Improved mechanical properties and strengthening mechanism with the altered precipitate orientation in magnesium alloys

Y.J.Wn, Y.Zeng,?, Y.C.Dou, D.C.Hu, X.Y.Qin, Q.Zeng, K.X.Sun, G.F.Qun

a Key Laboratory of Advanced Technologies of Materials, Ministry of Education, School of Material Science and Engineering, Southwest Jiaotong University,Chengdu 610031, China

b College of Materials Science and Engineering, Sichuan University of Science and Engineering, Zigong 643000, China

c Department of Materials, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom

Abstract

Keywords: Precipitate orientation; Precipitation strengthening; Grain boundary strengthening; Yield strength model.

1.Introduction

Magnesium (Mg) alloys, served as the lightest metallic structural materials, have great potential for improving the fuel efficiency and reducing carbon dioxide (CO2) emission of vehicles [1].Mg-3wt.%Al-1wt.%Zn (AZ31) alloy, a common commercial Mg alloy, is widely utilized in the field of transportation industry and aerospace applications due to the high ductility and good formability [2].However, the extensive applications of AZ31 alloy are restricted due to its low strength.

In general, precipitation strengthening is considered as a feasible method to improve the strength of Mg alloys [3].However, AZ31 Mg alloy is acknowledged as a non-heattreatable Mg alloy [4].During the process of aging treatment,β-Mg17Al12particles would precipitate in Mg matrix.The most commonly observed orientation relationship (OR)between Mg17Al12precipitates and Mg matrix is the Burgers OR,i.e., (011)β//(0001)α, [11]β//[20]α[5–7].It is noteworthy that the majority of Mg17Al12precipitates in Mg-Al alloys have habit planes (HPs) parallel or approximately parallel to the(0002)basal planes of Mg matrix(hereafter named basal plates) [7–9].Such basal plates do not raise appreciable strengthening due to its limited impediment of the dominant slip system in Mg alloys at room temperature (RT),i.e., basal slip [4].Thus, the strengthening effect of AZ31 Mg alloy is limited by the conventional aging treatment.So, it is urgentto find an effective way to improve the strength of AZ31 Mg alloy.

In terms of precipitation strengthening, the orientation of precipitate with Mg matrix plays an important role in the hardening effect [9,10].Nie [11]proposed a physical model to quantitatively investigate the effect of precipitate shape and orientation on dispersion strengthening based on Orowan strengthening theory for hexagonal-closed packed (HCP)metals and thus predicated that prismatic plates have a strong blocking effect on basal slip.As a result, the basal plates formed in the as-cast AZ91 alloy generally give poor strengthening compared to the precipitates formed in the prismatic plane of the as-cast Mg-Y-RE alloys (hereafter named prismatic plates) [4].However, such prismatic plates were predicted to have a weak blocking effect on prismatic slip which is weaker than basal plates.In addition, Robson et al.[12]also predicted that rod-shaped precipitates with their long-axes parallel to thec-axes of Mg crystals (hereafter namedc-axis rods) are more effective in hardening against basal slip and prismatic slip compared to sphere and basal plates.Although the Orowan model can well estimate the hardening effects on various slip modes, it is not suitable for twinning deformation because the Orowan model was found to underestimate grately the hardening effect on twinning.Recently, Fan et al.[10,13]developed a novel physical model to study the precipitation hardening effect of different types of precipitates (basal plates, prismatic plates,c-axis rods and spherical precipitates) on twinning deformation.It was found that the prismatic plates have the best hardening effect on both twinning and basal slip.From the aforementioned researches,it can be concluded that different types of precipitates lead to different strengthening responses.In this sense, precipitation is considered as an important tool for controlling the strength of individual slip and twin modes,thereby adjusting the asymmetry and improving the overall strength and ductility of Mg alloys [10].Inspired by the provious researches, the strength of AZ31 Mg alloy could be improved by regulating the orientation between precipitate and Mg matrix (hereafter named precipitate orientation).

For HCP magnesium and its alloys, deformation twinning plays an important role during plastic deformation process [14].Two common twinning modes were observed in Mg alloys.They were classified as {102} entension twins and {101} contraction twins since they result in an extension or contraction alongc-axis, respectively [14].In general,twinning can change the grain orientation of the Mg alloys[15,16].For extension twins, it reorients the lattice by ～86.3°along 〈11ˉ20〉 crystal directions [15].Moreover, {102} extension twins can be easily activated during compression along rolling direction (RD) or transverse direction (TD) or tension along normal direction(ND)in strong basal texture Mg alloys sheet [17].Recently, the interactions of precipitates and twins were reported in Refs.[10,18,19].These researches indicated that the precipitates in Mg alloys might increase the stress for twin growth or detwinning but does not prohibit them, and twinning generally does not shear precipitates but engulf them and lead only to a rigid body rotation of the precipitates by 3–4° with repect to its original position.That is, during the process of {102} extension twinning, the lattice for matrix would be reoriented by ～86.3°, while the precipitates would close to their original position.

Therefore, it is possible to tailor the precipitate orientation through controlling twinning and precipitation process.More recently, Liu et al.[8]reported a method for regulating the precipitate orientation in AZ80 alloys by coupling twinning, aging and detwinning processes (TAD processes).The results of microstructural observations indicated that the precipitate orientation was altered from basal precipitation to prismatic precipitation.Compression and tensile tests were performed to confirm that such change in precipitate orientation can remarkably improve the strength of as-rolled AZ80 Mg alloy sheet.Furthermore, a crystallography-based algorithm was proposed to predict the possible crystallographic orientation relationships (ORs) between the prismatic precipitates and the detwinned matrix, and the predictions were subsequently validated through experimental observation[20].The results showed that three new ORs betweenβ-Mg17Al12andα-Mg matrix were determined through experimental observation, which agreed well with the predictions through the algorithm after considering the 3.69° rotation of precipitates at twin boundary.It could be further deduced that the precipitates is not exactly parallel to prismatic plane because the lattice ortation angle is 86.3° and the precipitates still have a small rotation at twin boundary [20].Although this TAD process can regulate precipitate orientation and thus improve the overall strength, it seems to be cumbersome and the underlying strengthening mechanism was not discussed in depth.

Therefore, in the present work, an aging prior to twinning deformation process was applied to improve the mechanical properties of AZ31 alloy through altering the precipitate orientation.The mechanical properties between the aged sheet and the twinned sheet were compared to assess the strengthening effect of the altered precipitate orientation and twin boundary.Specifically, all samples used for testing mechanical properties were conducted along 45°to ND(in the ND-TD plane) to avoid the influence of texture on properties.Furthermore, the inherent mechanism of the improved strength and ductility in the sample containing the prismatic plates was analyzed in detail.

2.Materials and methods

The material used in this study is a commercial hot-rolled AZ31 Mg alloy sheet with a thickness of 10mm and a typical strong basal texture, as shown in Fig.1b.The experimental process is illustrated in Fig.1a, and described as follows.Firstly, to obtain uniformed precipitates, the as-received sheet was solution treated at 410°C for 8h, which still possessed a typical strong basal texture with a slightly decreased texture intensity, as shown in Fig.1c.Then, this sheet was aged at 180°C for 14h (T6 sheet).Cubic block samples with 10mm×10mm×15mm along ND, TD and RD were machined from the aged sheet (hereafter named sample A).Secondly, to transform the precipitate orientation, sampleA was compressed along TD at a constant strain rate of 10-3s-1(hereafter named sample AC).Two strain values (8 and 13%) were carried out to obtain the maximum twinning proportion, which expected most grains were completely twinned.Thus, the grain orientation will change fromc-axis// ND toc-axis // TD.Finally, the compressed samples were annealed at 250°C for 30min (hereafter named sample ACA).This treatment could have a slight influence on the texture, but the main grain orientation remainsc-axis // TD.

Fig.1.(a) A schematic diagram showing the sample produced in each step.The macro-texture of (b) the as-rolled AZ31 sheet and (c) the as-solutionized AZ31 sheet.(d) A schematic diagram showing the compression test process, and the grain orientation is illustrated in the test sample.In this condition, the c-axis of grain is 45° to the compressive axis.

To avoid the influence of texture on mechanical properties, all the compression test samples with a dimension of 4.5×4.5×7.5mm (length×width×height) were machined along 45° to ND (in the ND-TD plane).The test samples produced in each step were denoted as sample A-45°, sample AC-45° and sample ACA-45°, respectively (see Fig.1a).Mechanical properties were evaluated by compression test with a strain rate of 1×10-3s-1at RT using a MTS-CMT5105.Note that the compressive axis is along the height direction,as demonstrated in Fig.1d.All compression tests were repeated 3 times for each type of samples to get the representative results.

Morphology observations of the various samples were investigated by using an optical microscopy (OM, ZEISS Axio Lab A1) and a backscatter scanning electron microscopy(BSEM, TESCAN VEGA II LMU).The grain size (d) was determined by linear intercept method withd=1.74L (Lis the size of line intercept) [21].More than 200 grains were counted for each sample to obtain an average grain size.The evolution of the crystal orientation was analyzed by using an electron backscatter diffraction (EBSD, JEOL JSM-7800F)technique.Sample preparation for EBSD incorporated mechanical grinding, polishing with a diamond and colloidal silica slurry as well as electro-polishing at a voltage of 20V and an electric current of 0.1 A for 60s at a temperature of-40 °C in an AC2 electrolyte.All EBSD data were analyzed by using the channel 5 software.The samples for transmission electron microscopy (TEM) observations were prepared by ion-beam milling using a Gatan PIPS 695 and the precipitates were examined by using a JEOL2100 TEM operating at 200kV.

3.Results

3.1.Microstructure and texture evolution

Fig.2 shows the BSEM images of various samples.The microstructure of as-rolled sheet consists of the equiaxed grain structure ofα-Mg and a few irregular granular secondary phases (see Fig.2a).The microstructure of the solution treated AZ31 sheet is free of precipitates (see Fig.2b).After aging at 180 °C for 14h, some irregular granular precipitates disperse on theα-Mg matrix (see Fig.2c).Note that such a heat treatment has no obvious influence on the grain size of Mg-Al alloys, which is consistent with the results reported in Refs.[22,23].

Fig.3 shows the OM images of sample A, sample AC with a compression strain of 8 and 13% and sample ACA,respectively.The corresponding (0002) macro-pole figures of sample AC with a compression strain of 8 and 13% are also presented as insets.It is found that the average grain size of sample A is ～21.70μm.After compression along TD, the lamellar twins formed on the matrix.Fig.3b shows the microstructure of sample AC with a compression strain of 8%,the grain size is refined to 9.44μm, which is caused by the twin boundaries existing in the matrix.Similarly, the grain size of sample AC with a compression strain of 13% is refined to 11.85μm, as shown in Fig.3c.

Fig.2.BSEM images of the samples: as-rolled sheet (a), solid solution treated at 410°C for 8h (b) and aged at 180°C for 14h (c).

Fig.3.OM images of the samples: (a) sample A, sample AC with a compression strain of (b) 8% and (c) 13%, respectively, and (d) sample ACA.The twin boundaries are indicated by red arrows in Fig.3 (b) and (c).The corresponding (0002) macro-pole figures are presented in (b) and (c) as insets.The maximum texture intensity is given and marked by red word in the corresponding (0002) macro-pole figure (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

It was reported [24]that the compression strain of 8% almost causes a completely twinning deformation (with ～94%volume fraction) for a rolled AZ80 Mg alloy, which significantly decreases the twin boundaries in most grains.However,in the present work, profuse twin boundaries still exist inside the grains with the compression strain of 8%.Besides, as demonstrated in Fig.3b, although most of (0002) poles tilt to TD, a few (0002) poles still remain in the center in the sample AC with a compression strain of 8%.With further strain to 13%, the twin boundaries are remarkably decreased and the (0002) poles completely tilt to TD, resulting in the formation of a twin-texture withc-axis // TD, as shown in Fig.3c.Combined the results of the macro-texture and twin morphology, it proves that the sample AC with a compression strain of 13% is suitable for subsequent research.

In addition, annealing process was subjected to eliminate the hardening effect of dislocations or residual twin boundaries induced in the previous steps.Fig.3d shows the twin boundaries in sample ACA are significantly disappeared due to the annealing process, accompanied with coarser grains(average grain size of 22.44μm).

Variations of the texture and crystal orientation of the various samples are compared in Fig.4.Here, Fig.4a shows the inverse pole figure (IPF) map of sample A, and the corresponding (0002) pole figure is presented as inset.This sample exhibits a typically strong basal texture, where the basal(0002) planes are mostly parallel to RD-TD plane.Fig.4b presents the pole figure and IPF map of the sample A-45°.Note that the examined plane is vertical to the compressive axis with a cross-section of 4.5×4.5 mm2.Compared with sample A, the pole axis of (0002) pole figure of sample A-45° has a titled angle of 45° from the center to ND.It reveals that thec-axes of grains in sample A-45° are 45° to the compressive axis (see Fig.1d).Moreover, it is well known that{102} extension twin can be easily induced by compression along TD or RD for as-rolled Mg alloys sheet and {102}extension twin can trigger a drastic change ofc-axis with a crystallographic lattice reorientation of 86.3° [15].Therefore,as shown in Fig.4d, the major texture component in sample AC isc-axis // TD.It means that thec-axes of grains are largely oriented parallel to TD.Besides, according to the pole figure shown in Fig.4e, it can be found that the basal poles in sample AC-45° largely tilt towards ND with an angle of 45°, and thus thec-axes of grains are 45° to the compressive axis.It indicates the grain orientation in sample AC-45° is similar to that in sample A-45°.

Since the texture has a major effect on mechanical properties, the Schmid factor (SF) distribution for basal slip on< a >{0002}<11ˉ20>as well as the mean SF of sample A-45° and sample AC-45° were calculated from the EBSD raw data and are presented in Fig.4c and f.The mean SF for the basal slip of sample A-45° and sample AC-45° is 0.43 and 0.40, respectively.The distribution of the SF also indicates that the dominated SF of the grains in both sample A-45° and sample AC-45° concentrates between 0.4 and 0.5 for basal slip.Such grain orientations favor the activation of basal slip.

It was reported that the precipitates in Mg-Al alloys,proved to be Mg17Al12, usually presented as the shape of plates and distributed in the basal plane of matrix [25].In general, these precipitates would display a plate-shaped morphology when viewed along [0001]αdirection while present a lath-shaped morphology when viewed along [100]αdirection.Analogously, the possible morphologies of prismaticplates in AZ31 observed along different directions could also be predicted.The schematic morphologies of prismatic plates are depicted in Fig.5a.Compared to basal plates,prismatic plates would exhibit the lath shape when viewed along[0001]αdirection, while show plate shape when viewed along [100]αdirection.

Fig.4.EBSD inverse pole figure (IPF) maps of (a) sample A, (b) sample A-45°, (d) sample AC and (e) sample AC-45° The corresponding (0002) micro-pole figures are presented as insets.Distributions of the Schmid factor for basal slip in (c) sample A-45°and (f) sample AC-45°.

To identify the orientation of the precipitates in sample AC,TEM bright-field images viewed along [100]αand [0001]αdirection were obtained.Fig.5b shows the bright-field TEM images viewed along [100]αdirection of sample AC.It indicates that the plate-shaped Mg17Al12precipitates are the major morphologies with their broad face approximately parallel to the prismatic plane of the matrix.Meanwhile, the morphologies of these precipitates viewed [0001]αdirection are lath-shaped (see Fig.5c).The corresponding electron diffraction patterns are presented as insets.As aforementioned, the lattice rotation is 86.3°, and the precipitates usually have a small rotation (<4°) at twin boundry [10].Therefore, the precipitates are not exactly parallel to the prismatic planes of the twinned region.In the present work, it can be concluded that the plate-shaped precipitates in sample AC have the HPs with their broad face approximately parallel to one of the{100}αprismatic plane of the twinnedα-Mg matrix with a small rotation angle (<4°) during the interaction with twin boundaries.

3.2.Mechanical properties

Fig.6 shows the compressive properties of sample A-45°,sample AC-45° and sample ACA-45°.The details of compressive properties are summarized in Table 1.It can be clearly seen that, compared to sample A-45°, the compressive yield strength (CYS) of sample AC-45° and sample ACA-45° increased by～40MPa and ～20MPa, respectively.Moreover, the compression ratio of sample AC-45° prolonged by～22% compared to sample A-45°, while the compression ratio of sample ACA-45° is at the same level as sample A-45°(～23%).

Table 1The mechanical properties consist of the ultimate compressive strength(UCS), compressive yield strength (CYS) and compression ratio of sample A-45°, sample AC-45° and sample ACA-45°.

3.3.Fracture properties

As mentioned above, profuse twin boundaries still existed inside the grains in the sample AC-45°.These twin boundaries would exert an extra influence on fracture performance,such as void formation and growth [26].Therefore, the fracture performance of sample A-45° and sample ACA-45° was proposed to examine.

Fig.7 shows the SEM images of fracture performance of sample A-45° and sample ACA-45°.Particularly, the morphologies of sample A-45° and sample ACA-45° at a compression strain of 20% are displayed in Fig.7a and d.It can be seen that the micro-cracks initiate at grain boundaries in both samples.Some slip traces were observed on the surface of sample ACA-45° (marked with white arrow in Fig.7d) whereas not observed in sample A-45°, as confirmed in Fig.7a and d.Besides, no deformation twins are found in either sample.

Fig.7b, c and e, f show the morphologies of the fracture surface of sample A-45° and sample ACA-45°, respectively.The fracture surface of both samples composes by tear ridges,cleavage steps, cleavage surfaces and microvoids.However,compared to sample A-45°, more microvoids are observed in sample ACA-45°.

Fig.5.(a) A schematic diagram showing the morphologic characteristics of Mg17Al12 precipitates viewed along [100]α and [0001]α.Bright-field TEM images of sample AC (b) viewed along [100]α and (c) viewed along [0001]α.

Fig.6.Compressive stress-strain curve of sample A-45°, sample AC-45° and sample ACA-45°.

4.Discussion

4.1.The mechanism for the improved strength

As mentioned above, the precipitate orientation was altered from basal plane to prismatic plane by the aging prior to twinning deformation process, accompanied with the CYS improvement.In the present work, the influence of texture on the CYS can be avoided due to the similar grain orientation and close SF.Therefore, the possible CYS strengthening mechanism can be mainly divided into 3 parts, namely,(1) solid solution strengthening contribution,σss, (2) precipitation strengthening contribution,σpptand (3) grain boundary strengthening contribution,σgb.The contributions of these strengthening mechanisms to CYS are further quantitatively discuss as follows:

Fig.7.SEM images of (a) sample A-45°and (d) sample ACA-45° with a compression strain of 20%.The compression direction is indicated by blue arrow in (a).The fracture surface of (b, c) sample A-45° and (e, f) sample ACA-45° The regions surronded by red lines in (b) and (e) are magnified and shown in(c) and (f), respectively.The microcracks, cleavage steps, cleavage surfaces, microvoids and tear ridge are marked by yellow arrows, while the slip traces are marked by whilte arrows (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

4.1.1.Solid solution strengthening

Solid solution strengthening by Al [27], Zn [28], Sn [29],Rare-Earths (RE) [30–32]and other solutes is an important mechanism to improve the room and elevated temperature(RT and ET) strength of Mg alloys.To estimate the solid solution strengthening effect on basal slip, Yasi et al.[33]developed a model ofσssas a function of the solute concentration and a potency factor for each solute.Taken with Taylor factor,σssis given as follows:

wherem=4.5 is the Taylor factor,Mxis the potency factor of solutexandcxis the solute concentration in the matrix.However,the Al solutes would precipitate in the form of Mg17Al12particles during the aging process.Thus, in the present work,theσssof Al and Zn can be neglected due to their few solid solubility present in the matrix.

4.1.2.Precipitation strengthening

For precipitation strengthening, the structure, morphology and orientation of precipitates play important roles to determine the YS of Mg alloys [9,34].Specifically, the different precipitate orientation can bring significantly different strengthening effect on Mg matrix.Many researches[11,12,35,36]based on Orowan strengthening theory were carried out to predict the strengthening effect of different precipitate orientation.At the same time, these predictions were also verified by the experimental results [8,12,37].Many experimental researches of Mg alloys deformed at RT and theoretical considerations based on single-crystal data suggest that basal slip will dominate the RT deformation process due to the fact that the critical resolved shear stress (CRSS) of basal slip is much lower than non-basal slip systems [4].Specifically, as shown in Fig.4, the average SF for basal slip of the compression samples are both over 0.4, it comfirms that the deformation of AZ31 Mg alloys at yielding occurs by basal slip [4].This suggests that the CYS improvement mainly imputes to the hardening arising from basal slip.In order to quantify the hardening effect of basal plates and prismatic plates on basal slip, the increment of CRSS (Δτ) originated by the need for dislocations to bypass the two different precipitates was estimated as follows.TheΔτis given as follows[11]:

whereGis the shear modulus of the Mg matrix,bis the magnitude of the Burgers vector for the gliding dislocations,λis the effective planar inter-particle spacing on the slip plane,vis the Poisson’s ratio of the Mg matrix,dpis the mean planar diameter of the particles on the slip plane, andr0is the core radius of the dislocations, which is approximated to be the magnitude ofb[22].

Based on Eq.(2), the appropriate version of the Orawan equations predicting the strengthening effect of basal plates and prismatic plates on basal slip were developed by Nie[11].For basal plates, Eq.(2) is rewritten in the form

For prismatic plates, Eq.(2) is rewritten in the form

whereD, Tandfis the uniform diameter, thickness and volume fraction of the plate-shaped precipitates, respectively.

According to these equations,theΔτis usually determined by the size (i.e., the uniform diameterDand thicknessTof plates) and the volume fraction (f) of precipitates.In the present study, according to the TEM images, theD, T, andfof plates were confirmed as 32.5nm, 22.4nm and 0.04, respectively.For Mg alloys, theGandvis 16.5GPa and 0.35,respectively.As a consequence, the calculatedΔτof basal slip produced by basal plates and prismatic plates is 40.87 and 59.67MPa, respectively.Clearly, theΔτof basal slip produced by prismatic plates is ～20MPa higher than that produced by basal plates.This is the reason why the sample ACA-45° containing prismatic plates shows the higher CYS than sample A-45° containing basal plates.It is noteworthy that the CYS of sample AC-45° containing prismatic plates is higher than that of sample ACA-45° also containing prismatic plates.This additional strengthening effect should be attributed to the grain refinement and introduced dislocation caused by twinning deformation [38].This part will be discussed in detail in the next section.After annealing, the twin boundaries of sample AC-45° were significantly disappeared,as shown in Fig.3d.Therefore, the hardening effect of sample ACA-45° should be largely attributed to theΔτof basal slip produced by prismatic plates.

Although, in the present study, the influence of texture on the CYS can be avoided due to the similar grain orientation and close SF, it has great affect on the YS of Mg alloys indeed.According to the Schmid law [39], theσpptis given as follows:

wheremsis the SF for basal slip.Clearly, the lower SF for basal slip is, the higherσpptis.According to the discussion above, different precipitate orientations make the distinct strengthening effect on basal slip.Hence, for basal plates precipitated alloys,e.g.Mg-Al alloys etc., substituting Eq.(3) into Eq.(5), the appropriateσpptcan be rewritten as follows:

Similarly, for prismatic plates precipitated alloys,e.g.Mg-RE alloys etc., the appropriateσpptcan be rewritten as follows:

As discussed before, it is speculated that theσpptproduced by prismatic plates may always be larger than theσpptproduced by basal plates.To further clarify the different hardening effects on basal slip produced by basal plates and prismatic plates,a schematic diagram is plotted to show the effect of these plates on dislocation gilding on (0002) basal plane of the Mg matrix.As described in Fig.8, the slip plane represents the(0002)basal plane of Mg matrix;the red arrows represent the dislocation motion direction; the black dislocations represent the dislocations before slipping; the red dislocations represent the dislocations after slipping and the basal plates and prismatic plates are inserted in Mg matrix,respectively.It implies that basal plates exert a weak blocking effect on dislocation motion, thereby causing a relatively lowΔτ.Thus,the basal slip is easy to occur and the Mg alloys containing such precipitates usually exhibit a lower YS, such as Mg-Al alloy systems [4].However, according to the description of prismatic plates, it usually exerts a strong blocking effect on dislocation motion, thereby causing a highΔτ[11].Thus,the basal slip is hard to occur and the Mg alloys containing prismatic plates usually exhibit a higher YS, such as novel Mg-Gd-Y alloy systems [40,41]and Mg-Nd alloy systems[9,42].

4.1.3.Grain boundary strengthening

It is well-known that grain boundary strengthening is a feasible way to enhance the YS of Mg alloys due to the considerable strengthening coefficient [43].According to Hall-Petch relationship [43], theσgbis given as follows:

wherekis the Hall-Petch coefficient (158MPa)[43]anddis the average grain size.Clearly, the smaller grain size causes the great contribution to YS[43].Therefore, compared to sample A-45°and sample ACA-45°,the CYS improvement of sample AC-45° originated from grain refinement can be given as follows:

The average grain sizes of sample A-45°, sample AC-45°and sample ACA-45° were illustrated in Fig.3.Accordingly,the grain refinement contribution to YS of sample AC-45° is～12MPa higher than sample A-45° and sample ACA-45°.To reveal the potential mechanism, a schematic diagram describing the microstructure evolution during compression along TD is depicted in Fig.9.For compression along TD, the precipitate orientation was altered, accompanied with the formation of twin boundaries (red line) and dislocations (green symbol),thereby causing the grain refinement strengthening and dislocation strengthening [44], which make extra contributions to the YS.Thus, the sample AC-45° exhibits a greater strengthening effect.

4.1.4.A yield strength model

Combined the above strengthening mechanisms, a total YS(σy) model with the dominated basal slip in Mg alloy was developed as:

Fig.8.A schematic diagram showing the effect of the orientation of precipitate plates on dislocation gilding on basal plane of the magnesium matrix.The brown plates represent the plate-shaped precipitates.The F denotes the force applied on matrix and λ is the angle between the force axis and the slip direction.The red arrow represents the slip direction.The black “dislocation symbol” represents the state of the dislocation before slipping, while the red “dislocation symbol” represents the state of the dislocation after slipping (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

Fig.9.A schematic diagram describing the microstructure evolution during compression along TD.The brown plates represent the plate-shaped precipitates.The red lines denote the twin boundaries and the green “dislocation symbol” represents the dislocation caused by twinning deformation.The Mg crystal shows the grain orientation evolution during the compression process (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

Note that theσ0can be determined via the SF law[39]giving as follows:

whereτ0is the initial CRSS of basal slip(5MPa)[45],Δτ/msis considered asσppt, and thusσ0equals toτ0/ms.

The YS model is proposed to analyze the effect of multiple factors, including solute, precipitation behavior, grain boundary and texture, on the YS of Mg alloys.As for precipitation behavior, it refers to precipitate orientation, size and volume fraction.Hence, for basal plates precipitated alloys with dominated basal slip,e.g.Mg-Al alloysetc., substituting Eqs.(1),(6) and (8) into Eq.(10), the appropriate YS model can be rewritten as follows:

Similarly,for prismatic plates precipitated alloys with dominated basal slip,e.g.Mg-RE alloysetc., substituting Eqs.(1),(7) and (8) into Eq.(10), the appropriate YS model can be rewritten as follows

For a micro-alloyed or a peak aged Mg alloy, such as the aged AZ31 investigated here, the solid solution strengthening contribution can be neglected due to the rare solute concentration in the matrix.Conbined with the present experimental results, when we discuss the variation of the YS as a function ofDand SF, thefanddare assumed to be 0.04 and 22μm,respectively.Besides, the ratio ofTtoD, namely aspect ratio,is supposed to be 0.7.When we discuss the variation of the YS as a function ofdand SF, the precipitate size is assumed thatD=32nm andT=22nm.The SF is assumed to be 0.4 when we discuss the variation of the YS as a function ofDandd.Accordingly, the trend of the YS as the function ofD,dand SF is depicted in Fig.10.

As shown in Fig.10, the theoretical YS increases with the decreasingD, dand SF, whether the alloy containing pris-matic plates or basal plates.When the SF for basal slip is close to 0, the theoretical YS will extremely increase to more than 1000MPa.This is due to other deformation systems will dominate the plastic deformation process [46].For instance,the extruded Mg alloy bar owns a strong<100>fiber texture in which the basal planes largely parallel to the extrusion direction (ED) [37].When tested in tension or compression along ED, the SF for basal slip is 0.However, it demonstrated that the activation of prismatic slip controls the YS in tension and the activation of {102} twinning controls the YS in compression [37].To compare the YS of the alloy containing prismatic plates and basal plates, the YS ratio of the alloy containing prismatic plates to the alloy containing basal plates are depicted in Fig.10g–i.It is found that the YS ratio is always larger than 1 with the same varites of SF,dandD.It can further imply that the YS of the alloy containing prismatic plates is greater than that containing basal plates continuously, confirming that the Mg alloys formed the prismatic plates always exhibit the appreciable YS[9,42].

Fig.10.The variation of the YS as a function of D, d and SF of (a)–(c) the alloy containing basal plates and (d)–(e) the alloy containing prismatic plates.(g)–(i) The YS ratio of the alloy containing prismatic plates to the alloy containing basal plates as a function of D, d and SF.Specifically, (a), (d) and (g) the YS/YS ratio as a function of D and SF; (b), (e) and (h) the YS/YS ratio as a function of d and SF; (c), (f), (i) the YS/YS ratio as a function of d and D.

4.2.Effect of precipitate type on ductility

It was reported that although prismatic plates have a strong blocking effect on basal slip, the blocking effect on prismatic slip is relatively weak [11].Wang et al.[36]developed the appropriate Orowan equations to quantify the strengthening effect on prismatic slip in HCP metals.For basal plates, the appropriate version of the Orowan equation is given as

For prismatic plates,the appropriate version of the Orowan equation is given as

Based on the counted results ofD, Tandffrom the TEM images, theΔτof basal and prismatic slip produced by basal plates and prismatic plates are calculated and listed in Table 2.Furthermore, the total CRSS (τ) of basal and prismatic slip can be obtained via the equation [22]:τ=τ0+Δτ, whereτ0is the initial CRSS of basal slip and prismatic slip.Note that theτ0of basal and prismatic slip adopted in the present study equals to 5 and 85MPa [45], respectively.

Table 2The calculated results of Δτ and τ of basal and prismatic slip according to the developed Orowan equations in HCP structure.

Fig.11.The histograms represent the CRSS for basal and prismatic slip which hardened by basal and prismatic plates, respectively.The black dashed line shows a descreasing trend of the CRSS ratio of prismatic slip to basal slip with the precipitate orientation changed from basal plates to prismatic plates.

It is found that the CRSS increment for prismatic slip caused by basal plates and prismatic plates is 42.68 and 41.91MPa, respectively.Subsequently, the total CRSS for prismatic slip strengthened by prismatic plates (126.91MPa)is lower than that strengthened by basal plates (127.68MPa).

The calculated results of CRSS are also plotted in Fig.11.Obviously, the CRSS ratio of prismatic slip to basal slip(τprism/τbasal) in the sample containing prismatic plates (1.96)decreases compared to the sample containing basal plates(2.78).It was reported [27,47]that the descreased CRSS ratio of non-basal slip to basal slip decreased, provided more opportunity to activate non-basal slips, which can enhance the ductility of Mg alloys at RT.Specifically, there is a high activity of prismatic slip at RT with aτprism/τbasalbetween 1.1 and 2.5 [48].Eventually, prismatic slip might be activated in sample ACA-45°, resulting in maintaining excellent ductility.It could account for the phenomenon that the ductility and strength of sample AC-45° improved simultaneously, and the strength of sample ACA-45° enhanced but the ductility not decreased.

Generally, the presence of the cleavage surface is usually the characteristic of brittle fracture.On the contrary, the presence of micro void is usually the characteristic of ductile fracture [49].These two fracture characteristics were employed simultaneously in sample A-45°and sample ACA-45°.However, compared to sample A-45°, more microvoids were formed on the fracture surface of sample ACA-45°, which indicates that sample ACA-45° has better plastic deformation capacity than sample A-45°.This phenomenon might also confirm the activation of non-basal slip systems.More slip systems could provide more mobile dislocations and less deformation resistance in the latter period of the deformation,resulting in excellent ductility.In terms of sample AC-45°, it shows better ductility than sample ACA-45°.This additional improvement in ductility can be attributed to the grain refinement caused by twin boundary [38].

5.Conclusion

In the present study, the effects of altered precipitate orientation on mechanical properties in AZ31 Mg alloy were investigated, and the corresponding strengthening mechanisms were discussed in detial.The key conclusions are summarized as follows:

1.The grain orientation was oriented fromc-axis//ND tocaxis//TD due to {101ˉ2} extension twinning process.Thus,the precipitate orientation in AZ31 Mg alloy was altered from basal plates to prismatic plates.

2.The CYS of sample AC-45°and sample ACA-45°with the prismatic plates improved by ～40MPa and ～20MPa than sample A-45°, respectively.Meanwhile, the compression ratio of sample AC-45° raised by 22% than sample A-45.

3.A YS model was developed to analyze the strengthening mechanisms.It was revealed that the optimized strength was attritubed to the altered precipitate orientation, refined grain size and dislocations produced by aging prior to twinning deformation process.Particularly, prismatic plates always exert a stronger blocking effect on basal slip than basal plates under the same variates ofD, dand SF.

4.Theτprism/τbasal of the sample AC-45° strengthened by prismatic plate was lower than that of the sample A-45°strengthened by basal plate,which gives the chance to activate prismatic slip.These slip systems could provide more mobile dislocations and less deformation resistance in thelatter period of the deformation, resulting in excellent ductility.

Declaration of Competing Interests

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

Acknowledgments

The authors gratefully acknowledge the Fundamental Research Funds for the Project of Science & Technology Department of Sichuan Province (2018HH0026), National Natural Science Foundation of China (51701132, U1764253) and China Scholarship Council (201907005018).We also thank the Analytical and Testing Center of Southwest Jiaotong University for assistance with SEM and EBSD experiments.