Crimp feasibility of AZ31 magnesium alloy wide plate at warm temperatures responding to asymmetry

Fangkun Ning,Qichi Le,Jiashi Yan,Yonghui Jia

Key Laboratory of Electromagnetic Processing of Materials,Ministry of Education,Northeastern University,Shenyang 110819,China

Abstract The crimp feasibility of AZ31 Mg alloy wide plate responding to asymmetry and anisotropy at different temperatures was conducted by bending experiments and numerical simulation.Through the microstructural characteristic,mechanical properties,EBSD and FEM analysis,the results indicated that {10-12} twins and pyramidal 〈a〉 slip were dominated at the inner surface layer of the plate,while prismatic and pyramidal 〈a〉 slips were controlled at the outer layer when bending at 100°C,and their quantity decreased as the temperature elevation and vanished at 200°C.The fl xural deflectio increased gradually with the augment of fl xural temperature,while the fracture stress weakened.A large number of twins nucleated and grew in the coarse grain,causing major distribution proportion of high angular grain boundaries(HAGBs)at the compression part,which could improve its fl xural properties and affect subsequent strain contours,twins and recrystallization distribution.The offset of the neutral layer declined from 1.4125mm to 0.7261mm with the temperature rising from 100°C to 250°C when bending,while it was concentrated on 0.0338-0.0481mm when coiling,accounting for 0.26%-0.37% of the plate thickness.At last,the reel diameter descended with increasing the temperature and coiling rate.

Keywords: Plate coiling;Flexural deflection Fracture stress;Neutral layer;Schmid factor.

1.Introduction

Magnesium (Mg) alloys are found wide interest as the lightest commercialized metallic structural materials for the weight-saving purpose,high specifi strength,favorable electromagnetic shielding capability,and so on [1-5].Moreover,Mg alloy plates are widely used in the fiel of aviation,spaceflight automobile,electronic products,and biomaterials [6-9].Besides,Mg alloy wide sheet is one of the key materials for automobile lightweight;the weight can be reduced by more than 60% by replacing steel plate and lessened 30% by replacing aluminum alloy plate [10,11].At the SAIC MOTOR real vehicle test,a 10% mass reduction induces many benefits such as fuel-efficien improvement,pollution emission reduction,and enhancing crashworthiness.The material is deformed between rolls to produce plate to a homogeneous thickness and large area [12].The resulting sheet is then available for transportation and further processing in sheet metal forming procedures,which are viable for a large variety of applications.Thus,sheets are important products if the full potential of a class of materials is to be realized.However,affected by the hexagonal close-packed (HCP) structure,Mg alloys with limited-slip systems also exhibit limited strength,ductility,and plastic formability,making they prone to crack during their plastic deformation.Mg alloys have strong anisotropy in the rolling deformation process.Mg crystal cell has a small deformation resistance in the direction parallel to the basal plane,but a large deformation resistance in the direction perpendicular to the basal plane[13,14].Lee et al.[15] investigated that the bending formability of rolled AZ31 Mg alloy could be improved through precompression and subsequent annealing.Ma et al.[16,17]indicated that the persistent tensile preloads,promoting the directional movement of neutral layer,would weaken the bending properties of AZ31 Mg alloy.Han et al.[18] studied that the formability of Mg alloy sheet would be enhanced undergoing continuous bending and annealing.After rolling,the strong texture is formed in the normal direction,where it is difficul to continue to deform.Mg alloy has an obvious asymmetry of tension and compression,which seriously limits its extensive application[19].Due to the above deformation characteristics,the secondary forming of Mg alloy is hard [20].The strength differential effects in the forming process will cause cracks in the plate,which will lead to the fracture of the material.Fracture,caused by early cracks,has a fatal effect on the Mg alloy plate,so it is very important to control cracks initiation and propagation [21].The lower volume heat capacity and inferior thermal conductivity lead to temperature variation and heterogeneity,which make the edge part of the plate cooling faster than the middle part [22,23].Therefore,the cracks are prone to emerge on the edge during hot continuous rolling.The accuracy control of cracks,breadth,and shape is the key to realize large coil weight.

The conventional rolling process of Mg alloy could divide into fi e processes:(i)heating process(Mg alloy casting billet heating in a continuous heating furnace),(ii)transport process(hot billet transporting on conveying roller),(iii) rolling process (rough rolling),(iv) finishin process (hot-straightening before finishin rolling) and (v) coiling process (coiling in coiler furnace) [22].Nevertheless,after roughing the billet into a plate with medium thickness,the larger surface area and the rapid heat dissipation will increase the subsequent heating process and the difficult of finishin rolling.The temperature compensation has an important influenc on the process of Mg alloy plate rolling.Therefore,coiling the plate after roughing can effectively reduce the exposed area and heat dissipation to improve the yield of the plate after finish ing rolling.The present work aims to reveal the crimp feasibility of the plate between roughing and finishin at different temperatures.

2.Materials and methods

The experimental material was a commercialized AZ31 Mg alloy plate (as-rough-rolled) with a sample size of～×1600mm (width)×13mm (thickness) and the nominal chemical composition of Mg-3.05Al-0.98Zn-0.21Mn(wt.%).After the plate removing from the roughing mill,it was fed into the coiler,wound on the reel,and kept insulation in the coiling furnace.When the billet had been roughed,the plate was uncoiled from the coiling furnace into the next rolling process (Fig.1a).Coiling could be thought of as the bending of a plate at a certain time.Therefore,the coil behavior of a plate was investigated by taking samples from the plate.As shown in Fig.1c,the sample size is 130mm×30mm×13mm with thermocouple points on the side of the sample,and two round holes with a diameter of 6.5mm are drilled at both ends of the sample.The bending experiment schematic diagram is shown in Fig.1.The bending samples are insulated with aluminum silicate blanket around the sides,heated with heating rods at both ends and controlled by a temperature control cabinet.The simulation was carried out under the same process conditions as the bending experiment (Fig.1b) and the simulated plate was meshed and marked with nodes to facilitate analysis.

The bending experiment was completed by using the bending mold on the universal tensile testing machine,in which the fl xural stress-strain curves under various conditions were obtained.The diameters of the back-up rolls and upper rams were 30mm and 10mm respectively.The span was 90mm and the plate temperature was heated to 100-250°C with the median interval 50°C.The pressing speeds of the ram were set as 10mm/min and 30mm/min.The parameters of the bending simulation were consistent with the bending experiment.The coiling simulation was carried out on the reel with a diameter of 600mm and a crimp rate of 0.6m/s at the same temperature with bending.The samples for microstructure observation were machined from the RD-ND section.The microstructures were observed using the Olympus optical microscope (OM) and FEI NOVA fiel emission scanning electron microscope (SEM) with Oxford electron back-scatter diffraction (EBSD) probe.The macro-texture was analyzed using an XD8ADVANCE-A25 X-ray diffractometer (XRD,Bruker).

3.Results and discusses

3.1.Microstructural characteristic of the plate during coiling (bending)

Due to the Mg alloy is subjected to severe plastic deformation,the material inside generates more heat and the temperature of the surface layer is lower because of faster heat loss[24].Therefore,there are relatively large differences between the surface layer and the center layer of the Mg alloy plate.The AZ31 plate rolling schematic,as-rolled plate pole fig ures,grain size distributions,and microstructures are shown in Fig.2.As can be seen from the metallographic microstructures (Fig.2d,g),the grain size of the surface layer or the center layer is relatively uniform,but the average grain size of the surface layer (Fig.2c,8.1μm) is smaller than the center layer (Fig.2c,10.1μm).However,the intensity (I) of the basal texture of the surface layer is stronger than that of the center layer,as shown in Fig.2b(I=9.7)and Fig.2e(I=8.1)respectively.

The surface layer and the center layer of the Mg plate will generate differences in microstructure during the bending process due to the disparity of the as-rolled plate.When coiling the Mg plate,the inner side is subjected to compressive stress and the outer side is undergone tensile stress.As we all know,Mg alloys have inferior deformation performance at room temperature,especially for Mg plates with strong basal texture.During the coiling and bending deformation of the magnesium plate,{10-12}extension twinning exists when the compressive stress direction is applied perpendicular to thecaxis of the grain,and{10-11}compression twinning proceeds when the tensile stress direction is implemented perpendicular to thec-axis of the grain.Fig.3 is the microstructures of the AZ31 plate after bending at different temperatures.A large number of twins are observed in the comprehensive (inner)part (Fig.3a) of the plate,but few twins in the tensile (outer)part (Fig.3c) when bending at 100°C.The number of twins in the inner (Fig.3d) and outer (Fig.3f) position decreases at 150°C with almost no twins in the middle layer.When the fl xural temperature reaches 200°C or above,recrystallization occurs at the compression (Fig.3g) and tensile positions(Fig.3i),and fin recrystallization grains are generated at the original grain boundary and twin grain boundary.The recrystallization degree at 250°C (Fig.3j-l) is higher than that at 200°C.

Fig.1.(a) Coil rolling process,(b) Bending simulation diagram,(c) Bending samples,(d) Bending experiment schematic diagram.

Roodposhti et al.[25] studied the microstructure evolution of AZ31 Mg alloy under high temperature deformation and showed that {10-10} 〈1-210〉 prismatic slip and {10-11} 〈1-210〉 pyramidal slip were activated wrought at 175°C and 225°C respectively.The non-basal slip is not activated at low deformation temperature,and the deformation mainly depends on slip and twinning to coordinate the strain [26].The production of twin variants and twin types is related to the grain size,deformation temperature,strain rate,and grain orientation.Therefore,during the Mg alloy plate bending experiment,a large number of twins are generated to coordinate the plastic deformation.

3.2.Mechanical properties of the plate during coiling(bending)

The stress and strain in the bending process are obtained by Eqs.(3.1) and (3.2) and shown in Fig.4.

whereDis fl xural deflection mm;dsample thickness,mm;Lspan,mm;bsample width,mm;Pfl xural load,N.

As can be seen from Fig.4,with the increase of fl xural temperature,the fl xural stress of the sample decreases gradually,and the fracture fl xural strain augments gradually,which indicates that the bending performance of AZ31 Mg alloy rolled plate becomes better as the raising of temperature [27].At room temperature,only the (0001) basal slip of Mg alloy with two independent slip systems is activated.When the plastic deformation proceeds at a lower temperature,the deformation is mainly coordinated by the basal slip and twinning to relax the local stress concentration generated in the plastic deformation process [28].The prismatic slip and pyramidal slip in Mg alloy are activated with deformation temperature increment and more slip systems coherence strain can improve the plastic deformation ability of Mg alloy.When the Mg alloy is bent at a lower temperature (100-200°C),the curves of fl xural stress and strain are smooth at the initial stage of deformation,while the curves become zigzag as the number of deformation increases.The spacing of zigzag gradually increases with the augment of fl xural temperature and the phenomenon of zigzag disappears at 250°C.Some studies [14,29,30] have shown that the zigzag phenomenon is caused by the interaction between movable dislocation and solute atoms.At the beginning of the deformation,the slow solute atom diffusion velocity is not enough to produce dynamic strain aging,so the early deformation curves are smooth.The diffusion velocity of solute atoms accelerates as the augment of strain to pin dislocations.For the dislocations to move persistently,a large force is needed to get out of the pinning of solute atoms,resulting in the zigzag of the stress-strain curves.The average transfer velocity of the solute atoms is similar to that of the dislocations and the solute atoms no longer play a role in locking dislocations due to evaporation of solute atoms atmosphere when bending at 250°C.Therefore,the dynamic strain aging effect did not appear under this condition.

Fig.2.AZ31plate rolling schematics (a),surface and center pole figur (b,e) of as-rolled plate,grain size distribution (c,f) and microstructure (d,g) graphs.

The fl xural deflectio and fracture stress of the AZ31 plate at different temperatures are listed in Table 1.As seen from Table 1,the fl xural deflectio increases from 15.7mm to 24.9mm gradually with the augment of fl xural temperature,while the fracture stress weakens from 479MPa to 177MPa inch by inch.This is because,with the increase of fl xural temperature,the prismatic slip and pyramidal slip are activated to enhance the slip systems,which makes the deformation of magnesium alloy sheet easier.

Table 1 Flexural deflection and fracture stresses of AZ31 plate at different temperatures.

When the temperature rises from 100°C to 250°C with the interval 50°C,the deflectio variation reaches 15.9%,25.8%,and 8.7% and the fracture stress variation gets to 15.7%,59.8%,and 46.3% respectively.It can be seen that deflec tion and fracture stress are most affected when bending at 200°C.The relationship of temperature with critical resolved shear stress (CRSS) in Mg and Mg alloys is shown in Fig.5.It can be intuitively seen from Fig.5 that the CRSS of the basal slip and the prismatic slip are distinctly smaller than that of the pyramidal slip and the contraction twinning under the recrystallization temperature,but the CRSS of the tension twinning is smaller than that of the prismatic slip.From the above analysis,it can be concluded that the non-basal slip systems can activate at 200°C with lower CRSS [31,32] under the dual action of stress and temperature,making the material soft,deflectio incremental and fracture stress dropping significantl .

Fig.3.Microstructures of AZ31 plate after bending at different temperatures (a-c) 100°C,(d-f) 150°C,(g-i) 200°C,(j-l) 250°C.

Fig.4.Flexural stress-strain curves at various temperatures.

Fig.5.Relationship of temperature with CRSS in Mg and Mg alloys.

3.3.EBSD analysis of the plate during coiling (bending)

When the plate is coiled or bent,the material in the inner and outer layer is subjected to different force,which causes various rotation of the internal grains of the plate,resulting in different types of twins,strains,and recrystallization [13].The{10-11}twinning is activated at 100°C with larger CRSS[33],while the CRSS of the prismatic and pyramidal slips at 100°C is similar to them at room temperature as shown in Fig.5.Therefore,the EBSD analysis of inner and outer layer samples is conducted at 100°C [34].

Due to the different magnitude and direction of internal and external force,the plate is subject to yield asymmetry during coiling/bending.Because of the unique hexagonal closepacked structure of Mg alloy,diverse twinning types will be generated to coordinate the deformation when thec-axis of the crystal cell applied forces in different directions.From the comparison between the band contrast images (Fig.6a and d)and the microstructures (Fig.3a and c),it can be seen that there are more twins in the inner plate.Additionally,as shown in Fig.6b and e,thec-axis of the inner layer grains are parallel to the normal direction (ND),while thec-axis of slight grains in the outer layer is parallel to the transverse direction(TD) (red grains in Fig.6e).The misorientation angles are focused on the low angle grain boundaries (LABGs) at the tension part.However,a large number of twins nucleate and grow in the coarse grains,causing major distribution proportion of high angle grain boundaries(HAGBs,about 86°)at the compression part.The HAGBs at the inner side of the bent plate could improve its fl xural properties and affect subsequent strain contours,twins,and recrystallization distribution.

The strain contours and HAGBs-LAGBs maps under diverse deformation zones are shown in Fig.7.The green lines represent the LAGBs (θ＜10°),while the black lines refer to the HAGBs (θ＞10°).The regions with larger strain value in the strain counters also have plentiful LAGBs.The LAGBs are formed by the moving dislocations rearrangement and merging when they pile up to a certain extent in the deformation process.The denser of the LAGBs indicates that the deformation is more severe.The darker of the strain contours means the more likely to produce microcracks in the deformation process,resulting in plate fracture failure.From the above analysis,it can be seen that the stretched zone of the plate produces a larger strain when coiled,resulting in a greater tendency to crack.

Fig.8 shows the recrystallization and {10-12} twins distribution at different deformation zone.The recrystallization grains at the compression zone account for about 10%(Fig.8b),which is much larger than that at the tension zone.When the Mg alloy plate is bent at 100°C,a mass of twins are generated at the compression zone (Fig.8c) to coordinate deformation,while very tiny twins are generated at the tension zone (Fig.8f).Lu et al.[35] investigated dynamic recrystallization (DRX) of Mg and its alloys and indicated that DRX induced by twins producing when Mg alloys deformation at lower temperatures.Therefore,the number of recrystallized and substructured grains is also large in the part with more twins.

Fig.6.Band contrast images (a,d),IPF coloring maps (b,e),and misorientation distribution maps (c,f) of the compressive (a-c) and tensile (d-f) layer of plate.

Fig.7.Strain contours and HAGBs-LAGBs maps:(a,b) compressive side;(c,d) tensile side.

The micro-pole figure and inverse pole figure are shown in Fig.9.The texture intensity of the compression part is 7.45 and that of the tension part is 11.99.It can be seen from Fig.9a that the pole density points of (0001) pole figur are distributed along RD.Thus,it can be informed that the orientation of the grains of the compression part has transformed into RD (Fig.9b unit cell).However,at the tension part,the pole density points of (0001) pole figur are distributed along with ND.It can be inferred that the grain orientation of the tension part is mainly concentrated in the direction of ND(Fig.9d unit cell).

Fig.10 shows the macro-textures of the bent plate.By comparing Fig.10 to Fig.9,it can be found that the distribution of macro-textures is similar to that of micro-textures.The texture orientation at the compression zone is deflecte to RD and ND (deviating to RD 18°) at the same time,which is related to the quantity of the grains detected by XRD.This is mainly caused by the deviations in the test scope.The grains scanned by the EBSD were less than the grains localized by XRD,about 300-400 grains.Therefore,the micro-texture at the compression part is just concentrated on RD.

The plastic deformation of the material is mainly completed by sliding and twinning [36].With increasing the Schmid factor (SF),the probability of sliding system activation increases as well.In the process of plastic deformation,the evolution of texture mainly depends on the movement of the slip system and twin system,so the SF diagram obtained by EBSD can be used to explain the evolution of texture theoretically.Fig.11 is the SF statistics of three 〈a〉 slip systems loading in ND and RD.Fig.12 and Fig.13 are SFs of three 〈a〉 slip systems in the compression zone and tension zone,respectively.Applied force loading in ND,SF distribution of prismatic 〈a〉 slip system (pr＜a＞) is mainly concentrated at both ends,while the SFs of basal 〈a〉slip system (ba＜a＞) and pyramidal 〈a〉 slip system (py＜a＞)have a higher distribution in the interval greater than 0.35(Fig.11a).However,the SFs of pr＜a＞and py＜a＞are distributed in an interval greater than 0.4 (Fig.11b),which indicating that the deformation in compression zone is mainly accomplished by pr＜a＞and py＜a＞and the intensity of texture is partial to RD (Fig.10a).As shown in Fig.5,the CRSS value of {10-12} twins is between pr＜a＞and py＜a＞,so a large number of {10-12} twins are generated in the compression zone.

Fig.8.Recrystallization and {10-12} twins distribution maps:(a-c) compression zone;(d-f) tension zone.

Fig.9.Micro-pole figure and inverse pole figures (a,b) compression part;(c,d) tension part.

The SF distribution of pr＜a＞in the tension zone is roughly the same as that of the compression zone.However,the frequency of the SF of pr＜a＞is higher in the range of less than 0.15 when applied force loading in ND (Fig.11c),and SF of pr＜a＞has a higher frequency in the range greater than 0.4 when applied force loading in RD (Fig.11d).It is meant that deformation is prone to conduct loading in RD and is carried out by pr＜a＞in the tension zone.

Through EBSD analysis,we know that due to the different forces applied on the inside and outside of the material during coiling/bending,the orientation,type of the grains,SF,and texture intensity are different,which further affects the coil performance and coil formability of the plate.

3.4.FEM analysis

3.4.1.FEM analysis of the plate during bending

Fig.10.Macro textures of the bent plate:(a) compression zone,(b) tension zone.

The simulation time is based on the time required for plate fracture under each condition in the bending experiment.With increasing the temperature,the fracture defection and corresponding simulation time augment equally.Therefore,the simulation time at 100°C is 94.20 s while that is 149.40 s at 250°C.The simulation time and displacement corresponding to bending at different temperatures are shown in Table 2.It can be seen from the data in Table 2 that the experimental value of displacement is slightly smaller than the simulated value.The reason is that the head slows down before it stops during the bending experiment.However,it does not affect the stress of the material.Therefore,the deflectio of the plate neutral layer of the material is determined by bending simulation at different temperatures and stresses in the compression and tension zones.The neutral layer coefficien was obtained by Wang et al.[37] using a measuring method,but the exact offset was not acquired.In this paper,the offsets of plates at different temperatures are obtained by numerical analysis.

Table 2 Simulation time and displacement corresponding to bending at different temperatures.

Table 3 Neutral plane offset on bending at various temperatures.

Fig.14 is the schematic diagram of each parameter during bending,whereσcis bending stress on the compressive side,σtis bending stress on the tensile side,xd is neutral plane offset.According to the principle of material mechanics and the EBSD analysis,it can be obtained that the stresses on compression and tension zone are mainly controlled by {10-12}twinning,prismatic and pyramidal slips.Hence,the stress in the tension and compression zone can be represented as[38]:

Fig.11.Schmid factor statistics of three 〈a〉 slip systems loading in ND and RD:(a),(b) compression zone;(c),(d) tension zone.

Fig.12.Schmid factor of three 〈a〉 slip systems in compression zone:(a)-(c) loading in ND,(d)-(f) loading in RD.

Fig.13.Schmid factor of three 〈a〉 slip systems in tension zone:(a)-(c) loading in ND,(d)-(f) loading in RD.

whereNcandNtare distance compression and tension side to a neutral plane,respectively;Mis bending moment;Iis the cross-sectional secondary moment;XprandXpyare volume fraction of pr＜a＞and py＜a＞,respectively;σpr,σpy,andσtware the stress in the grains undergoing prismatic slip,pyramidal slip,and twinning,respectively.

In this research,twinning was nearly not observed in the tension zone of the bending plate,and the stresses in tension and compression zone are primarily administrated by pr＜a＞,py＜a＞,and py＜a＞,twinning,respectively.The yield stresses for pr＜a＞and py＜a＞are concluded by CRSS (τ) and SF (m)[39].According to the relationship between the CRSS formula and the familiar Hall-Petch relationship,the yielding behaviors can be expressed as Eqs.(3.5) and (3.6):

whereτprandτpyare the CRSS values of pr＜a＞and py＜a＞,respectively.kis the strength coefficien for the normal stress anddis The grain size.The average SFs,m,for pr＜a＞and py＜a＞at compression and tension zone are 0.267,0.343 and 0.436,0.417,respectively,which accord with thevalues measured by Wang and Choo [39].In addition,Liu et al.[40] demonstrate that pyramidal 〈c+a〉 dislocations can accommodate large plasticity through gliding on pyramidal planes,which can accelerate pyramidal 〈a〉 slip.

Fig.14.Schematic diagram of each parameter during bending.

Fig.15.Stresses of the inner and outer zones of the plate on bending at various temperatures (a) 100°C,(b) 150°C,(c) 200°C,(d) 250°C.

By combining Eqs.(3.3) and (3.4) with the simulation results (Fig.15,σcandσt),the neutral layer offset can be obtained and listed in Table 3.As the temperature augments,the neutral plane offset firs increases and then decreases,reaching the maximum at 150°C.With the increase of temperature,the strength differential effects decrease from 70MPa to 17MPa.The decline of the neutral layer offset and tensioncompression asymmetry is related to the fact that the nonbasal slip systems have been activated at 250°C.The offset of the neutral layer enhances abnormally (from 1.4125mm to 1.6094mm) at 150°C,which is since there are fewer actuated slip systems and a larger number of twins in the material,shown in Figs.5 and 3d and f,respectively.As can be seen from Fig.15,with the enhancement of bending deflectio and temperature,the influenc range of stress increases along RD,and that decreases along with ND,which also weakens the offset of the neutral layer.

3.4.2.FEM analysis of the plate during coiling

Fig.16.Stress field of coiling at various temperatures (a) 100°C,(b) 150°C,(c) 200°C,(d) 250°C.

Based on the above bending simulation of plates at various temperatures,the coiling simulation of the 13mm thickness wide plates at the same temperature is carried out and shown in Fig.16.When the plate is crimped,the stress state of the firs layer,taken as the research object,is relatively complex,and the subsequent layers are relatively smooth.As can be seen from Fig.16,the tensile stress of the outer layer of the curly plate gradually decreases with the increase of temperature.The maximum tensile stresses at 100,150,200,and 250°C are 177,158,128,and 114MPa respectively,which are similar to the bending simulation results and beyond the elastic stress.The stress in the inner layer of the plate is evenly distributed at the range of 100-200°C,but the stress in the inner layer becomes tensile stress in some places as the temperature increases,which is related to the friction between the inner layer and the reel.As the temperature rising,the magnesium alloy and its surface adhesion turn into mild and larger,resulting in an augment of the interfacial friction coefficien between the plate and the reel.Combined with the radius of the reel and the span of the bending experiment,the deflectio during bending can be obtained,and then the offset of the neutral layer can be obtained (see Table 4) under the same curvature as that during coiling.From the data in Table 4,it can be known that the offset of the neutral layer during crimp is one-third to one-fourth of that during bending fracture at the same temperature.The offset will shift back in the subsequent uncoiling process and the offset turns slightas the plate becomes thinner during rolling.The temperature has little effect on the offset of the plate neutral layer during coiling.Therefore,the crimp can be carried out in a wide temperature range after rough rolling,considering the factors of production efficien y and process cost,but the crimping temperature cannot be less than 100°C.

Table 4 Neutral plane offset on coiling at various temperatures.

Fig.17.Critical reel diameters at diverse temperatures.

Too low coiling temperatures will increase the power of the coiler,which is not conducive to the coil.Moreover,the increase of deformation resistance of the plate and the augment of springback will amplify the loose tendency of the plate.According to the elastic-plastic theory and the tension and compression asymmetry of the polycrystalline magnesium alloy,the reel diameter at different temperatures and crimp speed can be obtained.Fig.17 shows the relationship between critical reel diameter and temperature when the plate is crimped at different speeds.As can be seen from Fig.17,the diameter of the reel decreases as the temperature increases.But at the same temperature,the diameter of reel decreases with the increase of crimp speed.And the higher the temperature,the larger the diameter difference will be.The inner layer and outer layer are subjected to compressive stress and tensile stress respectively,and the middle layer material is gradually affected by the inner and outer stress influenc when crimped.In the Hall-Petch relation [39],kis an important parameter and represents the magnitude of boundary obstacle against deformation propagation.A new equation ofkput forward by Guan et al.[41],presents that the strong deformation anisotropy in Mg alloys leads to a complex texture effect onk,including the effects from both external and internal stresses.It can also be seen from Fig.3 that the grain size and morphology are distinct in the inner and outer layers of the plate.Therefore,when the stress value of the inner layer is equal to that of the outer layer,the critical reel diameter can be obtained.

4.Conclusions

The coiling feasibility of plate between roughing and fin ishing at different temperature were investigated by bending experiment and FEM analysis.The microstructural characteristics and mechanical properties of the plate were discussed;the EBSD analysis was carried out.The following conclusions were drawn:

(1) The inner and outer sides of the plate were subjected to distinct stresses when coiling at 100-250°C.A large number of twins were observed at the surface of the plate when bending at 100°C,and the number of twins decreases as the temperature elevation.

(2) The fl xural deflectio increased from 15.7mm to 24.9mm gradually with the augment of fl xural temperature,while the fracture stress weakened from 479MPa to 177MPa.The deflectio variation reached 15.9%,25.8% and 8.7% and the fracture stress variation got to 15.7%,59.8% and 46.3% respectively.And the deflec tion and fracture stress were most affected when bending at 200°C.

(3) The EBSD analysis of inner and outer layer samples conducted at 100°C showed that a large number of twins nucleated and grew in the coarse grain,causing major distribution proportion of HAGBs at the compression part.The HAGBs at the inner side of the bent plate could improve its fl xural properties and affect subsequent strain contours,twins,and recrystallization distribution.

(4) The offsets of plates at different temperatures are obtained by numerical analysis combining bending experiments and elastoplastic theory.The offset of the neutral layer declined from 1.4125mm to 0.7261mm with the temperature rising from 100°C to 250°C when bending,while the offset of the neutral layer was concentrated at 0.0338-0.0481mm.

Declaration of Competing Interest

The authors declare that they have no conflic of interest.

Acknowledgments

This work was financiall supported by the project from the National Key Research and Development Program of China (No.2016YFB0301104),the National Natural Science Foundation of China (No.51771043),and the Program of Introducing Talents of Discipline Innovation to Universities 2.0 (the 111 Project 2.0 of China,No.BP0719037).Special thanks are due to the instrumental or data analysis from Analytical and Testing Center,Northeastern University.