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Plastic deformation and fracture of ultrafine-grained Al–Mg alloys with a bimodal grain size distribution
Acta Materialia 54 (2006) 1759–1766 www.actamat-journals.com
Plastic deformation and fracture of ultrafine-grained Al–Mg alloys with a bimodal grain size distribution G.J. Fan b
a,*
, H. Choo a, P.K. Liaw a, E.J. Lavernia
b
a Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, USA Department of Chemical Engineering and Materials Science, University of California, Davis, CA 95616, USA
Received 26 September 2005; received in revised form 15 November 2005; accepted 30 November 2005 Available online 15 February 2006
Abstract Four different ultrafine-grained (ufg) Al–7.5 wt.% Mg alloys were synthesized by consolidation of a mixture of as-received and cryomilled Al–Mg powders with a ratio of 1:9, yielding a bimodal microstructure consisting of coarse grains (grain sizes, dcg, typically of several micrometers) evenly distributed in the ufg matrices (average grain sizes d = 120, 142, 197, and 338 nm). The deformation behavior under uniaxial compression and tension of the as-extruded alloys was investigated. The Ramberg–Osgood equation was used to fit the compressive stress–strain curves of the bimodal ufg alloys. The compressive yield stresses of the ufg matrices with different average grain sizes indicated a reduced slope in the Hall–Petch relation. The plastic deformation of the ufg Al–Mg alloys with a bimodal microstructure was highly localized. The fracture of the alloys was attributed to shear localization under the compressive tests, and to a combination of shear localization, cavitation, and necking under the tensile tests. 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Mechanical alloying; Aluminum alloys; Mechanical properties; Ultrafine-grained microstructure
1. Introduction Bulk ultrafine-grained (ufg) metals and alloys with grain sizes, d, typically in the range 100 nm to 1 lm have been the subject of much interests recently, primarily due to their excellent mechanical properties for potential engineering applications [1]. Due to the ufg structure, bulk ufg metals and alloys exhibit extraordinarily high strengths as well as excellent superplasticity at high strain rates compared with coarse-grained materials [2–7]. However, bulk ufg metals and alloys often show a limited ductility at room temperature, which was attributed to the lack of efficient hardening during plastic deformation and/or to the defects introduced during the processing [4,8]. Recently, it was found that ufg metals and alloys with a bimodal microstructure exhibit a combination of high strength and good ductility [9–15]. In this toughening strategy, the ufg matrix *
Corresponding author. E-mail address: [email protected] (G.J. Fan).
in the bimodal microstructure provides the high strength, while the relatively large grains of the order of micrometers contribute to the ductility. Bulk bimodal ufg metals and alloys can be synthesized by: (a) thermomechanical treatment involving severe plastic deformation, i.e., cold rolling or equal-channel angular pressing, followed by an appropriate thermal annealing under controlled conditions [10]; and (b) mechanical milling plus the consolidation of the milled powders mixed with certain volume fractions of the as-received coarsegrained powders [9,11]. The latter synthesis method has an apparent advantage in that a tailored bimodal microstructure can be conveniently achieved using a desired ratio of starting powders with a bimodal grain size distribution. The mechanical properties can be easily optimized via design of the appropriate bimodal microstructure. In this paper, we investigate bimodal Al–7.5 wt.% Mg alloys with ufg matrices having various average grain sizes, which were synthesized using a mechanical milling machine followed by hot pressing and extrusion. The plastic
1359-6454/$30.00 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2005.11.044
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deformation and fracture of the bimodal alloys under compression and tension are discussed in detail. It is shown that the plastic deformation of the bimodal ufg Al–7.5 wt.% Mg alloys is highly localized. The alloys display a negative strain rate sensitivity, which promotes the deformation localization. The compressive yield stresses of ufg matrices with varying average grain sizes, derived from fitting the compressive stress–strain curves of the bimodal ufg alloys using the Ramberg–Osgood equation [16], were found to deviate from the Hall–Petch relation established for coarse-grained counterparts. The effect of the coarse grains on the mechanical behaviors of the bimodal alloys, including yielding, plastic flow, and fracture, is discussed. The fracture mechanisms of the bimodal ufg Al–Mg alloys during the compression and tension tests are compared. 2. Experimental The Al–7.5 wt.% Mg powders were mechanically milled at a cryogenic temperature (190 C) for 8 h. Mechanical milling at room temperature always introduces undesired oxides. Oxidation reactions were kinetically suppressed during the cryogenic milling [14]. In addition, the grain size can be more effectively refined during cryogenic milling, due to the significantly suppressed thermal recovery at a cryogenic temperature. The as-cryomilled Al–Mg powders exhibit a narrow grain size distribution with an average grain size of about 30 nm [14]. The powders after cryomilling were mixed with as-received coarse-grained powders with a weight ratio of 9:1. The powder mixtures were consolidated via hot isostatic pressing at four different temperatures (275, 300, 325, and 350 C) and at a pressure of 150 MPa for 3 h, and by subsequent hot extrusion at 250 C. The experimental details regarding the process of the cryomilling, consolidation, and extrusion are published elsewhere [15]. The as-extruded bars were electrodischarge machined into rectangular and dog-bone specimens along the extrusion direction for the compressive and tensile tests, respectively. The microstructure and the surface morphology of the samples before and after plastic deformation were characterized by optical microscopy (OM), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). 3. Results 3.1. Microstructures Depending on the consolidation temperatures, the ufg matrix exhibits different average grain sizes, as listed in Table 1. With increasing consolidation temperature, the average grain sizes of the ufg matrix increase from 120 to 338 nm, while the average sizes of the coarse grains change from 2.7 to 3.5 lm. The as-extruded bars exhibit a bimodal microstructure, as shown in Figs. 1(a) and (b), which show OM images along and perpendicular to the extrusion direction. No porosity was noticed during the OM
Table 1 Four different bimodal ufg Al–Mg alloys consolidated at different temperatures, Tcons, with different average grain sizes, d, of the ufg matrix. The average grain size of the coarse-grained inclusions in the bimodal microstructure, dcg, the strain rate sensitivity, m, the yield stress of the ufg matrix, rM, and the asymptotic reference stress of the bimodal N , at e_ ¼ 102 s1 are also listed alloys, r Sample
Tcons (C)
d (nm)
dcg (lm)
m
rM (MPa)
r N (MPa)
I II III IV
275 300 325 350
120 142 197 338
2.7 3.0 3.1 3.5
0.01 0.0105 0.0087 0.0073
640 624 611 599
582 561 545 536
examinations. The large grains (white area of Figs. 1(a) and (b)) with grain sizes of the order of several micrometers were evenly distributed in the ufg matrix (gray area), and were elongated along the extrusion direction. Fig. 1(c) shows a typical TEM image of sample III, showing the ultrafine grains in the matrix. The grain size distribution statistics for sample III, shown in Fig. 1(d), clearly indicate a bimodal grain size distribution. The average grain sizes are about 197 nm for the ufg matrix and 3.1 lm for the coarse-grained inclusions in the bimodal microstructure. X-ray diffraction patterns indicate a face-centered cubicstructured Al(Mg) supersaturated solid solution in the asextruded state. 3.2. Plastic flow and fracture during compressive tests The rectangular samples (I–IV) were compressed along the extrusion direction at room temperature. The typical true stress–strain curves for sample III, compressed at different strain rates, e_ , ranging from 104 to 101 s1, are shown in Fig. 2. The samples show an excellent compressive ductility. Also, the flow stress, r, decreases with increasing the strain rate. For example, the flow stress r at a strain of 0.2 decreases with increasing e_ from r = 612 MPa at e_ ¼ 104 s1 to r = 575 MPa at e_ ¼ 101 s1 , indicating a negative strain rate sensitivity. The strain rate sensitivity, m, is defined by o log r m¼ . ð1Þ o log e_ e;T
The relationship between the flow stress and the strain rate is presented in Fig. 3(a) and Table 1, where m = 0.01, 0.0105, 0.0087, and 0.0073 for samples I–IV, respectively. The negative strain rate sensitivity indicates that the plastic deformation of bimodal ufg alloys is macroscopically localized and is associated with a dynamic strain aging (DSA) as often observed in coarse-grained aluminum alloys [17,18]. The strain rate sensitivity, m, as a function of the average grain size, d, for the ufg matrix is plotted in Fig. 3(b). With decreasing d, the value of m decreases and becomes more negative, indicating that reducing the grain sizes may promote the deformation localization. The surface morphologies were examined by OM and SEM for the samples compressed for different strain levels
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Flow stress σ (ε=0.2) (MPa)
(a)
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680 d = 120 nm d = 142 nm d = 197 nm d = 338 nm
m = -0.01
640
m = -0.0105
600 m = -0.0087
560
10
m = -0.0073 -6
-4
-2
10 10 . -1 Strain rate ε (s )
10
0
(b)
Fig. 1. OM images for the as-extruded bar along the extrusion direction (a) and perpendicular to the extrusion direction (b) for the sample III. The gray area is the ufg matrix, and the light area is the coarse grains being elongated along the extrusion direction. TEM image (c) for the gray area indicates that grain size is in the ultrafine regime. The average grain size for the ufg matrix, derived from the grain size-distribution statistics (d), is about 197 nm. The arrow in (a) indicates the extrusion direction.
Strain rate sensitivity m
-0.006
-0.008
-0.010
-0.012 100
200 300 Grain size d (nm)
400
Fig. 3. Compressive flow stresses at e = 0.2 as a function of the strain rate for the bimodal alloys with the ufg matrix having different average grain sizes d (a). A plot of the strain rate sensitivity m, determined from (a), as a function of the average grain sizes of the ufg matrices d (b).
Fig. 2. Compressive stress–strain curves for the sample III at different strain rates.
and strain rates. Figs. 4(a) and (b) display the OM images for sample III for e = 0.1 and 0.2 at e_ ¼ 102 s1 , respectively. At e = 0.1, contrast differences along the extrusion direction develop in the surface of the sample. These contrast differences (large elongated dimples) are due to the large localized plastic strain within the coarse grains in the bimodal structured samples, since a lower stress is required for plastic yielding of the coarse grains. The
Fig. 4. OM images for the sample III compressed at e_ ¼ 102 s1 to e = 0.1 (a) and e = 0.2 (b), respectively. The arrows indicate the compression direction, which is parallel to the extrusion direction.
plastic deformation of the large grains in the bimodal microstructure, therefore, contributes to the global plastic strain. At e = 0.2, besides the localized plastic deformation
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in the coarse grains of the bimodal microstructure, shear bands along about 45 to the direction of the applied load were observed. Shear bands were more clearly observed by SEM. Figs. 5(a)–(d) show the SEM images for sample III for e = 0.2 at e_ ¼ 102 s1 . A high density of shear bands is observed in the low-magnification SEM image in Fig. 5(a). The high-magnification SEM image in Fig. 5(b) indicates a highly localized plastic deformation within and around the shear band zone. In Figs. 5(c) and (d), the shear banding spacing is about 200 nm, which is almost the same as the average grain size (197 nm) of the ufg matrix in specimen III. Fig. 5(e) indicates that the sample fractures along a direction with a maximum shear force, i.e., approximately 45 to the loading direction. The fracture surface after the compressive test in Fig. 5(f) suggests that the samples experience extensive plastic deformation prior to fracture.
800
Compression 600 True stress σ (MPa)
1762
Tension 400
200 .
e = 10-2 s-1
0 0.0
0.1
0.2 True strain ε
0.3
0.4
Fig. 6. Tensile stress–strain curve of the sample III. For comparison the compressive stress–strain curve of the same sample is also included. Note that the sample exhibits an asymmetric yielding behavior. The yield stress is lower during tension than during compression.
3.3. Plastic flow and fracture during tensile tests
Fig. 5. SEM images showing the shear band formation on the surface of the sample III compressed at e_ ¼ 102 s1 to e = 0.2 at a low magnification (a) and high magnification (b). A coordinated shear band array with a shear band spacing around 200 nm is shown in a low magnification (c) and in a high magnification (d). A side view of the sample fractured after compression (e) and the corresponding fracture surface morphology (f). The white arrow in (a) is the compression direction.
The tensile behavior of the bimodal ufg Al–Mg alloys with different d for the matrix was also studied. Fig. 6 shows a typical tensile stress–strain curve of sample III at e_ ¼ 102 s1 . For comparison the compressive stress–strain curve of the same sample at the same strain rate is included in Fig. 6. The monolithic ufg Al–Mg alloy showed a very limited tensile ductility (less than 1%) [13]. The tensile ductility was enhanced in the current bimodal ufg Al–Mg alloy with a tensile elongation of about 8%. Compared with the compressive stress–strain curve, the tensile yield stress is lower than the compressive yield stress. The asymmetry of yielding in ufg and nanocrystalline (nc) metals and alloys has been reported previously [19–22]. The fracture surfaces after the tensile test were examined using SEM. As shown in Fig. 7(a) for a typical example of sample III deformed at e_ ¼ 102 s1 , the sample fractures along approximately 45 to the loading direction at the edge of the sample, while perpendicular to the loading direction in the middle of the sample. The inset in Fig. 7(a) is shown in Fig. 7(b). Cavitations were observed on the surface of the deformed sample, and were particularly concentrated close to the fracture area. Cavitations are frequently observed on the surface of materials subjected to superplastic deformation at high temperatures, which is often attributed to the unaccommodated plasticity leaving the cavitations behind during grain boundary sliding [23–25]. In the present case, the observed cavitations might be due to the unaccommodated strain between coarse grains and ufg grains, since coarse grains may experience significantly more plastic strain than ufg grains. The contrast differences due to localized deformation within the coarse grains were also noticed in Fig. 7(b). Necking was observed perpendicular to the applied stress. Note that
G.J. Fan et al. / Acta Materialia 54 (2006) 1759–1766
Fig. 7. The SEM images of the sample III fractured after a tensile test at e_ ¼ 102 s1 with a low magnification (a), with a high magnification (b), and the fracture surface morphology (c).
necking was not observed in the monolithic ufg Al–Mg alloy of the same composition (not shown here), implying that the coarse grains (about 10 vol.%) play an important role in improving the plasticity of the present bimodal ufg alloys. The coarse grains themselves not only participate in the plastic deformation, as observed by SEM in Fig. 7(b), but also help release the stress concentration in the ufg matrix, thereby delaying crack initiation and propagation. Shear bands were observed on the surface during the tensile test. Therefore, the combination of cavitation, necking, and shear localization is responsible for fracture during the tensile test. The fracture surface after the tensile test, shown in Fig. 7(c), exhibits a dimple structure, which is typical of many ufg and nc metals and alloys [5,26,27]. The dimple sizes range from 500 nm to 2 lm, which is about three times larger than the average grain size of the ufg matrix. 4. Discussion 4.1. Hall–Petch relation for the ufg Al–Mg alloys For coarse-grained materials, plastic deformation is mainly realized by the motion of dislocations, which pile up near the grain boundaries. Based on the dislocation pileup mechanism, grain refinement generally makes the materials stronger. The yield strength as a function of grain size can be described by a Hall–Petch relation [28,29]: r ¼ r0 þ kd 1=2 ;
ð2Þ
where r is the yield strength of the material, r0 and k are constants, and d is the grain size. The Hall–Petch equation
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indicates that the yield strength of the material is inversely proportional to the square root of the grain size, d. When the grain size is reduced to ultrafine or to nanometer scales, deformation mechanisms other than the dislocation pileup mechanism may be responsible for the plastic deformation [30–35]. The experimental evidences suggest that the strength starts to deviate from the Hall–Petch relation with a reduced k value, when the grain is reduced to the ultrafine-scale region [36,37]. The deviation of the Hall–Petch relation may be due to dislocation motion different from the dislocation pileups at the grain boundaries. Furthermore, an inverse Hall–Petch relation was observed when the grain size was reduced to 10–20 nm [38,39]. The observed inverse Hall–Petch relation may be attributed to the grain boundary activities responsible for the plastic deformation of nc materials. The yield strength of the ufg matrix in the bimodal microstructure was obtained by modeling the compressive stress–strain curves shown in Fig. 2. The bimodal ufg Al–Mg alloys were considered as composites, where the soft coarse grains were evenly distributed in the hard ufg matrix. The plastic flow of a composite material has been phenomenologically described by the Ramberg– Osgood equation, which takes into account the volume fraction and aspect ratio of the second phase in a composite [40]. The Ramberg–Osgood equation is expressed by [16] n r r e ¼ þ ae0 ; ð3Þ N r E is the true where e is the true strain of the composite, r stress of the composite, n is the stress exponent, E is Young’s modulus of the composite, a is a constant typically =E. r N is an asymptotic reference equal to 1, and e0 equals r stress of a bimodal ufg alloy, and can be expressed by 1 N ¼ r M þ c r ð4Þ ð rM rM Þ; n M ¼ rM ð1 þ bf Þ; r
ð5Þ
M is the asymptotic reference stress for the matrix, c where r is a constant ranging from 2.5 to 5, rM is the quasistatic yield strength of the ufg matrix, f is the volume fraction of coarse-grained polycrystals, and b is a constant, which depends on the volume fractions and the shape of the coarse grains. A typical fitted compressive stress–strain curve for a bimodal ufg Al–Mg alloy having 10 vol.% of coarse grains is shown in Fig. 8 for sample III. With the input of E ¼ 65 GPa, ae0 = 0.01, c = 3, b = 1, and f = 0.1, N ¼ 545 MPa, n = 35. Therefore, rM was the best fit yields r determined to be 611 MPa (see Table 1). The yield strength of the ufg Al–Mg matrix as a function of the grain size, d, is shown in the Hall–Petch plot in Fig. 9. These data have a 1% statistic error established during the compression test. The yield strength, r, for the coarse-grained alloys was described by r = 72.6 + 8247 · d0.5 [41]. In the current case, the yield strength starts to
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800
True stress σ (MPa)
600
Experimental fitted curve
400
200 Fig. 10. Typical bright-field TEM image for the sample III compressed at e_ ¼ 102 s1 for e = 0.2, showing the large amount of dislocations introduced in the ultrafine grains during the plastic deformation.
0 0.0
0.1 True strain ε
0.2
4.2. Plasticity of bimodal ufg Al–Mg alloys
Fig. 8. Compressive stress–strain curve for the sample III deformed at e_ ¼ 102 s1 with the fitted curve using Eq. (3).
1000
Stress (MPa)
800
600
400
200
0 0.00
0.04 0.08 -0.5 -0.5 d (nm )
0.12
Fig. 9. Hall–Petch plot for the ufg matrices in the bimodal Al–Mg alloys (j). The yield strengths of the coarse-grained Al–Mg alloys were obtained from Ref. [41] (h).
deviate from the Hall–Petch relation established for the coarse-grained alloys with a decreased k value when the grain sizes are less than several hundred nanometers. The yield strength r for the ufg Al–Mg alloys can be described by r = 495.4 + 1598 · d0.5. The reduced k value of the Hall–Petch relation suggests that the dislocation pileup mechanism responsible for the plastic deformation of the coarse-grained materials may be different from that of the ufg materials. In addition, dislocation activities may be still operative inside these ultrafine grains. Fig. 10 shows a bright-field TEM image for sample III compressed at e_ ¼ 102 s1 for e = 0.2. Traces of dislocations were clearly observed after the plastic deformation.
Ufg and nc metals and alloys often show extraordinarily high strengths, while their ductility is very low. Different toughening strategies have been proposed to improve the ductility of ufg and nc materials. One of the toughening strategies is to introduce a certain volume fraction of coarse grains with grain sizes typically of micrometers into the ufg or nc matrix, leading to a bimodal microstructure. In the present investigations, extensive plastic deformation was clearly observed in the coarse grains, as evidenced in Figs. 4 and 7(b). The observed extensive plastic deformation occurring in the coarse grains will eventually contribute to the global ductility of the bimodal materials. The existence of large grains may also release stress concentrations, thereby delay the early fracture of the sample, and allow further plastic deformation to take place in the ufg matrix, as evidenced in Fig. 10 showing the presence of dislocation activities in the ufg matrix during plastic deformation. However, a monolithic ufg Al–Mg alloy exhibits very little plastic strain without extensive dislocation activities during plastic deformation. The sample often fractures along a single dominant shear band, leading to a very limited ductility. However, extensive shear bands (Fig. 5(a)) were developed in the bimodal Al–Mg alloys. Multiple shear bands were often observed during plastic deformation of bulk metallic glass composites [42]. The difference between the bimodal ufg materials and bulk metallic glass composites is that localized shear banding is the only deformation mechanism for bulk metallic glassy matrices, while the dislocation motion is also responsible for the plastic deformation of the ufg matrix. The bimodal Al–Mg alloys exhibit an improved ductility compared with the monolithic ufg alloy. However, their strain rate sensitivity shows a negative value, an indication of the great tendency of localized deformation, leading to plastic instability and early necking during the tensile test. The negative strain rate sensitivity observed in the ufg bimodal Al–Mg alloys could be attributed to DSA, which is microscopically controlled by dynamic interactions between the mobile dislocations and diffusing solute atoms.
G.J. Fan et al. / Acta Materialia 54 (2006) 1759–1766 (a)
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(b)
Shear band
Necking
Severe plastic deformation within large grains Cavitation
Fig. 11. Schematics illustrating the surface features for the bimodal ufg Al–Mg alloy after compression (a) and after tension (b).
The negative strain rate sensitivity could also be due to shear band formation. In this case, the formation of shear bands is accompanied by heat release, leading to the softening of the sample. Considering that shear bands cause thermal softening of the samples and that a high e_ will promote shear band formation, a lower stress is required for plastic deformation at a high e_ , which could result in a negative strain rate sensitivity. Therefore, the negative strain rate sensitivity observed in the ufg bimodal Al–Mg alloys can be attributed to DSA associated with the interaction of mobile dislocations and solute atoms, and to the thermal softening associated with the formation of shear bands. 4.3. Fracture of ufg bimodal Al–Mg alloys during compression and tension The fracture surfaces after compression (Fig. 5(f)) and tension (Fig. 7(c)) show somewhat different features. Both fracture surfaces indicate that extensive plastic deformation occurs prior to fracture. However, the side surfaces of the flat specimens show different features for the samples after compression and tension tests, particularly for the surface close to the fracture area. These features are compared schematically in Fig. 11. For the compression test, the localized plastic deformation within the shear bands and large grains is highlighted. The plastic instability appears to be dominated by shear band propagation, since the fracture occurs along the maximum shear stress, i.e., approximately 45 to the applied load. For the tensile test, in addition to the localized plastic deformation within the shear bands and large grains, cavitations and necking were observed, which can cause plastic instability. Cavitations were particularly concentrated on the surface close to the fracture area, an indication that cavitation-controlled failure may be at least in part responsible for the fracture, along with necking-controlled failure. Cavitation- and necking-controlled failure will lead to the fracture surface perpendicular to the applied load. However, the fracture surfaces after the tensile test, shown in Fig. 7(a), always exhibit a combined feature, with the fracture surface perpendicular to the applied load at the center, and 45 to the applied load at both edges of the flat specimens, indicating that shear banding may also play a role during the
later stage of fracture of the present ufg bimodal Al–Mg alloys. 5. Conclusions The plastic deformation and fracture of ufg Al–Mg alloys with a bimodal microstructure have been studied. The bimodal microstructure was obtained by the consolidation and extrusion of mixtures of cryomilled powders and as-received coarse-grained powders with a volume fraction of 9:1, leading to large grains evenly distributed in the ufg matrix. Due to the different consolidation temperatures used, the ufg matrix exhibits different grain size distributions, with average grain sizes ranging from 120 to 338 nm. Several conclusions can be drawn from this study. 1. The plastic deformation of the bimodal ufg Al–Mg alloys is macroscopically localized, as evidenced by a negative strain rate sensitivity. The negative strain rate sensitivity decreased (more negative) as the average grain size of the ufg matrix decreased, which is related to DSA effects associated with the interaction between the mobile dislocations and the solute atoms, as well as the formation of shear bands. 2. The relationship between the yield strength and the grain sizes indicates that the yield strength of the ufg Al–Mg matrix deviates from the Hall–Petch relation established for coarse-grained counterparts. 3. The large grains in the bimodal microstructure not only contribute to the global ductility of the ufg Al–Mg alloys, but also delay plastic instability. Therefore, the large grains in the bimodal microstructure can effectively increase the ductility of the ufg Al–Mg alloys. 4. The plastic instability of the bimodal ufg Al–Mg alloys during the compressive test is controlled by shear band propagation, leading to the fracture surface with an angle of 45 to the applied stress; while the plastic instability during the tensile test is controlled by a combination of shear band propagation, cavitations, and necking, leading to combined features for the fracture surface different from those during the compressive test.
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Acknowledgements G.J.F., H.C., and P.K.L. acknowledge the financial support of the National Science Foundation International Materials Institutes (IMI) Program (DMR-0231320) with Dr. Carmen Huber as the director. E.J.L. acknowledges the financial support of the Office of Naval Research with Grant No. N00014-04-1-0370. References [1] Koch CC, Morris DG, Lu K, Inoue A. Mater Res Soc Bull 1999;24:54. [2] Nieman GW, Weertman JR, Siegel RW. J Mater Res 1991;6:1012. [3] Valiev RZ, Islamgaliev RK, Alexandrov IV. Prog Mater Sci 2000;45:103. [4] Ma E. Scripta Mater 2003;49:663. [5] Kumar KS, Van Swygenhoven H, Suresh S. Acta Mater 2003;51:5743. [6] Youssef KM, Scattergood RO, Murty KL, Koch CC. Appl Phys Lett 2004;85:929. [7] Fan GJ, Fu LF, Wang YD, Choo H, Ren Y, Liaw PK, et al. Phys Rev Lett (to be published). [8] Sanders PG, Eastman JA, Weertman JR. Acta Mater 1997;45:4019. [9] Tellkamp VL, Melmed A, Lavernia EJ. Metall Mater Trans 2001;32A:2335. [10] Wang YM, Chen MW, Zhou FH, Ma E. Nature 2002;419:912. [11] Fan GJ, Wang GY, Choo H, Liaw PK, Park YS, Han BQ, et al. Scripta Mater 2005;52:929. [12] Han BQ, Lee Z, Witkin D, Nutt S, Lavernia EJ. Metall Mater Trans 2005;36A:957. [13] Witkin D, Lee Z, Rodriguez R, Nutt S, Lavernia EJ. Scripta Mater 2003;49:297. [14] Rodriguez R, Hayes RW, Berbon PB, Lavernia EJ. Acta Mater 2003;51:911.
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Plastic deformation and fracture of ultrafine-grained Al–Mg alloys with a bimodal grain size distribution G.J. Fan b
a,*
, H. Choo a, P.K. Liaw a, E.J. Lavernia
b
a Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996, USA Department of Chemical Engineering and Materials Science, University of California, Davis, CA 95616, USA
Received 26 September 2005; received in revised form 15 November 2005; accepted 30 November 2005 Available online 15 February 2006
Abstract Four different ultrafine-grained (ufg) Al–7.5 wt.% Mg alloys were synthesized by consolidation of a mixture of as-received and cryomilled Al–Mg powders with a ratio of 1:9, yielding a bimodal microstructure consisting of coarse grains (grain sizes, dcg, typically of several micrometers) evenly distributed in the ufg matrices (average grain sizes d = 120, 142, 197, and 338 nm). The deformation behavior under uniaxial compression and tension of the as-extruded alloys was investigated. The Ramberg–Osgood equation was used to fit the compressive stress–strain curves of the bimodal ufg alloys. The compressive yield stresses of the ufg matrices with different average grain sizes indicated a reduced slope in the Hall–Petch relation. The plastic deformation of the ufg Al–Mg alloys with a bimodal microstructure was highly localized. The fracture of the alloys was attributed to shear localization under the compressive tests, and to a combination of shear localization, cavitation, and necking under the tensile tests. 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Mechanical alloying; Aluminum alloys; Mechanical properties; Ultrafine-grained microstructure
1. Introduction Bulk ultrafine-grained (ufg) metals and alloys with grain sizes, d, typically in the range 100 nm to 1 lm have been the subject of much interests recently, primarily due to their excellent mechanical properties for potential engineering applications [1]. Due to the ufg structure, bulk ufg metals and alloys exhibit extraordinarily high strengths as well as excellent superplasticity at high strain rates compared with coarse-grained materials [2–7]. However, bulk ufg metals and alloys often show a limited ductility at room temperature, which was attributed to the lack of efficient hardening during plastic deformation and/or to the defects introduced during the processing [4,8]. Recently, it was found that ufg metals and alloys with a bimodal microstructure exhibit a combination of high strength and good ductility [9–15]. In this toughening strategy, the ufg matrix *
Corresponding author. E-mail address: [email protected] (G.J. Fan).
in the bimodal microstructure provides the high strength, while the relatively large grains of the order of micrometers contribute to the ductility. Bulk bimodal ufg metals and alloys can be synthesized by: (a) thermomechanical treatment involving severe plastic deformation, i.e., cold rolling or equal-channel angular pressing, followed by an appropriate thermal annealing under controlled conditions [10]; and (b) mechanical milling plus the consolidation of the milled powders mixed with certain volume fractions of the as-received coarsegrained powders [9,11]. The latter synthesis method has an apparent advantage in that a tailored bimodal microstructure can be conveniently achieved using a desired ratio of starting powders with a bimodal grain size distribution. The mechanical properties can be easily optimized via design of the appropriate bimodal microstructure. In this paper, we investigate bimodal Al–7.5 wt.% Mg alloys with ufg matrices having various average grain sizes, which were synthesized using a mechanical milling machine followed by hot pressing and extrusion. The plastic
1359-6454/$30.00 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2005.11.044
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deformation and fracture of the bimodal alloys under compression and tension are discussed in detail. It is shown that the plastic deformation of the bimodal ufg Al–7.5 wt.% Mg alloys is highly localized. The alloys display a negative strain rate sensitivity, which promotes the deformation localization. The compressive yield stresses of ufg matrices with varying average grain sizes, derived from fitting the compressive stress–strain curves of the bimodal ufg alloys using the Ramberg–Osgood equation [16], were found to deviate from the Hall–Petch relation established for coarse-grained counterparts. The effect of the coarse grains on the mechanical behaviors of the bimodal alloys, including yielding, plastic flow, and fracture, is discussed. The fracture mechanisms of the bimodal ufg Al–Mg alloys during the compression and tension tests are compared. 2. Experimental The Al–7.5 wt.% Mg powders were mechanically milled at a cryogenic temperature (190 C) for 8 h. Mechanical milling at room temperature always introduces undesired oxides. Oxidation reactions were kinetically suppressed during the cryogenic milling [14]. In addition, the grain size can be more effectively refined during cryogenic milling, due to the significantly suppressed thermal recovery at a cryogenic temperature. The as-cryomilled Al–Mg powders exhibit a narrow grain size distribution with an average grain size of about 30 nm [14]. The powders after cryomilling were mixed with as-received coarse-grained powders with a weight ratio of 9:1. The powder mixtures were consolidated via hot isostatic pressing at four different temperatures (275, 300, 325, and 350 C) and at a pressure of 150 MPa for 3 h, and by subsequent hot extrusion at 250 C. The experimental details regarding the process of the cryomilling, consolidation, and extrusion are published elsewhere [15]. The as-extruded bars were electrodischarge machined into rectangular and dog-bone specimens along the extrusion direction for the compressive and tensile tests, respectively. The microstructure and the surface morphology of the samples before and after plastic deformation were characterized by optical microscopy (OM), scanning electron microscopy (SEM), and transmission electron microscopy (TEM). 3. Results 3.1. Microstructures Depending on the consolidation temperatures, the ufg matrix exhibits different average grain sizes, as listed in Table 1. With increasing consolidation temperature, the average grain sizes of the ufg matrix increase from 120 to 338 nm, while the average sizes of the coarse grains change from 2.7 to 3.5 lm. The as-extruded bars exhibit a bimodal microstructure, as shown in Figs. 1(a) and (b), which show OM images along and perpendicular to the extrusion direction. No porosity was noticed during the OM
Table 1 Four different bimodal ufg Al–Mg alloys consolidated at different temperatures, Tcons, with different average grain sizes, d, of the ufg matrix. The average grain size of the coarse-grained inclusions in the bimodal microstructure, dcg, the strain rate sensitivity, m, the yield stress of the ufg matrix, rM, and the asymptotic reference stress of the bimodal N , at e_ ¼ 102 s1 are also listed alloys, r Sample
Tcons (C)
d (nm)
dcg (lm)
m
rM (MPa)
r N (MPa)
I II III IV
275 300 325 350
120 142 197 338
2.7 3.0 3.1 3.5
0.01 0.0105 0.0087 0.0073
640 624 611 599
582 561 545 536
examinations. The large grains (white area of Figs. 1(a) and (b)) with grain sizes of the order of several micrometers were evenly distributed in the ufg matrix (gray area), and were elongated along the extrusion direction. Fig. 1(c) shows a typical TEM image of sample III, showing the ultrafine grains in the matrix. The grain size distribution statistics for sample III, shown in Fig. 1(d), clearly indicate a bimodal grain size distribution. The average grain sizes are about 197 nm for the ufg matrix and 3.1 lm for the coarse-grained inclusions in the bimodal microstructure. X-ray diffraction patterns indicate a face-centered cubicstructured Al(Mg) supersaturated solid solution in the asextruded state. 3.2. Plastic flow and fracture during compressive tests The rectangular samples (I–IV) were compressed along the extrusion direction at room temperature. The typical true stress–strain curves for sample III, compressed at different strain rates, e_ , ranging from 104 to 101 s1, are shown in Fig. 2. The samples show an excellent compressive ductility. Also, the flow stress, r, decreases with increasing the strain rate. For example, the flow stress r at a strain of 0.2 decreases with increasing e_ from r = 612 MPa at e_ ¼ 104 s1 to r = 575 MPa at e_ ¼ 101 s1 , indicating a negative strain rate sensitivity. The strain rate sensitivity, m, is defined by o log r m¼ . ð1Þ o log e_ e;T
The relationship between the flow stress and the strain rate is presented in Fig. 3(a) and Table 1, where m = 0.01, 0.0105, 0.0087, and 0.0073 for samples I–IV, respectively. The negative strain rate sensitivity indicates that the plastic deformation of bimodal ufg alloys is macroscopically localized and is associated with a dynamic strain aging (DSA) as often observed in coarse-grained aluminum alloys [17,18]. The strain rate sensitivity, m, as a function of the average grain size, d, for the ufg matrix is plotted in Fig. 3(b). With decreasing d, the value of m decreases and becomes more negative, indicating that reducing the grain sizes may promote the deformation localization. The surface morphologies were examined by OM and SEM for the samples compressed for different strain levels
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Flow stress σ (ε=0.2) (MPa)
(a)
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680 d = 120 nm d = 142 nm d = 197 nm d = 338 nm
m = -0.01
640
m = -0.0105
600 m = -0.0087
560
10
m = -0.0073 -6
-4
-2
10 10 . -1 Strain rate ε (s )
10
0
(b)
Fig. 1. OM images for the as-extruded bar along the extrusion direction (a) and perpendicular to the extrusion direction (b) for the sample III. The gray area is the ufg matrix, and the light area is the coarse grains being elongated along the extrusion direction. TEM image (c) for the gray area indicates that grain size is in the ultrafine regime. The average grain size for the ufg matrix, derived from the grain size-distribution statistics (d), is about 197 nm. The arrow in (a) indicates the extrusion direction.
Strain rate sensitivity m
-0.006
-0.008
-0.010
-0.012 100
200 300 Grain size d (nm)
400
Fig. 3. Compressive flow stresses at e = 0.2 as a function of the strain rate for the bimodal alloys with the ufg matrix having different average grain sizes d (a). A plot of the strain rate sensitivity m, determined from (a), as a function of the average grain sizes of the ufg matrices d (b).
Fig. 2. Compressive stress–strain curves for the sample III at different strain rates.
and strain rates. Figs. 4(a) and (b) display the OM images for sample III for e = 0.1 and 0.2 at e_ ¼ 102 s1 , respectively. At e = 0.1, contrast differences along the extrusion direction develop in the surface of the sample. These contrast differences (large elongated dimples) are due to the large localized plastic strain within the coarse grains in the bimodal structured samples, since a lower stress is required for plastic yielding of the coarse grains. The
Fig. 4. OM images for the sample III compressed at e_ ¼ 102 s1 to e = 0.1 (a) and e = 0.2 (b), respectively. The arrows indicate the compression direction, which is parallel to the extrusion direction.
plastic deformation of the large grains in the bimodal microstructure, therefore, contributes to the global plastic strain. At e = 0.2, besides the localized plastic deformation
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in the coarse grains of the bimodal microstructure, shear bands along about 45 to the direction of the applied load were observed. Shear bands were more clearly observed by SEM. Figs. 5(a)–(d) show the SEM images for sample III for e = 0.2 at e_ ¼ 102 s1 . A high density of shear bands is observed in the low-magnification SEM image in Fig. 5(a). The high-magnification SEM image in Fig. 5(b) indicates a highly localized plastic deformation within and around the shear band zone. In Figs. 5(c) and (d), the shear banding spacing is about 200 nm, which is almost the same as the average grain size (197 nm) of the ufg matrix in specimen III. Fig. 5(e) indicates that the sample fractures along a direction with a maximum shear force, i.e., approximately 45 to the loading direction. The fracture surface after the compressive test in Fig. 5(f) suggests that the samples experience extensive plastic deformation prior to fracture.
800
Compression 600 True stress σ (MPa)
1762
Tension 400
200 .
e = 10-2 s-1
0 0.0
0.1
0.2 True strain ε
0.3
0.4
Fig. 6. Tensile stress–strain curve of the sample III. For comparison the compressive stress–strain curve of the same sample is also included. Note that the sample exhibits an asymmetric yielding behavior. The yield stress is lower during tension than during compression.
3.3. Plastic flow and fracture during tensile tests
Fig. 5. SEM images showing the shear band formation on the surface of the sample III compressed at e_ ¼ 102 s1 to e = 0.2 at a low magnification (a) and high magnification (b). A coordinated shear band array with a shear band spacing around 200 nm is shown in a low magnification (c) and in a high magnification (d). A side view of the sample fractured after compression (e) and the corresponding fracture surface morphology (f). The white arrow in (a) is the compression direction.
The tensile behavior of the bimodal ufg Al–Mg alloys with different d for the matrix was also studied. Fig. 6 shows a typical tensile stress–strain curve of sample III at e_ ¼ 102 s1 . For comparison the compressive stress–strain curve of the same sample at the same strain rate is included in Fig. 6. The monolithic ufg Al–Mg alloy showed a very limited tensile ductility (less than 1%) [13]. The tensile ductility was enhanced in the current bimodal ufg Al–Mg alloy with a tensile elongation of about 8%. Compared with the compressive stress–strain curve, the tensile yield stress is lower than the compressive yield stress. The asymmetry of yielding in ufg and nanocrystalline (nc) metals and alloys has been reported previously [19–22]. The fracture surfaces after the tensile test were examined using SEM. As shown in Fig. 7(a) for a typical example of sample III deformed at e_ ¼ 102 s1 , the sample fractures along approximately 45 to the loading direction at the edge of the sample, while perpendicular to the loading direction in the middle of the sample. The inset in Fig. 7(a) is shown in Fig. 7(b). Cavitations were observed on the surface of the deformed sample, and were particularly concentrated close to the fracture area. Cavitations are frequently observed on the surface of materials subjected to superplastic deformation at high temperatures, which is often attributed to the unaccommodated plasticity leaving the cavitations behind during grain boundary sliding [23–25]. In the present case, the observed cavitations might be due to the unaccommodated strain between coarse grains and ufg grains, since coarse grains may experience significantly more plastic strain than ufg grains. The contrast differences due to localized deformation within the coarse grains were also noticed in Fig. 7(b). Necking was observed perpendicular to the applied stress. Note that
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Fig. 7. The SEM images of the sample III fractured after a tensile test at e_ ¼ 102 s1 with a low magnification (a), with a high magnification (b), and the fracture surface morphology (c).
necking was not observed in the monolithic ufg Al–Mg alloy of the same composition (not shown here), implying that the coarse grains (about 10 vol.%) play an important role in improving the plasticity of the present bimodal ufg alloys. The coarse grains themselves not only participate in the plastic deformation, as observed by SEM in Fig. 7(b), but also help release the stress concentration in the ufg matrix, thereby delaying crack initiation and propagation. Shear bands were observed on the surface during the tensile test. Therefore, the combination of cavitation, necking, and shear localization is responsible for fracture during the tensile test. The fracture surface after the tensile test, shown in Fig. 7(c), exhibits a dimple structure, which is typical of many ufg and nc metals and alloys [5,26,27]. The dimple sizes range from 500 nm to 2 lm, which is about three times larger than the average grain size of the ufg matrix. 4. Discussion 4.1. Hall–Petch relation for the ufg Al–Mg alloys For coarse-grained materials, plastic deformation is mainly realized by the motion of dislocations, which pile up near the grain boundaries. Based on the dislocation pileup mechanism, grain refinement generally makes the materials stronger. The yield strength as a function of grain size can be described by a Hall–Petch relation [28,29]: r ¼ r0 þ kd 1=2 ;
ð2Þ
where r is the yield strength of the material, r0 and k are constants, and d is the grain size. The Hall–Petch equation
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indicates that the yield strength of the material is inversely proportional to the square root of the grain size, d. When the grain size is reduced to ultrafine or to nanometer scales, deformation mechanisms other than the dislocation pileup mechanism may be responsible for the plastic deformation [30–35]. The experimental evidences suggest that the strength starts to deviate from the Hall–Petch relation with a reduced k value, when the grain is reduced to the ultrafine-scale region [36,37]. The deviation of the Hall–Petch relation may be due to dislocation motion different from the dislocation pileups at the grain boundaries. Furthermore, an inverse Hall–Petch relation was observed when the grain size was reduced to 10–20 nm [38,39]. The observed inverse Hall–Petch relation may be attributed to the grain boundary activities responsible for the plastic deformation of nc materials. The yield strength of the ufg matrix in the bimodal microstructure was obtained by modeling the compressive stress–strain curves shown in Fig. 2. The bimodal ufg Al–Mg alloys were considered as composites, where the soft coarse grains were evenly distributed in the hard ufg matrix. The plastic flow of a composite material has been phenomenologically described by the Ramberg– Osgood equation, which takes into account the volume fraction and aspect ratio of the second phase in a composite [40]. The Ramberg–Osgood equation is expressed by [16] n r r e ¼ þ ae0 ; ð3Þ N r E is the true where e is the true strain of the composite, r stress of the composite, n is the stress exponent, E is Young’s modulus of the composite, a is a constant typically =E. r N is an asymptotic reference equal to 1, and e0 equals r stress of a bimodal ufg alloy, and can be expressed by 1 N ¼ r M þ c r ð4Þ ð rM rM Þ; n M ¼ rM ð1 þ bf Þ; r
ð5Þ
M is the asymptotic reference stress for the matrix, c where r is a constant ranging from 2.5 to 5, rM is the quasistatic yield strength of the ufg matrix, f is the volume fraction of coarse-grained polycrystals, and b is a constant, which depends on the volume fractions and the shape of the coarse grains. A typical fitted compressive stress–strain curve for a bimodal ufg Al–Mg alloy having 10 vol.% of coarse grains is shown in Fig. 8 for sample III. With the input of E ¼ 65 GPa, ae0 = 0.01, c = 3, b = 1, and f = 0.1, N ¼ 545 MPa, n = 35. Therefore, rM was the best fit yields r determined to be 611 MPa (see Table 1). The yield strength of the ufg Al–Mg matrix as a function of the grain size, d, is shown in the Hall–Petch plot in Fig. 9. These data have a 1% statistic error established during the compression test. The yield strength, r, for the coarse-grained alloys was described by r = 72.6 + 8247 · d0.5 [41]. In the current case, the yield strength starts to
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800
True stress σ (MPa)
600
Experimental fitted curve
400
200 Fig. 10. Typical bright-field TEM image for the sample III compressed at e_ ¼ 102 s1 for e = 0.2, showing the large amount of dislocations introduced in the ultrafine grains during the plastic deformation.
0 0.0
0.1 True strain ε
0.2
4.2. Plasticity of bimodal ufg Al–Mg alloys
Fig. 8. Compressive stress–strain curve for the sample III deformed at e_ ¼ 102 s1 with the fitted curve using Eq. (3).
1000
Stress (MPa)
800
600
400
200
0 0.00
0.04 0.08 -0.5 -0.5 d (nm )
0.12
Fig. 9. Hall–Petch plot for the ufg matrices in the bimodal Al–Mg alloys (j). The yield strengths of the coarse-grained Al–Mg alloys were obtained from Ref. [41] (h).
deviate from the Hall–Petch relation established for the coarse-grained alloys with a decreased k value when the grain sizes are less than several hundred nanometers. The yield strength r for the ufg Al–Mg alloys can be described by r = 495.4 + 1598 · d0.5. The reduced k value of the Hall–Petch relation suggests that the dislocation pileup mechanism responsible for the plastic deformation of the coarse-grained materials may be different from that of the ufg materials. In addition, dislocation activities may be still operative inside these ultrafine grains. Fig. 10 shows a bright-field TEM image for sample III compressed at e_ ¼ 102 s1 for e = 0.2. Traces of dislocations were clearly observed after the plastic deformation.
Ufg and nc metals and alloys often show extraordinarily high strengths, while their ductility is very low. Different toughening strategies have been proposed to improve the ductility of ufg and nc materials. One of the toughening strategies is to introduce a certain volume fraction of coarse grains with grain sizes typically of micrometers into the ufg or nc matrix, leading to a bimodal microstructure. In the present investigations, extensive plastic deformation was clearly observed in the coarse grains, as evidenced in Figs. 4 and 7(b). The observed extensive plastic deformation occurring in the coarse grains will eventually contribute to the global ductility of the bimodal materials. The existence of large grains may also release stress concentrations, thereby delay the early fracture of the sample, and allow further plastic deformation to take place in the ufg matrix, as evidenced in Fig. 10 showing the presence of dislocation activities in the ufg matrix during plastic deformation. However, a monolithic ufg Al–Mg alloy exhibits very little plastic strain without extensive dislocation activities during plastic deformation. The sample often fractures along a single dominant shear band, leading to a very limited ductility. However, extensive shear bands (Fig. 5(a)) were developed in the bimodal Al–Mg alloys. Multiple shear bands were often observed during plastic deformation of bulk metallic glass composites [42]. The difference between the bimodal ufg materials and bulk metallic glass composites is that localized shear banding is the only deformation mechanism for bulk metallic glassy matrices, while the dislocation motion is also responsible for the plastic deformation of the ufg matrix. The bimodal Al–Mg alloys exhibit an improved ductility compared with the monolithic ufg alloy. However, their strain rate sensitivity shows a negative value, an indication of the great tendency of localized deformation, leading to plastic instability and early necking during the tensile test. The negative strain rate sensitivity observed in the ufg bimodal Al–Mg alloys could be attributed to DSA, which is microscopically controlled by dynamic interactions between the mobile dislocations and diffusing solute atoms.
G.J. Fan et al. / Acta Materialia 54 (2006) 1759–1766 (a)
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(b)
Shear band
Necking
Severe plastic deformation within large grains Cavitation
Fig. 11. Schematics illustrating the surface features for the bimodal ufg Al–Mg alloy after compression (a) and after tension (b).
The negative strain rate sensitivity could also be due to shear band formation. In this case, the formation of shear bands is accompanied by heat release, leading to the softening of the sample. Considering that shear bands cause thermal softening of the samples and that a high e_ will promote shear band formation, a lower stress is required for plastic deformation at a high e_ , which could result in a negative strain rate sensitivity. Therefore, the negative strain rate sensitivity observed in the ufg bimodal Al–Mg alloys can be attributed to DSA associated with the interaction of mobile dislocations and solute atoms, and to the thermal softening associated with the formation of shear bands. 4.3. Fracture of ufg bimodal Al–Mg alloys during compression and tension The fracture surfaces after compression (Fig. 5(f)) and tension (Fig. 7(c)) show somewhat different features. Both fracture surfaces indicate that extensive plastic deformation occurs prior to fracture. However, the side surfaces of the flat specimens show different features for the samples after compression and tension tests, particularly for the surface close to the fracture area. These features are compared schematically in Fig. 11. For the compression test, the localized plastic deformation within the shear bands and large grains is highlighted. The plastic instability appears to be dominated by shear band propagation, since the fracture occurs along the maximum shear stress, i.e., approximately 45 to the applied load. For the tensile test, in addition to the localized plastic deformation within the shear bands and large grains, cavitations and necking were observed, which can cause plastic instability. Cavitations were particularly concentrated on the surface close to the fracture area, an indication that cavitation-controlled failure may be at least in part responsible for the fracture, along with necking-controlled failure. Cavitation- and necking-controlled failure will lead to the fracture surface perpendicular to the applied load. However, the fracture surfaces after the tensile test, shown in Fig. 7(a), always exhibit a combined feature, with the fracture surface perpendicular to the applied load at the center, and 45 to the applied load at both edges of the flat specimens, indicating that shear banding may also play a role during the
later stage of fracture of the present ufg bimodal Al–Mg alloys. 5. Conclusions The plastic deformation and fracture of ufg Al–Mg alloys with a bimodal microstructure have been studied. The bimodal microstructure was obtained by the consolidation and extrusion of mixtures of cryomilled powders and as-received coarse-grained powders with a volume fraction of 9:1, leading to large grains evenly distributed in the ufg matrix. Due to the different consolidation temperatures used, the ufg matrix exhibits different grain size distributions, with average grain sizes ranging from 120 to 338 nm. Several conclusions can be drawn from this study. 1. The plastic deformation of the bimodal ufg Al–Mg alloys is macroscopically localized, as evidenced by a negative strain rate sensitivity. The negative strain rate sensitivity decreased (more negative) as the average grain size of the ufg matrix decreased, which is related to DSA effects associated with the interaction between the mobile dislocations and the solute atoms, as well as the formation of shear bands. 2. The relationship between the yield strength and the grain sizes indicates that the yield strength of the ufg Al–Mg matrix deviates from the Hall–Petch relation established for coarse-grained counterparts. 3. The large grains in the bimodal microstructure not only contribute to the global ductility of the ufg Al–Mg alloys, but also delay plastic instability. Therefore, the large grains in the bimodal microstructure can effectively increase the ductility of the ufg Al–Mg alloys. 4. The plastic instability of the bimodal ufg Al–Mg alloys during the compressive test is controlled by shear band propagation, leading to the fracture surface with an angle of 45 to the applied stress; while the plastic instability during the tensile test is controlled by a combination of shear band propagation, cavitations, and necking, leading to combined features for the fracture surface different from those during the compressive test.
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