Deformation and failure behavior of heterogeneous Mg/SiC nanocomposite under compression

Xi Luo,Jinling Liu,*,Leigang Zhang,Xu He,Ke Zhao,Linan An

aState Key Laboratory of Traction Power & School of Mechanics and Engineering,Southwest Jiaotong University,Chengdu,Sichuan,610031,China

b Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province,Southwest Jiaotong University,Chengdu,Sichuan,610031,China

c Department of Materials Science and Engineering,University of Central Florida,Orlando,FL,32816,United States

Abstract The heterogeneous magnesium(Mg)matrix nanocomposite with dispersed soft phase exhibits high strength and toughness.Herein,the deformation behavior and failure process were investigated to reveal the unique mechanical behavior of the heterogeneous microstructure under compression.The extensive plastic deformation is accompanied by the flattenin and tilting of the soft phase,inhibiting strain localization and leading to strain hardening.Moreover,a stable crack multiplication process is activated,which endows high damage tolerance to the heterogeneous Mg matrix nanocomposites.The fina failure of the composite is caused by crack coalescence in the shear plane along a tortuous path.The presence of dispersed soft phases within the hard matrix induces a noticeable change in mechanical response.Especially,the malleability of the heterogeneous Mg matrix nanocomposite is two and ten times higher than that of pure Mg and the homogeneous Mg matrix nanocomposite,respectively.The current study provides a novel strategy to break the trade-off between strength and toughness in metal matrix nanocomposites.? 2021 Chongqing University.Publishing services provided by Elsevier B.V.on behalf of KeAi Communications Co.Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/)Peer review under responsibility of Chongqing University

Keywords:Magnesium matrix nanocomposites;Heterogeneous structure;Malleability;Microstructural evolution.

1.Introduction

The excellent combination of strength and toughness in magnesium matrix nanocomposites(Mg-NCs)is always pursued to improve the energy efficien y and maximize the safety factor of resulting components[1,2].Unfortunately,these two properties are often mutually exclusive,where high strength is often accompanied by a drastic decrease in toughness[3-5].Hence,the introduction of heterogeneous microstructure at the mesoscale has been proposed as a novel strategy to evade the trade-off between strength and toughness[6-8].Hereby,a new class of Mg-NCs with controllable inhomogeneous distribution of reinforcement has been developed[9-14].In general,such heterogeneous composites consist of regions with discrepant mechanical properties,i.e.,a reinforcement-rich region(hard phase)and a reinforcement-lean region(soft phase).For example,Habibi et al.[10]reported a hierarchical Mg matrix nanocomposite,where Al2O3/Al composite is dispersed in Mg matrix as the hard phase which results in an optimal combination of strength and ductility.Liu et al.[12]proposed an effective approach to generate a heterogeneous structure by one-step ball milling.The as-synthesized heterogeneous Mg-NCs,where SiC nanoparticles are nonuniformly distributed in the pure Mg matrix arising from the core-shell structure of ball-milled composite powder,are composed of two different phase structures with micrometer dimension(one is the pure Mg region without reinforcement(soft phase)and another is the composite region with SiC nanoparticle-reinforcement in the pure Mg matrix(hard phase)),and exhibits an enhanced strain-to-failure under compression which is almost fi e times higher than that of its homogeneous counterpart where the SiC particles with the same volume fraction are uniformly distributed in pure Mg matrix.

Furthermore,the deformation and fracture behavior of heterogeneous composites have been widely studied to reveal the mechanism of significantl improved toughness[15-17].Overall,a majority of studies were focused on the tensile behavior and accordingly proposed several mechanisms,such as strain partitioning[18],back-stress strengthening[19],delayed necking[20],as well as crack deflectio and bridging toughening mechanisms[21-23].However,the deformation and fracture behavior of heterogeneous composites under compressive loading have been rarely investigated.Fan et al.[24]primarily proposed that the heterogeneous grain size distribution in a bimodal Al-Mg alloys contributes to the global ductility under compression and argued that the propagation of multiple shear bands is the ultimate cause of fracture.Jiang et al.[25]investigated the strain map of B4C/Al trimodal nanocomposites after compression and revealed that the regions without nanoparticles suffered more severe deformation than the nanoparticle-reinforced regions at the initial deformation stage.Vogt et al.[26]observed the deformed microstructure of heterogeneous B4C/Al composites under dynamic compressive loading and indicated that the extensive axial microcracks were generated near the reinforcement,which were accompanied by the structural kinking and grain growth,inducing the strain-softening effect.He et al.[27]analyzed the fracture surface of heterogeneous Mg-based nanocomposites after compression and proposed that the pullout of the soft phase plays an important role in toughening the composite.

Although the reported results can explain the compressive behavior of heterogeneous nanocomposites,a few critical issues still need to be investigated in detail.For instance,the previous research is mainly focused on the heterogeneous composites with a high content of reinforcements,which generally exhibit a poor ability of plastic deformation and obvious strain softening after yielding due to the premature emergence of microcracks[26,28].However,the high deformability is required to facilitate the processing and forming,which can be attained by reducing the content of reinforcements[29].Furthermore,the evolution of heterogeneous structure under compression and the influenc of heterogeneous structure on the crack generation and propagation are unclear.Hence,a systematic study is required to investigate the structural evolution and damage process under compression.

In this work,a heterogeneous Mg matrix nanocomposite(Hetero-Mg-NC)reinforced by SiC nanoparticles(5 vol.%)was fabricated by powder metallurgy,and its compressive mechanical properties at room temperature were evaluated.Moreover,this study focused on analyzing the microstructure evolution of Hetero-Mg-NC under compression and made attempts to reveal its deformation,damage and fracture behavior.

2.Materials and met hod

2.1.Preparation of heterogeneous Mg matrix nanocomposites

The heterogeneous Mg matrix nanocomposite was produced through one-step ball milling and subsequent sintering.The starting powders were commercial Mg with a particle size of?150μm(Tianjin Kermel Chemical Reagent Co.,Ltd.,Tianjin,China)andβ-SiC nanoparticles with an average size of 20 nm(MTI Corporation,Richmond,CA,USA).Briefl,95 vol.% of Mg powder and 5 vol.% of SiC powder were mixed under argon atmosphere and ball-milled in a planetary mill(Nanjing Nanda Instrument Plant,Nanjing,China)at room temperature.A rotational speed of 180 r/min and a ballto-powder ratio of 10:1 were used.The as-milled composite powder was consolidated into a dense bulk with a diameter of 30 mm and a height of 6 mm by a hot oscillatory pressing sintering system(OPS-2020,Chengdu Efiel Materials Technology Co.,Ltd.,Chengdu,China)at 575 °C and 50 MPa.A complete description of the preparation process can be found elsewhere[12].Meanwhile,pure Mg sample was also fabricated following the same consolidation process here using the same raw material.Additionally,a conventional Mg matrix nanocomposite containing 5 vol.% uniformly-distributed SiC nanoparticles(referred to as Homo-Mg-NC)was obtained for comparison,which was same as the sample in ref.[5].

2.2.Microstructural characterization

The microstructure of Hetero-Mg-NCs was characterized by a scanning electron microscope(SEM,FEI Quanta FEG 250)and a high-resolution transmission electron microscope(TEM,JEOL,2100F).SEM samples were polished to a 0.5μm finis through a metallographic routine and SEM images were taken using the back-scattered electron(BSE)mode with an accelerating voltage of 20 keV and a working distance of 10.5 mm.TEM samples were prepared by ionmilling(Gatan PIPS-691)and TEM was operated under an accelerating voltage of 200 keV.The structural parameters of soft phase and the distribution of microcracks under different strains were measured by ImageJ software based on dozens of SEM images.

2.3.Mechanical characterization

The compression tests of Hetero-Mg-NC,with a loading direction parallel to the sintering direction(SD),were performed at room temperature using a universal testing system(Instron 2367,Illinois Tool Works Inc.,MA,USA)with a strain rate of 1×10-3s-1.The specimens for quasistatic uniaxial compression tests were machined into the shape of cylinders with a diameter of 2.5 mm and a height of 5 mm.In order to explore the microstructural evolution under compression,the specimens,cut from the same sample,were compressed to the true strain of 0.3%,10%,16%,22%,30%and 35% from the initial height respectively,and a semiquantitative analysis based on SEM images was carried out.

Table 1The results of quasistatic compressive test for pure Mg,Homo-Mg-NC and Hetero-Mg-NC.

3.Results

3.1.Microstructure of heterogeneous Mg matrix nanocomposite

Fig.1a and b show the typical back-scattered electron(BSE)and TEM images of the Hetero-Mg-NC,revealing an obvious heterogeneous structure where SiC nanoparticles are nonuniformly distributed within the Mg matrix.Herein,such heterogeneous characteristics divide the nanocomposite into two regions,where Mg with a high volume fraction of SiCp represents the hard phase and pure Mg without SiCp represents the soft phase.It can be seen that the hard phase is continuous and separates the soft phase into fla e-like islands.Based on several BSE images,statistics on the structural parameters of the soft phase are plotted in Fig.1c-e.The average area of the isolated soft phases is found to be about 77.2μm2and the calculated volume fraction of the soft phase is approximately 27.4%,which can be effectively controlled by the ball milling process.The soft-phase shape is evaluated by the length ratio of the long axis to the short axis,which is denoted as the aspect ratio(λ).In the Hetero-Mg-NC,the soft phase,with an aspect ratio of 3.52±0.32,shows a fla e-like shape.In addition,the arrangement of the fla e-like soft phases is evaluated by the angle(θ)between the long axis of the soft phase and transverse direction(TD),as define in Fig.1f.It can be seen that the arrangement angle ranges from-90° to 90°,revealing a disordered arrangement.Moreover,the BSE images and corresponding EDS maps of Hetero-Mg-NC,pure Mg,and Homo-Mg-NC are displayed in Fig.S1,Supplementary material.It shows the difference of microstructure and characterization of the distribution of SiC nanoparticle-reinforcement in these samples.

3.2.Compressive behavior

Fig.2a shows the representative compressive true stressstrain curve of the Hetero-Mg-NC,together with pure Mg and Homo-Mg-NC tested under the same conditions.Clearly,these materials exhibit markedly distinct mechanical responses and the corresponding compressive properties,including yield strength,ultimate strength,plastic strain and malleability.These data of compressive properties are calculated from the true stress-strain curves and listed in Table 1.The yield strength of the Hetero-Mg-NC is as high as 200 MPa,showing a 159.5% increase over that of pure Mg(76 MPa),and even superior to the performance of most Mg alloys and composites[1,30-32].Additionally,it is surprising to fin that the Hetero-Mg-NC still maintains comparable or even better plastic strain(16.5%)than pure Mg with a significan increase in strength,which has not been observed in homogeneous composites before.In the case of Homo-Mg-NC,the plastic strain decreases to 2.9%,only 17.6% of the value of the Hetero-Mg-NC.Furthermore,the strain-hardening rateΘ(Θ=dσ/dε)of the Homo-Mg-NC shows a drastic drop after yielding.In comparison,the Hetero-Mg-NC renders a more stable and much higherΘthan that of Homo-Mg-NC(Fig.2b).In particular,after the stress reaches the ultimate strength(274 MPa),the Hetero-Mg-NC continues to deform rather than abrupt failure.Its fina failure strain reaches up to 45.1%,which is about two and ten times higher than that of pure Mg and the Homo-Mg-NC,respectively.These results indicate that the Mg matrix nanocomposite with a heterogeneous structure possesses better malleability than pure Mg and the homogeneous one.

The inset picture in Fig.2a exhibits the specimens of the Hetero-Mg-NC before and after failure.After such a large deformation,the specimen maintains structural integrity rather than breaking into several pieces,which is different from the off-axial failure characteristics of the Homo-Mg-NC[5].Moreover,a discontinuous main crack is observed on the specimen surface,which is around 45° to the loading direction,as marked by the red-colored line.It can be seen that the shear failure dominates the failure mode of Hetero-Mg-NC.

3.3.Microstructural evolution under compressive load

To explore the relationship between performance and microstructural evolution of the Hetero-Mg-NC under compressive load,a semi-quantitative analysis was carried out to analyze structural changes of the soft phase and damage distribution at various strains.A series of samples were separately compressed to the trure strain of 0.3%,10%,16%,22%,30% and 35% from the initial height,almost covering the complete deformation process(Fig.S2a).To better observe the heterogeneous structure,the deformed specimens were sectioned into two parts along the compressive direction(Fig.S2b).Finally,the as-polished longitudinal sections were observed by SEM.

3.3.1.Structural evolution of soft phase

The observations were focused on the middle region of the samples,aiming to capture the deformation and reduce the localized effect of the loading head.Fig.3 presents the representative microstructure of Hetero-Mg-NC compressed to different strains.From the viewpoint of overall deformation,the heterogeneous structure always exists but its morphology undergoes distinct changes with increasing macro strains:(i)the soft phases are gradually squashed and(ii)oriented in a certain direction;(iii)the damage initiates in the later deformation stage,which will be discussed in the next section.To more intuitively and quantitatively describe structural evolution,a large number of scans were carried out on each group of samples with different strains.The detailed structural parameters of the soft phase at different strains,e.g.,aspect ratio(λ)and angle of arrangement(θ),were obtained by statistical analysis.

Fig.1.The microstructure of heterogeneous Mg matrix nanocomposite:(a)BSE-SEM image taken along the SD;(b)TEM image and corresponding selected area electron diffraction(SAED)patterns;the distribution of(c)size,(d)aspect ratio(λ)and(e)arrangement angle(θ)of the soft phase;(f)the schematic diagram of the arrangement angle.

Fig.2.Compressive behaviors of Hetero-Mg-NC,pure Mg and Homo-Mg-NC:(a)Compressive true stress-strain curves and(b)strain-hardening rate vs.true strain.The inset figur in(a)shows the specimens before and after compression test,and the discontinuous main crack on the failure specimen was marked by the red-colored line for clarity.(For interpretation of the references to colour in this figur legend,the reader is referred to the web version of this article.)

Fig.3.The internal microstructure of Hetero-Mg-NC at different macro strains:(a)0.3%;(b)10%;(c)16%;(d)22%;(e)30%;and(f)35%.The loading direction is indicated by the white arrow.

Fig.4.The distribution of aspect ratio(λ)of the soft phase at various strains:0.3%,10%,16%,22%,30% and 35%.The mean value ofλand standard deviation are also included.

Fig.4 displays the aspect ratio(λ)distribution of the soft phase under different strains(0.3-35%)to reveal the shape evolution.Compared with the initial(undeformed)state(Fig.1d),the proportion of the largeλincreases with increasing macro strain and the distribution range ofλis gradually broadened from 1-9 to 1-16.The mean values are used to evaluate the fla y degree of the soft phase at each state.As mentioned above,the mean value ofλof the initial structure is about 3.52.However,after a low compressive strain of 0.3%,theλdramatically increases to 4.13(Fig.4a).Although the specimen is in the macroscopic elastic stage,its mean aspect ratio of soft phase shows an increase of ?17% over the undeformed status.It can be seen that the soft phase has suffered a large plastic deformation even at the very early deformation stage.Then,λcontinues to increase and reaches 5.73 at the strain of 35%,which is 66.6% higher than the initialλ.One can remark that the shape of the soft phase became more fla during compression.

The histograms of the arrangement angle(θ)distribution at different strains are shown in Fig.5.Similarly,the mean angle at each state was calculated to represent the arrangement of the soft phase.In the undeformed sample(Fig.1e),the mean value ofθis found to be 0°,which indicates that the long-axis direction of the soft phase is approximately perpendicular to the loading direction.When the samples are strained to 0.3%,10%,16% and 22%,the mean values ofθare found to be 0°,-0.2°,-0.3° and-0.7°,respectively,showing a slight change.Herein,the negative sign indicates that the long-axis of the soft phase rotates clockwise,as schematically illustrate in Fig.1f.Nevertheless,when the sample continues to deform to 30% strain,a sharp transition of the arrangement angle is observed that its mean value shows an increase of 157.1% compared to that at the previous state(ε=22%).Then,the mean value ofθkeeps growing and reaches-5.7° at the strain of 35%.However,unlike the aspect ratio,the angle distribution of the soft phase becomes narrow and concentrated with the increase of strain.The results indicate that the soft phase was tilting along a certain direction during deformation.

3.3.2.Damage evolution

The aforementioned results(Fig.3)demonstrate that the structural evolution of the soft phase is also accompanied by the initiation and evolution of damage.Fig.6 shows the highmagnificatio SEM images of the samples at the applied strain of 0.3% and 10%.One should note that the microcracks were not observed in the sample with a strain of 0.3%(Fig.6a).When the strain is increased to 10%,the inner section is still free of cracks except for the slight structural changes,as illustrated in Fig.6b.This indicates that the heterogeneous Mg matrix composite experienced a nondestructive elastic-plastic deformation at least until the macro strain reached 10%.

Referring to the stress-strain curve(Fig.2a),the sample entered a stable strain-hardening stage after the elastic stage.Until the strain reached?16%,the strain hardening terminated.Hence,further observations are focused on the microstructure of the sample with a critical strain of 16%,as show in Fig.7a and b.Obviously,several minor cracks appeares inside the sample,which are marked by the dotted circles.In the current state,the cracks,with a length of about 1.2μm,are mainly distributed at the interface between the soft and hard phases.With careful observation(Fig.7b),the microcracks preferred to initiate at the end of long-axis of the soft phase due to stress concentration[33].Fig.7c and d display the microstructure of the sample under the strain of 22%,showing a larger number of cracks compared to the previous status(ε=16%).The newly generated cracks are found at the interface but also within the soft and hard phases(Fig.7d).Interestingly,despite an obvious increase in crack concentration,the crack size remains almost the same and the crack length ranges from 2 to 4μm.Thus,it can be seen that the cracks tend to dispersedly initiate within the material instead of forming a large crack during this stage.

Fig.5.The distribution of arrangement angle(θ)of the soft phase at various strains:0.3%,10%,16%,22%,30% and 35%.The mean value ofθand standard deviation are also included.

Fig.6.The high-magnificatio SEM images of the samples compressed to the strain of(a)0.3% and(b)10%.These SEM images can confir the absence of crack.

However,the status of cracks changed when the strain is increased to 30%.As shown in Fig.8a,several large cracks were formed and arranged along a particular angle.The high-magnificatio SEM images of Region-A,-B and-C,as marked in Fig.8a,show some interesting features.First,the large cracks exhibit a wing-like shape(Fig.8b),which implies that the cracks propagate towards two sides after nucleation and their further propagation seem to be well inhibited.The average size of large crack is calculated to be?10μm,which is around ten times larger than the initial crack size at the strain of 16%.More remarkably,these large cracks exhibit a specifi arrangement direction which is consistent with the direction of maximum shear stress(Fig.8c).Furthermore,a large number of dispersed microcracks are observed in Region-C far away from the large cracks(Fig.8d),and their sizes are similar to those of the cracks formed under the macro-strain of 16%.It is noteworthy that the direction of these small cracks is disordered and random,which is in sharp contrast to the alignment of large cracks.

The applied strain is further increased to 35% and the corresponding cross-sectional SEM images are shown in Fig.9.It can be seen from Fig.9a that a major crack at an angle of approximately 52° with respect to the loading direction was developing.In current case,the crack length can be up to 200μm which has increased markedly compared with the previous state(ε=30%).The high-magnificatio observations were then performed to reveal more detail.The firs attention was paid to the region marked in Fig.9a,where a distinct shear deformation band was observed(Fig.9b).Also,the soft phase within and around the band readjusted its orientation as possible as parallel to the direction of maximum shear stress,which implies the occurrence of localized shear deformation.Another point of concern is the crack propagation and coalescence,as illustrated in Fig.9c.Herein,the small-scale bridging,deflectio and branching of cracks were revealed.The crack bypassed a few soft and hard phases and demonstrated a tortuous path in a wave-like pattern.In general,these features play a key role in toughening composite and provide strong evidence to explain the excellent malleability of the heterogeneous composites.

Fig.7.The damage characterization of the samples at the strain of(a,b)16% and(c,d)22%.The yellow dotted circles in(a)and(c)mark the positions of microcracks.(b)A microcrack initiates at the interface between the soft and hard phases when the applied strain reaches 16%;(d)the microcracks generate within the soft and hard phases when the strain reaches 22%.(For interpretation of the references to colour in this figur legend,the reader is referred to the web version of this article.)

4.Discussion

4.1.Coordinated deformation of heterogeneous Mg matrix nanocomposites

The results described in previous sections demonstrate the changes in heterogeneous structure under different strains,i.e.,variation in aspect ratio,arrangement angle of the soft phase,and damage evolution.To further describe the variation of these parameters with respect to strain during the whole compressive process,these scattered data points are fitte with curves,respectively.The corresponding fittin curves are summarized in Fig.10.According to the transition points of the stress,i.e.,the yield point and peak-stress point,the entire process can be generally divided into three stages:elastic stage(StageⅠ),hardening stage(StageⅡ)and softening stage(StageⅢ).Clearly,these parameters present different evolution laws with increasing strain and play a key role in determining different stages.

During the elastic stage,the aspect ratio of soft phase exhibits a steep increase,whereas the arrangement angle almost remains unchanged and no cracks are observed.As is seen,the flattenin of the soft phase is dominant rather than the tilting.It is noteworthy that the current microstructure has undergone irreversible changes,which indicates that the soft phase has partially suffered premature plastic deformation.Considering that the soft phase is arranged approximately perpendicular to the loading direction,it is reasonable to use the variation of short-axis length to evaluate the plastic strain of the soft phase along the loading direction.Hence,the average plastic strainˉε(i)of the soft phase can be calculated by applying the following equation:ˉε(i)=(si-s0)/s0,whereirepresents the macro strain at different stages(i=0 represents the initial state)andsidenotes the mean value of short-axis length of the soft phase at the strain ofi.As shown in Fig.11,at the macro strain of 0.3%,the average plastic strain of the soft phase is up to 3%,verifying that a higher strain is primarily localized within the soft phase.

Fig.8.The damage characterization of the sample compressed to the strain of 30%:(a)A low-magnificatio SEM image;(b-d)The corresponding highmagnificatio observations of Region-A,-B,and-C,as marked in(a).

Actually,the occurrence of localized plastic deformation during the macro elastic stage is commonly observed in heterogeneous materials due to the difference in mechanical properties of constituents[34].In the Hetero-Mg-NC,the soft phase is pure Mg with coarse grains and the hard phase is SiC nanoparticles reinforced Mg matrix composite(Fig.1b).The difference in yield strength between the soft and hard phases is noticeable.Reasonably,the yield strengths of the soft and hard phases can be estimated using the measured values of pure Mg(76 MPa)and homogeneous composite(406 MPa),respectively.When the applied strain is 0.3%,the transient stress extracted from the stress-strain reaches up to?176 MPa,which is lower than the yield strength of the hard phase but much higher than that of the pure Mg(soft phase).Hence,the soft phase is likely to experience plastic deformation even in the early stage of deformation.Moreover,since the grain size in the soft phase is larger than that in the hard phase(Fig.1b),there is a lower density of obstacles to suppress the dislocation movement.Thus,the dislocations can easily glide and,macroscopically,result in a conspicuous change in the shape of the soft phase.

Fig.9.The damage characterization of the sample compressed to the strain of 35%:(a)A low-magnificatio SEM image:(b)the high-magnificatio observation of a region near the crack tip,showing an obvious shear deformation band;and(c)a closer observation to the propagating cracks.

However,the shape of soft phase cannot keep changing rapidly due to the constraint of the surrounding hard phase and,obviously,its variation slows down in the subsequent deformation process.Specificall,the aspect ratio of the soft phase exhibited a slight increase during Stage II,whereas the arrangement angle and damage remained unchanged.It can be seen that the flattenin of soft phase still plays the dominant role in Stage II.Correspondingly,the average plastic strain of the soft phase at various macro strains was calculated.For instance,at the macro strain of 10%,theis found to be 14%.In order to reveal the degree of strain localization,we introduce the relative differenceas an indicator to evaluate the gap between average strainof the soft phase and macro strainε(i),which is shown by the orange-colored curve in Fig.11.Compared with the value of macro strain at 0.3%,the gapΔ(10%)is significantl reduced,which implies that the deformation of the soft phase is inhibited to a certain extent.The underlying reasons for this may be explained by the following possible points.

Fig.11.Quantitative analysis of the plastic deformation of the soft phase based on the variation in short-axis length with increasing strain,where the curve with circle represents the average plastic strainˉε(i)of the soft phase with increasing strains and the curve with square represents the relative differenceΔbetween the average strainˉε(i)of the soft phase and macro strain ε(i).

Fig.10.The variation in(a)aspect ratio(λ)and arrangement angle(θ)of the soft phase as well as(b)crack length with increasing strains.The schematic illustrations in the upper and right corners of(a)represent flattenin and tilting of the soft phase,respectively.

On the one hand,the soft phase becomes stronger and its ability to resist deformation is improved with increasing strain.As mentioned above,a noticeable strain partitioning exists between the soft and hard phases,where the soft phase accommodates more strain due to its lower yield strength.To coordinate the deformation of the hard phase,a plastic strain gradient in the soft phase near the interface builds up so that the induced back-stress strengthening makes the soft phase stronger,as reported elsewhere[34-36].Besides,the deformation resistance of the soft phase during deformation can be further enhanced owing to the interaction and entanglement of geometrically necessary dislocations and movable dislocations.On the other hand,the hard phase begins to yield at this stage,which leads to a gradual shift of strain partitioning from the soft phase to the hard phase[25].The plastic deformation of hard phase,to a certain extent,relieves the drastic deformation of soft phase.

Although the aforementioned factors effectively retard the shape change of the soft phase and even reduce the deformation incompatibility between the soft and hard phases to a certain extent,the incompatibility cannot be completely eliminated due to the inherent mechanical differences between two phases.As the applied strain continues to increase,the incompatibility is gradually aggravated and leads to the accumulation of the local shear stress.Hence,under the action of shear stress,the soft phase continues to deform and macroscopically begins to present the change in arrangement angle(StageⅢ).In particular,the arrangement angle varies exponentially during the later deformation stage,making the tilting of the soft phase dominant instead.It is worth noting that the shape changes of the soft phase caused by the local plastic deformation in the firs two stages mainly manifest in the flattenin rather than the tilting of soft phase,and,however,this transformation in StageⅢcan be ascribed to the formation and evolution of the local shear band.As shown in Figs.8 and 9,the soft phase exhibits an obvious rotation compared with the initial state,especially those of which within and near the shear band readjust their orientation as much as possible to parallel to the shear direction.

Apart from the above discussion about the underlying reasons behind the structural evolution of the soft phase,there are some findings First,the flattenin of the soft phase widely occurs in the whole sample,which implies that the Hetero-Mg-NC undergoes an extensive plastic deformation due to the presence of dispersed soft phase[37].The dispersed soft phase,acting as a deformation-prone region,affects the stress/strain distribution during deformation and plays a critical role in dispersing stress concentration and inhibiting strain localization[38].With increasing strains,the plastic deformation of soft phase can release the stress and further suppress the degree of strain localization,leading to a sustainable strain hardening,as shown in Fig.2b.After a long strain-hardening stage,the Hetero-Mg-NC enters a stable strain-softening stage and,subsequently,the tilting of soft phase becomes apparent.Herein,the tilting of soft phase reflect the development of the shear band.The progressive evolution of the arrangement angle of the soft phase,as illustrated in Fig.10a,demonstrates the stable development of the shear band,which facilitates in retaining the ductility of Hetero-Mg-NC[39].

4.2.Initiation and evolution of cracks in heterogeneous Mg matrix nanocomposite

With the increase of applied strain,the occurrence of internal damage is an inevitable result.Based on the previous observations(Fig.7a),the damage,i.e.,appearance of microcracks,was firs detected when the strain reaches?16%.Then,accompanied by the shape change of soft phase,the damage accumulated and evolved progressively(Figs.7-9),which eventually led to the failure of composite.

The formation of cracks,which can directly affect the damage behavior of the material,is a primary issue in discussing the failure of the novel heterogeneous composites.As is well-known,crack nucleation is closely related to the local stress state,and voids/cracks tend to form at the place where the local stress exceeds the maximum load-bearing strength[40].Herein,the deformation of heterogneous composite is always non-uniform at microscopic scale owing to obvious differences in mechanical properties of various phases,making it possible for the voids to nucleate in multiple locations,as illustrated in Fig.12a.Due to the significan mechanical incompatibility between soft and hard phases,their interface is a preferred site of stress concentration[41].As confirme by the substantial SEM results,the majority of voids and microcracks are indeed distributed at the interface between the soft and hard phases,a small portion of them appearing inside the phases.

After the void nucleation occurring at the interface,there is an intriguing findin that these voids did not grow into a large crack at once,but instead held at a relatively stable size.As illustrated in Fig.10b,the crack length within the strain of 16-25%increased from 1.2μm to 2.1μm,showing a rather slow growth rate.The dimensional stability of the cracks during this stage can be attributed to the initial small size of cracks as well as the loading constraints on cracks.It is known that the crack-induced stress concentration is directly related to the crack size[42].Herein,the crack-induced local stress concentration is comparatively small due to the thumbnail size of the incipient cracks during deformation,which does not exceed the ultimate strength of the local region.Hence,rapid crack growth was not observed.Additionally,under external compressive loading,the crack-perpendicular compressive stress can cause crack closure and further hinder crack growth[43].On the other hand,there is a plastic zone in the vicinity of the crack tip.In the case of interfacial cracks,the soft phase effectively relieves the nearby stress concentration through plastic deformation so as to further suppress the growth of cracks,which can also be confirme strongly by the obvious flatten ing and tilting of the soft phase,as shown in Figs.4 and 5.

Accompanied by the pinning of initial cracks,crack multiplication occurred(Fig.12b).To be specific some new cracks continuously initiated at other locations and the number of cracks gradually increased with increasing strains(Fig.7).Instead of highly concentrating in a narrow region nearby the early cracks,these newly-formed tiny cracks exhibited a diffused distribution,which is different from the manifestation of crack multiplication at the front edge of the cracks in other cases[22].In general,the renucleating cracks are roughly located around the crack tip due to the strong stress concentration.However,benefitin from the small size of cracks and excellent load-induced constraint,the crack-induced stress concentration seems less obvious in our Hetero-Mg-NC.The relatively small disturbance of a local stress fiel by crack-induced stress facilitates the undamaged part continue undertaking the plastic deformation.Therefore,with increasing strain,the new cracks sequentially initiate at those sites where the excess of stress level cannot be fully accommodated by local plastic strain,which is similar to the situation in the initial crack-free specimen.

Fig.12.The crack evolution diagram of the Hetero-Mg-NC under compression.(a)Microcracks nucleate at multiple locations.(b)Crack multiplication occurs without an obvious increase in crack size.(c)Accompanied with the formation of shear band,cracks within the band are deformed and elongated along the shear axis.(d)Crack propagation and coalescence result in a tortuous crack path.

As crack multiplication proceeded,there was a noticeable transition from the diffused damage to the localized damage.As shown in Fig.8,the cracks in Region-A exhibited larger dimensions and inclined at an angle of about 45° to the compressive axis,which significantl contrasts with the small size and random arrangement of the cracks in Region-C.The emergence of these discrepancies between different regions can be associated with the formation of the shear band.When a shear band forms,the strain localization occurs within the band and,in turn,the cracks within the band are deformed and elongated along the shear axis under the action of shear stress,as illustrated in Fig.12c.However,the plastic deformation and crack growth in the regions far away from the shear band are gradually reduced due to the aggravation of strain localization within the intense shear band.Hence,the subsequent deformation behavior and crack evolution within the shear zone directly determine the fina failure of the material.It is worth noting that the additional cracks will generate within the shear band due to mechanical incompatibility between the soft and hard phases.With the increase of crack size and density,the interaction between cracks intensifie and then triggers the propagation and coalescence of cracks.

The crack propagation is a rather complicated process,which needs to be discussed.First,with respect to a single crack in the present case,the propagation path is not straight forward but tortuous on a local scale(Fig.12d),which can be attributed to the crack itself propagation mode and the surrounding heterogeneous structure.Under far-fiel compressive loading,the crack generally propagates in a mixed propagation mode,i.e.,the combination of tensile stress-induced crack opening and shear stress-induced crack sliding.Consequently,under the action of tensile stress and shear stress at the crack tip,the crack propagation direction deviates from the initial crack direction,showing a wing-like pattern[44].In general,the wing-like crack is often observed in brittle materials[45]and seldom mentioned in ductile materials since crack propagation in ductile materials is accompanied by crack blunting,which hides the trail of wing-like crack.However,for our studied heterogeneous composite which consists of the hard(brittle)and soft(ductile)phases,the wing-like propagation path of the crack in hard phase can be readily observed(Fig.9c).In addition,the effect of heterogeneous structure is also quite significant As the soft phase is the“weak”region compared to the hard phase,the cracks are easily attracted or captured by the dispersed soft phase in front of the crack tip[22].When a crack propagates to the soft phase,according to the maximum strain energy release rate criterion[46],the crack preferentially bypasses the soft phase and propagates along the interface because of the higher strain localization at the interface.Only when the crack propagation along the interface is hindered,e.g.,the angle between crack direction and interface is large,the crack will propagate into the neighboring soft phase[47].Hence,the series of direction selection makes the crack propagation path rugged.

Meanwhile,crack propagation occurs in multiple cracks,which reduces the crack spacing.When the spacing is reduced to a certain extent,the strong strain localization between two cracks eventually causes crack coalescence and forms a main crack.It should be noted that,even though the above-mentioned factors induce the cracks to propagate and coalesce in a tortuous path,the main trend is still dominated by the maximum shear stress.Overall,the crack propagationcoalescence path is roughly along the direction of maximum shear stress(Fig.9a),revealing the ultimate shear failure.

4.3.Contribution of heterogeneous structure to malleability

The heterogeneous Mg matrix nanocomposite studied here exhibited superior compressive performance to pure Mg and its homogeneous counterpart(Fig.2),particularly showing the excellent malleability.Based on microstructural evolution and damage analysis,it is considered that the excellent malleability mainly derives from the extensive plastic deformation and remarkable crack tolerance.

From the compressive testing results,the Hetero-Mg-NC exhibits a sustainable strain hardening and its plastic strain is up to?16%.However,the single hard phase,i.e.,the homogeneous Mg matrix composite with the same content of nanoparticles,shows a high strength but with a limited plastic strain(?3%)after yielding.The brittle-like performance of Homo-Mg-NC can be ascribed to the extreme stress concentration and severe strain localization.If there is no other effective way to release stress concentration,the strain is localized in a small region and the cracking occurs at relatively lower strains.In contrast,the introduction of the soft phase can adjust stress distribution and disperse stress concentration[18],thereby inhibiting strain localization and retarding the occurrence of cracking,which is indirectly demonstrated by extensive plastic deformation of soft phase(Fig.10).Moreover,the dispersed soft phase within the hard matrix may also improve the overall malleability.In the Hetero-Mg-NC,the soft phase suffers complex multiaxial stress transferred from the neighboring hard phase.The presence of complex stress may contribute to activate additional slip and twinning systems[11],facilitating the plastic deformation of soft phase in the hetero-Mg-NC.As evidenced in Fig.11,the average strain of the soft phase at the end of strain-hardening stage reaches?21%,which is significantl higher than the plastic strain of pure Mg(?14%).However,further research is required to fully understand the effect of such a heterogeneous structure on the deformation modes of Mg.

After exceeding the strain-hardening limit,the Hetero-Mg-NC underwent a progressive strain softening and eventually failed at the strain of?45%,which is in sharp contrast to the catastrophic failure of the Homo-Mg-NC.Based on the previous research[5],the Homo-Mg-NC was prone to failure by splitting under compression,and its off-axis main crack was the result of unstable propagation of the airfoil crack.Despite the presence of secondary cracks,the Homo-Mg-NC essentially lacks the ability to restrain crack growth.Once a crack is formed,the driving force for crack growth is always larger than the crack growth resistance.Meanwhile,the strong stress concentration induces crack growth and finall leads to a rapid fracture.However,in the case of Hetero-Mg-NC,the situation is obviously different.The inspection of the internal section of deformed samples under different strains revealed the stable crack multiplication process,where the crack size remains the same but the crack density increases with increasing strain.Overall,the Hetero-Mg-NC demonstrated an outstanding crack tolerance.When the damage accumulated to a certain extent,the shear band formed which caused the cracks located within the band to propagate and coalesce.As discussed in Section 4.2,the tortuous crack propagationcoalescence path reveals the occurrence of local crack deflection which is considered to be an extrinsic toughening mechanism in heterogeneous materials.In consideration of the aforementioned mechanisms,the Hetero-Mg-NC continued to withstand up to the strain of?30%before failure since the initial damage was firs observed at the macro strain of?16%.

5.Conclusions

The heterogeneous Mg matrix nanocomposite(Hetero-Mg-NC)exhibited superior malleability to pure Mg and corresponding homogeneous Mg matrix nanocomposite(Homo-Mg-NC).The deformation,damage,and fracture behavior of the Hetero-Mg-NC was investigated using microstructural observation and semi-quantitative analysis to understand the physical origin of the improved performance.Compared with the Homo-Mg-NC,the excellent malleability of the Hetero-Mg-NC under compression mainly derived from the extensive plastic deformation and remarkable crack tolerance.The following conclusions can be drawn from the current results:

1.The soft phase in Hetero-Mg-NC undertook a severe plastic deformation during the whole deformation process,as indicated by the flattenin and subsequent tilting of the soft phase along the shear axis.

2.The large plastic deformation of the soft phase inhibited strain localization within the hard phase and at the interface,delaying the formation of cracks and leading to a sustainable strain hardening.

3.Benefitin from the small size of initiated cracks and excellent loading constraints,a stable crack multiplication process occurred in the Hetero-Mg-NC,achieving a high damage tolerance under compression.

4.The tortuous crack propagation-coalescence path was observed due to the mixed crack propagation mode and the presence of soft phase,which contributed to the excellent malleability of Hetero-Mg-NC.

Conflic of interest

The authors declare no conflict of interest.

Acknowledgments

This work was financiall supported by the National Natural Science Foundation of China(Grant No.51871187),Department of Science and Technology of Sichuan Province(Grant No.2020YFG0140),and Fundamental Research Funds for the Central Universities(Grant No.2682019LK04).

Supplementary materials

Supplementary material associated with this article can be found,in the online version,at doi:10.1016/j.jma.2021.04.008.