Plastic instability and texture modification in extruded Mg-Mn-Nd alloy

Sng Kyu Woo, Risheng Pei, Tll Al-Smmn, Dietmr Letzig, Sngong Yi

aMagic-Magnesium Innovation Center, Institute for Materials and Process Design, Helmholtz-Zentrum Geesthacht, Geesthacht 21502, Germany

b Institut für Metallkunde und Materialphysik, RWTH Aachen University, Aachen 52056, Germany

Abstract Even though Mg alloys containing Mn and rare earth elements lead to higher ductility and lower yield asymmetry due to the weak texture after extrusion, plastic instability, commonly known as the Portevin-Le Chatelier (PLC) effect, causes unexpected fragility in the service environment.In the present study, the PLC phenomenon and texture development during the deformation of Mg-Mn and Mg-Mn-Nd extruded alloys were investigated under various temperatures and strain rates.The addition of Nd causes not only texture weakening but also severe PLC phenomenon.The PLC phenomenon was significantly affected by the temperatures and the strain rates, which causes a difference in mechanical properties and development of texture.In the conditions of high temperature and low strain rate, the strength increased while the elongation decreased significantly, and obvious PLC phenomenon with severe serration and negative strain rate sensitivity.The initial texture was maintained even after deformation only under severe PLC conditions, and this is due to the restriction of basal slip and suppression of lattice rotation in PLC conditions.The series of results indicate that the PLC phenomenon causes a reduction of formability even at high temperature.

Keywords: Magnesium; Plastic instability; Portevin-Le Chatelier effect; Manganese; Neodymium; Texture.

1.Introduction

It has been widely accepted until recently that the microalloying of rare earth (RE) elements and/or Ca to Mg forms a significantly weaker texture during thermo-mechanical treatments, in comparison to commercial AZ-based alloys [1-8].The weak texture, e.g.a wider distribution of (0001) basal poles, allows the activation of dislocation slip on the basal plane, which is the dominant deformation mechanism of Mg alloys.The texture weakening with altering the basal-type orientation to a more randomized orientation distribution leads to an improved room temperature (RT) ductility and formability, reduced tensile/compressive anisotropy, and a balanced strain hardening.In addition to the texture weakening, the addition of RE and Ca affects the activities of various deformation mechanisms of the Mg alloys.Recent studies showed that Mg alloys containing Mn and a single RE element have an obvious trend to form a weak texture after extrusion.These weakened texture profiles lead to higher ductility and reduced asymmetry in tensile and compressive yield strengths[5,9,10].

Plastic instability, commonly known as the Portevin-Le Chatelier(PLC)effect,appears as unstable plastic flow during mechanical tests of structural materials such as steel, Al, Cu,and Mg based alloys.The occurrence of instability phenomena manifests in the form of ‘serration flow’ or ‘jerky flow’in the plastic range, within a specific range of strain rate and temperature [11-13].The PLC phenomenon has a diverse influence on various material properties.It increases the flow stress, maximum tensile strength, and work hardening rate,while the ductility decreases with decreasing strain rate sensitivity (SRS) coefficient and fracture toughness [11].Thus,it causes an unexpected vulnerability in the service environment or during the thermomechanical processes.This phenomenon has been extensively studied to understand the un-derlying mechanisms for engineering materials, such as steel,Cu and Al alloys.Recently, the direction of research has been extended to Mg alloys.Although several mechanisms have been proposed so far, the mechanism of PLC and its influence on the mechanical properties have not yet been clearly identified.Therefore, a further systematic study is still required according to the characteristics of each alloy system because various factors act in combination depending on the alloying element.

Recent studies reported the occurrence of the PLC phenomenon in Mg alloys, especially in Mg alloys containing RE elements [14-16].Nevertheless, there is still a lack of understanding the relationship between the plastic instability and microstructure and/or texture of Mg-Mn alloys.Even though the Mg-Mn-RE alloys obviously have the advantages from the texture weakening after extrusion, there is a concern that the properties are severely deteriorated due to the plastic instability at certain deformation conditions.The present study aims to investigate the PLC phenomenon in Mg-Mn and Mg-Mn-Nd extruded alloys under various temperatures and strain rates.The focus of the present study is laid to verify the correlation between the PLC phenomenon and texture evolution.The deformation conditions, at that the PLC effect is evident, were selected, and then the correlation between the mechanical behavior and the resulting deformation texture was analyzed in detail.

2.Experimental procedure

Pure Mg ingot and Mg-Mn and Mg-Nd master alloys were used for casting.The raw materials with nominal compositions of M1 (Mg-1 wt.%Mn) and MN11 (Mg-1 wt.%Mn-1 wt.%Nd) were molten in a steel crucible under a protective gas atmosphere.The melt was poured into a cylindrical steel mold preheated at 500 °C and quenched with the mold in water.After homogenization heat treatment for 16 h at 450 °C,the billets for extrusion were machined to 49 mm in diameter.The machined billets were preheated to 300 °C and then directly extruded through a circle die of 8 mm in diameter.The extrusion ratio and ram speed were 37.5:1 and 2.5 mm/s,respectively.Table 1 shows the chemical composition of M1 and MN11 alloys measured by spark optical emission spectroscopy (OES).

Table 1Chemical composition of Mn-based alloys measured by spark OES.

The specimens for microstructural observation were cut from the extruded bars and mounted using epoxy resin.The mounted specimens were mechanically ground using SiC papers up to #2400 grit and then polished using 3 μm diamond paste and water-free oxide polishing suspension.The polished specimens were etched using a mixed solution of 1 mL of nitric acid, 20 mL of distilled water, 20 mL of acetic acid, and 70 mL of ethylene glycol.The microstructures of specimens were observed using an optical microscope (OM, Nikon Optiphot 200).

The global texture was measured using an X-ray diffractometer (XRD, PANalytical X’Pert PRO MRD) with Cu Kαradiation.A beam size of 2 × 1 mm2 was employed to measure 6 pole figures, the (100), (0001), (101), (102),(110), and (103) up to a tilt angle of 70°.Normalized and background-corrected pole figures were used to calculate the orientation distribution function by using an open source code MTEX [17].The complete pole figures and inverse pole figures in the extrusion direction were calculated to present the texture.

The mechanical properties of the extruded alloys were examined using round-shaped specimens with a gauge length of 20 mm and a diameter of 4 mm.Tensile tests were carried out using a universal testing machine (Zwick, Z050)equipped with a heating furnace at various temperatures (RT and 150 °C) and strain rates (10?2/s, 10?3/s, and 10?4/s)in the extrusion direction.Prior to the mechanical loading,the specimens were preheated at the testing temperature for 10 min to ensure temperature uniformity over the specimen.After the tensile test, the specimens were immediately quenched in a water bath at RT in order to avoid the microstructure change due to slow cooling.Furthermore, strain rate jump tests were carried out to determine the SRS,mvalue.The strain rates were increased in 5 steps from 10?4to 10?2/s at each testing temperature.

Electron backscatter diffraction(EBSD)was carried out using a field emission gun scanning electron microscope (Zeiss,Ultra 55) equipped with an EDAX/TSL EBSD system with a Hikari detector.Longitudinal sections of the tensile specimens were ground and mechanically polished.Then, electrolytic polishing was carried out using a Struerse AC2 solution.EBSD measurements were performed at an accelerating voltage of 15 kV and a step size of 0.3 μm.The acquired EBSD data was analyzed using MTEX and TSL OIM analysis software.

3.Results

Fig.1 shows the optical micrographs of the as-extruded M1 and MN11 alloys.Both alloys show a fully recrystallized microstructure with equiaxed grains, resulting from dynamic recrystallization during extrusion.The M1 alloy shows an inhomogeneous grain size distribution, and the average grain size is classified into two groups: 14.9 ± 1.1 μm and 36.2 ± 1.0 μm.The MN11 alloy has a relatively uniform grain size distribution, and the average grain size is 8.8 ± 1.0 μm.The finer grain structure in the latter is attributed to the Nd addition.Extruded Mg-Mn-Nd alloys contain a large amount of Nd solute, the Mg-Nd intermetallics and thermally stable Mn-containing particles [5,9,10,18].The addition of Nd causes a change in the fraction and shape of the Mn-containing particles.These microstructural changes effectively inhibit grain growth.

Fig.1.Microstructure of extruded (a) M1 and (b) MN11 alloys observed using an optical microscope.

Fig.2.The recalculated (100) and (0001) pole figures (a, b) and inverse pole figures (c, d) of the extruded M1 (a, c) and MN11 (b, d) alloys obtained using X-ray diffraction.

Fig.2 shows the recalculated (100) and (0001) pole figures and the inverse pole figures of the extruded M1 and MN11 alloys obtained from XRD measurements.The M1 alloy shows a strong ‘basal-type’ texture in which the majority of the grains have the basal planes parallel to the extrusion direction (ED), Figs.2(a) and (c).Accordingly, the inverse pole figure shows high intensities along the arc between＜100＞and＜20＞poles.The＜100＞fiber component parallel to the ED, i.e.main deformation axis, is commonly formed by round extrusion of commercial Mg alloys [5,19,20].The addition of Mn is known to promote the formation of the basal-type texture of Mg alloys [20,21].The MN11 alloy shows a distinct texture with the basal poles largely tilted away from the ED, and the main texture components are represented by＜201＞and＜33＞components in the ED,Figs.2(b) and (d).The MN11 has a much weaker texture intensity than the M1 alloy, 2.7 m.r.d.(multiple of random distribution) and 4.6 m.r.d., respectively.Texture weakening has been reported in the Nd containing Mg alloys at a wider range of extrusion conditions such as temperature and speed, whilethe distribution of main components slightly varies with the extrusion conditions [5,9].Such texture with the tilted basal poles from the ED are classified as ‘RE texture’ components[5,9,10,19,21,22].

Fig.3.(a) Tensile stress-strain curves obtained at different temperatures and strain rates for M1 alloys, and the magnified stress-strain curves of the selected area at (b) RT and (c) 150 °C.

Fig.4.(a) Tensile stress-strain curves obtained at different temperatures and strain rates for MN11 alloys, and the magnified stress-strain curves of the selected area at (b) RT and (c) 150 °C.

Tensile stress-strain curves of the M1 and MN11 alloys obtained at different temperatures, RT and 150 °C, and initial strain rates, 10?2/s, 10?3/s, and 10?4/s, are shown in Figs.3 and 4, respectively.Table 2 shows the yield strength (YS), ultimate tensile strength (UTS), uniform elongation (UEl.) and fracture elongation (FEl.) corresponding to the flow curves under each condition measured in Figs.3 and 4.In the case of the M1 alloy, UTS and UEl.were measured in the curve after the yield point, to exclude abnormal peaks observed at the initial curve.Fig.3(b) and (c) show a magnified view of the flow curve in the selected area at RT and 150 °C, respectively.The selected area was determined near the UTS where the serration was prominent in order to compare the different serration behaviors according to testing conditions.At RT, theM1 alloy shows relatively high stress and low elongation.At 150°C,the fracture elongation significantly increased,accompanying the decrease in the strength.The distinct mechanical properties at different testing temperatures result from the difference in the dominant deformation mechanisms.While the dislocation slip is the main deformation mechanism at RT,thermally activated mechanisms, such as grain boundary sliding (GBS), dynamic recrystallization, the occurrence of creep driven by dislocation climb or diffusion, are responsible at high temperature [23,24].In the case of the M1 alloy, the flow stress was significantly reduced and the elongation is significantly increased, as the constraint of activating dislocation slip due to the strong basal texture at RT is alleviated by the reduced critical resolved shear stress (CRSS) values at 150 °C.By comparing the flow curves at different strain rates, there is a clear tendency that the flow stress increases as the strain rate increases, and the fracture elongation does not show a large difference with the variation of strain rates.Noteworthy is that serration is observed in some of the flow curves of the M1 alloy [Figs.3(b) and (c)].While the serration of the flow curve is almost negligible at RT, it becomes remarkable at 150 °C and a low strain rate of 10?4/s.

Table 2Tensile mechanical properties along the ED measured for the M1 and MN11 alloys at different temperatures (YS: yield strength, UTS: ultimate tensile strength, UEl.: uniform elongation and FEl.: fracture elongation).

The counterpart flow curves of the MN11 alloy at the same testing conditions are presented in Fig.4.In the MN11 alloy with the RE texture components, as shown in Fig.2(b)and (d), the activation of dislocation slip is relatively easy in comparison to the M1 alloy.When a tensile load is applied in the ED, Schmid factor for basal slip is initially high due to the tilted basal plane to the loading axis.Easier activation of the basal slip, as a result of a geometrical advantage, is generally accepted to promote enhanced ductility [14,21].The flow curves of the MN11 alloy with those properties differ from those of the M1 alloy.The tendency of increasing the stress as the strain rate increases is similar to that of the M1 alloy, but unlike the M1 alloy, the elongation also tends to decrease as the strain rate increases.At RT, similar to the M1 alloy, significant serration was not observed [Fig.4(b)].On the other hand, the results at 150 °C are noteworthy.Compared with the results at RT, the stress decreased slightly,but the elongation also decreased.In addition, evident serrations were observed at strain rates of 10?3/s and 10?4/s [cf.inset in Fig.4(a)].In Fig.4(c), the serration observed at a strain rate of 10?4/s is clearly much more prominent compared to other conditions.In the latter case of severe serration, the difference in stress between the highest and lowest serration points,Δσ, ranged from 5 ≤Δσ≤10 (MPa).It is clearly distinguished from the weak serrations under other conditions withΔσof 1 or less.As shown in Fig.4(a) and(c), the serration behaviors at 10?3/s and 10?4/s are classified into different types [11,16,25,26].‘TypeA’ band has a relatively small amplitude, but a large amplitude may appear periodically in the long range.It is can be subdivided according to these patterns.‘TypeB’ band characteristically a large amplitude accompanied by a stress drop in very short periods.This pattern is observed periodically over the long range.‘TypeC’ band results in a stress drop of large amplitude and a pseudo-periodic pattern is formed with large period.The serration at 10?3/s corresponds to the typeA, while a mixed type of serration similar to typeBis observed at the strain rate of 10?4/s.The variation of the serration type is attributed to the temperature increase, from typeAto typeBand typeC.TypeAserration is often observed at high strain rates or low temperatures, while typeCserration is observed at low strain rates and high temperatures.The type of serration is found to depend on the ’pinning nature’ between the dislocations and solute atoms according to varying strain rate and temperature.The pinning and unpinning abilities of the solute atoms to the dislocation is the predominant factor of the diverse serration behaviors.Unlike at RT, the stress increased and the elongation decreased significantly as the strain rate decreases.It is known to be due to the PLC effect associated with severe serration, which is prominently observed in the high temperature flow curve [11-13].

The degree to which the properties vary depending on the strain rate is expressed as SRS, m-value, which is considered an important parameter to explain better formability at higher temperatures [27,28].SRS is influenced by the alloy composition and microstructural factors such as grain size, texture and twinning and experimental conditions such as strain rate and temperature[22,29-32].In general,in a commercial alloy such as AZ31 alloy, them-value is in the range of 0 to 0.01,and the m-value tends to increase with increasing temperature and strain rate [29,30].The SRS parameter ‘m’ is expressed as Eq.(1.1), whereσ1 andσ2 are the flow stresses at each strain rates ˙ε1 and ˙ε2, and ‘n’ is the strain sensitivity coefficient [27,33].

The most common way to measure the SRS is to carry out each tensile test at different constant strain rates, as shown in Figs.3 and 4.However, due to deformation history and recovery, the microstructure may change for each test, and it affects the calculated m-value.Alternatively, SRS is of-ten evaluated by the strain jump test technique [31,34,35], or a stress relaxation test [36].These tests have the advantage of being performed with a fixed specimen microstructure, so that SRS can be accurately and reliably measured.Fig.5(a)shows the variation in flow stress according to the strain rate change, which was measured via the strain rate jump tests.Fig.5(b) shows the result of m-values calculated from the data sets shown in Fig.5(a).While the stress increase with the strain rate is obvious at RT in both alloys, the SRS of the MN11 alloy at high temperature varies with the range of the strain rates.At the range of the higher strain rate the SRS is positive, while a negative SRS is shown at the low strain rate range.It clearly indicates a negativem-value, unlike the other three conditions, which all have positive values in Fig.5(b).In particular, the trend is more pronounced at a low strain rate.

Fig.5.(a) Variation in flow stress with strain rate in each condition measured via the strain rate jump test, and (b) calculated m-value of the measured data in (a) with a variation of strain rates of M1 (black) and MN11 (red) alloys at RT (solid line) and 150 °C (dash line) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

Fig.6 shows the EBSD orientation maps measured from longitudinal sections of the tensile samples of the MN11 alloy fractured at different testing conditions.The orientation maps and inverse pole figures were measured at two different areas of the fractured samples, one at the area nearby the fracture surface (F) and the other at the uniformly deformed area (U).For the uniformly deformed area (U), an area where necking did not occur at least 5 mm away from the fracture tip (F)was selected to have a deformation similar to that of UEl.The examined alloys have similar values of UEl.under all conditions, Table 2, and they are considered to have undergone the same deformation at the area (U).The PLC phenomenon is most prominently observed at the testing condition of 150 °C and 10?4/s.At the testing condition of 150 °C and 10?2/s,the PLC phenomenon significantly diminished as the strain rate increases, and the sample tested at RT and 10?4/s is also almost free from the PLC phenomenon with the temperature decrease.The deformation degree should be relatively large at the area(F),where elongated grains along the loading direction are observed.In general, the deformation of commercial AZ-based alloys at elevated temperature accompanies dynamic recrystallization (DRX) and grain growth.The grain structure at the area (F) in Fig.6, does not show traces of DRX, which is believed to be restricted at 150 °C in the examined alloy.At the area near the fracture surface (F) of the sample tested at 150 °C and 10?4/s, the＜201＞component in the loading direction is maintained from the initial texture.On the contrary, the specimens with weak serration of the flow stress curves, i.e.tested at 150 °C and 10?2/s, and at RT and 10?4/s, clearly show the development of＜100＞component in the loading direction.The same comparison was made in the uniform deformation region (U), i.e.away from the fracture tip and necking zone.The specimen tested at 150 °C and 10?4/s maintained the initial texture with the intensity distribution along the arc from＜101＞and＜201＞to＜22＞and＜21＞components.Both of the other specimens did not fully maintain the initial texture.However, in the 150 °C and 10?2/s specimen, only a slight change was observed, whereas at RT and 10?4/s, it deviated from the initial texture and showed a complete＜100＞component.A change in texture in terms of intensity of＜100＞component was listed in the following order.Initial state ≈150 °C and 10?4/s (U)＜150 °C and 10?4/s (F) ≈150 °C and 10?2/s(U)＜RT and 10?4/s (U) ≤150 °C and 10?2/s (F) ≈RT and 10?4/s (F).This texture variety has a similar order to the PLC strength.

4.Discussion

4.1.Changes in microstructure, texture, and PLC effect according to Nd addition

The addition of Nd to the Mg-Mn alloy results in the grain refinement and the texture weakening accompanying the formation of RE texture components (Figs.1 and 2).The possible mechanisms for grain refinement were reported that fineand thermally stable Mn and Nd containing phases inhibit the grain growth by pinning [9,10].The underlying mechanism of texture weakening by the addition of RE is still controversial.Diverse mechanisms have been reported by many research groups, e.g.nucleation of recrystallization at shear or twin bands [1,7,9,21,37,38], enhanced non-basal slip activity [39,40], and the orientated grain growth controlled by solute drag or particle pinning along the grain boundaries[7,8,41-43].Of course, it is likely that several mechanisms act simultaneously.Nd is considered as an effective texture modifier among REs, and is known to contribute to an increase in ductility and a decrease in yield anisotropy through texture weakening[5,9,10].Such improvement of the mechanical properties of the Mg-Mn alloy by the Nd addition is supported by the stress strain curves at RT, Figs.3 and 4, of the present study.As such, the addition of Nd is considered to be a promising alloying element to achieve the desired mechanical properties by means of microstructure and texture modification.Nevertheless, it should be noted that severe serration of the stress strain curves takes place at a specific temperature and strain rate range, as shown in Fig.4.The M1 alloy does not show serration in the flow curves at RT, while it is partially observed at 150 °C and 10?4/s, Fig.3(c).In the MN11 alloy, a weak serration is observed already at RT,and the occurrence of the serration is severe at 150 °C, especially at the low strain rate.With decreasing the strain rate,the flow stress increases and the elongation decreases significantly in MN11 alloy at 150 °C, which is clearly depicted by a negative SRS(nSRS)value under the corresponding loading conditions.As such, nSRS is well-known as an indication of dynamic strain aging (DSA), which is considered as a major mechanism of the PLC phenomenon [11,26,33,44].DSA is defined as the interaction between the mobile dislocations and the diffusing solute atoms.According to this mechanism,the mobile dislocations act as a carrier of plastic deformation and move unsteadily between obstacles.Recently, extensive theoretical studies of the PLC effect and its mechanisms have been reported in the literature, including various novel simulations and insights into the nature of nucleation and the motion of the strain bands [33,45,46].In other studies, it has been quite discussed that DSA cannot explain all cases of nSRS [11,33,44,47].H?hner [48, 49]suggested that in order to satisfy nSRS, the DSA and the long-range dislocation interaction does not occur independently, but must be combined with each other.In this case, an unstable plastic flow is observed.When Nd is added, a large amount of Nd solute is present in the extrusion bar [9, 10].In order to control the movement of dislocation via interaction of Nd solute with mobile dislocation, diffusion of Nd solute and slow dislocation movement are required.At 150 °C and low strain rate of 10?4/s this condition is likely to be satisfied, as shown in Fig.4(a).Hence, it is reasonably inferred that DSA caused by Nd solute induces nSRS and causes PLC phenomenon.Several recent studies have reported DSA and PLC phenom-ena occurring in Mg alloys containing Nd such as Mg-Zn-Nd[15,16]and Mg-Y-Nd [32].

Fig.6.The EBSD orientation maps from longitudinal sections of alloys and the corresponding inverse pole figures for the area nearby the fracture surface(F) and uniformly deformed area (U) after tensile test under each condition of MN11 alloy; (a) 150 °C_10?2/s, (b) 150 °C_10?4/s, and (c) RT_10?4/s.

4.2.Correlation between PLC phenomenon and texture according to temperature and strain rate in MN11 alloy

There is a consensus that the addition of RE to the Mg alloy significantly affects the evolution of the microstructure during deformation at high temperatures.This is often explained by the retardation of dynamic recovery (DRV) and DRX due to solute drag or boundary pinning [1,7,21,39].This is very important for altering the basal-type texture,as the DRX kinetics is controlled by the amount of stored energy in the deformed microstructure and nucleation during static recrystallization.The results of Figs.3-6 show the interrelationship among the microstructural change caused by the addition of Nd, mechanical properties, texture development and PLC phenomenon.It is obvious that there is a very close relationship between the development of the texture and the occurrence of PLC phenomenon [46,50,51].The results of the present study clearly show that the texture and PLC phenomenon are strongly dependent on the alloying element and experimental conditions.Even in the case of the same initial texture, the resulting texture from the tensile deformation varies in correspondence with the PLC occurrence.The tensile specimens deformed at three different conditions corresponding to the degree of serration show distinct deformation textures, Fig.6.Lattice rotation during uniaxial tension commonly results in the formation of＜100＞texture component, as shown in Fig.6(a)and (c).However, in the specimen deformed at 150 °C and 10?4/s, Fig.6(b), the texture rarely changed and the initial texture was maintained.In other words, plastic spin was suppressed by some factors.It is also believed that the factor is related to the observation of strong serration under this condition.

In order to analyze the slip system that is dominantly activated during deformation under each condition in-grain misorientation axes (IGMA)analysis was conducted based on the EBSD results.This analysis provides insight into the local rotation of the crystal lattice due to dislocation slip [39,52,53].For example, deformation due to prismatic＜a＞slip induces lattice rotation around the＜0001＞axis,while basal＜a＞and pyramidal II＜c + a＞slip cause the lattice rotation around＜100＞and pyramidal＜a＞slip around＜102＞axes.In this work, the misorientation angle of 0.5°-2° was used in the IGMA analysis.Specimens deformed under conditions of RT and 10?4/s, 150 °C and 10?4/s, and 150 °C and 10?2/s which show a clear difference in texture as shown in Fig.6, were analyzed and compared.The grains with a GOS (grain orientation spread) of 1° or more were selected for the IGMA analysis.Fig.7 shows the IGMA distribution of the specimen deformed at RT and 10?4/s, showing weak serration.In Fig.7, among the grains of GOS＞1° in the uniformly deformed area (U), the IGMA analysis was performed on the grains selected according to the orientation.The grain orientations showing strong intensity in Fig.6 were analyzed by dividing into two IGMA types.Fig.7(a) shows the grains having their＜201＞poles in the ED, and the grains with＜100＞poles in the ED are shown in Fig.7(b).In the case of RT and 10?4/s specimen, a similar number of grains locate at＜201＞and＜100＞poles.The IGMA for the grains in Fig.7(a) show a relatively high concentration in the＜0001＞axis.Therefore, it is considered that the prismatic＜a＞slip was predominantly activated.On the other hands,＜100＞grains selected IGMA in Fig.7(b) show a relatively high concentration in the＜100＞axis, which means basal slip was predominantly activated for these selected grains.These results show that the activated slip system differs according to the grain orientations, and thus various slip systems are activated upon deformation.In the case of RT and 10?4/s specimen in Fig.7, activation of prismatic slip and basal slip leads lattice rotation, resulting in the strong intensity of＜100＞poles after fracture as shown in Fig.6(c).Fig.8 shows IGMA distributions of the specimen deformed at 150 °C and 10?4/s,which shows strong serration.In this specimen, a large number of deformed grains are selected at the＜201＞poles,while only a few grains locate at the＜100＞poles.The IGMA for the grains in Fig.8(a) show a relatively high concentration in the＜0001＞axis.Therefore, it is considered that the prismatic＜a＞slip was predominantly activated with other non-basal slips.Even though only a small number of grains in Fig.8(b) were analyzed, a high concentration was clearly distinguished in the＜0001＞axis.That is, the same IGMA is identified in the two different grain orientations in this specimen.It is indicated that activation of basal slip is strongly restricted regardless of grain orientations in 150 °C and 10?4/s specimen with strong serration.This could be related to the selective segregation of Nd solute atoms on the basal plane around basal dislocations.By DSA, the basal slip is hardened and the activation of non-basal slip is promoted at 150 °C and 10?4/s.That is the PLC effect contributes to maintaining the initial RE texture by suppressing lattice rotation during deformation.In addition, the reduction of the CRSS of non-basal slip at 150 °C should be also one of the reasons.This may also explain the result of relatively weak＜100＞pole of another specimen at 150 °C, in Fig.6(a),compared to RT specimen.Fig.9 shows IGMA distributions of the specimen deformed at 150 °C and 10?2/s, which also shows relatively weak serration.Similar to 150 °C and 10?4/s specimen in Fig.8,the high concentration in the＜0001＞axis is shown, but the grains with＜100＞poles in the ED show high concentration in the＜100＞axis, similar to RT and 10?4/s specimen in Fig.7.This means that more basal slip is activated with prismatic＜a＞slip in this specimen, and it may indicate a relative dominance of the effect of temperature rather than that of strain rate.However, it is believed that the lower strain rate contributes to a stronger suppression of basal slip, so that lattice rotation is more restricted in the 150 °C and 10?4/s specimen.

Another important deformation mechanism is GBS, especially at elevated temperature and moderate strain rate.The occurrence of the GBS, especially the GBS induced by the grain boundary diffusion, is considered to weaken the textureby accepting the grain rotation during deformation [54,55].The GBS is in general accompanied by fine grains formed in the vicinity of grain boundaries as a result of DRX [56,57].However, as shown in Fig.6, the samples of the present study do not show such DRXed microstructures, and the relatively high flow stress is observed during the deformation of MN11 alloy at the elevated temperatures.These observations are not manifested in the occurrence of the boundary diffusion-based GBS, such that the texture formation is not caused by the GBS.

Fig.7.Inverse pole figure maps (top) and corresponding IGMA analysis results (bottom) on the uniformed area (U) of RT_10?4/s specimen corresponding in Fig.6(c); (a) and (b) represent the selected grains from inverse pole figure marked as purple and blue, respectively (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

Lattice rotation during the deformation is also influenced by the secondary phases[58,59].Table 3 and Fig.10 show the fraction of stable phases of the M1 and MN11 alloys calculated using the thermodynamic software PANDAT.While the fractions of the Mn-containing phases are not significantly different in both alloys, the fraction of the Nd-containing phases in the MN11 alloy is much higher than the Mncontaining phase.At 450 °C, all Nd-containing phases are dissolved, but thermally stable Mn-containing phases are not completely dissolved.During the extrusion and air-cooling the Mn-containing phase is mostly precipitated, whereas theNd-containing phases are not fully precipitated and a large amount of Nd solute is dissolved in the as-extruded bars.Such a large amount of dissolved Nd solute can induce the PLC by interaction with mobile dislocations.The fraction,distribution, and shape of the Mn and Nd-containing phases change during high temperature deformation [9,10,60,61].Especially the diffusion and precipitation of the Nd-containing phase is facilitated when the sample is exposed to the thermal environment for a long time during the low strain rate defor-mation at 150 °C.These results elucidate that the dynamic microstructural change during deformation affects not only the PLC phenomenon but also the development of the texture.It seems that the large number of dynamic precipitates formed in this way maintained the initial texture by suppressing the lattice rotation.In order to suppress lattice rotation by the precipitate, a condition in which a very slow deformation rate is applied for a long time in a thermal environment must be satisfied, which corresponds very well to the condition for the occurrence of the PLC phenomenon.From this point of view, not only the interaction between the Nd solute atom and the dislocation, but also the interaction between the dislocation and the precipitate can be regarded as the possible mechanism for the PLC phenomenon of the Nd-containing alloys.

Table 3Fraction of stable phases of M1 and MN11 alloys at difference temperatures calculated by thermodynamic calculation software PANDAT (in wt.%).

Fig.8.Inverse pole figure maps (top) and corresponding IGMA analysis results (bottom) on the uniformed area (U) of 150 °C_10?4/s specimen corresponding in Fig.6(b); (a) and (b) represent the selected grains from inverse pole figure marked as purple and blue, respectively (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

The dislocation density remaining in the deformed material, i.e.geometrically necessary dislocations (GNDs), can be visually expressed using a kernel average misorientation(KAM) map [39,62].Fig.11 and Table 4 show the KAM map and the relative fraction according to the misorientation angle interval of area (U) in Fig.6 in each specimen.In general, the deformed grains have a relatively high KAM due to the high density of GNDs, and low KAM in recrystallized grains [63].As shown in Fig.11, all specimens show uniform deformation.The sample deformed at RT and 10?4/s,Fig.11(c),shows the highest KAM value.The other two specimens have relatively low KAM values because they were deformed at 150 °C.Comparing the specimens deformed at different temperatures, the 150 °C and 10?2/s specimen in Fig.11(a) shows a relatively larger fraction of a lower KAM value overall.In general, localized misorientation decreases as the deformation temperature increases, due to the increase in the DRV fraction [64], which corresponds well with the results of Figs.11(b) and (c).When the strain rate is low,localized misorientation decreases, because DRV occurs during deformation at low strain rate [64,65].Accordingly, it is expected that the 150 °C and 10?4/s specimen should have a lower KAM value than the 150 °C and 10?2/s specimen.But the results in Figs.11(a) and (b) do not correspond to this,but rather show a higher KAM value in 150 °C and 10?4/s specimen.It means that the stored strain energy is higher in the 150 °C and 10?4/s specimen with strong serration thanthat of 150 °C and 10?2/s specimen.This indicates that a large number of dislocations are accumulated during the deformation process due to the PLC effect and the restriction of dynamic recovery.The higher GNDs of the former is elucidated by the stronger dislocation interaction with solute or precipitate, or pile-up by PLC effect.This corresponds very well to the reversal of the trend in flow curves (Fig.4).That is, the flow stress of 10?4/s specimen was higher than that of 10?2/s specimen at the same temperature.As mentioned above, this result is related to the microstructure change during high temperature deformation due to the effect of the Nd addition.Serration in flow is observed only when sufficient long-range diffusion of obstacles such as solute or forest dislocation is involved [11,33,66-68].In this case, the movement of dislocation must be controlled by clustering as an obstacle for a certain amount of time, and the solute moves to the junction of forest and mobile dislocation to increase the strength and inhibit dislocation movement (pinning).After that, when the aging rate is slowed and the dislocation is suddenly released, stress drop occurs (unpinning), and this process is expressed as nSRS and severe serration.Depending on the strain rate and temperature, the time for dislocation movement and clustering formation and action varies.Based on these, nSRS and serration occur under conditions where dislocation and clusters can continuously interact.At high temperature, the deformation at 150 °C and 10?4/s accompanying the severe serration satisfies this condition, DSA and nSRS are induced.Thus the specimen at this condition has a relatively high GNDs at high temperature deformation compare to higher strain rate specimen.Accordingly, the misorientation degrees, in Figs.11(a) and (b), match well to the conditions of the occurrence of PLC.

Table 4The fraction in the range of kernel average misorientation angle of each specimen corresponding to Fig.11 (in%).

Fig.9.Inverse pole figure maps (top) and corresponding IGMA analysis results (bottom) on the uniformed area (U) of 150 °C_10?2/s specimen corresponding in Fig.6(a); (a) and (b) represent the selected grains from inverse pole figure marked as purple and blue, respectively (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

Fig.10.Equilibrium phase fraction of the (a) M1 and (b) MN11 alloys calculated using thermodynamic calculation software PANDAT.

Fig.11.Kernel average misorientation (KAM) distribution maps (top) and the relative fraction according to the misorientation interval in each specimen(bottom); (a) 150 °C_10?2/s, (b) 150 °C_10?4/s, and (c) RT_10?4/s.

5.Conclusion

In this study, the texture and the mechanical properties under various temperatures and strain rates of the extruded Mg-Mn and Mg-Mn-Nd alloys were compared,and the correlation between the PLC phenomenon and the texture according to the Nd addition was analyzed.The main results of the present study are summarized below.

(1) The addition of Nd leads to the texture weakening and occurrence of the PLC phenomenon in an extruded Mg-Mn alloy tested in uniaxial tension at ambient and 150 °C.

(2) The PLC effect (serrated flow behavior) is significantly facilitated at 150°C and low strain rates between 10?3/s and 10?4/s.

(3) The relationship between flow stress and strain rate is reversed at 150 °C with the occurrence of the PLC effect, i.e.the stress level rises with decreasing strain rates.

(4) Under the condition of severe serration in the plastic flow, the deformed sample maintains the initial extrusion rare earth-type texture, which indicates that lattice rotation was suppressed during tensile deformation at 150 °C.

(5) The decrease in high-temperature ductility despite maintaining the weakened texture and increasing the deformation temperature is due to the plastic instability associated with the occurrence of the PLC phenomenon.

Conflict of interest

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.

Acknowledgment

The authors are grateful for the financial support of German Research Foundation (DFG) (Grant Nr.Yi103/3-1 and AL1343/8-1).