm of thermo-kinetic synergy are still on the way,which could be divided into three aspects:

(1) Enriching the components of the Taiji diagram.Lots of works are still required to be done to fully understand the rule of thermo-kinetic synergy at a more fundamental level.Although the thermo-kinetic correlation and connection have been revealed here,their physical origin should be further illuminated.Additionally,the development of thermo-kinetic database of Mg alloys for the accurate quantification of ΔGand GS is indispensable.

(2) Optimizing the original processing path by rotating the Taiji diagram clockwise.The correspondence between the thermo-kinetic pair of ΔG-GS and the cooperation of different structural factors should be further revealed,thereupon then,the microstructural evolution during processing of the material could be directionally selected via the thermo-kinetic control for ΔG-GS to attain the objective mechanical properties.By doing so,the original processing path could be optimized by taking full advantage of the cooperation of the acquainted structural factors,usually with the saved manufacturing cost.

(3) Designing the innovative processing path by rotating the Taiji diagram anticlockwise.Providing the required strength-ductility balance of the material,new processing paths for accumulating high ΔGand maintaining high GS could be created without the consideration for the participated structural factors,due to the always existence of structural factors (i.e.,the disabled one is always replaced by the functional one) for transmitting ΔG-GS.By doing so,some undiscovered structural factors may emerge for taking part into a specific thermo-kinetic accumulation process,which could be captured and documented in the database of structural factor groups,thus being utilized for developing new strengthening and toughening mechanisms.

Acknowledgements

The authors are grateful for the financial support from the Natural Science Foundation of China (Nos.52130110,52171013 and 51790481),the Research Fund of the State Key Laboratory of Solidification Processing (Nos.2019-TZ-01 and 2019-BJ-02),the Fundamental Research Funds for the Central Universities (No.3102020QD0412),and “2020-2022 Youth Talent Promotion Project” of China Association for Science and Technology.The authors are obliged to associate professor Wenchao Yang in Northwestern Polytechnical University for his assistance of data collection.