In-situ analysis of slip transfer and heterogeneous deformation in tension of Mg-5.4Gd-1.8Y-1.5Zn alloy

Shaosong Jiang,Yong Jia,Xiaojun Wang

School of Materials Science and Engineering,Harbin Institute of Technology,Harbin,150001,China

Received 25 July 2019;received in revised form 27 November 2019;accepted 13 January 2020 Available online 2 June 2020

Abstract Slip transfer is influential in determining damage nucleation of polycrystalline material.The interactions between dislocations and grain boundaries(GBs)was investigated using in-situ tension test in a multi-directionally forged Mg-5.4Gd-1.8Y-1.5Zn(wt%)alloy.It was found that strain accommodation of individual grains by means of slip occurred more easily than slip transfer when several slip systems were operable.The basal-basal slip transfer occurred when the GB misorientation was smaller than 34.2°,whereas basal-pyramidal type took place when the crystallographic misorientation was larger than 48.8°.The product of Luster-Morris mfactor and the sum of the Schmid factors of the two correlated slip systems indicated that the threshold for basal-basal slip transfer may exist,however,basal-pyramidal slip transfer shows no such threshold and is more complicated.These results presented here demonstrated that besides the geometrical alignment,the deformation details(such as the number of operable slip systems)and stress state in each individual grain must be considered.

Keywords:Slip transfer;Mg-RE alloy;Heterogeneous deformation;In-situ tensile test.

1.Introduction

Heterogeneous deformation of polycrystals has been an intense field of research[1,2].During deformation,the mechanical integrity and continuity of GBs are maintained,and abundant studies have proven that GBs act as effective barriers for dislocation motion[3-7].It is also possible that plastic deformation takes place across GBs through the traverse of dislocations[1,8-11].High-angle or low-angle GBs,which facilitates or hinders the mobility of dislocations,will determine the mechanical behavior of polycrystalline metals[12,13].The strain field,accommodated by the GBs,will influence the boundary energy and,consequently,cohesion and nucleation of the crack[8,14-16].Thus,a thorough understanding of the localized deformation at or near GBs will be necessary to establish an accurate model capable of predicting the damage nucleation.

Full-field homogenization in crystal plasticity modeling,using crystal plasticity finite element method(CPFEM)or spectral methods by fast Fourier transformation(FFT),has the potential to accurately predict the mechanical properties of polycrystalline metals[17,18].The principal advantage of CPFEM or spectral solver would be their great flexibility to handle the complicated internal and/or external boundary condition.However,simulations generally show partial agreements with experimental measures and exhibit rather shaper orientation gradients near GBs[19-21].This is because one consequence of the crystalline anisotropy is the spatially heterogeneous boundary conditions,resulting from stress or strain concentrations that normally precedes the onset of fracture.Dislocation pile-ups and geometrically necessary dislocations at GBs,which accommodates the strain gradients,is generally ignored in crystal plasticity modeling.Therefore,to predict effective materials properties,strain field interactions between dislocations and GBs must be quantitatively understood and imported into the crystal plasticity modeling.

Fig.1.Geometric relationship between the incoming slip system and outgoing slip system across GBs for a bicrystal

To introduce the grain boundaries properties into the mesoscale model,a clear understanding of the details of the microstructural hierarchy and stress state near GBs is necessary.Slip transfer process across GBs has a double-sided effect on mechanical properties as this phenomenon promotes or prevents crack initiation.M.Jiménez et al.[22]found that the short cracks propagated along the easy slip transfer path across the GBs in Ni-based superalloys.Britton et al.[11]measured the stress field at the head of the blocked slip band using high-angular resolution electron backscatter diffraction(HREBSD)and found that blocked slip bands with or without stress concentration are instructive for studying fracture initiation and propagation mechanism.Wang et al.[23]reported that slip transfer enables mechanical twinning to occur in an adjacent grain despite the fact that the twins have a very low Schmid factor relative to the global(uniaxial tensile)stress tensor in commercial purity titanium.

In the past research,multiple criteria have been proposed to assess the ease of slip transfer in polycrystalline metals,including geometric parameter and stress criteria.The geometric relationship of the slip transfer is indicated in Fig.1.Themparameter,from Luster and Morris[24],considers the coplanarity of incoming and outgoing slip system and is promising to predict the slip transfer:

whereψrepresents the angle between a pair of slip planes normal andκis the angle between the incoming and outgoing slip directions.Themfactor lies in the range of 0～1,where 1 means that dislocations could traverse GBs without resistance and 0 represents GB is impenetrable.Nonetheless,in-situstraining and diffraction-contrast electron tomography in TEM experiments show that the interactions between lattice dislocations and GBs have a rather complicated process and that the emitted slip system is governed by the magnitude of the residual boundary dislocation[25].Atomic and molecular dynamics simulations demonstrate that many other factors,such as local resolved stress,boundary structures,and the boundary strain energy density,also determine the slip transmission process[26-28].

While most of the studies focus on the nucleation of dislocation at the head of blocked dislocations,there is very limited work investigating the threshold criterion for slip transmission.Hémery et al.[29]researched slip transfer between primaryαnodules in Ti-6Al-4V and confirmed thatmparameter is a convincing indicator of the probability of slip transfer.Bieler et al.[30]investigated the slip transfer cases within near-cube oriented grains in pure Al and found that,besides the geometric alignments between slip systems,the deformation details in each grain also play an important role.The purpose of this work is to extract the threshold for slip transfer and analyze the heterogeneous deformation near GBs in a Mg-5.4Gd-1.8Y-1.5Zn alloy.Such work would contribute to crystal plasticity modeling used to address the deformation kinematics.

2.Experimental procedure

The as-cast magnesium alloy with a nominal composition of 5.4 wt% Gd,1.8 wt% Y,and 1.5 wt% Zn was provided from Shenyang Institute of Metal Research with coarse grain diameter about 220μm.To refine the grain size,the alloy was forged.Before forging the ingots were homogenized at 500°C for 12 h followed by rapid cooling in the water.As general hot-deformation process,like rolling and extrusion,produces strong basal texture and the multi-directional forging results in weak texture,the alloy was multi-directionally forged at 450°C by six passes.Thus,the effect of the texture on the initiation of the slip systems is excluded from the alloy.After forging,the wrought alloy was heated up to 210°C for 24 h to achieve peak aging.

The dog-bone tensile specimens having a thickness of 0.8 mm,gauge width of 1.8 mm,and gauge length of 7 mm,were cut from the aged alloy by electrical discharge machining.Specimens surface were ground using silicon carbide paper with various grit sizes and then polished using colloidal silica suspension.To obtain a stress-free surface for electron backscatter diffraction(EBSD)characterization,the specimen surface was electro-polished at a voltage of 10 V and the temperature of-20 °C using an electrolyte solution of 10 vol.%perchloric acid with 90 vol.% alcohol for 100 s.The grain orientation of the tensile specimen was measured using EBSD before and afterin-situtension in a field-emission gun scanning electron microscope(FEG-SEM),a Nova NanoSEM 430 instrument(FEI Company,Hillsboro,OR),equipped with a Nordlys EBSD detector(Oxford Instruments,Abingdon,Oxfordshire).Images were made using an acceleration voltage of 20 kV and a current of 6.1 nA.Automated beam scanning on the sample surface covered an area of 0.8 mm2with a step size between points of 0.9μm.Afterin-situtension,the number of nonindexed or incorrectly indexed electron backscatter patterns(EBSPs)increased,and therefore a medium level of zero-solution extrapolation was performed by Channel 5 software.

Table 1Possible slip systems for the alloy;the same coloring scheme represents the same family of crystallographic planes and is used throughout this study.

A tension test was carried out at room temperature within the NanoSEM 430 instrument chamber,using a voltage of 10 kV,which is sensitive to surface topography.The dog-bone specimen was stressed at a strain rate of 1×10?3s?1and was mounted horizontally on the 2 kN tensile stage(Deben,London,UK)driven by a dual threaded leadscrew to allow real-time observation of the gauge section.The displacement was stopped at different strains up to 22% to monitor slip bands.

The crystallographic orientation data was imported into a MATLAB toolbox[31]to calculate slip lines on the sample surface and themfactor from Luster-Morris.The MATLAB toolbox also plots pairs of cell lattice orientations with highmvalues around GBs,corresponding to the appropriate slip system and slip traces.The computed slip traces,according to the cross product of slip plane normal and sample surface normal(i.e.T=nsp×e,whereTis the slip bands vector,nsprepresents the slip plane normal vector in sample coordinate system,andeis[001]),is compared to the SEM micrograph of slip lines.Theoretical slip lines that deviate from experimental observation by more than 5° are not considered in the following analysis.The possible slip systems initiated during tension are listed in Table 1 and are colored according to three different hexagonal close-packed(HCP)slip planes.The basal,prismatic,and pyramidal slip traces are colored blue,red,and gold respectively throughout this study.

3.Results

3.1.Microstructure evolution

The inverse pole figures(IPFs)in the tensile direction(X direction)and the corresponding pole figures(PFs)of the sample at the same area before tension and after～22% strain are shown in Fig.2.The arrow indicates the same grain in Fig.2a and Fig.2c.It should be mentioned that the rumpled surface after straining affects the EBSP data acquisition,but does not influence the precision of the orientation data.The constituent grains in Fig.2a have a wide distribution of sizes,from 10μm to 100μm.The orientation of each grain is displayed in different colors in IPFs,and as shown in Fig.2c,the fraction of<10-10>fiber texture colored in blue increases with strain.After straining,the grains have developed a sharper texture(as indicated by the circular inset in Fig.2d)where four prismatic plane poles are distinct in the deformed pole figure,indicating that prismatic slip has rotated the grains to this more stable orientation[32].In addition,there is an increase in the strength of the clustering of<0001>poles perpendicular to X-axis in Fig.2d(from 5.6 to 6.5 times random).The poles of the<0001>texture component in PF that are parallel to the X direction(tensile direction),which are illustrated by the square inset in Fig.2b,rotate nearly 90° toward the Y direction in Fig.2d,suggesting the formation of tensile twins(i.e.<-1011>{10-12}tensile twins rotate<2-1-10>axis by 86.2°).

3.2.Slip transfer analysis

3.2.1.Analysis strategy

The portion of the tensile specimen surface after straining is shown in Fig.3,and it appears that heterogeneous deformation occurs for most of the grains,as evidenced by welldefined boundary ledges and rough topography.Slip lines are visible on the sample surface and are kinked or curved due to the surface rumpling,which would influence the interpretation of slip traces.It seems that a single slip system dominates the deformation within each grain and the operated slip system number varies from grain to grain.

Since it is impossible to monitor the slip lines evolution in real-time within the SEM.The identification of the incoming or outgoing slip assumes that if the basal-basal slip transfer occurs,the one with the higher Schmid factor is identified as the incoming slip.If the basal-pyramidal slip occurs,the basal slip was considered as the incoming slip.This is because at room temperature the CRSS of basal slip is much smaller than the pyramidal slip with typical CRSSnon-basal/CRSSbasalratios ranging between 20 and 100.The evaluation of themfactor associated with the pair of slip systems at GB 1 is given using the method illustrated in Table 2.The coloring scheme of slip systems is identical to slip planes in Table 1.The slip that commenced on a specific slip system is determined by the critical resolved shear stress(CRSS)and the Schmid factor,and thus,the slip systems are ranked according to the Schmid factor in the table ofmfactor.It should be noted that as the local stress tensors may vary substantially from grain to grain,so the ranking of the Schmid factor is only approximate.The leftmost column of Table 2 notes the slip system number among all potential slip systems(3{0001},3{10-10},and 6{11-22})for grain 565,and the magnitude of the Schmid factor for these slip systems are arranged in decreasing order,which is listed in the second column.Similarly,the slip system number in the top row of Table 2 for grain 568 are sorted by corresponding Schmid factor.For a bicrystal,twelve slip systems within each grain results in a 12×12 array with 144mfactors,and eachmvalue involves the geometry of two slip systems.Slip systems with Schmid factor larger than 0.25 are considered in Table 2,which produces 24mvalues;mfactors associated with the observed basal and pyramidal slip systems in Fig.3a are shown in bold.

Fig.2.EBSD inverse pole figure(IPF)in the tensile direction for the tensile specimen(a)before straining and(c)after～22% strain.The corresponding pole figures of(b)undeformed and(d)strained sample are adjacent.The fraction of the<10-10>texture component colored in blue in Fig.2c increases with strain,indicating the occurrence of the prismatic slip.

Table 2mvalue related to the geometry of two slip systems at GB 1;the slip systems are ranked according to the Schmid factor.The mfactor associated with slip lines near GB 1 are highlighted in bold.

Table 2mvalue related to the geometry of two slip systems at GB 1;the slip systems are ranked according to the Schmid factor.The mfactor associated with slip lines near GB 1 are highlighted in bold.

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The magnitude of the Schmid factors for grain 568 ranges between 0.297 and 0.48,while grain 565 has only four slip systems with Schmid factor greater than 0.25.Although basal slip dominates the deformation at room temperature,nonbasal and cross-slip are also observed in polycrystalline magnesium alloys.Slip systems having lower Schmid factors are also possible when the CRSS reaches some critical value.One way of identifying a meaningfulmfactor is to check the upper left portion of Table 2,as this part constitutes slip systems interactions that are likely to act.This method developed by Bieler is useful in understanding the potential for slip transfer[30].

In the following analysis,strain field interactions between slip bands and GBs are categorized as follows:(a)slip transfer is not observed,where sharp topography develops at GBs region;(b)slip transfer does happen without ledges or with faint topography.

3.2.2.Slip transfer does not happen

As mentioned above,the surface topography of grain 565 and 568 are shown in the scanning electron micrograph of Fig.3a.Due to the curved topography,slip bands of grain 568 follows the“C-type”path,and the curvature of slip lines increases as the bands approach grain boundaries.By virtue of the orientation data,it can be known that for grain 568,the basal plane is nearly parallel to the tensile stress axis,and for this extreme orientation the slip deformation forms as steps on the sample surface.The basal plane of grain 565 is oriented nearly 45°to the applied stress direction,and,therefore,dense slip lines that are parallel to one another are observed.The slip trace calculations based upon the orientation data indicate that basal slip commences in grain 565,while slip operates on the pyramidal plane in grain 568.Slip lines on the sample surface are closely aligned with the computed slip traces,as illustrated in Fig.3a.In grain 565,slip occurs along<2-1-10>-type directions on the(0001)plane(slip system 1 or 2),as indicated by the blue dashed line;while the(2-1-12)[-2113]slip system,represented by the gold line in Fig.3,commences in grain 568(slip system 10).

Fig.3.(a)Surface topography of the tensile specimen after straining,where it appears that a single slip system is dominant for most of the grains.The operated slip systems in grain 565 and 568 are represented by the blue and gold lines;The number in the circle denotes the slip system in Table 1.(b)Visualization of the bold mvalue in Table 2 associated with the geometry of two slip systems in the hexagonal unit cell:the blue and gold lines represent the basal and pyramidal slip traces,respectively.Because of the distinct GB ledge,slip transfer across GB 1 is not observed.

The possible slip traversing parameters for grain 565 and 568 are listed in Table 2.The highestmfactor,0.91,accompanies with second highly stressed slip system in grain 565,but the other slip system(slip system 12 ranked 5th)is not observed in the SEM photograph for grain 568.The computed slip traces at boundary 1 result in themfactor of 0.7 or 0.81,which are associated with the geometry of two slip systems in the hexagonal unit cell as visualized in Fig.3b.Themvalues of 0.7 or 0.81,resulting from the most highly stressed slip system in grain 565(slip systems 2 and 1),correspond to slip system 10 in grain 568,which has the 3rdhighest value of the Schmid factor.However,the well-defined boundary ledge at boundary 1 indicates heterogeneous strain between grain 565 and 568,such that slip transfer seems unlikely.

As shown in Fig.4,it appears that dislocations traverse GB 2 during deformation;rather,the slip lines on either side of the GB 2 are misaligned with each other and the existence of a boundary ledge indicates heterogeneous strain between grain 456 and 457.Two sets of parallel yet intersecting sets of slip lines can be observed in grain 456;slip trace calculations based on orientation data predict that(-2112)[2-1-13]pyramidal slip and basal slip operate in these two grains,as indicated in Fig.4a.It is noteworthy that grain 456 is oriented in an unfavorably orientation-that is,the basal plane is parallel to the applied stress and in this condition,the Schmid factor of basal slip system approaches zero,as listed in the last row of Table 3.Still,slip occurs within{0001}plane,which means that stress tensors in the alloy are relatively complex(thus,as defined in section 3.2.1,the ranking of the Schmid factor is only approximate).In addition to the distinct boundary ledge,given that the poor geometric alignment between two operated slip system with themvalue of 0.6,slip transfer across boundary 2 is highly unlikely.

Table 3Schmid factor values for grain 456 and 457 and the mfactor for boundary 2.The mfactor 0.6,which is typeset in bold,corresponds to the operated slip system in grain 456 and 457.

Table 3Schmid factor values for grain 456 and 457 and the mfactor for boundary 2.The mfactor 0.6,which is typeset in bold,corresponds to the operated slip system in grain 456 and 457.

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Table 4mfactor between potential slip systems in grain 335 and 334 and corresponding Schmid factors.Two sets of operated slip systems produce mfactor 0.77 or 0.85.

Table 4mfactor between potential slip systems in grain 335 and 334 and corresponding Schmid factors.Two sets of operated slip systems produce mfactor 0.77 or 0.85.

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3.2.3.Slip transfer occurs convincingly

Fig.5 demonstrates that slip lines traverse boundary 3 with misorientation angle of 76° as the GB is not effective in prohibiting dislocation motion.The GB seems transparent,and in this case no boundary ledge forms,indicating homogeneous strain in both grains.It seems that slip lines in grain 335 could be from either the slip system 10 or 7;the upper right portion of slip bands is more consistent with the slip system 10,whereas the lower parts are nearly aligned with slip system 7.Also,the slip systems 10 and 7 in grain 335 have similarly high Schmid factors;however,the slip system 10 is highly misaligned with the initiated slip system 3 in grain 334(m=0.34),as underlined in Table 4.The computed slip system traces in grain 335 disagree with observations because the topography of the sample surface is sloped toward the lower left corner in Fig.5a,such that the inclined slip lines for slip system 7 in grain 335 look more like slip system 10.The geometrical configurations between observed slip systems 7 and 3 in grain 335 and 334 results inmfactor,0.77,which is shown in bold in Table 4,and both of the slip systems correspond to the highest Schmid factor.Considering the lower value of the Schmid factor for basal slip system 2,which has 7thhighest Schmid factor in grain 334,and complex stress tensors during tension,another m?factor,0.85,is also possible and is illustrated in Fig.5c.

Fig.4.(a)Scanning electron micrograph showing slip lines at boundary 2 with misorientation 68.2° between grain 456 and 457.It appears that slip transfer occurs at boundary 2,however distinct boundary ledge indicates heterogeneous deformation between two grains.(b)The slip trace calculations,in comparison to slip lines in Fig.4a,demonstrate that pyramidal and basal slip occur in two grains as indicated by the dashed lines,both of which correspond to highest Schmid factor.The poor alignment between two slip systems at boundary 2 and the boundary ledge show that slip transfer across boundary 2 is prohibited in this case.

Fig.5.(a)Scanning electron micrograph overlaid with IPF map shows continuous slip or dislocation motion through boundary 3 with misorientation 76°between grain 334 and 335.(b)The mfactor is obtained by geometrical relationships between observed slip systems at boundary 3 with values 0.77 or 0.85.

Slip transfer initiated from basal to basal plane in a bicrystal is also observed in this study,where the blue slip system 3 traverses the boundary 4 with themfactor of 0.99,as illustrated in Fig.6a.Grain 455 and 459 having an angle of misorientation 3.7°is oriented unfavorably,in which the basal plane is almost perpendicular to the applied stress direction,such that the CRSS has small value on{0001}plane.As shown in Fig.6b,the magnitude of the Schmid factor for the operated basal slip system in two grains has a lower ranking.Actually,slip on a pyramidal plane is most favorable relative to the tensile axis,but pyramidal slip system is not observed in these grains,illustrating the significance of different CRSS values for different slip systems.

Fig.6.(a)Scanning electron micrograph overlaid with IPF map showing slip transfer takes place at boundary 4 with misorientation 3.7°,in comparison with GB 3 illustrated above.(b)The basal slip system operates in grain 455 and 459,resulting in the mfactor of 0.99.

3.2.4.Statistics from 94 observations

As mentioned previously,slip transfer across GBs seems independent of the crystallographic misorientation.In this section,statistical results in conjunction with 94 grain boundaries are used to identify the relationships between the slip transfer events and geometrical configuration at the common boundary,as shown in Fig.7,where the relationships are plotted asmvalue versus grain boundary misorientation.Slip transfer from basal to prismatic plane is not observed in this study,and the observed slip transfer events from basal to basal and basal to pyramidal planes are represented by blue and gold triangles respectively.In addition,the maximummvalue in each case is displayed in solid squares in a similar way,indicating that the observed cases are sometimes different from the maximum m?value.The×symbols denote the cases when slip transfer is prohibited at the boundary,and the relevant maximummparameter is also noted in the figure.Statistical results in Fig.7 indicate that a highmvalue,larger than 0.9,is associated with low-angle grain boundaries(more specifically,the degree of misorientation<23.8°)and highangle grain boundaries with angles of misorientation greater than 48.8°-that is,themvalues follow the downward trend when the angle of GBs misorientation ranges between 6.5°and 48.8°.Several slip transfer parameters have values less than the maximummfactor.It can be clearly seen that slip transfer by basal to basal plane occurs when the grain boundary misorientation is smaller than 34.2°,and basal-pyramidal type takes place when the angle of misorientation is greater than 48.8°.It’s not clear why slip transfer is not observed when the geometrical relationships between incoming and outgoing slip systems have good coplanarity,but stress state adjacent to the boundary area certainly plays an important role in determining the slip transfer process.Furthermore,Fig.7 suggests that the threshold value of the slip transfer parameter,m,should larger than 0.77 in this alloy.

Fig.7.(a)Plot of factor versus grain boundary misorientation for the alloy.Basal to basal slip is observed when the GB misorientation is smaller than 34.2°,and basal-pyramidal type occurs when the angle of misorientation is larger than 48.8°.

3.3.Fracture mechanisms

Heterogeneous deformation of polycrystals not only varies from grain to grain,but significant orientation gradients arise within each grain,as demonstrated in Fig.8b.The higher degree of misorientation is seen in the brighter yellow color.The kernel average misorientation(KAM)map,which is a local misorientation map,indicates that a higher level of misorientation and therefore strain develops around GBs compared to the interior of grains.High strain or high misorientation are generally seen at grain triple junctions during tension.Heterogeneous deformation within grains is expected to induce localized stress concentrations and promote local cracking.As indicated in Fig.8a,a crack propagates along the GB,in which grain 76 and 92 are oriented in hard and soft orientations respectively.In fact,small cracks tend to form at some points with both hard and soft orientation more often than regions that are both hard[1,33],where the extent and magnitude of dislocation motion in two grains give rise to the incompatible shape change.

Fig.8.(a)Scanning electron micrograph showing crack propagation,in which a crack propagates between grain 76 and 92;(b)kernel average misorientation(KAM)map of grains analyzed in Fig.8a.The higher degree of misorientation and therefore strain is seen in the bright yellow.High strain or high misorientation are observed around the GBs and at grain triple junctions.

4.Discussion

Slip transfer in the rare earth magnesium alloy has been studied using anin-situtensile test.Basal to basal slip with the sametype Burgers vector is identified;whereas basal to pyramidal slip involvesand-type slip direction when the crystallographic misorientation is large.Previous work by Wang et al.[33]indicates that basal-prismatic slip transfer is mostly seen in an extruded Mg-10Gd-3Y-0.5Zr(wt.%)alloy with strong basal texture when the GBs have misorientation angles larger than 75°.In contrast to Wang’s work,observed slip transfer is most often basal-pyramidal type in this study when the angles of the GBs misorientation are greater than 48.8°.The maximum texture strength value of 5.6,relative to that from a random distribution in Fig.2b,indicates that the initial material has a weak texture.The difference in slip transfer type illustrates the significance of crystallographic orientation and texture on slip activity for these two alloys.

Since the slip system with higher Schmid factor is most likely to activate and therefore enables slip transfer.The effect of the Schmid factor is evaluated in Fig.9,which plots the product ofmfactor and the sum of the Schmid factors versus the angles of the GB misorientation.Considering the different CRSS for basal and pyramidal slip,slip transfer types of basal-basal and basal-pyramidal are displayed separately in Fig.9a and b.For the data points representing slip transfer cases,values ofmtimes the sum of the two Schmid factors,SF,are expected to concentrate in the upper region of the figure under the assumption of uniaxial stress state.However,there is significant variation and scatter in the calculated results.The dashed line in Fig.9a indicates that a threshold for basal to basal slip may exist,below which instances of no slip transfer are most often observed and the slip transfer events occasionally arise.Basal to pyramidal slip has a wide range of Schmid factors on slip systems as shown in Fig.9b,and significant scatter in the calculated results ofmtimesSF indicates a complex threshold criteria for basal to pyramidal slip.The reason for the considerable scatter in the calculated data points is probably because the local stress tensors differ from uniaxial tension,which affects the Schmid factors.

In agreement with previous studies,dislocations traversing GBs can take place in HCP polycrystals when pairs of slip systems have relatively high values ofmfactor.However,in spite of the fact that there is favorable geometrical continuity between slip systems from one grain into the other,instances of no slip transfer are increasingly observed when crystallographic misorientation larger than 6.3°,as shown in Fig.7.The slip transfer process is a function of the orientation of slip components upon which the stresses are taken to act.Coincident with the slip activity is the introduction of a complex stress state adjacent to the GBs.Crystal plasticity modeling provides that during deformation,the stress tensor within individual grain deviate from the uniaxial stress state[17],and this further affects the driving force for dislocation motion.The effect of the stress tensor,which can be predicted using CPFEM and/or measured by high angular resolution EBSD,needs to be examined in further work.

As indicated in Fig.10a,sometimes the continuity of slip lines on the sample surface are clear(i.e.slip bands intersect at the common point across GB),but the presence of boundary ledge indicates heterogeneous strain on either side.Fig.10a demonstrates that more than one slip system operates in grain 204:basal and pyramidal slip system are both active in this grain.Although there is a highmfactor(Fig.10b),the magnitude of lattice distortion from the primary slip system in grain 204 causes incompatible deformation among two grains,such that slip transfer enabling a homogeneous strain is not significant in this case.The aligned slip traces with the presence of boundary ledge is also reported in a near-cube oriented Aluminum alloy[30].Additionally,cross slip process by which screw dislocations move from(-2112)plane to(11-22)plane along the<2-1-13>type direction is observed in grain 204,and thus wavy slip lines are observed on grains surface.Investigations by transmission electron microscopy(TEM)reveal that the addition of rare earth element dramatically changes the slip activity in magnesium alloys[34,35].Cross-slip is often reported in FCC metals;for magnesium alloy density functional theory and first-principle calculations suggest that the stacking fault energies(SFEs)decrease with the addition of rare earth element,and the stacking fault acts as nucleation source fordislocation[36-38].Therefore,pyramidal slip can operate and cross slip would be possible in an HCP crystal structure.

Fig.9.The product of factor and the sum of the Schmid factors versus the angles of the GBs misorientation for(a)basal to basal slip and(b)basal to pyramidal slip respectively.The dashed line in Fig.9a suggests that the threshold criterion for basal to basal slip may exist.

Fig.10.(a)It appears that basal to pyramidal slip takes place from grain 201 to 204;however,the boundary opens apart,indicating heterogeneous strain on either side.Meanwhile,more than one slip system operates in grain 204 and cross-slip occurs from pyramidal type plane to another.(b)mvalue of 0.78 for the observed basal-pyramidal slip pair.

The strain state on the sample surface is analyzed based upon the crystallographic orientation data.As might be expected,poor alignment between slip systems across GBs may make dislocations traversing GBs more difficult during tension;rather the blocked dislocations introduce geometrically necessary dislocations(GNDs),which causes lattice distortion near GBs.Fig.11 gives an enlarged portion of strain maps on the deformed specimen surface,as indicated by the rectangle insets in Fig.2c.The local lattice curvature measured by a KAM map is used to examine the relationship with the angle of GBs misorientation.Small orientation changes adjacent to GBs region can be found in the Fig.11b,which means that there are some accumulations of GNDs along some boundaries.The grain reference orientation deviation(GROD)angle map in Fig.11c visualizes the long-range orientation gradients within the individual grains and demonstrates that nonuniform deformation develops within each grain.In addition,the GB misorientation map of Fig.11d indicates that there is no relationship between the density of GNDs and the high or low angle GBs.

Fig.11.(a)SEM images showing the surface topography of the tensile specimen after straining;(b)KAM map,(c)GROD angle map,and(d)GB misorientation map of Fig.11a.

The fact that slip transfer cases on the sample surface are highly aligned may suggest that due to the lack of constraint of adjacent grains the free surface facilitates the nucleation of dislocation at the GBs.Although only specimen surface is examined byin-situtension test,the maximum stress within structural parts occurs at surface positions for many common loading situations.Consequently,most of the time the failure of engineering materials is originating from the cracks on the component surface.Therefore,the deformation behavior on surface grains still has a significant influence on its failure mechanism[1].

5.Conclusion

A combination ofin-situtension test and EBSD orientation data is used to investigate the slip transfer process and heterogeneous deformation of a forged Mg-5.4Gd-1.8Y-1.5Zn alloy.The following conclusions can be drawn:

1 Slip transfer process of basal-basal and basal-pyramidal type is observed for the material with weak texture.Basalbasal slip occurs when the GBs misorientation smaller is than 34.2°,whereas basal-pyramidal type takes place when the crystallographic misorientation is larger than 48.8°.

2 As a non-sufficient but necessary condition for slip transfer cases,the Luster-Morris factor,m,should larger than 0.77 for this alloy.

3 Strain accommodation of individual grains by means of slip occurred more easily than slip transfer when several slip systems were operable in this alloy.

4 The product ofmfactor and the sum of the Schmid factors demonstrates that the threshold for basal-basal slip may exist,however,there is significant scatter in the calculated results ofmtimesSF for basal to pyramidal slip,indicating complex stress tensor within the grains to initiate pyramidal slip.

5 Besides the geometrical criterion,the stress state in each grain plays an important role in determining the slip transfer process.The effect of the stress tensor,which can be predicted using crystal plasticity modeling,needs to be examined in further work.

Acknowledgements

The authors acknowledge the funding support from National Natural Science Foundation of China via grant 51775135.

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.