Biwu Zhu,Xio Liu,?,Cho Xie,Wenhui Liu,Chngping Tng,Liwei Lu

a Key Laboratory of High Temperature Wear Resistant Materials Preparation Technology of Hunan Province,Hunan University of Science and Technology,Xiangtan 411201,China

b The Faculty of Mechanical Engineering and Mechanics,Ningbo University,Ningbo 315211,China

Abstract As-extruded AZ31 magnesium alloy samples were compressed at ambient temperature and strain rates of 1000–3000 s?1.The fracture surfaces of cracked samples,the evolution of microstructures and macrotextures were detected.The received fl w curves exhibit an abnormal behavior at strain rates above 1500 s?1.A strain constitutive model based on strain equivalent principle was applied to analyze the f ow curves of the damaged samples.The results indicate that the abnormal f ow behaviors of the fractured samples are related to the increasing area of crack surfaces,and kinetic energy during dynamic crack nucleation and propagation.The initiation of the micro-crack also causes obvious fl w softening in the cracked samples.The shapes of fl w stresses of the intact samples are affected by twinning.

Keywords:Magnesium alloy;Flow behavior;Fracture;Micro-crack;Twinning.

1.Introduction

Magnesium alloys are excellent candidates for several structural applications in the automotive and aerospace industries[1–5].In some structural applications,components are subjected to the wide range of strain rates such as explosive forming,high speed machining and shock loading.Therefore,the mechanical behavior,f ow behavior and microstructure evolution are of great interest particularly for automotive and aerospace industries where some critical components have to show appropriate resistance to failure under severe loading conditions such as car crash.Actually,the materials may display a very different mechanical behavior,f ow behavior and microstructure evolution under high strain rate in contrast to the quasi-static deformation due to the existence of dynamic stress wave[6,7].

The dominant deformation modes in magnesium are the{0001}＜11–20＞ basal slip system and the{10–12}＜10–11＞extension twinning,especially at high strain rate and low temperature[8–10].Su et al.[11]rolled the AZ31 magnesium alloy at average strain rates of 171–592 s?1at low temperature and found that twinning was activated to accommodate plastic deformation.Dixit et al.[12]compressed as-extruded pure magnesium along the extrusion direction under a strain rate of 1000 s?1.Their results showed that extension twinning caused grain reorientation,in addition,extension twinning and dislocation activity were required to accommodate plastic deformation.Guo et al.[13]carried out compressive deformation on AM80 magnesium alloy at room temperature and at strain rates of 450–2300 s?1using the Split–Hopkinson pressure bar and indicated that twinning play an important role in deformation at super high strain rate.In our previous study[14],it was found that{10–12}＜10–11＞ extension twins were favored during compression of as-extruded AZ31 samples and leaded to basal plane reorientation from hard slip to considerable softer orientations at relatively small strain.

Fig.1.Initial microstructures:(a)initial Optical structure and(b)initial texture.

Fig.2.The true stress–strain curves under different strain rates at room temperature.

Dynamic recrystallization is favored in magnesium alloys due to low stacking fault energy.Lv et al.[15]carried out a hot compression on Mg-2.0Zn-0.3Zr-0.9Y alloy and indicated that dynamic recrystallization could cause the fl w softening.Zhu et al.[16]and Su et al.[11]observed that twinninginduced dynamic recrystallization reduced the work hardening rate.Molodov et al.[17]took place a plane strain compression along ＜11–20＞ direction on specially oriented magnesium single crystals at room temperature with a strain rate of 0.001s?1and found that recrystallized grains were detected in numerous bands,which were associated with{10–11}contraction twinning within the primary extension twinned matrix.Accordingly,dynamic recrystallization could occur at wide temperature ranges,even at ambient temperature.

Fig.3.The morphology of samples after compression under high strain rates and different strains(a)0.08;(b)0.1;(c)0.14;(d)0.27;(e)0.25;(f)0.23.

Fig.4.Superficia areas of crack surfaces for the fractured samples.

The initiation of twinning,dynamic recrystallization and the crack during deformation can influenc the f ow behavior[18–22].Poliak and Jonas[18]indicated that the onset of dynamic recrystallization corresponded to an inflec tion point in the θ-σ curve and proposed second derivative method,which were verifie by many studies[18–20].Jiang et al.[21,22]showed that the shape of fl w curve was determined by the type of twinning.Barnett[23]indicated that the f ow stress strongly depended on texture and deformation mode.Our previous research[14]found that initiation of twinning and dynamic recrystallization was related to an inflectio point in the θ-σ curve.The nucleation and growth of the micro-crack are one key mechanism for relaxing stress during plastic deformation.Although the fracture mechanism in fin grains is different from that in coarsen grains[24,25],the initiation of the crack would consume the strain energy to provide surface energy for the formation of the crack surface,inducing the f ow softening[26].

Fig.5.SEM images of the fracture surfaces in fractured samples under different strain rates:(a)˙ε=1500 s?1,ε=0.14;(b)˙ε=2000 s?1,ε=0.27;(c)˙ε=2800 s?1,ε=0.25;(d)˙ε=3000 s?1,ε=0.25.

In the present study,dynamic compression tests were carried out on as-extruded AZ31 magnesium alloy at room temperature and strain rates of 1000–3000 s?1.The superficia areas of crack surface for fractured samples were calculated to investigate the fl w behavior.The micro-cracks in fractured samples were detected and its effects on f ow behavior were also discussed.The dynamic recrystallization behavior was determined by microtexture corresponding to recrystallized grains.The influence of dynamic recrystallization and twinning on fl w behavior were also studied.

2.Experimental method

The alloy used in the present investigation was AZ31 magnesium alloy(3.19wt.%Al and 0.81wt.%Zn).The material was received in the form of extruded bars with a diameter of 25mm.The bars were annealed at 470°C for 3h.Cylindrical specimens with a diameter of 8mm and a height of 4mm were machined from the centers of the as-extruded bars.The initial microstructures are displayed in Fig.1.It can be seen that the initial optical structure shows equiaxed grains and the initial texture displays typical fibe texture.

The specimens were impacted to selected strains along the extrusion direction(ED)at room temperature with different strain rates(1000 s?1,1250 s?1,2000 s?1,2800 s?1and 3000 s?1)by the Split–Hopkinson pressure bar.A series of strain rings were used to limit the strain amount,the graphite was used to lubricate the interface between the specimen and the pressure bars,and the pulse shaping technique was employed to produce a desired profil of incident pulse to ensure constant strain-rate deformation in specimen.To check the repeatability of the results,two and four experiments were conducted for each condition.

In order to observe the microstructure of intact samples,cross-sections parallel to the compression axis were cut from the deformed specimens.These were mounted and polished to a 1200 grit surface finis using SiC papers.Polishing was then carried out with diamond paste through the sequence of 3,1 and 0.05μm.The polished samples were etched with a solution containing 5g picric acid,10ml distilled water,100ml alcohol and 5ml acetic acid for times that varied from 18 to 22s.Then,the evolution of microstructure was detected by optical microscopy.

Fig.6.Microstructures of different areas at a strain rate of 1500 s?1.

To measure the microtexture of intact samples,crosssections parallel to the compression axis were polished to a 1200 grit surface finis using SiC papers.Polishing was then carried out with diamond paste through the sequence of 3,1 and 0.5μm.It was followed by an electrochemical polishing in AC2 solution.Then,the Electron back scatter diffraction(EBSD)micrographs were obtained in a FEI Nova400 SEM equipped with the HKL data acquisition system and the fracture surfaces in fractured samples were observed by JSM-6380LV SEM.

In order to calculate the superficia areas of crack surfaces for the fractured samples,the boundary sizes of crack surfaces were measured and then CAD software was used to draw the geometry of crack surfaces.Finally,the superficia areas of crack surfaces were estimated.

3.Results and discussion

The true stress–strain curves under different strain rates at room temperature are displayed in Fig.2.It is worth noting that the f ow stresses do not increase with increasing strain rate.The fl w stress at 2000 s?1is higher than those at 2800 s?1and 3000 s?1.The fl w curve at 1250 s?1displays abrupt hardening after yield stress due to the fact that the work hardening rate dramatically increases with strain rate,while the f ow curves at 1500 s?1,2000 s?1,2800 s?1and 3000 s?1exhibit gradually hardening after yield stress,followed by softening after peak stress.These suggest that the fl w behavior at strain rates above 1500 s?1is abnormal.

The morphology of samples after compression under high strain rates is exhibited in Fig.3.The samples at strain rates of 1000 s?1and 1250 s?1are intact,while the fracture occurs under strain rates of 1500 s?1,2000 s?1,2800 s?1and 3000 s?1.It can be observed that the samples under strain rates of 2800 s?1and 3000 s?1are severely cracked.

3.1.The fl ow behavior of the fractured samples

3.1.1.The effect of fracture morphology on fl ow behavior

Under high strain rate,the growth of the crack called dynamic cracking requires a kinetic energy for the fast crack growth.It is generally known that the nucleation of the multicrack and the demand of kinetic consume the strain energy to generate new surfaces during the damage process,leading to the fact that the true stress–strain curve drops dramatically[26,27].The increase of superficia area of crack surfaces will consume more strain energy,contributing to the increment of softening in the true stress–strain curve.

Fig.7.Microstructures of different areas at a strain rate of 2000 s?1.

Aiming to study the effect of superficia area of crack surfaces on fl w stress,the approximate superficia area of crack surface for the corresponding fractured samples are calculated and exhibited in Fig.4.It can be obviously seen that the superficia areas of crack surfaces under strain rates of 1500 s?1and 2000 s?1are small,while those under strain rates of 2800 s?1and 3000 s?1are relatively big.

The fracture surfaces of crack samples are shown in Fig.5.It can be seen from Fig.5(a)that only several dimples are observed on the fracture surfaces at a strain rate of 1500 s?1in Fig.5(a),while tongue pattern and river pattern are mainly detected in the facture surfaces in Fig.5(a)–(d).The formation of dimples may be caused by fin grains for the occurrence of dynamic recrystallization.The tongue and river patterns,as the characterization of the brittle fracture,may be caused by two facts:(i)the slip system cannot accommodate the plastic deformation within coarse grain under high strain rate;and(ii)the formation of twinning leads to stress concentration through the dislocation pile-ups on the twin boundary,inducing the cracking along the twin boundary under high strain rate.These suggest that sample rupture is due to quasicleavage fracture,and the brittle fracture is the main fracture mode.Thus,the formation of same superficia area of crack surfaces could be considered as consuming the same strain energy.

As shown from Fig.3,the samples at 1500 s?1,2000 s?1,2800 s?1and 3000 s?1rupture,resulting in the lower f ow stress in contrast to that at 1250 s1.In Fig.4,the samples at 2800 s?1and 3000 s?1are severely fractured and form large superficia area of crack surfaces.Then,the consumption of strain energy is larger than those at 1500 s?1and 2000 s?1.Therefore,the f ow stresses of 2800 s?1and 3000 s?1are lower than those at 1500 s?1and 2000 s?1.

3.1.2.The effect of micro-crack on fl ow behavior

The f ow stress will be affected by the micro-crack during deformation.The microstructures of different areas at strain rates of 1500 s?1,2000 s?1and 2800 s?1are exhibited in Figs.6–8,separately.It can be seen that the main cracks,micro-cracks and twins are observed.The initiation and propagation of micro-cracks causes substantial softening at 1500–3000 s?1,resulting in the fact that the f ow stress is lower than that at 1250 s?1after yield stress.The number of microcracks increases with increasing strain rate.Substantial small twins and intersecting twins are observed around the crack.The formation of deformation twinning would cause the local transformed strains and local stresses through the dislocation reaction and pile-ups at the twin boundary,resulting in interfacial crack nucleation and growth around twins[26].In addition,some of the micro-cracks’morphologies are similar to twins.This may be attributed to the fact that the crack may grow along twin boundary,due to strain incompatibility and high stress concentration around twin boundary[28].It also can be seen from Figs.6 to 8 that some of micro-cracks initiate at triple joint of three neighboring grains.Triple joint of three neighboring grains has high stress concentration for dislocation pile-ups during deformation,providing the driving force for the initiation of the micro-crack[29].

Fig.9.Microstructures under different strain rates:(a)˙ε=1000 s?1 and(b)˙ε=1250 s?1.

According to damage mechanics,any true strain constitutive equation for a damage material is derived in the same as the strain constitutive equation without damage material.Then,a strain constitutive model based on strain equivalent principle was proposed by Lemaitre[30],and shown as follows:here,is the effective stress;σis the true stress;E is the elastic modulus;D is the damage variable.

The damage variable was displayed in the following Eq.(2):

here,A is the sectional area;? is the damaged sectional area.

According to Eqs.(1)and(2),the increase of the damaged sectional area causes the increase of damage variable,followed by the decrease of true stress at the same strain.The formation of the micro-crack is one type of damage inside the material.Thus,the increase of micro-cracks leads to the increase of damaged section area.In Figs.6–8,the number of micro-cracks increases with strain rate.This leads to the fact that the f ow stresses decrease with increasing strain rate in the strain rate interval 1500–3000 s?1.

3.2.The fl ow behavior of intact samples

The microstructures of intact samples are detected and shown in Fig.9.Twins are detected,while the number of twins slowly increases with strain rate.The recrystallized bands are also observed.

Fig.11.Texture corresponding to recrystallization under different strain rates:(a)˙ε=1000 s?1 and(b)˙ε=1250 s?1.Here ED is the compression direction.

The EBSD maps of intact samples are shown in Fig.10.Here,thick black lines are correspondence to grain boundaries(θ＞15°),red lines correspond to{10–12}extension twins,green lines represent to{10–11}contraction twins,yellow lines show{10–11}–{10–12}double twinning,and pink lines display{10–12}–{10–12}extension-extension twinning.Substantial extension twins are detected at strain ratesof 1000 s?1and 1250 s?1,while several contraction twins are observed at a strain rate of 1000 s?1.Twinning will affect the shape of the f ow stress.Contraction twins are responsible for the concave down shape of stress–strain curve,and extension twinning causes the sigmoid shape[21–23].Therefore,a concave down shape forms at 1000 s?1for the initiation of contraction twinning.

At high strain rate,the twins and dislocation are mainly affected by strain rate[31].The dislocation slip alternated with twining is the apparent deformation characteristic for magnesium alloy at room temperature[13].At room temperature and high strain rate,the time for dislocation motion decreases,resulting in the requirement of substantial twins to accommodate the uniform plastic deformation and the rapid increase of dislocation density.The area fraction of twins,assumed to be equivalent to the volume fraction,was measured using a point counting analysis with a rectangular net[13,32].The area fractions of twins at 1000 s?1and 1250 s?1are 23%and 32%,respectively.The number of twin increases with strain rate,followed by the increment of twin boundaries.These twin boundaries inhibit dislocation motion and induce dislocation pile-ups,finall causing that the dislocation density increases.According to the relationship between fl w stress and dislocation densityσ=αμ ρ(hereαis the Taylor factor,μis the shear modulus,andρis the dislocation density.),the dislocation density dramatically increases,contributing to the dramatic increase of f ow stress.Therefore,the f ow stress at 1250 s?1is much higher than that at 1000 s?1after yield stress.

The texture of intact samples related to recrystallization is displayed in Fig.11.Blue color represents the recrystallized grain,red color is related to matrix grains or twins and yellow color corresponds to sub-structure.The c-axis of most grains is vertical to extrusion direction.The initial texture in Fig.1 shows a typical fibe texture and c-axis of most grains is vertical to extrusion direction.This indicates that the changes of texture at 1000 s?1and 1250 s?1with a small strain can be ignored.However,it also can be seen that several grains rotate nearly 90°indicating the occurrence of twinning.The orientation of some recrystallized grains only deviates from the matrix a small angle for the occurrence of dynamic recrystallization on the boundary of matrix grain,while some of the recrystallized grains departure from the twins a small angle,due to the fact that twinning induces dynamic recrystallization.In the present condition,the recrystallized volume fractions are small at 1000 s?1and 1250 s?1with a small strain.Therefore,the work hardening is still higher than the softening caused by the dynamic recrystallization,causing the rapid increase in the fl w stress under a small strain.Therefore,f ow softening leaded by dynamic recrystallization is not obvious.

4.Conclusions

The f ow stresses of as-extruded AZ31 magnesium alloys under high strain rates display abnormal behavior.After analyzing the effects of the fracture morphology,the micro-crack,and microstructure on the fl w stress,the main results of the analysis can be summarized as follows:

1.The formation and propagation of the crack consumes the strain energy,leading to fl w softening.The superficia areas of crack surfaces can determine the f ow behavior,and big superficia areas of crack surface are corresponding to low f ow stress in the fractured samples.

2.The initiation of micro-cracks within the cracked samples also contributes to f ow softening.According to strain equivalent principle of damage mechanics,the increase of micro-crack is responsible for the decrease of f ow stress,causing that the f ow stresses decrease with increasing strain rate in the strain rate range of 1500–3000 s?1.

3.Twinning is the one key factor influencin the shape of fl w curves in intact samples.The softening caused by dynamic recrystallization can be neglected under small strain for small recrystallized volume fraction.

Acknowledgments

The authors gratefully acknowledge research support from the National Natural Science Foundation of China(grant nos.51601062 and 51605159)and the National Natural Science Foundation of Hunan(2018JJ3180).