Research on deformation mechanism of AZ31 magnesium alloy sheet with non-basal texture during uniaxial tension at room temperature:A visco-plastic self-consistent analysis

Li Hu,Huyun Lv,Lixin Shi,*,Yu Chen,Qing Chen,To Zhou,*,Mingo Li,Mingo Yng

aCollege of Material Science and Engineering,Chongqing University of Technology,Chongqing 400054,China

b Southwest Technology and Engineering Research Institute,Chongqing 400039,China

Abstract The relationship between activities of involved deformation mechanisms and the evolution of microstructure and texture during uniaxial tension of AZ31 magnesium alloy with a rare non-basal texture has been thoroughly investigated in the present study by means of electron backscattered diffraction(EBSD)measurement and visco-plastic self-consistent(VPSC)modeling.These results show that except basalslip and prismaticslip,{10¯12}extension twin(ET)also plays a significant role during plastic deformation.With the increasing tilted angle between loading direction and rolling direction(RD)of sheet,the activity of{10¯12}ET possesses a decreasing tendency and its role in plastic deformation changes from the one mainly sustaining plastic strain to the one mainly accommodating local strain between individual grains.When{10¯12}ET serves as a carrier of plastic strain,it mainly results in the formation of basal texture component(c-axis//ND,normal direction).By comparison,when the role of{10¯12}ET is to accommodate local strain,it mainly brings about the formation of prismatic texture component(c-axis//TD,transverse direction).At large plastic deformation,the competition between basalslip and pyramidalslip is responsible for the concentration of tilted basal poles towards ND within all deformed samples.The larger difference is between the activities of basalslip and pyramidalslip,the smaller separation is between these two tilted basal poles.Besides,VPSC modeling overestimates volume fractions of{10¯12}ET in samples with angle of 0 to 30° between loading direction and RD of sheet because interactions between twin variants are not included in VPSC modeling procedure at the present form.In addition,as compatible deformation between individual grains cannot be considered in VPSC modeling,the predicted volume fractions of{10¯12}ET in samples with angle of 45 to 90° between loading direction and RD of sheet are smaller than the correspondingly measured results.© 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/)

Keywords:AZ31 magnesium alloy;Non-basal texture;Plastic deformation;VPSC.

1.Introduction

Owing to their remarkably low density,high specific stiffness and strength,magnesium alloys have long been treated as a promising light-weight material to tackle the increasingly serious energy crisis.However,the widespread applications of magnesium alloys are still hindered by industrial practitioners because of their poor formability at room temperature[1].In fact,this shortcoming originates from the intrinsic characteristics of hexagonal close-packed(HCP)structure in magnesium alloys,which leads to the limited slip systems[2].Extensive research has confirmed that basalslip{0001}<11¯20>and prismaticslip{10¯10}<11¯20>can only sustain the plastic strain perpendicular to thec-axis of grains and provide only two independent slip systems each.Therefore,they cannot accommodate all the strains for polycrystalline plasticity since at least five independent slip systems are needed during plastic deformation of metallic materials,which is called the von Mises condition[3].Additional deformation mode,namely pyramidalslip{11¯22}<11¯23>or{10¯12}extension twin(ET),has to participate in the plastic deformation and accommodate the plastic strain along thec-axis of grains[4].Moreover,{10¯11}compression twin(CT)has also been observed during plastic deformation of magnesium alloys and it is closely related to texture softening,reduction of work hardening rate,strain concentration and early failure or fracture of deformed samples[5,6].Given the aforementioned complex deformation mechanisms in magnesium alloys,the detailed understanding of roles of various deformation mechanisms during plastic strain is of great necessity to guide the design of ductile magnesium alloys and further broaden the correspondingly industrial applications.

Over the past few decades,numerous investigations,especially the ones with the assistance of experimental measurement and/or crystal plasticity modeling,have attempted to identify,quantify or clarify the contribution and significance of various deformation mechanisms that lead to the complex deformation behavior of magnesium alloys under different strain paths.For instance,Chapuis et al.[7]and Wang et al.[8]confirmed that the in-plane tensile behavior of AZ31 magnesium alloy sheet is mainly accommodated by basalslip and prismaticslip.In comparison,Guo et al.[9]reported that the through-thickness tensile deformation of AZ31 magnesium alloy is sustained by not only basalslip and prismaticslip but also{10¯12}ET.In addition,Wang et al.[10]studied the uniaxial compression behavior of AZ31 magnesium alloy along normal direction(ND)and transverse direction(TD).Their investigation claimed that{10¯12}ET occurs at the onset of plastic deformation and quickly grows to consume the parent grains,whereas{10¯11}CT also nucleates at the early stage of plastic strain and then multiplies in the grains reoriented by{10¯12}ET.Besides,Agnew et al.[11]investigated the role of pyramidalslip during through-thickness compression of AZ31 magnesium alloy and confirmed that pyramidalslip serves as the second most active deformation mechanism after basalslip.However,it is worth noting that these foregoing investigations are mainly limited to magnesium alloys with typical basal texture,which is usually formed during the rolling process of fabricating sheet.As for magnesium alloys with non-basal texture,the focus of current research mainly lays on how to tailor the initial basal texture.For example,Kuang et al.[12]fabricated the AZ31 magnesium alloy sheet with TD-split bimodal texture by using single pass large strain electro-plastic rolling(LSER).He et al.[13]successfully introduced an orthogonal four-peak distribution of basal texture in the fabricated AZ31 magnesium alloy sheet by applying in-plane pre-compression,pre-stretching and annealing treatment.Study on the effects of non-basal texture on mechanical properties and/or formability of magnesium alloys are seldom reported,let along the relationship between microstructure evolution and the corresponding activities of deformation mechanisms during plastic deformation[14].

Therefore,the current investigation aims at elucidating relationship between microstructure evolution and activities of involved deformation mechanisms in magnesium alloy with non-basal texture.The adopted material in the present study is AZ31 magnesium alloy sheet fabricated by the newly developed processing technology,viz.equal channel angular rolling and continuous bending process with subsequent annealing(ECAR-CB-A).Texture characterization convinced that this manufactured AZ31 magnesium alloy sheet is with a rare non-basal texture,whose two basal poles tilt about±40°away from ND to rolling direction(RD)[14,15].Uniaxial tension experiments along different loading directions at room temperature are then conducted and these deformed samples are characterized by means of electron backscattered diffraction(EBSD)measurement.Subsequently,numerical investigation by using the visco-plastic self-consistent(VPSC)model is performed to correlate activities of deformation mechanisms with microstructure evolution.It has been generally accepted that among these reported crystal plasticity models,VPSC model developed by Lebensohn and Toméhas been termed as a most popular one due to its high forecasting accuracy,extraordinary computation efficiency and outstanding robustness in algorithms[17,18].

2.Experimental and modeling procedures

2.1.Uniaxial tension experiments and microstructure characterization

In the present study,AZ31 magnesium sheet with nonbasal texture was manufactured by the ECAR-CB-A process.The detailed processing procedures and processing parameters about the ECAR-CB-A process have been well documented in the work of Tu et al.[15].Then,dog-bone shaped specimens with the gauge length of 22.5mm and cross-section of 6mm×1.2mm were taken from the fabricated AZ31 magnesium sheet via electro-discharge machining(EDM).The corresponding sampling strategy is depicted in Fig.1,where the angles between gauge direction and RD of sheet are identified to be 0,30,45,60 and 90°.Tensile tests were hereafter performed on a SANS testing machine at a constant strain rate of 0.001s-1and at room temperature.The deformation degree was chosen to be 6 and 12%.To be concise in the following sections,these samples deformed in uniaxial tension would be called UT-0° sample,UT-30° sample,UT-45°sample,UT-60° sample and UT-90° sample,respectively.

Evolution of microstructure and texture within all undeformed and deformed samples were characterized on the RDTD planes by means of EBSD measurement.The corresponding aspect about sample preparation is as follows:RD-TD planes of these samples are mechanically polished by using 1200-grit SiC paper and then electro-polished in ACII electrolyte.The corresponding components of this solution include 50ml C3H8O,37.5g C6H8O7·H2O,20.75g NaCNS,400ml C2H6O,5g C9H7NO,9ml H2O and 7.5ml HClO4.

Fig.1.Schematic illustration of sampling strategy for tension specimens with different tilted angles between the gauge direction and RD of sheet.

Fig.2.Microstructure and texture of undeformed sample:(a)Inverse pole figure(IPF)map;(b)Grain boundaries(GB)map;(c)(0002),(10¯10)and(10¯11)pole figures.

The duration time of electrolytic polishing,polishing voltage and current were chosen to be 180s,20V and 0.03A,respectively.Afterwards,EBSD investigation was performed on a FEI Nova 400 scanning electron microscope equipped with an HKL-Nordlys Max detector.To obtain a good indexing quality,a relatively large step size of 2.0μm is adopted for the undeformed sample in the present study,while a relatively small step size of 1.5μm is applied for these deformed samples.All EBSD data were further post-processed with the assistance of Channel 5 analysis software and MTEX toolbox[19].The corresponding microstructure and texture of undeformed sample is shown in Fig.2,which includes the inverse pole figure(IPF)map,grain boundaries(GB)map and pole figures.It is obvious that the fabricated AZ31 magnesium sheet possesses a rare non-basal texture with two tilted basal poles away from ND to RD.The grain morphology in Fig.2(a)is with typical characteristic of equiaxed microstructure and the average grain size is identified to be 14.45μm.Moreover,Fig.2(b)demonstrate that the microstructure of undeformed sample is nearly twin-free and has a few low angle boundaries(LABs)whose misorientation ranges from 2 to 15°.All these aforementioned observations are quite consistent with the reported results in Chen et al.[14]and Song et al.[16].

2.2.VPSC-based crystal plasticity modeling

VPSC model is applied to simulate the plastic deformation behavior of AZ31 magnesium alloy with a rare non-basal texture during uniaxial tension tests.Some complete descriptions of VPSC model are available in the literature[17,20].In fact,VPSC model possesses the capability to account for not only the anisotropy of properties in single grain but also the anisotropy of properties in polycrystalline aggregate.The constitutive behavior at grain level is described by a non-linear rate-sensitivity equation as follows:

where˙εijandσklstand for the correspondingly deviatoric strain rate and stress.˙γ0servers as a normalization factor and is set to the macroscopic strain rate of 0.001s-1.The exponent n reflects the rate-sensitivity and a value of 20 is adopted in the present study to simulate plastic deformation of HCP materials,as advised in the VPSC manual.In addition,refers to the Schmid tensor associated with slip and twinning modes,and it can be calculated on the basis of normal vector(ns)and Burgers vector(bs).τsis the critical revolved shear stress(CRSS)on specific slip/twinning mode.The corresponding evolution ofτsis associated with accumulated shear strain(Γ)for individual deformation mechanisms and can be described by the following extended Voce equation.

whereτ0,τ1,θ0,θ1stand for adjustable parameters which control the hardening behavior of each deformation mode.In addition,VPSC model takes into account the hardening effect,which results from the interaction between different deformation mechanisms.Therefore,a coupling coefficient hss′is introduced to reflect these interactions by the following equation:

where hss′stands for the self-hardening coefficient when s=s′,whereas hss′infers to the latent-hardening coefficient when s/=s′.Δτsequals to the increment of CRSS in a slip/twinning mode.

To model the contribution of twin to texture development and track the evolution of twin volume fraction,the predominant twin reorientation(PTR)scheme proposed by Toméet al.[21]has been successfully embedded into VPSC code.The principle of PTR scheme is as follows:At each incremental step,by comparing the accumulated twin volume in each grain with a threshold value Vthres,whether or not a given grain should be reoriented can be determined by the following equation:

where Ath1and Ath2are two artificial material constants and they are associated with the evolution of twin volume fraction in different twining modes.The proposal of Chapuis et al.[22]is as follows:for{10¯12}ET,the values of Ath1and Ath2are 0.7 and 0.1,whereas for{10¯11}CT,the values of Ath1and Ath2are 0.05 and 0.05.Moreover,Veffand Vaccumrefer to the effective twin fraction and the accumulative twin fraction in a grain,respectively.

Fig.3.Comparison between experimental stress-strain curve and the correspondingly predicted one of AZ31 magnesium alloy with a rare non-basal texture under uniaxial tension along RD of sheet(The initial texture obtained by EBSD measurement and by discretizing the ODF are also included).

In the present study,plastic deformation of AZ31 magnesium alloy is assumed to be accommodated by basalslip,prismaticslip,pyramidalslip,{10¯12}ET and{10¯11}CT.These involved deformation mechanisms would lead to great difficulty about parameter identification in VPSC model because at least 12 material parameters would be needed in simulating plastic deformation of magnesium alloy[23].Therefore,a minimum parameter approach proposed by Hutchinson et al.[23]has been adopted in the present study.Only a measured true stress-strain curve of uniaxial tension along RD of sheet,as shown in Fig.3,has been used to verify the material parameters in VPSC model.These fitted material parameters are exhibited in Table 1,where the fundamental CRSS values are obtained by taking an approximate average of reported results of single crystal tests[23–26].Obviously,the predicted true stress-strain curve agrees well with the measured result.Though only a few material parameters are included,Chen et al.[27]reported that these predicted texture evolution and activities of deformation mechanisms by using a minimum parameter approach are acceptable when simulating plastic deformation behavior of AZ31 magnesium alloy.Lastly,in order to get accurate simulation results by using VPSC model,it is important to obtain an appropriate input data of initial orientations,which can reflect the texture characteristics of as-received AZ31 magnesium alloy sheet with a rare non-basal texture.This issue can be handled by discretizing the orientation distribution function(ODF)of measured EBSD data with the help of MTEX toolbox.The specific contents about orientation discretization can be found in[28,29].From Fig.3,it is obvious that(0002)and(10¯10)pole figures based on the extracted 5000 orientations shows high consistency with respect to the corresponding ones on account of EBSD data.

3.Results

3.1.Measured and predicted texture evolution during uniaxial tension

Fig.4 compares the measured and predicted texture evolution of various samples along different loading directions during uniaxial tension.It is obvious that these predicted(0002)pole figures show good accordance with the measured ones at both deformation degree of 6 and 12%.This aspect further confirms the validity of the fitted material parameters in the present study.In addition,it can be found that with the progression of plastic strain,a new TD-component texture(caxis//TD)marked by white dash box gradually appears within all deformed samples,especially for the UT-0° sample.Chen et al.[14]have also reported this phenomenon and concluded that this dramatic texture change surely arises from the con-tribution of activated{10¯12}ET within deformed samples.Moreover,along with the increase of tilted angle between loading direction and RD of sheet,there exists an apparently weakened tendency about the concentration of tilted basal poles towards ND.This observation can further be verified by comparing the correspondingly measured and predicted results about the separated angles between two points with maximum pole density in tilted basal poles,as shown Table 2.On the one side,the predicted results show minor differences by comparison with the correspondingly measured ones.For example,the measured and predicted results about separated angles are 71.3 and 70.5° at deformation degree of 6%,55.6 and 56.2° at deformation degree of 12%.On the other side,these measured differences(Δθ)between the separated angles in the case of deformation degree of 6 and 12% decrease from 15.7 to 4.7°,while the correspondingly predicted ones also decrease from 14.3 to 2.2°.These observations apparently show a decreasing tendency about the difference(Δθ)with the increasing tilted angle between loading direction and RD of sheet.

Table 1Material parameters of VPSC model with a minimum parameter approach.

Table 2The measured and predicted results about separated angles between two points with maximum pole density in tilted basal poles at different deformation degree and the corresponding difference(Δθ).

3.2.Measured and predicted microstructure evolution during uniaxial tension

Figs.5 and 6 are composed of IPF maps and depict the microstructure evolution of all 6%-deformed samples and 12%-deformed samples along different loading directions during uniaxial tension.As Chen et al.[14]have reported that{10¯12}ET is identified to be the dominant twinning mechanism during plastic deformation of AZ31 magnesium alloy sheet with a rare non-basal texture,in the present study{10¯12}ETs are also be focused on and are highlighted by bright color,while the rest is being partly greyed out.It is obvious that loading direction has an important influence on the activation of{10¯12}ET during uniaxial tension.The amount of{10¯12}ET possesses a decreasing tendency along with the increasing tilted angle between loading direction and RD of sheet.This aspect can further be verified by the correspondingly calculated volume fractions of{10¯12}ET within deformed samples,as shown in Table 3.As for UT-0° sample,it contains the largest volume fractions of{10¯12}ET within both 6%-deformed sample(0.161)and 12%-deformed sample(0.204).By comparison,UT-90° sample only possesses the minimal volume fractions of{10¯12}ET at both 6%-deformed sample(0.045)and 12%-deformed sample(0.068).Moreover,the predicted evolution of volume fraction about{10¯12}ET is calculated and shown in Fig.7,where these experimental values are also included and plotted by polygons with different colors.In all deformed samples,the predicted volume fractions of{10¯12}ET overall increase with the progression of plastic strain.However,the larger is the tilted angle between loading direction and RD of sheet,the smaller is the predicted volume fraction of{10¯12}ET.In addition,it is worth noting in Fig.7 that all deformed samples can be classified into two categories:these(UT-0° sample and UT-30° sample)overestimating the volume fractions of{10¯12}ET in numerical investigation and these(UT-45° sample,UT-60° sample and UT-90° sample)underestimating the volume fractions of{10¯12}ET in numerical investigation.

Table 3Measured volume fractions of{10¯12}ET within all deformed samples during uniaxial tension along different loading directions.

4.Discussion

4.1.Effect of loading direction on predicted activities of deformation mechanisms

Fig.4.(0002)pole figures showing the comparison between measured and predicted texture evolution of various samples along different loading directions during uniaxial tension at room temperature:(a)UT-0° sample;(b)UT-30° sample,(c)UT-45° sample;(d)UT-60° sample,(e)UT-90° sample.(TD-component texture marked by white dash box emerges near the TD of sheet with the increasing plastic strain).

Fig.5.IPF maps of 6%-deformed samples along various loading directions during uniaxial tension at room temperature:(a)UT-0° sample;(b)UT-30° sample;(c)UT-45° sample;(d)UT-60° sample;(e)UT-90° sample.

Fig.8 demonstrates the predicted slip and twinning activities of various samples during uniaxial tension.As plastic strain instead of deformation degree is applied in VPSC model,translation equation ofεplasticstrain=ln(1+εengineeringstrain)is adopted for uniaxial tension deformation and the corresponding plastic strain values with respect to 6 and 12% deformation degree are calculated to be 0.058 and 0.113,respectively.It can be seen from Fig.8 that as for the twinning modes,{10¯12}ET largely participates in the plastic deformation at the onset of uniaxial tension(to plastic strain of 0.03),afterwards its contribution is gradually weakening with the increasing plastic strain.It has been generally accepted that{10¯12}ET can accommodate plastic strain along thec-axis of grains and possesses the smallest CRSS by comparison with other deformation mechanisms except for basalslip[30,31].Consequently,it possesses a relatively large amount of activation at early stage of plastic deformation.Moreover,as the tilted angle between thec-axis of most grains and loading direction increases from about 50° in UT-0° sample to nearly 90° in UT-90° sample,the elongation along thec-axis is extensively prohibited[18].This aspect leads to the reduced contribution of{10¯12}ET,as shown in Fig.8.In terms of{10¯11}CT,its activities only maintain at a low level and contribute very small to the plastic deformation within all deformed samples.

As for the slip modes,with the progression of plastic strain,the predicted activities of prismaticslip are gradually enhanced,while the predicted activities of basalslip possess a decreasing tendency.This aforementioned observation can be further verified by analyzing the Schmid factor(SF)of each slip mode,which indicates the difficulty of activation during plastic deformation.Based on the EBSD data of all samples,the corresponding results of statistical analysis about SF are shown in Fig.9 and Table 4.As for basalslip,during deformation the percentage of SF value in the rage of 0.3–0.5 and the average SF value both possess a decreasing tendency along with the increasing tilted angle between loading direction and RD of sheet.With respect to prismaticslip,the percentage of SF value in the rage of 0.3–0.5 and the average SF value both exhibit an increasing tendency along with the increasing tilted angle between loading direction and RD of sheet.Besides,Fig.8 demonstrates that basalslip and prismaticslip are two dominant deformation mechanisms for AZ31 magnesium alloy with a rare non-basal texture during uniaxial tension along different loading directions.This phenomenon also occurs in AZ31 magnesium alloy with typical basal texture during in-plane uniaxial tension,as reported by Agnew et al.[11]and Chapuis et al.[22].However,the loading direction has an obvious impact on the contribution of basalslip and prismaticslip to plastic strain.Fig.8 depicts that in UT-0°sample,basalslip is the most important slip mode during plastic deformation,and prismaticslip serves as the secondary one.However,along with the increasing tilted angle between loading direction and RD of sheet,prismaticslip begins to sustain more plastic strain by comparison with basalslip.Clearly,prismaticslip,not basalslip,has been turned into the prominent deformation mechanism in UT-90° sample.Lastly,it is interesting to find in Fig.8 that the predicted activities of pyramidalslip grow gradually with the increasing tilted angle between loading direction and RD of sheet.This issue seems to be contradictory to the correspondingly statistical analysis of SF value in Fig.9 and Table 4,where there only exists minor change about the percentage of SF value in the rage of 0.3–0.5 and the average SF value.Generally speaking,pyramidalslip would be activated with difficulty at room temperature due to its large CRSS and it mainly serves as a compatibility deformation mechanism for magnesium alloys[32,33].In the present study,along with the increasing tilted angle between loading direction and RD of sheet,the reduced activities in{10¯12}ET would hinder the plastic strain along thec-axis of grains.Consequently,pyramidalslip has to be activated more frequently in order to satisfy the necessity of deformation along thec-axis of grains.

Fig.6.IPF maps of 12%-deformed samples along various loading directions during uniaxial tension at room temperature:(a)UT-0° sample;(b)UT-30°sample;(c)UT-45° sample;(d)UT-60° sample;(e)UT-90° sample.

Table 4The average SF values of basalslip,prismaticslip and pyramidalslip within five samples during uniaxial tension.

Fig.7.Predicted volume fractions of{10¯12}ET for all tensile samples.(Experimental volume fractions of{10¯12}ET at deformation degree of 6 and 12% are included and plotted by polygons with different colors).

4.2.Contribution of involved deformation mechanisms to texture evolution

To date numerous investigations have been conducted in order to elucidate the roles of various deformation mechanisms to texture evolution of magnesium alloys during uniaxial tension and a consensus has been arrived over this issue[14,33–35]:the activities of basalslip and{10¯12}ET are beneficial for rotating ofc-axis of grains towards ND,whereas the motion of pyramidalslip leads to the rotation ofc-axis of grains towards loading direction during uniaxial tension.Moreover,prismaticslip mainly results in a rotation of grains around theirc-axis and{10¯11}CT only provides slight contribution to the plastic strain as well as texture evolution.Consequently,the observed phenomenon about texture evolution shown in Fig 4 should be collectively ascribed to the activities of basalslip,{10¯12}ET and pyramidalslip.To more precisely assess the relationship between the activities of involved deformation mechanisms and the corresponding texture evolution in the present study,grain orientations obtained from VPSC modeling are further divided into two classes.One of them possesses misorientations(larger than 60°)with respect to the correspondingly initial orientations.The other contains the remaining orientations in the predicted results.Clearly,the former class is mainly ascribed to the activation of{10¯12}ET which could result in the rotation around its<1¯210>axis by about 86.3°.In addition,the latter class is attributed to the joint action of remaining deformation mechanisms,especially for basalslip and pyramidalslip.Finally,the corresponding(0002)pole figures,which are based on these two groups of orientations,are constructed and shown in Fig.10 and Fig.11,respectively.It is obvious in Fig.10(a)that at deformation degree of 6%,{10¯12}ETs within UT-0° sample mainly contribute to the formation of basal texture component(c-axis//ND)and its role in the formation of prismatic texture component(c-axis//TD)is negligible.Along with the increasing tilted angle between loading direction and RD of sheet,the density of basal texture component is gradually reduced and the density of prismatic texture component is gradually enhanced.Especially in UT-90° sample,{10¯12}ETs mainly bring about the formation of prismatic texture component.Meanwhile,Fig.11(a)depicts that the collective action of involved deformation mechanisms except for{10¯12}ET actually results in a negligible change of texture.This observation is mainly ascribed to the fact that dislocation slip would only result in a gradual change of texture[14].Considering that at early stage of plastic deformation,there exists relatively large amount of activities of{10¯12}ET within UT-0°sample and UT-30° sample,as shown in Fig.8,it can be concluded that the concentration of tilted basal poles towards ND within these samples should be mainly ascribed to the contribution of{10¯12}ET.With the progression of plastic strain,the role of{10¯12}ET to the formation of prismatic texture component are gradually enhanced within all deformed samples.Fig.10(c)shows that at deformation degree of 21%,{10¯12}ET apparently results in a strong prismatic texture component and a weak basal texture component within all deformed samples.These observations provide strong evidence that in the case of large plastic deformation,{10¯12}ET has little influence on the concentration of tilted basal poles towards ND in(0002)pole figure.However,Fig.11(b)and(c)demonstrate that within UT-0° sample and UT-30° sample there still exists observable phenomenon about the concentration of tilted basal poles towards ND,while these exists negligible change about the separation of two tilted basal poles within the remaining samples.Given consideration that the activity of basalslip is substantially larger than the one of pyramidalslip within UT-0° sample and UT-30° sample,as shown in Fig.8,the concentration effect resulted from basalslip should be far better than the splitting effect derived from pyramidalslip.This aspect finally results an observable concentration of tilted basal poles towards ND in(0002)pole figure at large plastic strain.In terms of UT-90° sample,Fig.8 depicts that there exists relatively small difference between the activities of basalslip and pyramidalslip.Accordingly,the concentration effect resulted from basalslip should be largely offset by the splitting effect derived from pyramidalslip.This aspect finally brings about a negligible concentration of tilted basal poles towards ND in(0002)pole figure.

Fig.8.Predicted slip and twinning activities of various samples during uniaxial tension:(a)UT-0° sample;(b)UT-30° sample,(c)UT-45° sample;(d)UT-60°sample,(e)UT-90° sample.

4.3.Effect of twin variant on predicted volume fraction of{101¯2}ET

From Figs.5 and 6,it can be seen that{10¯12}ET plays an important role on the microstructure evolution of AZ31 magnesium alloy with a rare non-basal texture during uniaxial tension.Although its role on texture evolution can be effectively predicted,there exists some difference between the measured volume fractions of{10¯12}ET and the correspondingly predicted ones,as shown in Fig.7.In fact,it is well known that there are six twin variants of{10¯12}ET in magnesium alloys during plastic deformation and the selective activation of various twin variants is extensively dependent on the strain path[36].To further investigate the twinning behavior and explore the cause of difference between the predicted volume fractions of{10¯12}ET and the correspondingly measured ones,eight representative grains per deformed sample are selected from Fig.5 and they are then thoroughly analyzed by using IPF maps and(0002)pole figures,as shown in Fig.12.In the present study,the selected eight grains per deformed sample could be further divided into two groups:(i)four grains with theirc-axis inclined about 20°–60° towards ND and(ii)four grains with theirc-axis tilted about 60°–90° towards ND.

Fig.9.Statistical analysis of SF values on basalslip,prismaticslip and pyramidalslip during uniaxial tension:(a)UT-0° sample;(b)UT-30° sample,(c)UT-45° sample;(d)UT-60° sample,(e)UT-90° sample.

Fig.10.Predicted(0002)pole figures based on the activities of{10¯12}ET within deformed samples during uniaxial tension:(a)At deformation degree of 6%;(b)At deformation degree of 12%;(c)At deformation degree of 21%.

Fig.11.Predicted(0002)pole figures based on the activities of deformation mechanisms other than{10¯12}ET within deformed samples during uniaxial tension:(a)At deformation degree of 6%;(b)At deformation degree of 12%;(c)At deformation degree of 21%.

Fig.12.IPF maps and(0002)pole figures of selected eight grains per deformed sample at deformation degree of 6%:(a)UT-0° sample;(b)UT-30° sample,(c)UT-45° sample;(d)UT-60° sample,(e)UT-90° sample.

As for grains with theirc-axis inclined about 20°–60° towards ND,IPF maps demonstrate that only one or two twin variants occur during plastic deformation and they mainly rotate their initial orientations to the region near TD.In terms of grains with theirc-axis tilted about 60°–90° towards ND,the number of activated twin variants is gradually decreasing along with the increasing tilted angle between loading direction and RD of sheet.For example,there exist up to four twin variants within UT-0° sample,while only one twin variant emerges within UT-90° sample.Moreover,the corresponding(0002)pole figures depict that these twin variants mainly rotate their initial orientations to the area close to RD.Guo et al.[9]have claimed that as for{10¯12}ET during plastic deformation,the role of sustaining plastic strain means the activation of more twin variants,whereas the role of accommodating plastic strain between individual grains indicates the activation of less twin variants.Consequently,we have reason to believe that compare to the role of accommodating plastic strain,{10¯12}ETs in UT-0° sample and UT-30° sample prefer to sustain plastic strain.Meanwhile,{10¯12}ETs within UT-90° sample are inclined to accommodate plastic strain between individual grains.Based on the aforementioned analysis,the reason leading to the overestimation of predicted volume fractions of{10¯12}ET in UT-0° sample and UT-30° sample,as shown in Fig.7,can be disclosed.Because many twin variants tend to activate within a grain,twin-twin interactions occur more frequently,and thus hinder the twin growth[37].However,this“barrier effect”is not included in the VPSC modeling procedure at the present form,where all self-hardening coefficients and latent-hardening coefficients are set to unity.One potential access to tackle this issue is that this“barrier effect”would be considered indirectly by modifying the self-hardening coefficient of{10¯12}ET.With respect to the rest samples,although the aforementioned“barrier effect”is relatively weak and can be neglected in the VPSC modeling because there are much less interactions between twin variants,activation of{10¯12}ET is mainly ascribed to be the compatible deformation between individual grains.Unfortunately,this aspect has not been appropriately considered in the present form of VPSC code,and finally results in the underestimation of predicted volume fractions of{10¯12}ET in UT-45° sample,UT-60° sample and UT-90°sample,as shown Fig.7[17].

5.Conclusions

Through the combination of experimental investigation and numerical simulation,the relationship between the activities of involved deformation mechanisms and evolution of microstructure and texture during uniaxial tension of AZ31 magnesium alloy with a rare non-basal texture has been thoroughly investigated in the present study.The following conclusions can be obtained.

(1)Except for basalslip and prismaticslip,{10¯12}ET deeply participates in the plastic deformation.With the increasing tilted angle between loading direction and RD of sheet,the activity of{10¯12}ET reduces gradually and its role in plastic deformation changes from the one mainly sustaining plastic strain to the one mainly accommodating local strain between individual grains.

(2)The formation of TD-component texture during uniaxial tension is mainly ascribe to the activities of{10¯12}ET.For UT-0°sample and UT-30°sample,the concentration of tilted basal poles towards ND is observable at early stage of plastic deformation.This aspect is mainly attributed to the activities of{10¯12}ET.At large plastic deformation,the competition between basalslip and pyramidalslip is responsible for the concentration of tilted basal poles towards ND within all deformed samples.The larger difference is between the activities of basalslip and pyramidalslip,the smaller separation is between these two tilted basal poles.

(3)Because of taking no account of interaction between twin variants in the VPSC modeling,the predicted volume fractions of{10¯12}ET in UT-0° sample and UT-30° sample are larger than the correspondingly measured ones.In addition,as compatible deformation between individual grains can not be modeled in the VPSC modeling,the predicted volume fractions of{10¯12}ET in the remaining samples are smaller than the correspondingly measured ones.

Declaration of Competing Interest

None.

Acknowledgments

This work was supported by the National Natural Science Foundation of China(Grant Nos.51805064,51701034,51822509),the Scientific and Technological Research Program of Chongqing Municipal Education Commission(Grant Nos.KJQN201801137),the Basic and Advanced Research Project of CQ CSTC(Grant Nos.cstc2017jcyjAX0062,cstc2018jcyjAX0035).