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Anisotropy of dynamic behavior of extruded AZ31 magnesium alloy
Materials Science and Engineering A 527 (2010) 2915–2924
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Anisotropy of dynamic behavior of extruded AZ31 magnesium alloy G. Wan c,a , B.L. Wu a,c,∗ , Y.D. Zhang a,b , G.Y. Sha a , C. Esling b a
Shenyang Institute of Aeronautical Engineering, 110136, Shenyang, China LETAM University of Metz-CNRS UMR, 7078, France c Nanjing University of Aeronautics and Astronautics, 210016, Nanjing, China b
a r t i c l e
i n f o
Article history: Received 12 October 2009 Received in revised form 4 January 2010 Accepted 6 January 2010
Keywords: Magnesium Texture Dynamic behavior Anisotropy Twinning Slip
a b s t r a c t Textures always exert an intensive influence on the deformation and fracture of magnesium alloys. A hot extruded AZ31 alloy with intensive texture was selected for impact tests with the impact direction parallel to the respective normal, extrusion and transverse directions (ND, ED and TD) of the initial extrusion plate. The results showed that the stress–strain response of the alloy is highly anisotropic and sensitive to the strain rate. The maximum flow stress can reach nearly as high as 600 MPa for TD impact. Microstructure responses show that when impacted along normal direction, {1 0 −1 1}–{1 0 −1 2} double twins is common in large grains, however, small grains show {1 0 −1 2} tension twins. After impacted along transverse direction, grains of the alloy are evidently refined and the texture changes from {0 0 0 1}1 1 −2 0 to that with {0 0 0 1} pole in TD direction. The stress–strain, microstructure and orientation responses could well be interpreted with the Schmid factor distributions. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Magnesium alloys are attractive materials for aerospace and automotive industries due to their high specific strength. However, they have limited formability at room temperature, which mainly arises from the limited number of slip systems in the hexagonal close packed (HCP) structure [1–3]. Consequently, twinning is an important mechanism to accommodate the deformation of polycrystalline magnesium alloys [4–7]. Magnesium alloys will be improved in plasticity at elevated temperature for processing. After deformation during processing, the texture always forms and results in a pronounced anisotropy of the mechanical properties of magnesium alloys [8–11]. At present, most of the investigations have dealt with the mechanical behavior under conventional tensile or compression. However materials components will be potentially subjected to impact loads in some services. The behavior of materials under impact loading that results in a very high strain rate, is quite complicated. El-Magd and Abouridouane [12] indicated in their work that under impact loading, the dynamic plastic response of the lightweight wrought alloy is mainly controlled by strain rate sensitivity and the adiabatic character of the deformation process. Generally magnesium alloys have high anisotropic trend. Textures always
∗ Corresponding author at: Shenyang Institute of Aeronautical Engineering, 110136, Shenyang, China. Tel.: +86 24 89723976; fax: +86 24 89724198. E-mail address: [email protected] (B.L. Wu). 0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2010.01.023
exert an intensive effect on their deformation and fracture. This would enhance the complicity of the dynamic behavior. Recently, Tucker and co-workers [13] investigated the anisotropic effects on the strain rate dependence of AZ31B alloy and showed that stress–strain responses at high strain rate in the normal, rolling and transverse directions (ND, RD and TD) were evidently different. They concluded that the texture of the material played a significant role in the plastic deformation at both quasi-static and high strain rates due to twin–slip interactions. A similar work for AZ31 alloy was also presented, in which impact direction (ID) was aligned in 0◦ , 45◦ and 90◦ with the ND and the twinning mechanism for the 90◦ and the slip mechanism for 0◦ and 45◦ impact were concluded, respectively [14]. Experimental results showed that twinning plays an important role when the strain rate is high or the grain size is large [15,16]. So twinning would be a favored mechanism to accommodate the deformation of a magnesium alloy which has large grains and was compressed at high strain. In the present work, a plate of hot extruded AZ31 alloy with partially dynamically recrystallized grains was selected for impact tests. The influence of the texture on the dynamic mechanical behavior was investigated and the responses of the microstructure were analyzed. 2. Experimental The investigated material was AZ31 magnesium alloy with the chemical composition of Mg–3.0Al–1.0Zn (in mass.%). A square bar of 100 mm × 20 mm × 20 mm was cut from an as-received extruded plate with size of 800 mm in length (extrusion direction, ED),
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Fig. 1. Schematic showing of the impact samples cut from the as-received AZ31 plate.
250 mm in width (Transverse direction, TD) and 20 mm in thickness (Normal direction, ND), and then annealed at 250 ◦ C for 2.5 h as the initial state of the alloy. Three groups of cylindrical samples with size of Ø8 mm × 8 mm were cut out of the center of the annealed square bar for the impact tests. The axial directions of the respective samples were parallel to the ND, TD and ED of the extruded plate. The relative positions between the extruded plate, the annealed square bar and the impact samples are schematically shown in Fig. 1. The impact tests were performed with the Split Hopkinson Pressure Bar (SHPB). The samples were impacted in their axial directions. The ID is corresponding to ND for Sample group A, TD for Sample group B and ED for Sample group C, respectively. For each group, the samples were impacted under two gas gun pressures (0.2 MPa and 0.5 MPa). During the test, the samples were put between the incident and transmitter bars. The incident, reflection and transmission strain-time waves were recorded by the data collection system of the equipment, and then the true stress, true strain and strain rate of each impact were calculated according to the equations below [17], from which the true stress–strain relationships were obtained. =
A Eεt (t) A0
2C0 ε=− L0 ε˙ =
(1)
t
εr (t)d
(2)
2C0 (ε (t) − εt (t)) L0 i
(3)
o
where , ε and ε˙ are true stress, true strain and strain rate. εi (t), εr (t) and εt (t) are incident, reflection and transmission strain-time waves. E, C0 and A are Young’s elastic modulus of the impacting bar, elastic wave rate in the bars and the sectional area of the bars. The initial sectional area and length of the impact samples are denoted A0 and L0 .
Fig. 2. EBSD orientation micrograph of the initial microstructure of the alloy observed in the transverse section.
The global texture analyses were performed by measuring incomplete pole figures with a Fangyuan D2000 X-ray goniometer using Schulz reflection method. The range of the tilt angle ˛ is 0–70◦ and of the azimuthal angle ˇ is 0–360◦ at 5◦ steps. Electron back-scattered diffraction (EBSD) measurements were carried out in a JEOL6500F field emission SEM equipped with an automatic orientation acquisition system (Oxford Instruments-HKL Channel 5) to measure the local texture. The orientation map of the initial state was acquired from the ND-ED plane and that for the impacted samples were measured from the impacted plane. 3. Results 3.1. Initial microstructure and texture Fig. 2 shows the orientation micrograph in the ND-ED plane of the initial state of the alloy (extrusion + 250 ◦ C/2.5 h annealing). The blue lines in the figure indicate the boundaries whose misorientation angle is larger than 5◦ . The colors of the grains correspond to their orientations. From the picture, it can be seen that the microstructure is composed of two kinds of grains, the large grains clearly elongate along the ED and the small equiaxied grains distribute between the large elongated grains. The elongation of the large grains indicate that they have not recrystallized during the annealing but remained in the as worked state, while the equiaxied shape of the small grains suggests that they are fully recrystallized. The texture of the overall microstructure in Fig. 2 is displayed with
Fig. 3. Pole figures of the initial microstructure shown in Fig. 2.
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ented around {0 0 0 1}1 1 −2 0; whereas the small grains tend to have deviated {0 0 0 1} plane texture. 3.2. Stress–strain response
Fig. 4. Highlighted large elongated grains in the microstructure shown in Fig. 2.
the {0 0 0 1} and {1 0 −1 0} pole figures in Fig. 3. It can be seen that the texture of the initial state of the alloy is very close to the {0 0 0 1}1 1 −2 0 component. This observation is consistent with the X-ray global texture analysis. As the grain size is very inhomogeneous, distinguishing the texture of the large elongated grains from that of the small grains is useful. With the “subset” function of Channel 5 software, the large elongated grains are selected and shown in Fig. 4. Their corresponding pole figures with scattered data are displayed in Fig. 5. The pole figures of the remaining small grains are shown in Fig. 6. It is seen that the large grains are ori-
Fig. 7 shows the dynamic stress–strain curves of Sample group A, B and C impacted along ND (Fig. 7(a)), TD (Fig. 7(b)) and ED (Fig. 7(c)) under two strain rates for each group, respectively. The higher strain rate corresponds to the 0.5 MPa gas gun pressure and the lower strain rate to the 0.2 MPa pressure in the figure. All the three samples were impacted to fracture under 0.5 MPa or higher strain rate, while those under 0.2M Pa or lower strain rate were not. It was found that for all the three directions, the flow stress increases with the strain. When impacted along ND, the beginning flow stresses under the two strain rates are higher than those of the samples impacted along the other directions. However, the d/dε–ε slope curves derived from –ε data of impacted samples indicate that the deformation hardening rate (d/dε) of the impacted samples varies in quite different ways in the three directions, as shown in Fig. 8. The hardening rate of the ID//ND impacted samples decreases drastically from the very beginning; whereas those of the ID//TD and ID//ED impacted samples rise at the beginning and drop after reaching the maximum. The relative reduction of the height at rupture was considered as a measure of the impact ductility of the material [12]. The dynamic impact ductility of the samples also shows evidently anisotropy. The sample (impacted along TD) possesses the highest impact reduction (about 0.30) at the strain rate of 1766 s−1 . At this high reduction, the maximum flow stress reaches nearly as high as 600 MPa.
Fig. 5. Pole figures with scattered data of the highlighted large elongated grains in Fig. 4.
Fig. 6. Pole figures of the remaining small grains in Fig. 2.
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Fig. 7. True stress–strain curves of the samples impacted with (a) ID//ND, (b) ID//TD and (c) ID//ED under two stage gas gun pressures.
Another important phenomenon is that flow stress shows different strain rate sensitivity from ND impact to TD and ED impact. The flow stress increases with increasing strain rate in ND (Fig. 7(a)), but decreases in TD (Fig. 7(b)) and ED (Fig. 7(c)) impact. In summary, the mechanical behaviors of the three groups of sample impacted along different directions show strong anisotropy. 3.3. Microstructures and orientations response The orientation micrographs of the samples impacted with ID//ND, ID//TD and ID//ED under 0.2 MPa gas gun pressure corresponding to low strain rate are shown in Fig. 9(a), Fig. 10(a) and Fig. 11(a). The corresponding pole figures are displayed in Fig. 9(b),
Fig. 8. d/dε–ε slope curves of the samples impacted with (a) ID//ND, (b) ID//TD and (c) ID//ED under two stage gas gun pressures.
Fig. 10(b) and Fig. 11(b). From Fig. 9, it is seen that after impacted along ND, the microstructure still consists of large grains and small grains. The only difference from the initial microstructure is that a little of twins appear in both the large grains and the small grains. Detailed analysis revealed that the twins in the large grains have mainly 38◦ misorientation around 1 1 −2 0 with the matrix that are {1 0 −1 1}–{1 0 −1 2} double twins [18,19], while the twins in the small grains possess 86◦ misorietation around 1 1 −2 0 with the matrix that are {1 0 −1 2} tension type. Fig. 9(b) displays {0 0 0 1} and {1 0 −1 0} pole figures of the microstructure in Fig. 9(a). The main component is close to that of the initial texture but with noticeable deviation. This deviation
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Fig. 9. EBSD orientation micrograph (a) and pole figures (b) of the sample impacted along ND at the rate of 1766 s−1 .
may result from the inaccuracy of sample sectioning and local texture inhomogeneity. The unreasonable pole intensity (as high as 84.99) is due to the insufficient number of grains. However, after impacted along TD at the strain rate of 933 s−1 , the microstructure is obviously refined (Fig. 10(a)) in contrast to the initial microstructure. The remaining large grains are in the course of fragmentation by twinning, as outlined in Fig. 10(a). The twins appear as the 1 1 −2 0 86◦ tension type. In addition to the refinement of the microstructure, it was found that the orientation changes from the initial {0 0 0 1}1 1 −2 0 to that with {0 0 0 1} pole in TD (the c-axis is parallel to TD). After impacted along ED at strain rate of 802 s−1 , the orientation micrograph shows large {1 0 −1 2} tension twins (green and yellow parts) in the original large grain where the white lines indicate the twin boundaries (Fig. 11(a)). It can be found that unlike those in the case of ID//TD, large grains in this case are not evidently refined during twinning. However, the orientation of the large grains changes from the initial {0 0 0 1}1 1 −2 0 to two distinct components with the c-axis perpendicular to ND and about 30◦ tilt from ED, as shown in Fig. 11(b). The two components possess 86◦ rotation around different 1 1 −2 0 axis from the initial component, suggesting that the two orientations are the two tension twin variants with respect to the initial orientation. 4. Discussion
that the anisotropy is resulted from textures, it is helpful to understand the relationships between the dynamic mechanical behavior, orientations and microstructures. In general, magnesium can be deformed by crystallographic slip and twinning. The principal slip system of magnesium alloy is the basal a at room temperature. However, non-basal slip is also an important means for deformation at room temperature [20]. Koike et al. [21] reported, in an ECAE AZ31 alloy with an average grain size of 8 m that, 40% of dislocation segments were of the non-basal type. Previous research concluded that the prismatic a slip in magnesium alloys is active at room temperature [22]. Pyramidal c+a slip is also potential deformation system at room temperature [2]. This often takes place in the case of controlled-loading experiments of single crystal Mg or in the case of Mg–Li and Mg–Y alloys [23,24]. In addition to dislocation slip, magnesium exhibits a strong propensity for mechanical twinning. Generally, tension, contraction twins and the double twins are observed in magnesium alloys [19]. The {1 0 −1 2} tension twinning is preferred when there is an extension strain component parallel to the c-axis [25]. The {1 0 −1 1} contraction twinning is reported to be activated when there is a contraction strain component parallel to the c-axis [26]. In the present work, the extruded alloy has deviated {0 0 0 1} plane texture for the small grains and {0 0 0 1}1 1 −2 0 orientation for the large grains. When an impact load is applied on the magnesium alloy along ND, TD and ED, deformation mechanisms of grains are different under the three conditions.
4.1. Deformation mechanisms
4.2. Schmid factors
The above results show an obvious anisotropic dynamic mechanical behavior of the alloy under impact loading. As we know
The slip and twining systems of a grain will have different Schmid factors when compression load is applied in 0 0 0 2,
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Fig. 10. EBSD orientation micrograph (a) and pole figures (b) of the sample impacted along TD at the rate of 1865 s−1 .
1 0 −1 0 and 1 1 −2 0, as schematically shown in Fig. 12. Schmid factors of basal a slip, prismatic a slip, pyramidal c+a slip, {1 0 −1 2} tension twinning and {1 0 −1 1} contraction twinning with the load in the above directions are calculated and listed in Table 1. In the present investigation, the orientation of the most large elongated grains is close to {0 0 0 1}1 0 −1 2, so for the three impact indirections (ID//ND, ID//TD and ID//ED), they undergo the load in 0 0 0 2, 1 0 −1 0 and 1 1 −2 0 crystallographic directions, respectively. Despite of the strong {0 0 0 1}1 0 −1 2 component in the initial alloy, there still remain large amount of grains deviating from this orientation. So when impacted along ND, TD and ED, the Schmid factors for different deformation systems of each grain will be determined by its individual orientation. Fig. 13 displays the Schmid factor maps of the initial microstructure in Fig. 2, where ID is supposed to be parallel to ND, TD and ED, respectively. It can be seen that in the case of ID//ND, large elongated grains have low Schmid factors for basal a slip, but that of some small grains is high. For prismatic a slip, the Schmid factors are low for almost all the grains, however, the Schmid factors for tension and contraction twinning are high for almost all the grains, especially for large elongated grains. It should be noted that small grains have higher Schmid factors for {1 0 –1 2} tension twinning than that for {1 0 −1 1} contraction twinning. In the case of ID//TD, Schmid factors of most grains for basal a slip are very low, but they are very high for prismatic a slip. These grains also have higher Schmid factors for the two twinning systems. In the case of ID//ED, The Schmid factors are just distributed similarly to those in the case of ID//TD. The only difference is that
for prismatic a slip, the Schmid factors of many small grains are slightly lower than those of the sample of ID//TD, and the Schmid factors of the large elongated grains for {1 0 −1 2} tension and {1 0 −1 1} contraction twinning are lower.
4.3. Dynamic response From the above clarification of the Schmid factors for different systems in large and small grains, we can expect that except for basal slip occurring in small grains with higher Schmid factors, twinning would be an important mechanism for the deformation of the samples under the impact along ND. Two kinds of twins (double twins in large elongated grains and tension twins in the small grains) are mainly observed (Fig. 9(a)). For the double twinning, {1 0 −1 1} contraction twins form first and then {1 0 −1 2} extension twins are propagated within them [19]. The reason for the {1 0 −1 1}–{1 0 −1 2} double twins with high critical resolved shear stress (CRSS) of the contraction twin to form in the large elongated grains is that during a rapid deformation under impact loading, twinning, a high speed deformation mode, is appropriate to accommodate the strain. In addition, the {1 0 −1 1}–{1 0 −1 2} double twins in the large elongated grains have large size in length and small size in thickness. This would result in the reduced elastic strain energy according to E = (c/r)s2 [27], where E is elastic strain energy; c and r represent the thickness and length of the twin respectively, is the shear modulus and s is the twinning shear. Therefore, the {1 0 −1 1}–{1 0 −1 2} double twins are difficult to form in the small grains because of the small r value. In contrary, the {1 0 −1 2} tension twins were easy to form in the small grains due to their lower CRSS and higher Schmid factors.
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Table 1 Calculated Schmid factors. Deformation system
{0 0 0 1}1 1 −2 0 slip
{1 0 −1 0}1 1 −2 0 slip
{1 1 −2 2}1 1 −2 3 slip
{1 0 −1 2}1 0 −1 1 twinning
{1 0 −1 1}1 0 −1 2 twinning
ID//0 0 0 2 ID//1 0 −1 0 ID//1 1 −2 0
0.0000(6) 0.0000(6) 0.0000(6)
0.0000(6) 0.0000(2)/0.4330(4) 0.0000(2)/0.4330(4)
0.44598(6) 0.0000(2) 0.33449(4) 0.44600(2) 0.1115(4)
0.49896(6) 0.49811(2)/0.124528(4) 0.0000(2)/0.373583(4)
0.41526(6) 0.420399(2)/0.1051(4) 0.0000(2)/0.315299(4)
Number in parentheses indicates number of the deformation systems with the same Schmid factor value.
In addition to twinning in large grains, because there is high contraction stress along the c-axis, the large grains have high Schmid factors for pyramidal c+a slip (Table 1). This deformation mode has been revealed, discussed as above, in the case of controlled-loading experiments of single crystal Mg, to which the stress situation of the large grains is very similar in the present study. So pyramidal c+a slip would be predominantly deformation mode because of its lower CRSS than that of contraction twinning. Normally, dislocation slip has less effect on grain reorientation than twinning, this can be derived from the pole figures of the sample after impact (Fig. 9(b)), in which texture is less changed unlike those in the samples impacted along TD and ED directions. Table 2 displays CRSS values for some deformation modes in magnesium or its alloys. It is seen that pyramidal c+a slip and {1 0 −1 1} contraction twinning have very high CRSS (45–81 and 76–153 MPa, respectively), so high stress is needed to activate the deformation modes. Therefore, the samples show higher stresses at the beginning of the deformation than those impacted along the other two directions (Fig. 7). In the case of ID//TD, except for basal a slip, all deformation mechanisms list in Fig. 13 have high Schmid factors for most grains.
Fig. 12. Schematic showing of the impact load aligned in 0 0 0 2, 1 0 −1 0 and 1 1 −2 0 crystallographic directions.
The oriented large grains would result in more stress concentration and they are difficult to deform by basal a slip, but easier twinning to a high strain because of the big r value. Because the c-axis of most large grains is perpendicular to impact direction, there is tension stress along the c-axis. So twinning in large grains is mainly tension type in this case. The prismatic a slip with a CRSS ratio of 1–3 to basal a slip [2] would be activated as tension twinning does. Twinning and Slip are easy at the beginning of the deformation. Twin variants, as well as twin–slip interaction, makes large grains
Fig. 11. EBSD orientation micrograph (a) and pole figures (b) of the sample impacted along ED at the rate of 1603 s−1 .
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refined during deformation. The refinement is favored under adiabatic condition. After refinement, slip plays an important role for further deformation, but twin/grain boundaries impose impedance to the subsequent dislocation slip and result in a rapid hardening (Hall-petch effect). During grain refinement, the texture changes to that with {0 0 0 1} pole in TD (Fig. 10(b)). This result is very similar to that found in the conventional compression reported in Ref. [6]. That means after twinning, most of refined grains have c-axis parallel to impact direction. This texture change sends the hard direction to the deformation direction, thus gives also rise to a rapid hardening. Hardening process corresponds to the part of the curves with d2 /dε2 > 0 in Fig. 8(b). The texture evolution is connected with tension twinning, during which the orientation is changed by the misorientation of 1 1 −2 0 86◦ between the tension twins and the matrix. {1 0 −1 2} tension twinning in Zr has a similar contribution to reorientation as in Mg alloy [35]. However, in the above reference, the initial orientation of grains is deviated 50–90◦ from ND of the rolling plane. So after {1 0 −1 2} tension twining, the basal pole rotates around 1 1 −2 0 by approximately 85◦ towards ND of the pole figure. On the contrast, the initial orientation of the large grains in the present study is {0 0 0 1}1 1 −2 0, so after {1 0 −1 2} tension twinning, the basal pole rotates around 1 1 −2 0 by approximately 86◦ towards TD. Although reorienta-
tion trajectories in the present work were different from those in the above reference, the reorientation mechanism was identical. In the case of ID//ED, Schmid factors for slip and twinning are similar to those in the case of ID//TD, but they are a little lower for twinning. Unlike in the case of ID//TD, in which ID is parallel to 1 0 −1 0 direction of large grains, in the case of ID//ED, ID is parallel to 1 1 −2 0 direction of large grains. So it is convenient to simultaneously activate two variants of tension twinning by shearing along two 1 0 −1 1 directions of 1 . So after impacted along extrusion direction, the large grains show {1 0 −1 2} tension twin variants, but they are not evidently refined. As the twin variants swept the large part of the large grain, resultant orientation of the alloy is dominated by the orientation of the latter twin variants (Fig. 11(b)). Generally, the yield stress of a material under dynamic load is much higher than that under quasi-static load and this phenomenon has been widely observed in various metal or alloy systems [17,36,37]. In the present investigation, the maximum flow stress of the sample, impacted along TD at strain rate of 1766 s−1 , is quite close to 600 MPa. From the stress–strain curves (Fig. 7(b)), it can be seen that the strain hardening rate is positive and very high for TD impacts. So the maximum flow stresses could get high if the compact ductility is also very high. The drastic increase of strain
Fig. 13. Schmid factor maps of the initial microstructure in Fig. 2.
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Table 2 CRSS for some deformation modes in magnesium and its alloys. Deformation system
Basal a slip
Prismatic a slip
Pyramidalc+a slip
{1 0 −1 2} tension twinning
{1 0 −1 1}contraction twinning
CRSS (MPa)
0.45–0.81[28–32]
39.2[33,34]
45–81[1,24]
2.0–2.8[2]
76–153[2]
hardening rate with the increase of strain rate in the magnesium alloys has been observed in AM20, AM50 and AM60 magnesium alloys at a nominal strain rate range from 0.001 s−1 to approximately 1700 s−1 by Song et al. [38]. However, even with the high strain hardening rate, the maximum flow stress during compressive impact, reported in Ref. [13,14], is just 480 MPa and 400 MPa along TD in AZ31B and AZ31 alloys, respectively. The maximum stresses are much lower than the present results. This difference is resulted from the different maximum reductions (0.18 and 0.06 in Ref. [13,14] and 0.30 in our work). The difference originally comes from the different microstructures that determine the different deformation mechanisms. In our case, the microstructure is composed of very large grains with intense {0 0 0 1}1 0 −1 2 texture. This sharp texture brings the tension twinning plane in a favorable orientation. In addition, the large grains favor twinning as a deformation mechanism. Unlike dislocation slip, twinning mode is surely advantageous to obtain high ductility as there are no premature cracks easily induced. The phenomenon that the flow stress increases with the increase of grain size has been observed by Kim et al. [39]. In the present study, the ductility of the AZ31 alloy impacted along TD and ED is much higher than that of the same alloy with basal plane parallel to ED (also compressive direction) under quasi-static compression reported by Wang and Huang [40]. This is because tension twinning is activated heavily in large grains with {0 0 0 1}1 1 −2 0 initial orientation under the impact load along TD and ED. However, under the quasi-static compression, tension twinning is limited in the alloy when the grains sizes are small and uniform, which can be seen in the deformed microstructures given in Refs. [40,41]. 4.4. Strain rate sensitivity As mentioned above, the flow stress decreases with the increase of the strain rate under conditions of ID//TD and ID//ED. This is exhibited as negative strain rate sensitivity. The modified Cowper–Symonds equation can be used to describe the effect of strain rate on the flow stress of a material [38]:
⁄
. 1P
u − k0 ε ( ) =1+ 0 u − ky C
2 − 1 .
.
ln(ε2/ε1)
5. Summary The present study of dynamic behavior of extruded AZ31 magnesium has shown the different responses of stress-strain when the samples were impacted along ND, TD and ED directions. When impacted along ND, the beginning flow stress is higher than those when impacted along other two directions. Although strain hardening is positive for all the three directions, the hardening rate varies in different ways. In ND, the hardening rates are high at the beginning but decrease continuously. On the contrary, in TD and ED, the hardening rates are low at beginning but then increase rapidly. The sample (impacted along TD) possesses the highest impact reduction (about 0.30) at the strain rate of 1766 s−1 . The maximum flow stress can reach nearly as high as 600 MPa at this strain rate. The flow stress is strain rate sensitive in all the three directions. It is positive for ND and negative for TD and ED. Microstructure and orientation responses show that when impacted along ND, {1 0 −1 1}–{1 0 −1 2} double twins forms dominantly in the large grains which are remained from the extrusion and annealing, however small grains show {1 0 −1 2} tension twins. After impacted along TD, the grains of the alloy are evidently refined. {1 0 −1 2} tension twinning as well as dislocation slip are effective for grain refinement and in this case, microtexture changes from {0 0 0 1}1 1 −2 0 to {0 0 0 1} pole in TD. After impacted along extrusion direction, {1 0 −1 2} tension twin variants are also observed in the large grains but they are not evidently refined. As the twin variants swept the large part of the large grains, resultant orientation of the alloy is dominated by those of the twin variants. The stress–strain, microstructure and orientation responses could well be interpreted with the Schmid factor distributions. Acknowledgements
(4)
where 0 , y and u are the static flow, yield and ultimate stress, respectively, ε˙ is the strain rate, C and P are strain rate sensitive material constants and k is the parameter that describes the strain rate sensitivity of the strain hardening. According to Eq. (4), if the flow stress decreases with increasing strain rate, the sensitivity material constant P would be negative. The strain rate sensitivity parameter, ˇ, can also be quantified as [17] ˇ=
of the tested material certainly exerts influence on the deformation behaviors of the material during the impact under the three specific directions. To clearly reveal the mechanism of the strain rate sensitivity of the flow stress, further investigation is needed.
(5)
where the compressive stress 2 and 1 are obtained from the tests conducted at the average strain rates of ε2 and ε1 , respectively, and are calculated at the same strain. According to Eq. (5), the sensitivity parameters at strain of 0.1 for ID//ND, ID//TD and ID//ED are 50.19 MPa, −72.72 MPa and −90.02 MPa, respectively. This indicates that strain rate sensitivity is quite different for the three directions. The difference in the strain rate sensitivity under the three deformation conditions may be related to the different deformation mechanisms (slip or twinning or both). The initial texture
This work is supported by the financial support from the National Foundation of Natural Science (No. 50771067). The author B. L. Wu acknowledges LETAM UMR 7078 CNRS for the invited professorship. The authors acknowledge the fruitful discussion with Professor M. Humbert and Professor M-J Philippe. References [1] X.Y. Lou, M. Li, R.K. Boger, S.R. Agnew, R.H. Wagoner, International Journal of Plasticity 23 (2007) 44–86. [2] J. Koike, Metallurgical and Materials Transaction A 36A (2005) 1689–1695. [3] Y.N. Wang, J.C. Huang, Materials Chemistry and Physics 81 (2003) 11–26. [4] M.H. Yoo, Metallurgical and Materials Transactions A 12A (1981) 409–418. [5] Robert Gehrmann, M. Matthias, Frommert, Gunter Gottstein, Materials Science and Engineering A 395 (2005) 338–349. [6] J. Jiang, A. Godfrey, W. Liu, Q. Liu, Materials Science and Engineering A 483–484 (2008) 576–579. [7] Huajie Yang, Shuming Yin, Chongxiang Huang, Zhefeng Zhang, Shiding Wu, Shuxin Li, Yandong Liu, Advanced Engineering Materials 10 (2008) 955–959. [8] S. Kleiner, P.J. Uggowitzer, Materials Science and Engineering A 379 (2004) 258–263. [9] S.Ya. Betsofen, A.A. Il’in, A.A. Ashmarin, A.A. Shaforostov, Russian Metallurgy (Metally) 3 (2008) 252–258. [10] J.A. del Valle, F. Carren, O.A. Ruano, Acta Materialia 54 (2006) 4247–4259.
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[11] Y.V.R.K. Prasad, K.P. Rao, Materials Science and Engineering A 487 (2008) 316–327. [12] E. El-Magd, M. Abouridouane, International Journal of Impact Engineering 32 (2006) 741–758. [13] T. Matthew, Tucker, F. Mark, Horstemeyer, M. Phillip, Gullett, Haitham El Kadiri, R. Wilburn, Scripta Materialia 60 (2009) 182–185. [14] Y.A.N.G. Yong-biao, W.A.N.G. Fu-chi, T.A.N. Cheng-wen, W.U. Yuang-yuan, C.A.I. Hong-nian, Transaction of Nonferrous Metals Society of China 18 (2008) 1043–1046. [15] L. Jiang, J.J. Jonas, R.K. Mishra, A.A. Luo, A.K. Sachdev, S. Godet, Acta Materialia 55 (2007) 3899–3910. [16] M.R. Barnett, Scripta Materialia 59 (2008) 696–698. [17] Su-Tang Chiou, Hsien-Lung Tsai, Woei-Shyan Lee, Journal of Materials Processing Technology 209 (2009) 2282–2294. [18] Mark Denis Nave, Scripta Materialia 51 (2004) 881–885. [19] Lan Jiang, J. John, Jonas, A. Alan, Luo, K. Anil, Sachdev, Stephane Godet, Scripta Materialia 54 (2006) 771–775. [20] J. Koike, R. Ohyama, Acta Materialia 53 (2005) 1963–1972. [21] J. Koike, T. Kobayashi, T. Mukai, H. Watanabe, M. Suzuki, K. Maruyama, K. Higashi, Acta Materialia 51 (2003) 2055–2065. [22] Z. Keshavarz, M.R. Barnett, Materials Forum 29 (2005) 382–386. [23] T. Obara, H. Yoshinga, S. Morozumi, Acta Metallurgica 21 (1973) 845–853. [24] S.R. Agnew, M.H. Yoo, C.N. Tome, Acta Materialia 49 (2001) 4277–4289. [25] M.R. Barnett, Materials Science and Engineering A 464 (2007) 1–7.
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Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Anisotropy of dynamic behavior of extruded AZ31 magnesium alloy G. Wan c,a , B.L. Wu a,c,∗ , Y.D. Zhang a,b , G.Y. Sha a , C. Esling b a
Shenyang Institute of Aeronautical Engineering, 110136, Shenyang, China LETAM University of Metz-CNRS UMR, 7078, France c Nanjing University of Aeronautics and Astronautics, 210016, Nanjing, China b
a r t i c l e
i n f o
Article history: Received 12 October 2009 Received in revised form 4 January 2010 Accepted 6 January 2010
Keywords: Magnesium Texture Dynamic behavior Anisotropy Twinning Slip
a b s t r a c t Textures always exert an intensive influence on the deformation and fracture of magnesium alloys. A hot extruded AZ31 alloy with intensive texture was selected for impact tests with the impact direction parallel to the respective normal, extrusion and transverse directions (ND, ED and TD) of the initial extrusion plate. The results showed that the stress–strain response of the alloy is highly anisotropic and sensitive to the strain rate. The maximum flow stress can reach nearly as high as 600 MPa for TD impact. Microstructure responses show that when impacted along normal direction, {1 0 −1 1}–{1 0 −1 2} double twins is common in large grains, however, small grains show {1 0 −1 2} tension twins. After impacted along transverse direction, grains of the alloy are evidently refined and the texture changes from {0 0 0 1}1 1 −2 0 to that with {0 0 0 1} pole in TD direction. The stress–strain, microstructure and orientation responses could well be interpreted with the Schmid factor distributions. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Magnesium alloys are attractive materials for aerospace and automotive industries due to their high specific strength. However, they have limited formability at room temperature, which mainly arises from the limited number of slip systems in the hexagonal close packed (HCP) structure [1–3]. Consequently, twinning is an important mechanism to accommodate the deformation of polycrystalline magnesium alloys [4–7]. Magnesium alloys will be improved in plasticity at elevated temperature for processing. After deformation during processing, the texture always forms and results in a pronounced anisotropy of the mechanical properties of magnesium alloys [8–11]. At present, most of the investigations have dealt with the mechanical behavior under conventional tensile or compression. However materials components will be potentially subjected to impact loads in some services. The behavior of materials under impact loading that results in a very high strain rate, is quite complicated. El-Magd and Abouridouane [12] indicated in their work that under impact loading, the dynamic plastic response of the lightweight wrought alloy is mainly controlled by strain rate sensitivity and the adiabatic character of the deformation process. Generally magnesium alloys have high anisotropic trend. Textures always
∗ Corresponding author at: Shenyang Institute of Aeronautical Engineering, 110136, Shenyang, China. Tel.: +86 24 89723976; fax: +86 24 89724198. E-mail address: [email protected] (B.L. Wu). 0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2010.01.023
exert an intensive effect on their deformation and fracture. This would enhance the complicity of the dynamic behavior. Recently, Tucker and co-workers [13] investigated the anisotropic effects on the strain rate dependence of AZ31B alloy and showed that stress–strain responses at high strain rate in the normal, rolling and transverse directions (ND, RD and TD) were evidently different. They concluded that the texture of the material played a significant role in the plastic deformation at both quasi-static and high strain rates due to twin–slip interactions. A similar work for AZ31 alloy was also presented, in which impact direction (ID) was aligned in 0◦ , 45◦ and 90◦ with the ND and the twinning mechanism for the 90◦ and the slip mechanism for 0◦ and 45◦ impact were concluded, respectively [14]. Experimental results showed that twinning plays an important role when the strain rate is high or the grain size is large [15,16]. So twinning would be a favored mechanism to accommodate the deformation of a magnesium alloy which has large grains and was compressed at high strain. In the present work, a plate of hot extruded AZ31 alloy with partially dynamically recrystallized grains was selected for impact tests. The influence of the texture on the dynamic mechanical behavior was investigated and the responses of the microstructure were analyzed. 2. Experimental The investigated material was AZ31 magnesium alloy with the chemical composition of Mg–3.0Al–1.0Zn (in mass.%). A square bar of 100 mm × 20 mm × 20 mm was cut from an as-received extruded plate with size of 800 mm in length (extrusion direction, ED),
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Fig. 1. Schematic showing of the impact samples cut from the as-received AZ31 plate.
250 mm in width (Transverse direction, TD) and 20 mm in thickness (Normal direction, ND), and then annealed at 250 ◦ C for 2.5 h as the initial state of the alloy. Three groups of cylindrical samples with size of Ø8 mm × 8 mm were cut out of the center of the annealed square bar for the impact tests. The axial directions of the respective samples were parallel to the ND, TD and ED of the extruded plate. The relative positions between the extruded plate, the annealed square bar and the impact samples are schematically shown in Fig. 1. The impact tests were performed with the Split Hopkinson Pressure Bar (SHPB). The samples were impacted in their axial directions. The ID is corresponding to ND for Sample group A, TD for Sample group B and ED for Sample group C, respectively. For each group, the samples were impacted under two gas gun pressures (0.2 MPa and 0.5 MPa). During the test, the samples were put between the incident and transmitter bars. The incident, reflection and transmission strain-time waves were recorded by the data collection system of the equipment, and then the true stress, true strain and strain rate of each impact were calculated according to the equations below [17], from which the true stress–strain relationships were obtained. =
A Eεt (t) A0
2C0 ε=− L0 ε˙ =
(1)
t
εr (t)d
(2)
2C0 (ε (t) − εt (t)) L0 i
(3)
o
where , ε and ε˙ are true stress, true strain and strain rate. εi (t), εr (t) and εt (t) are incident, reflection and transmission strain-time waves. E, C0 and A are Young’s elastic modulus of the impacting bar, elastic wave rate in the bars and the sectional area of the bars. The initial sectional area and length of the impact samples are denoted A0 and L0 .
Fig. 2. EBSD orientation micrograph of the initial microstructure of the alloy observed in the transverse section.
The global texture analyses were performed by measuring incomplete pole figures with a Fangyuan D2000 X-ray goniometer using Schulz reflection method. The range of the tilt angle ˛ is 0–70◦ and of the azimuthal angle ˇ is 0–360◦ at 5◦ steps. Electron back-scattered diffraction (EBSD) measurements were carried out in a JEOL6500F field emission SEM equipped with an automatic orientation acquisition system (Oxford Instruments-HKL Channel 5) to measure the local texture. The orientation map of the initial state was acquired from the ND-ED plane and that for the impacted samples were measured from the impacted plane. 3. Results 3.1. Initial microstructure and texture Fig. 2 shows the orientation micrograph in the ND-ED plane of the initial state of the alloy (extrusion + 250 ◦ C/2.5 h annealing). The blue lines in the figure indicate the boundaries whose misorientation angle is larger than 5◦ . The colors of the grains correspond to their orientations. From the picture, it can be seen that the microstructure is composed of two kinds of grains, the large grains clearly elongate along the ED and the small equiaxied grains distribute between the large elongated grains. The elongation of the large grains indicate that they have not recrystallized during the annealing but remained in the as worked state, while the equiaxied shape of the small grains suggests that they are fully recrystallized. The texture of the overall microstructure in Fig. 2 is displayed with
Fig. 3. Pole figures of the initial microstructure shown in Fig. 2.
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ented around {0 0 0 1}1 1 −2 0; whereas the small grains tend to have deviated {0 0 0 1} plane texture. 3.2. Stress–strain response
Fig. 4. Highlighted large elongated grains in the microstructure shown in Fig. 2.
the {0 0 0 1} and {1 0 −1 0} pole figures in Fig. 3. It can be seen that the texture of the initial state of the alloy is very close to the {0 0 0 1}1 1 −2 0 component. This observation is consistent with the X-ray global texture analysis. As the grain size is very inhomogeneous, distinguishing the texture of the large elongated grains from that of the small grains is useful. With the “subset” function of Channel 5 software, the large elongated grains are selected and shown in Fig. 4. Their corresponding pole figures with scattered data are displayed in Fig. 5. The pole figures of the remaining small grains are shown in Fig. 6. It is seen that the large grains are ori-
Fig. 7 shows the dynamic stress–strain curves of Sample group A, B and C impacted along ND (Fig. 7(a)), TD (Fig. 7(b)) and ED (Fig. 7(c)) under two strain rates for each group, respectively. The higher strain rate corresponds to the 0.5 MPa gas gun pressure and the lower strain rate to the 0.2 MPa pressure in the figure. All the three samples were impacted to fracture under 0.5 MPa or higher strain rate, while those under 0.2M Pa or lower strain rate were not. It was found that for all the three directions, the flow stress increases with the strain. When impacted along ND, the beginning flow stresses under the two strain rates are higher than those of the samples impacted along the other directions. However, the d/dε–ε slope curves derived from –ε data of impacted samples indicate that the deformation hardening rate (d/dε) of the impacted samples varies in quite different ways in the three directions, as shown in Fig. 8. The hardening rate of the ID//ND impacted samples decreases drastically from the very beginning; whereas those of the ID//TD and ID//ED impacted samples rise at the beginning and drop after reaching the maximum. The relative reduction of the height at rupture was considered as a measure of the impact ductility of the material [12]. The dynamic impact ductility of the samples also shows evidently anisotropy. The sample (impacted along TD) possesses the highest impact reduction (about 0.30) at the strain rate of 1766 s−1 . At this high reduction, the maximum flow stress reaches nearly as high as 600 MPa.
Fig. 5. Pole figures with scattered data of the highlighted large elongated grains in Fig. 4.
Fig. 6. Pole figures of the remaining small grains in Fig. 2.
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Fig. 7. True stress–strain curves of the samples impacted with (a) ID//ND, (b) ID//TD and (c) ID//ED under two stage gas gun pressures.
Another important phenomenon is that flow stress shows different strain rate sensitivity from ND impact to TD and ED impact. The flow stress increases with increasing strain rate in ND (Fig. 7(a)), but decreases in TD (Fig. 7(b)) and ED (Fig. 7(c)) impact. In summary, the mechanical behaviors of the three groups of sample impacted along different directions show strong anisotropy. 3.3. Microstructures and orientations response The orientation micrographs of the samples impacted with ID//ND, ID//TD and ID//ED under 0.2 MPa gas gun pressure corresponding to low strain rate are shown in Fig. 9(a), Fig. 10(a) and Fig. 11(a). The corresponding pole figures are displayed in Fig. 9(b),
Fig. 8. d/dε–ε slope curves of the samples impacted with (a) ID//ND, (b) ID//TD and (c) ID//ED under two stage gas gun pressures.
Fig. 10(b) and Fig. 11(b). From Fig. 9, it is seen that after impacted along ND, the microstructure still consists of large grains and small grains. The only difference from the initial microstructure is that a little of twins appear in both the large grains and the small grains. Detailed analysis revealed that the twins in the large grains have mainly 38◦ misorientation around 1 1 −2 0 with the matrix that are {1 0 −1 1}–{1 0 −1 2} double twins [18,19], while the twins in the small grains possess 86◦ misorietation around 1 1 −2 0 with the matrix that are {1 0 −1 2} tension type. Fig. 9(b) displays {0 0 0 1} and {1 0 −1 0} pole figures of the microstructure in Fig. 9(a). The main component is close to that of the initial texture but with noticeable deviation. This deviation
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Fig. 9. EBSD orientation micrograph (a) and pole figures (b) of the sample impacted along ND at the rate of 1766 s−1 .
may result from the inaccuracy of sample sectioning and local texture inhomogeneity. The unreasonable pole intensity (as high as 84.99) is due to the insufficient number of grains. However, after impacted along TD at the strain rate of 933 s−1 , the microstructure is obviously refined (Fig. 10(a)) in contrast to the initial microstructure. The remaining large grains are in the course of fragmentation by twinning, as outlined in Fig. 10(a). The twins appear as the 1 1 −2 0 86◦ tension type. In addition to the refinement of the microstructure, it was found that the orientation changes from the initial {0 0 0 1}1 1 −2 0 to that with {0 0 0 1} pole in TD (the c-axis is parallel to TD). After impacted along ED at strain rate of 802 s−1 , the orientation micrograph shows large {1 0 −1 2} tension twins (green and yellow parts) in the original large grain where the white lines indicate the twin boundaries (Fig. 11(a)). It can be found that unlike those in the case of ID//TD, large grains in this case are not evidently refined during twinning. However, the orientation of the large grains changes from the initial {0 0 0 1}1 1 −2 0 to two distinct components with the c-axis perpendicular to ND and about 30◦ tilt from ED, as shown in Fig. 11(b). The two components possess 86◦ rotation around different 1 1 −2 0 axis from the initial component, suggesting that the two orientations are the two tension twin variants with respect to the initial orientation. 4. Discussion
that the anisotropy is resulted from textures, it is helpful to understand the relationships between the dynamic mechanical behavior, orientations and microstructures. In general, magnesium can be deformed by crystallographic slip and twinning. The principal slip system of magnesium alloy is the basal a at room temperature. However, non-basal slip is also an important means for deformation at room temperature [20]. Koike et al. [21] reported, in an ECAE AZ31 alloy with an average grain size of 8 m that, 40% of dislocation segments were of the non-basal type. Previous research concluded that the prismatic a slip in magnesium alloys is active at room temperature [22]. Pyramidal c+a slip is also potential deformation system at room temperature [2]. This often takes place in the case of controlled-loading experiments of single crystal Mg or in the case of Mg–Li and Mg–Y alloys [23,24]. In addition to dislocation slip, magnesium exhibits a strong propensity for mechanical twinning. Generally, tension, contraction twins and the double twins are observed in magnesium alloys [19]. The {1 0 −1 2} tension twinning is preferred when there is an extension strain component parallel to the c-axis [25]. The {1 0 −1 1} contraction twinning is reported to be activated when there is a contraction strain component parallel to the c-axis [26]. In the present work, the extruded alloy has deviated {0 0 0 1} plane texture for the small grains and {0 0 0 1}1 1 −2 0 orientation for the large grains. When an impact load is applied on the magnesium alloy along ND, TD and ED, deformation mechanisms of grains are different under the three conditions.
4.1. Deformation mechanisms
4.2. Schmid factors
The above results show an obvious anisotropic dynamic mechanical behavior of the alloy under impact loading. As we know
The slip and twining systems of a grain will have different Schmid factors when compression load is applied in 0 0 0 2,
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Fig. 10. EBSD orientation micrograph (a) and pole figures (b) of the sample impacted along TD at the rate of 1865 s−1 .
1 0 −1 0 and 1 1 −2 0, as schematically shown in Fig. 12. Schmid factors of basal a slip, prismatic a slip, pyramidal c+a slip, {1 0 −1 2} tension twinning and {1 0 −1 1} contraction twinning with the load in the above directions are calculated and listed in Table 1. In the present investigation, the orientation of the most large elongated grains is close to {0 0 0 1}1 0 −1 2, so for the three impact indirections (ID//ND, ID//TD and ID//ED), they undergo the load in 0 0 0 2, 1 0 −1 0 and 1 1 −2 0 crystallographic directions, respectively. Despite of the strong {0 0 0 1}1 0 −1 2 component in the initial alloy, there still remain large amount of grains deviating from this orientation. So when impacted along ND, TD and ED, the Schmid factors for different deformation systems of each grain will be determined by its individual orientation. Fig. 13 displays the Schmid factor maps of the initial microstructure in Fig. 2, where ID is supposed to be parallel to ND, TD and ED, respectively. It can be seen that in the case of ID//ND, large elongated grains have low Schmid factors for basal a slip, but that of some small grains is high. For prismatic a slip, the Schmid factors are low for almost all the grains, however, the Schmid factors for tension and contraction twinning are high for almost all the grains, especially for large elongated grains. It should be noted that small grains have higher Schmid factors for {1 0 –1 2} tension twinning than that for {1 0 −1 1} contraction twinning. In the case of ID//TD, Schmid factors of most grains for basal a slip are very low, but they are very high for prismatic a slip. These grains also have higher Schmid factors for the two twinning systems. In the case of ID//ED, The Schmid factors are just distributed similarly to those in the case of ID//TD. The only difference is that
for prismatic a slip, the Schmid factors of many small grains are slightly lower than those of the sample of ID//TD, and the Schmid factors of the large elongated grains for {1 0 −1 2} tension and {1 0 −1 1} contraction twinning are lower.
4.3. Dynamic response From the above clarification of the Schmid factors for different systems in large and small grains, we can expect that except for basal slip occurring in small grains with higher Schmid factors, twinning would be an important mechanism for the deformation of the samples under the impact along ND. Two kinds of twins (double twins in large elongated grains and tension twins in the small grains) are mainly observed (Fig. 9(a)). For the double twinning, {1 0 −1 1} contraction twins form first and then {1 0 −1 2} extension twins are propagated within them [19]. The reason for the {1 0 −1 1}–{1 0 −1 2} double twins with high critical resolved shear stress (CRSS) of the contraction twin to form in the large elongated grains is that during a rapid deformation under impact loading, twinning, a high speed deformation mode, is appropriate to accommodate the strain. In addition, the {1 0 −1 1}–{1 0 −1 2} double twins in the large elongated grains have large size in length and small size in thickness. This would result in the reduced elastic strain energy according to E = (c/r)s2 [27], where E is elastic strain energy; c and r represent the thickness and length of the twin respectively, is the shear modulus and s is the twinning shear. Therefore, the {1 0 −1 1}–{1 0 −1 2} double twins are difficult to form in the small grains because of the small r value. In contrary, the {1 0 −1 2} tension twins were easy to form in the small grains due to their lower CRSS and higher Schmid factors.
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Table 1 Calculated Schmid factors. Deformation system
{0 0 0 1}1 1 −2 0 slip
{1 0 −1 0}1 1 −2 0 slip
{1 1 −2 2}1 1 −2 3 slip
{1 0 −1 2}1 0 −1 1 twinning
{1 0 −1 1}1 0 −1 2 twinning
ID//0 0 0 2 ID//1 0 −1 0 ID//1 1 −2 0
0.0000(6) 0.0000(6) 0.0000(6)
0.0000(6) 0.0000(2)/0.4330(4) 0.0000(2)/0.4330(4)
0.44598(6) 0.0000(2) 0.33449(4) 0.44600(2) 0.1115(4)
0.49896(6) 0.49811(2)/0.124528(4) 0.0000(2)/0.373583(4)
0.41526(6) 0.420399(2)/0.1051(4) 0.0000(2)/0.315299(4)
Number in parentheses indicates number of the deformation systems with the same Schmid factor value.
In addition to twinning in large grains, because there is high contraction stress along the c-axis, the large grains have high Schmid factors for pyramidal c+a slip (Table 1). This deformation mode has been revealed, discussed as above, in the case of controlled-loading experiments of single crystal Mg, to which the stress situation of the large grains is very similar in the present study. So pyramidal c+a slip would be predominantly deformation mode because of its lower CRSS than that of contraction twinning. Normally, dislocation slip has less effect on grain reorientation than twinning, this can be derived from the pole figures of the sample after impact (Fig. 9(b)), in which texture is less changed unlike those in the samples impacted along TD and ED directions. Table 2 displays CRSS values for some deformation modes in magnesium or its alloys. It is seen that pyramidal c+a slip and {1 0 −1 1} contraction twinning have very high CRSS (45–81 and 76–153 MPa, respectively), so high stress is needed to activate the deformation modes. Therefore, the samples show higher stresses at the beginning of the deformation than those impacted along the other two directions (Fig. 7). In the case of ID//TD, except for basal a slip, all deformation mechanisms list in Fig. 13 have high Schmid factors for most grains.
Fig. 12. Schematic showing of the impact load aligned in 0 0 0 2, 1 0 −1 0 and 1 1 −2 0 crystallographic directions.
The oriented large grains would result in more stress concentration and they are difficult to deform by basal a slip, but easier twinning to a high strain because of the big r value. Because the c-axis of most large grains is perpendicular to impact direction, there is tension stress along the c-axis. So twinning in large grains is mainly tension type in this case. The prismatic a slip with a CRSS ratio of 1–3 to basal a slip [2] would be activated as tension twinning does. Twinning and Slip are easy at the beginning of the deformation. Twin variants, as well as twin–slip interaction, makes large grains
Fig. 11. EBSD orientation micrograph (a) and pole figures (b) of the sample impacted along ED at the rate of 1603 s−1 .
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refined during deformation. The refinement is favored under adiabatic condition. After refinement, slip plays an important role for further deformation, but twin/grain boundaries impose impedance to the subsequent dislocation slip and result in a rapid hardening (Hall-petch effect). During grain refinement, the texture changes to that with {0 0 0 1} pole in TD (Fig. 10(b)). This result is very similar to that found in the conventional compression reported in Ref. [6]. That means after twinning, most of refined grains have c-axis parallel to impact direction. This texture change sends the hard direction to the deformation direction, thus gives also rise to a rapid hardening. Hardening process corresponds to the part of the curves with d2 /dε2 > 0 in Fig. 8(b). The texture evolution is connected with tension twinning, during which the orientation is changed by the misorientation of 1 1 −2 0 86◦ between the tension twins and the matrix. {1 0 −1 2} tension twinning in Zr has a similar contribution to reorientation as in Mg alloy [35]. However, in the above reference, the initial orientation of grains is deviated 50–90◦ from ND of the rolling plane. So after {1 0 −1 2} tension twining, the basal pole rotates around 1 1 −2 0 by approximately 85◦ towards ND of the pole figure. On the contrast, the initial orientation of the large grains in the present study is {0 0 0 1}1 1 −2 0, so after {1 0 −1 2} tension twinning, the basal pole rotates around 1 1 −2 0 by approximately 86◦ towards TD. Although reorienta-
tion trajectories in the present work were different from those in the above reference, the reorientation mechanism was identical. In the case of ID//ED, Schmid factors for slip and twinning are similar to those in the case of ID//TD, but they are a little lower for twinning. Unlike in the case of ID//TD, in which ID is parallel to 1 0 −1 0 direction of large grains, in the case of ID//ED, ID is parallel to 1 1 −2 0 direction of large grains. So it is convenient to simultaneously activate two variants of tension twinning by shearing along two 1 0 −1 1 directions of 1 . So after impacted along extrusion direction, the large grains show {1 0 −1 2} tension twin variants, but they are not evidently refined. As the twin variants swept the large part of the large grain, resultant orientation of the alloy is dominated by the orientation of the latter twin variants (Fig. 11(b)). Generally, the yield stress of a material under dynamic load is much higher than that under quasi-static load and this phenomenon has been widely observed in various metal or alloy systems [17,36,37]. In the present investigation, the maximum flow stress of the sample, impacted along TD at strain rate of 1766 s−1 , is quite close to 600 MPa. From the stress–strain curves (Fig. 7(b)), it can be seen that the strain hardening rate is positive and very high for TD impacts. So the maximum flow stresses could get high if the compact ductility is also very high. The drastic increase of strain
Fig. 13. Schmid factor maps of the initial microstructure in Fig. 2.
G. Wan et al. / Materials Science and Engineering A 527 (2010) 2915–2924
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Table 2 CRSS for some deformation modes in magnesium and its alloys. Deformation system
Basal a slip
Prismatic a slip
Pyramidalc+a slip
{1 0 −1 2} tension twinning
{1 0 −1 1}contraction twinning
CRSS (MPa)
0.45–0.81[28–32]
39.2[33,34]
45–81[1,24]
2.0–2.8[2]
76–153[2]
hardening rate with the increase of strain rate in the magnesium alloys has been observed in AM20, AM50 and AM60 magnesium alloys at a nominal strain rate range from 0.001 s−1 to approximately 1700 s−1 by Song et al. [38]. However, even with the high strain hardening rate, the maximum flow stress during compressive impact, reported in Ref. [13,14], is just 480 MPa and 400 MPa along TD in AZ31B and AZ31 alloys, respectively. The maximum stresses are much lower than the present results. This difference is resulted from the different maximum reductions (0.18 and 0.06 in Ref. [13,14] and 0.30 in our work). The difference originally comes from the different microstructures that determine the different deformation mechanisms. In our case, the microstructure is composed of very large grains with intense {0 0 0 1}1 0 −1 2 texture. This sharp texture brings the tension twinning plane in a favorable orientation. In addition, the large grains favor twinning as a deformation mechanism. Unlike dislocation slip, twinning mode is surely advantageous to obtain high ductility as there are no premature cracks easily induced. The phenomenon that the flow stress increases with the increase of grain size has been observed by Kim et al. [39]. In the present study, the ductility of the AZ31 alloy impacted along TD and ED is much higher than that of the same alloy with basal plane parallel to ED (also compressive direction) under quasi-static compression reported by Wang and Huang [40]. This is because tension twinning is activated heavily in large grains with {0 0 0 1}1 1 −2 0 initial orientation under the impact load along TD and ED. However, under the quasi-static compression, tension twinning is limited in the alloy when the grains sizes are small and uniform, which can be seen in the deformed microstructures given in Refs. [40,41]. 4.4. Strain rate sensitivity As mentioned above, the flow stress decreases with the increase of the strain rate under conditions of ID//TD and ID//ED. This is exhibited as negative strain rate sensitivity. The modified Cowper–Symonds equation can be used to describe the effect of strain rate on the flow stress of a material [38]:
⁄
. 1P
u − k0 ε ( ) =1+ 0 u − ky C
2 − 1 .
.
ln(ε2/ε1)
5. Summary The present study of dynamic behavior of extruded AZ31 magnesium has shown the different responses of stress-strain when the samples were impacted along ND, TD and ED directions. When impacted along ND, the beginning flow stress is higher than those when impacted along other two directions. Although strain hardening is positive for all the three directions, the hardening rate varies in different ways. In ND, the hardening rates are high at the beginning but decrease continuously. On the contrary, in TD and ED, the hardening rates are low at beginning but then increase rapidly. The sample (impacted along TD) possesses the highest impact reduction (about 0.30) at the strain rate of 1766 s−1 . The maximum flow stress can reach nearly as high as 600 MPa at this strain rate. The flow stress is strain rate sensitive in all the three directions. It is positive for ND and negative for TD and ED. Microstructure and orientation responses show that when impacted along ND, {1 0 −1 1}–{1 0 −1 2} double twins forms dominantly in the large grains which are remained from the extrusion and annealing, however small grains show {1 0 −1 2} tension twins. After impacted along TD, the grains of the alloy are evidently refined. {1 0 −1 2} tension twinning as well as dislocation slip are effective for grain refinement and in this case, microtexture changes from {0 0 0 1}1 1 −2 0 to {0 0 0 1} pole in TD. After impacted along extrusion direction, {1 0 −1 2} tension twin variants are also observed in the large grains but they are not evidently refined. As the twin variants swept the large part of the large grains, resultant orientation of the alloy is dominated by those of the twin variants. The stress–strain, microstructure and orientation responses could well be interpreted with the Schmid factor distributions. Acknowledgements
(4)
where 0 , y and u are the static flow, yield and ultimate stress, respectively, ε˙ is the strain rate, C and P are strain rate sensitive material constants and k is the parameter that describes the strain rate sensitivity of the strain hardening. According to Eq. (4), if the flow stress decreases with increasing strain rate, the sensitivity material constant P would be negative. The strain rate sensitivity parameter, ˇ, can also be quantified as [17] ˇ=
of the tested material certainly exerts influence on the deformation behaviors of the material during the impact under the three specific directions. To clearly reveal the mechanism of the strain rate sensitivity of the flow stress, further investigation is needed.
(5)
where the compressive stress 2 and 1 are obtained from the tests conducted at the average strain rates of ε2 and ε1 , respectively, and are calculated at the same strain. According to Eq. (5), the sensitivity parameters at strain of 0.1 for ID//ND, ID//TD and ID//ED are 50.19 MPa, −72.72 MPa and −90.02 MPa, respectively. This indicates that strain rate sensitivity is quite different for the three directions. The difference in the strain rate sensitivity under the three deformation conditions may be related to the different deformation mechanisms (slip or twinning or both). The initial texture
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