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The influence of grain size on the mechanical properties of nanocrystalline aluminium
NamStmmm~
Matcdala. Vol. 9,PP. 611-614.1997 l~eviw ~kieaceLid @ 1997 A~m Memllurg~ Inc. Printedinthe USA. All dghm rmerved
Pergamon
0965-9773:97 $17.00 + .00
PII S0965-9773(97)00137.2
THE INFLUENCE OF GRAIN SIZE ON THE MECHANICAL PROPERTIES OF NANOCRYSTALLINE ALUMINIUM E. BONETTI, L. PASQUINI, E. SAMPAOLESI Dipartimento di Fisica, Universita di Bologna and Istituto Nazionale per la Fisica della Materia, Viale Berti Pichat 6/2, 1-40127 Bologna, Italy. ABSTRACT Uniaxial tensile tests were performed at room temperature on nanocrystalline aluminium (n-AO prepared by mechanical attrition and cold consolidation with average grain size in the 20-40 nm range. The stress-strain curves analysis shows an enhanced tensile strength and a reduced ductility of n-Al with respect to the coarse-grained material. Anyway, the strength increase is much lower than predicted by extrapolation of the Hall-Petch relation to nanometer sized grains. Moreover, the strengthening rate (Hall Petch coefficient) is strongly reduced in comparison with coarse-grained AI. The observed behaviour is discussed in connection with microstructure evolution during mechanical attrition. ~ 1997 Acta Metailurgica Inc.
~TRODUCTION Mechanical properties of nanocrystalline materials (NCM) display an increasing interest because they are significantly different from those of the coarse grained (CG) counterpart. Dramatic changes in mechanical propertiessuch as hardness, strength and ductility,occur when the grain sizeis progressivelyreduced to the nanometer scale(I).It has bccn pointed out that confinement effects(2) may be responsiblefor specificchanges in the mechanisms of deformation. The plasticbehaviour of metals, which in the bulk situationstronglydepends on dislocation activity (generation and dynamics), starts to differ substantiallyentering the nanometer regime because of the reduced availabilityof mobile dislocationsin the increased confined nanophase grains (3). The strengthof a polycrystallinematerial can be enhanced by decreasing the grain size; the phcnomcnological relationbetween the yield stress(%) and the average grain size (d) can be expressedby the well-known HaII-Petchequation (4, 5): % = Co + k d "If2
611
[ll
612
E BONETrl,L PASQ~NJAND E SAMPAOLES~
where Oo (friction stress) and k (H-P coefficient) are material constants. Anyway, the grain size dependence of yield stress in NCM cannot be obtained by a simple extrapolation of the HP relation to the nanometer scale (6-9); in some cases, even negative values of the H-P coefficient k have been reported (10). In the present paper some results will be presented regarding the mechanical behaviour of nanocrystalline aluminium (n-A1). The aim of this research is to investigate the influence of grain size on the mechanical properties in the nanometer range.
EXPERIMENTAL Pure aluminium powders (44 ~tm, Alfa products, 99.9% purity) were used for the present experiments. Mechanical attrition (MA) was performed by a SPEX mixer-mill model 8000 using hardened steel balls and a tungsten carbide vial; the ball-to-powder weight ratio was 4 to 1. The powders were milled for five different times (2, 4, 8, 16, 32 h) in order to follow the microstructural evolution of the material. The consolidation procedure consisted in cold pressing the milled powders in a die with a rectangular section of 15 x 5 mm 2 under a uniaxial pressure of 1 GPa. In this way bar-shaped samples with a thickness of about 0.8 mm were obtained. Density measurements based on the Archimedes principle yield values ranging from 95 to 98 % of the fully dense value. The uniaxial tensile tests were performed at room temperature with a rigid tensile machine at a constant strain rate of 104s 1. The 0.2% offset was used as the yield stress. The average grain size reached at the different milling times (table 1) was estimated by Xray diffraction line-broadening analysis (11). Complementary TEM analysis showed a wide distribution of grain sizes (12): crystallite dimensions up to 50 nm were observed even at the higher milling times.
RESULTS AND DISCUSSION In fig. 1 the stress-strain curves of n-Al (32 h milling, d = 21 nm) and CG-A1 (d ~ 100 gin) are compared: a significant strength increase is observed in n-Al (Oy = 26 MPa) with respect to CG-AI (Oy = 13.5 MPa). Anyway, Oy of n-Al strongly disagrees with the H-P prediction; in fact, the extrapolation ofeq. [1] (using A1 parameters found in (13)) to d = 20 tun gives Oy ~ 500 MPa. As shown in fig. 2 and table 1, the increase in strength with decreasing grain size persists in the nanometer regime: in fact, a grain size reduction from 40 nm to 21 nm results in a yield stress increase of about 40%. The strengthening rate (with decreasing grain size) is illustrated in fig. 3, where Oy is plotted as a function o f d -rE (H-P co-ordinates); a least-squares linear fit in accordance with eq. [1] gives the following estimate for k and Oo: k = (400 + 80) MPa x nm ]/2 Oo = (6 + 2) MPa. The H-P coefficient k is lowered by about a factor five with respect to CG-A1 (13). These results seem to confirm that the H-P equation is inadequate to describe the strengthening behaviour over a wide grain size range, i.e. from CG material down to NCM.
THE INFLUENCEOF GRAIN SIZE ON THE MECHANICALPROPERTIESOF NANOCRYSTAUJNEALUMINUM
*
o a.,k132h • a-./kl 2h
_ I
n-A132h
.
=
~
e
~
-
613
-
o x = 20 M P a
17.5 M P a
tO
o.o
oi~
s~m t~)
Figure 1. Stress-strain curves for n-Al milled 32 h (d = 21 rim) and CG-AI (d = 100 txm).
,b Smmia~ )
~i~
2o
Figure 2. Stress-strain curves for n-Al milled 2h (d = 40 nm) and 32h (d = 21 nm).
Recently reported data (6-9) prove that the strengthening rate decreases with decreasing grain size. Both extrinsic features (such as pores and flaws in the cold-consolidated samples (6, 7)) and changes in deformation mechanisms (8) have been taken into account to explain the deviation from H-P behaviour occurring when the nanoscale is reached. As regards our results, the influence of the synthesis technique must be stressed. In fact, samples obtained at short milling times are characterised not only by a larger grain size, but also by a higher structural heterogeneity and dislocation density, thus making difficult to isolate the contribution of the grain size reduction to the observed mechanical behaviour. The strain reached at failure (of) in n-A1 ranges from 0.6% to 1.9% (table 1), typical values being around 1%, one order of magnitude lower than those pertaining to CG samples (el > 20%). Only n-Al obtained after 32 h milling exhibits an appreciable plastic yielding that permits to reach a 2% strain at failure. A significant reduction of ductility was also observed by Nieman et al in n-Pd and n-Cu (6). On the contrary, Gertsman et al (8) recently found evidence of rather good ductility in n-Cu. The situation is quite controversial because of the not well understood influence of extrinsic features upon the brittle behaviour of n-metals. TABLE 1 Tensile Tests Data on n-Al: d = Grain Size; % = Yield Stress; ~f = % Strain at Failure; d~dt = Strain Rate. Milling time (h)
d(nm)
Wma)
2
40 +4
17.5
1.2
0.8 x 10 "4
4
35+4
17
0.8
1 x 10 -4
8
28 + 3
18.5
0.7
1 x 10 -4
16
27 + 3
19.5
0.6
0.9 x 10 -4
32
21+2
26
1.9
1 × 10 ~
ds/dt ( s -~ )
E BONE'rn, L PASQUINIANDE SAMPAOLESI
614
25
•
CG-AI
.o-° tO
.............. ""
k = 400 M P a n m 1/2
d-ta(nm)-ta
Figure 3. Hall-Petch plot in n-Al (grain size 20+40 nm); CG-AI is represented by A.
CONCLUSIONS Tensile tests on n-Al indicate a deviation from the H-P prediction, in agreement with previously reported results on Pd and Cu. Anyway, samples prepared by MA are characterised by a broad grain size distribution, particularly at the lowest milling times. Moreover, a much higher dislocation density is encountered during the first stages of milling. Keeping in mind all these considerations, conclusions have to be drawn cautiously: in fact, in a heterogeneous system different deformation mechanisms could be simultaneously operating. It is interesting to note that an appreciable increase of ductility occurs after 32 h milling. Since mass density measurements indicate no dependence on the milling time, this result cannot be explained in terms of extrinsic features. More likely the enhanced ductile behaviour of n-A1 32 h is associated with the long time milling process, that determines a best refined microstructure with a narrow crystal size distribution and reduced defects content.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8
R.W. Siegel and G.E. Fougere, NanoStruct. Mater. 6, 205 (1995). R.W. Siegel, MRS Bulletin XV, 60 (1990). R.W. Siegel, Enc. of Appl. Physics, Vol 11, p.1, G.L. Trigg, ed., VCH, Weinheim (1994). E.O. Hall, Proc. Phys. Soc. London B64, 747 (1951). N.J. Petch, J. Iron Steel Inst. 174, 25 (1953). G.W. Nieman, J.R. Weertman and R.W. Siegel, J. Mater. Res. 6, 1012 (1991). G.W. Nieman, J.R. Weertman and R.W. Siegel, NanoStruct. Mater. 1, 185 (1992). V.Y. Gertsman, M. Hoffmann, H. Gleiter and R. Birringer, Acta metall, mater. 42, 3539 (1994) 9 M. Hoffmann and R. Birringer, Acta mater. 44, 2729 (1996) 10. A.H. Chokshi, A. Rosen, J. Karch and H. Gleiter, Scripta Metall. 23, 1679 (1989). 11. S. Enzo, G. Cocco and P.P. Macri, Key Eng. Mater 81-83, 49 (1993). 12. M. Re, M.Alvisi, E. Bonetti and L. Tapfer, Microsc. Microanal. Microstruct. 6, 673 (1995) 13. P. Polukhin, S. Gorelik and V. Vorontsov, Physicalprinciples ofplastic deformation, Mir Publisher, Moscow (1984).
Matcdala. Vol. 9,PP. 611-614.1997 l~eviw ~kieaceLid @ 1997 A~m Memllurg~ Inc. Printedinthe USA. All dghm rmerved
Pergamon
0965-9773:97 $17.00 + .00
PII S0965-9773(97)00137.2
THE INFLUENCE OF GRAIN SIZE ON THE MECHANICAL PROPERTIES OF NANOCRYSTALLINE ALUMINIUM E. BONETTI, L. PASQUINI, E. SAMPAOLESI Dipartimento di Fisica, Universita di Bologna and Istituto Nazionale per la Fisica della Materia, Viale Berti Pichat 6/2, 1-40127 Bologna, Italy. ABSTRACT Uniaxial tensile tests were performed at room temperature on nanocrystalline aluminium (n-AO prepared by mechanical attrition and cold consolidation with average grain size in the 20-40 nm range. The stress-strain curves analysis shows an enhanced tensile strength and a reduced ductility of n-Al with respect to the coarse-grained material. Anyway, the strength increase is much lower than predicted by extrapolation of the Hall-Petch relation to nanometer sized grains. Moreover, the strengthening rate (Hall Petch coefficient) is strongly reduced in comparison with coarse-grained AI. The observed behaviour is discussed in connection with microstructure evolution during mechanical attrition. ~ 1997 Acta Metailurgica Inc.
~TRODUCTION Mechanical properties of nanocrystalline materials (NCM) display an increasing interest because they are significantly different from those of the coarse grained (CG) counterpart. Dramatic changes in mechanical propertiessuch as hardness, strength and ductility,occur when the grain sizeis progressivelyreduced to the nanometer scale(I).It has bccn pointed out that confinement effects(2) may be responsiblefor specificchanges in the mechanisms of deformation. The plasticbehaviour of metals, which in the bulk situationstronglydepends on dislocation activity (generation and dynamics), starts to differ substantiallyentering the nanometer regime because of the reduced availabilityof mobile dislocationsin the increased confined nanophase grains (3). The strengthof a polycrystallinematerial can be enhanced by decreasing the grain size; the phcnomcnological relationbetween the yield stress(%) and the average grain size (d) can be expressedby the well-known HaII-Petchequation (4, 5): % = Co + k d "If2
611
[ll
612
E BONETrl,L PASQ~NJAND E SAMPAOLES~
where Oo (friction stress) and k (H-P coefficient) are material constants. Anyway, the grain size dependence of yield stress in NCM cannot be obtained by a simple extrapolation of the HP relation to the nanometer scale (6-9); in some cases, even negative values of the H-P coefficient k have been reported (10). In the present paper some results will be presented regarding the mechanical behaviour of nanocrystalline aluminium (n-A1). The aim of this research is to investigate the influence of grain size on the mechanical properties in the nanometer range.
EXPERIMENTAL Pure aluminium powders (44 ~tm, Alfa products, 99.9% purity) were used for the present experiments. Mechanical attrition (MA) was performed by a SPEX mixer-mill model 8000 using hardened steel balls and a tungsten carbide vial; the ball-to-powder weight ratio was 4 to 1. The powders were milled for five different times (2, 4, 8, 16, 32 h) in order to follow the microstructural evolution of the material. The consolidation procedure consisted in cold pressing the milled powders in a die with a rectangular section of 15 x 5 mm 2 under a uniaxial pressure of 1 GPa. In this way bar-shaped samples with a thickness of about 0.8 mm were obtained. Density measurements based on the Archimedes principle yield values ranging from 95 to 98 % of the fully dense value. The uniaxial tensile tests were performed at room temperature with a rigid tensile machine at a constant strain rate of 104s 1. The 0.2% offset was used as the yield stress. The average grain size reached at the different milling times (table 1) was estimated by Xray diffraction line-broadening analysis (11). Complementary TEM analysis showed a wide distribution of grain sizes (12): crystallite dimensions up to 50 nm were observed even at the higher milling times.
RESULTS AND DISCUSSION In fig. 1 the stress-strain curves of n-Al (32 h milling, d = 21 nm) and CG-A1 (d ~ 100 gin) are compared: a significant strength increase is observed in n-Al (Oy = 26 MPa) with respect to CG-AI (Oy = 13.5 MPa). Anyway, Oy of n-Al strongly disagrees with the H-P prediction; in fact, the extrapolation ofeq. [1] (using A1 parameters found in (13)) to d = 20 tun gives Oy ~ 500 MPa. As shown in fig. 2 and table 1, the increase in strength with decreasing grain size persists in the nanometer regime: in fact, a grain size reduction from 40 nm to 21 nm results in a yield stress increase of about 40%. The strengthening rate (with decreasing grain size) is illustrated in fig. 3, where Oy is plotted as a function o f d -rE (H-P co-ordinates); a least-squares linear fit in accordance with eq. [1] gives the following estimate for k and Oo: k = (400 + 80) MPa x nm ]/2 Oo = (6 + 2) MPa. The H-P coefficient k is lowered by about a factor five with respect to CG-A1 (13). These results seem to confirm that the H-P equation is inadequate to describe the strengthening behaviour over a wide grain size range, i.e. from CG material down to NCM.
THE INFLUENCEOF GRAIN SIZE ON THE MECHANICALPROPERTIESOF NANOCRYSTAUJNEALUMINUM
*
o a.,k132h • a-./kl 2h
_ I
n-A132h
.
=
~
e
~
-
613
-
o x = 20 M P a
17.5 M P a
tO
o.o
oi~
s~m t~)
Figure 1. Stress-strain curves for n-Al milled 32 h (d = 21 rim) and CG-AI (d = 100 txm).
,b Smmia~ )
~i~
2o
Figure 2. Stress-strain curves for n-Al milled 2h (d = 40 nm) and 32h (d = 21 nm).
Recently reported data (6-9) prove that the strengthening rate decreases with decreasing grain size. Both extrinsic features (such as pores and flaws in the cold-consolidated samples (6, 7)) and changes in deformation mechanisms (8) have been taken into account to explain the deviation from H-P behaviour occurring when the nanoscale is reached. As regards our results, the influence of the synthesis technique must be stressed. In fact, samples obtained at short milling times are characterised not only by a larger grain size, but also by a higher structural heterogeneity and dislocation density, thus making difficult to isolate the contribution of the grain size reduction to the observed mechanical behaviour. The strain reached at failure (of) in n-A1 ranges from 0.6% to 1.9% (table 1), typical values being around 1%, one order of magnitude lower than those pertaining to CG samples (el > 20%). Only n-Al obtained after 32 h milling exhibits an appreciable plastic yielding that permits to reach a 2% strain at failure. A significant reduction of ductility was also observed by Nieman et al in n-Pd and n-Cu (6). On the contrary, Gertsman et al (8) recently found evidence of rather good ductility in n-Cu. The situation is quite controversial because of the not well understood influence of extrinsic features upon the brittle behaviour of n-metals. TABLE 1 Tensile Tests Data on n-Al: d = Grain Size; % = Yield Stress; ~f = % Strain at Failure; d~dt = Strain Rate. Milling time (h)
d(nm)
Wma)
2
40 +4
17.5
1.2
0.8 x 10 "4
4
35+4
17
0.8
1 x 10 -4
8
28 + 3
18.5
0.7
1 x 10 -4
16
27 + 3
19.5
0.6
0.9 x 10 -4
32
21+2
26
1.9
1 × 10 ~
ds/dt ( s -~ )
E BONE'rn, L PASQUINIANDE SAMPAOLESI
614
25
•
CG-AI
.o-° tO
.............. ""
k = 400 M P a n m 1/2
d-ta(nm)-ta
Figure 3. Hall-Petch plot in n-Al (grain size 20+40 nm); CG-AI is represented by A.
CONCLUSIONS Tensile tests on n-Al indicate a deviation from the H-P prediction, in agreement with previously reported results on Pd and Cu. Anyway, samples prepared by MA are characterised by a broad grain size distribution, particularly at the lowest milling times. Moreover, a much higher dislocation density is encountered during the first stages of milling. Keeping in mind all these considerations, conclusions have to be drawn cautiously: in fact, in a heterogeneous system different deformation mechanisms could be simultaneously operating. It is interesting to note that an appreciable increase of ductility occurs after 32 h milling. Since mass density measurements indicate no dependence on the milling time, this result cannot be explained in terms of extrinsic features. More likely the enhanced ductile behaviour of n-A1 32 h is associated with the long time milling process, that determines a best refined microstructure with a narrow crystal size distribution and reduced defects content.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8
R.W. Siegel and G.E. Fougere, NanoStruct. Mater. 6, 205 (1995). R.W. Siegel, MRS Bulletin XV, 60 (1990). R.W. Siegel, Enc. of Appl. Physics, Vol 11, p.1, G.L. Trigg, ed., VCH, Weinheim (1994). E.O. Hall, Proc. Phys. Soc. London B64, 747 (1951). N.J. Petch, J. Iron Steel Inst. 174, 25 (1953). G.W. Nieman, J.R. Weertman and R.W. Siegel, J. Mater. Res. 6, 1012 (1991). G.W. Nieman, J.R. Weertman and R.W. Siegel, NanoStruct. Mater. 1, 185 (1992). V.Y. Gertsman, M. Hoffmann, H. Gleiter and R. Birringer, Acta metall, mater. 42, 3539 (1994) 9 M. Hoffmann and R. Birringer, Acta mater. 44, 2729 (1996) 10. A.H. Chokshi, A. Rosen, J. Karch and H. Gleiter, Scripta Metall. 23, 1679 (1989). 11. S. Enzo, G. Cocco and P.P. Macri, Key Eng. Mater 81-83, 49 (1993). 12. M. Re, M.Alvisi, E. Bonetti and L. Tapfer, Microsc. Microanal. Microstruct. 6, 673 (1995) 13. P. Polukhin, S. Gorelik and V. Vorontsov, Physicalprinciples ofplastic deformation, Mir Publisher, Moscow (1984).