On the Strain Rate Sensitive Characteristics of Nanocrystalline Aluminum Alloys

  • Sreedevi Varam
  • K. Bhanu Sankara Rao
  • Koteswararao V. RajulapatiEmail author
Conference paper
Part of the The Minerals, Metals & Materials Series book series (MMMS)


For structural applications, ductility is essential along with high strength in nanocrystalline (nc) materials. In general, ductility is controlled by strain hardening and strain rate sensitivity. In conventional materials which are coarse grained, the deformation is mainly dislocation based and accumulation of these dislocations results in work hardening. The deformation mechanisms that are operative in nc materials are distinct and the strain hardening ability is limited in nc materials. Strain rate sensitivity (SRS) and activation volume are the two key parameters which govern the underlying deformation mechanisms in nc materials. Higher SRS value could be an indication of better ductility levels. In general, nanocrystalline single phase fcc metals showed increased SRS, where as bcc metals showed decreased SRS. The addition of second phase effects the overall SRS of the nano composite/alloy. Since producing nc materials in bulk quantities is a challenge, nanoindentation, which can be performed on smaller sized samples, is an useful technique to study SRS and activation volume. Strain rate sensitive characteristics of Al and its alloys are reviewed in this paper. Our earlier work as well as the available literature data on these alloys showed that the nature and structure of the second phase dispersions greatly influence the SRS.


Nanocrystalline Deformation mechanisms Nanoindentation Strain rate sensitivity Activation volume 


The strength of engineering materials can be improved by grain refinement through Hall-Petch strengthening [1]. Nanocrystalline/nanostructured materials having average grain sizes <100 nm, exhibited improved physical and mechanical properties as compared to conventional coarse grained materials [2, 3, 4, 5, 6]. Nanocrystalline (nc) Al and Al alloys are potential candidates for structural applications as they possess high specific strength. Several processing routes [7, 8, 9, 10, 11, 12, 13, 14] have been employed to synthesize nc materials. Ball milling and severe plastic deformation techniques are used in producing bulk quantities of these materials [7, 12].

The deformation mechanisms that are operative in nc materials are distinct from the responsible mechanisms in conventional coarse grained materials [4]. The experimental data revealed higher strength values in nc single phase materials but the ductility levels were observed to be on the lower side [15]. Ductility is dependent on strain hardening exponent. But, the strain hardening ability is limited in nc materials since they do not deform mainly by dislocation motion. A comprehensive understanding on the effect of strain hardening rate on ductility of nc materials is yet to be established. The important parameters in plastic deformation process are strain rate sensitivity (SRS) and activation volume [16]. Materials with higher SRS value showed better ductility [17, 18]. The relationship between SRS and ductility in superplastic materials was studied and, the general trend of increasing ductility with increasing SRS was investigated for various materials experimentally [19, 20]. Koch [21] indicated that the second phase addition delays the localized deformation during tensile loading conditions, which results in improved ductility in nc materials. Studies on strain rate sensitive characteristics of bulk multi-phase nc materials in which both the matrix and the dispersed second phase are in nano size, are very limited as on today [22].

This paper discusses the strain rate sensitive characteristics of nc Al based alloys. Strain rate sensitivity of various nc alloys—Al–Pb, Al–W, Al–Pb–W, Al–Zn, Al–Mg and Al–Cu is discussed in detail. Nanocrystalline Al–Pb and Al–W alloy powders were produced using a high energy ball milling. The nc alloy powders were then consolidated using uni-axial pressing and spark plasma sintering. The Al–Pb–W alloy was in situ consolidated using high energy ball milling. Rate sensitive deformation behavior of these materials has been studied by nanoindentation. Nanoindentation is being extensively used to study various mechanical properties of nc materials and the underlying deformation mechanisms can be understood.

Elastic modulus and hardness are obtained from load-displacement curves of nanoindentation. Hardness is estimated from the maximum load applied, P max and the contact area under load, A as per Eq. (1) [23]
$$ H = \frac{{P_{max} }}{A} $$
The contact area which is a function of contact depth, \( h_{c} \) of the indenter and for a Berkovich indenter, it is calculated as per the below equation [23].
$$ A = C_{0} h_{c}^{2} + C_{1} h_{c}^{1} + C_{2} h_{c}^{1/2} + C_{3} h_{c}^{1/4} + \cdots + C_{8} h_{c}^{1/128} $$
where, \( C_{0} \) = 24.56, \( C_{1} \) = 1.6991E+4, \( C_{2} \) = −1.1537E+6, \( C_{3} \) = 1.1977E+7, \( C_{4} \) = −3.0602E+7 and \( C_{5} \) = 1.9918E+7. It is simplified as: \( A = 24.56 h_{c}^{2} \). Elastic modulus of the sample, E s , is calculated from the reduced modulus using the below equation [23, 24]
$$ \frac{1}{{E_{r} }} = \frac{{\left( {1 - \nu_{i}^{2} } \right)}}{{E_{i} }} + \frac{{\left( {1 - \nu_{s}^{2} } \right)}}{{E_{s} }} $$
where, E r is the reduced modulus, E i and ν i are the Young’s modulus and Poisson’s ratio of the diamond indenter which are 1140 GPa and 0.07 respectively. ν s is the Poisson’s ratio of the sample.
SRS and activation volume (\( \upsilon^{*} \)) are important parameters in understanding the dependence of flow stress on loading rate [1]. The flow stress, \( \sigma \) is dependent on the strain, \( \varepsilon \), loading rate/strain rate, \( \dot{\varepsilon } \), temperature, \( T \) and microstructure, \( S \) i.e., \( \sigma = f\left( {\varepsilon , \dot{\varepsilon }, T, S} \right) \) [25] which may be further depicted as per Eq. (4)
$$ {\text{d}}\upsigma = \left( {\frac{{\partial\upsigma}}{{\partial\upvarepsilon}}} \right){\text{d}}\upvarepsilon + \left( {\frac{{\partial\upsigma}}{{\partial {\dot{\upvarepsilon }}}}} \right){\text{d}}{\dot{\upvarepsilon }} + \left( {\frac{{\partial\upsigma}}{{\partial {\text{T}}}}} \right){\text{dT}} + \left( {\frac{{\partial\upsigma}}{{\partial {\text{S}}}}} \right)dS $$
At constant temperature and microstructure, the flow stress is related to the strain rate as per the power law equation [26]
$$ \sigma = \sigma_{0} \left( {\frac{{\dot{\varepsilon }}}{{\dot{\varepsilon }_{0} }}} \right)^{m} $$
SRS or strain rate exponent \( m \), can be obtained using Eq. (6) [26]:
$$ m = \frac{\partial \ln \sigma }{{\partial \ln \dot{\varepsilon }}} $$
Strength, \( \sigma \) can be estimated from the hardness, \( H \) obtained from nanoindentation data and the relationship between hardness and strength as per Tabor’s relation [27] is given as: \( \sigma \approx H/3 \). Activation volume, \( \upsilon^{*} \) can be calculated from the following equations [28, 29].
$$ \upsilon^{*} = \sqrt 3 kT\left({\frac{{\partial { \ln }{{\dot{\upvarepsilon }}}}}{{\partial {\upsigma }}}} \right) = 3\sqrt 3 kT\left({\frac{{\partial { \ln }{{\dot{\upvarepsilon }}}}}{{\partial {\text{H}}}}} \right) $$

Nanoindentation can be performed at various loading rates. The effective strain rate (\( \dot{\varepsilon } \)) can be calculated by dividing the loading rate with maximum load applied. The slope of the plot between yield stress and strain rate on logarithmic scale gives the SRS. The activation volume is obtained from the slope of the plot between \( \sqrt 3 kT { \ln }(\dot{\varepsilon }) \) and yield stress.

Strain Rate Sensitive Characteristics

Ultrafine-grained (ufg) metals and alloys exhibited improved ductility along with high strength [30, 31, 32]. The higher SRS values obtained in these materials were correlated to improved ductility levels. Experimental investigations by Wei et al. [33] showed higher SRS values for nc face centered cubic (fcc) metals and lower SRS values for body centered cubic (bcc) metals when compared to conventional coarse grained materials. When second phase dispersions which are nano sized, are present in the nc matrix, they seem to be effecting the strain rate sensitive properties to a great extent. The strain rate sensitive characteristics of ufg and nc Al and its alloys are discussed in the following sections.

Nanocrystalline Al

Ultrafine-grained (ufg) Al (99.5% pure) produced by severe plastic deformation [34] showed increased SRS value of 0.014, when compared to that of coarse grained Al (0.004) at room temperature. SRS was measured using strain rate jump tests during compression. SRS values obtained for ufg Al and coarse grained Al at 250 °C were 0.25 and 0.025 respectively indicating enhanced ductility levels in case of ufg Al. Based on these experimental findings, May et al. [34] indicated that the deformation mechanisms in ufg Al mainly involve diffusion processes that occur near grain boundaries. Nanocrystalline Al thin films synthesized by pulsed direct current magnetron sputtering [35] exhibited enhanced SRS values. The values of SRS and activation volume measured using strain rate jump tests for nc Al thin film (150 nm thick) were 0.037 ± 0.006 and 35 ± 4b 3 respectively, where b being the Burgers vector of Al.

Nanocrystalline bulk Al samples (~42 nm grain size) were synthesized using ball milling and uni-axial pressing [36]. The average hardness obtained using nanoindentation was 1.67 ± 0.09 GPa for an applied maximum load of 8000 µN. The stress vs strain rate plots on logarithmic scale for different peak loads are shown in Fig. 1 [36]. An average SRS of 0.035 ± 0.017 was obtained for applied peak forces of 1000, 5000 and 8000 µN. It was suggested that in nc materials, grain boundary mediated deformation processes were involved during plastic deformation. The high SRS values obtained could be indicative of reasonable ductility levels in nc Al.
Fig. 1

Variation of yield stress with strain rate for nanocrystalline Al at maximum peak forces of 1000, 5000 and 8000 µN [36]

Nanocrystalline Al–Pb Alloys

Nanocrystalline two-phase materials comprising of Al and Pb were synthesized using ball milling followed by spark plasma sintering at 573 K [37]. The structural characteristics of bulk nc Al–2 at.%Pb alloy (20 mm diameter × 3 mm thickness) are shown in Fig. 2. The X-ray diffractograms (Fig. 2b) of the bulk sample (Fig. 2a) revealed a two phase structure which did not show any solid solution formation. The bright-field and dark-field images obtained from transmission electron microscopy (TEM) (Fig. 2c, d) showed nanocrystalline structure. The Al grains were of ~53 nm in size with narrow size distribution as shown in Fig. 2e. High resolution TEM micrographs (Fig. 3a) showed Pb particles of about 6 nm in diameter. It is clear from Fig. 3b that Pb phase is segregated at the nc Al grain boundaries and it is also present inside the grains as fine Pb particles with a narrow size distribution (Fig. 3c).
Fig. 2

Structural details of bulk nanocrystalline Al–2at.%Pb alloy a Spark plasma sintered bulk sample, b X-ray diffractograms of various nc Al–Pb alloys, c, d Bright-field and dark-field TEM micrographs of the sample and e nc Al grain size distribution [37]

Fig. 3

High resolution TEM micrographs of nc Al–2at.%Pb alloy a Micrograph showing Pb particles of ~6 nm in Al matrix, b High angle annular dark-field image of the sample showing Pb particles segregated at Al grain boundaries as well as distributed within the Al grains, c Size distribution of Pb particles with an average particle size of ~6 nm [37]

Indentations were performed by applying different peak loads of 1000, 2000 and 4500 µN with loading rates of 100, 500 and 1000 µN/s for each peak force using a nanoindenter. The hardness values of nc Al–Pb alloys were observed to be increasing with the addition of Pb up to 2 at.%, then they decreased as shown in Fig. 4a. Similar trend was observed from both microindentation as well as nanoindentation data. The overall hardness of the nc Al–2at.%Pb composite was governed by the competition between particle strengthening and grain boundary softening as depicted in Fig. 4b. Lead phase enhanced the SRS of nc Al–Pb alloys with increasing amount of Pb addition as shown in Fig. 4c. Al–4at.%Pb alloy showed a high SRS value of 0.1. It is clear from the figure that the second phase particles are definitely contributing to the enhanced SRS values which might result in improved ductility as suggested by Koch [21]. Lead present in the grain boundaries might be influencing the SRS via some grain boundary mediated processes leading to higher SRS. The activation volume values measured for various nc Al–Pb alloys were in the range of 2.84–6.15b3, which were much lower when compared to those of conventional materials, suggesting that dislocations are not governing the activation volume. Instead, it is expected that the interfaces viz., grain boundaries and matrix/particle boundaries are responsible for the enhanced SRS and low activation volume measured.
Fig. 4

Hardness and strain rate sensitivity (SRS) of various nc Al–Pb alloys a Variation of obtained hardness values with Pb content, indentations have been performed at various loads using microindentation and nanoindentation, b Variation of hardness with Pb content, the plot obtained from predictions, the rule of mixtures plot and the experimental data obtained from Vickers microhardness with 50 g load are shown, c Variation of SRS with Pb content indicating the increase in SRS with increasing Pb content [37]

Nanocrystalline Al–W Alloys

A bulk nc Al–10at.%W alloy was synthesized by ball milling and spark plasma sintering at 748 K [38]. The TEM micrographs as shown in Fig. 5a, b revealed the presence of Al12W intermetallic particles of ~175 nm in size (Fig. 5d) in an nc Al matrix of 40 nm (Fig. 5c). The nanoindentation studies showed a high hardness value of 5.42 ± 0.33 GPa. The hardness increased with increasing loading rate as shown in Fig. 6a. A SRS value of 0.025 ± 0.002 was measured (Fig. 6b). Activation volume was calculated using the nanoindentation data and the sample showed lower activation volume of 1.63–3.88b3. The high hardness value of the nanocomposite was attributed to the presence of uniformly distributed second phase particles of nc Al12W in an nc aluminum matrix. It was suggested that the interfacial regions which include the grain boundaries and triple junctions in the matrix and reinforcement, boundaries between matrix and particles etc. could be governing the activation volume and SRS of the bulk Al–10at.%W nanocomposite.
Fig. 5

Structural details of bulk nc Al–10at.%W alloy including a bright-field and b dark-field TEM micrographs, c Al grain size distribution showing an average grain size of ~40 nm and d the grain size distribution of the second phase particles having an average size of ~175 nm [38]

Fig. 6

Nanoindentation data of bulk nc Al–10at.%W alloy, a Variation of hardness with loading rate at peak forces of 6000 and 8000 µN and b Variation of yield stress with strain rate on logarithmic scale showing the SRS value obtained from the slope of the plot [38]

Nanocrystalline Al–Pb–W Alloys

Investigations on nc Al–1at.%Pb–1at.%W alloy which was in situ consolidated during ball milling, resulted in high SRS and low activation volume values of 0.071 ± 0.004 and 4.71b3 respectively [39]. The variation of flow stress with strain rate is shown in Fig. 7a for different peak forces. It was suggested that grain boundary mediated deformation processes are responsible for obtained high SRS values. The SRS and activation volume are plotted for various alloy compositions in Fig. 7b. Addition of 1at.%Pb to Al resulted in enhancement of SRS to a value of 0.043. When 1at.%W was added along with 1at.%Pb, SRS further enhanced to 0.071. There seem to be not much variation in the activation volume of these alloys. Though, the addition of fcc Pb increased the SRS and the addition of bcc W decreased the SRS when these elements were added to nc Al individually, the simultaneous addition of fcc Pb and bcc W to nc Al matrix resulted in the increase in the overall SRS value to 0.071.
Fig. 7

Nanoindentation data of in situ consolidated nc Al–1at.%Pb–1at.%W alloy, a Variation of flow stress with strain rate on natural logarithmic scale and b SRS and activation volume values for different alloy compositions indicating enhanced SRS for an alloy with Pb and W addition [39]

Ultrafine-Grained Al–Zn Alloy

Investigations [30, 31] were carried out on ufg Al–30wt%Zn alloy produced using high pressure torsion, a severe plastic deformation process. SRS was measured using depth-sensing nanoindentation which revealed unusually high values for SRS as shown in Fig. 8 (adopted from [30]). The authors emphasized that SRS and ductility have a close relationship. At room temperature, the alloy showed SRS of 0.22 and high ductility was achieved with elongations of ~150%. The unusual elongation values were attributed to the presence of Zn-rich layer at the grain boundaries of Al which led to grain boundary sliding mechanism through diffusion of Zn atoms along the grain boundaries.
Fig. 8

Hardness versus strain rate plots on natural logarithmic scale for conventional and ultra-fine grained Al–30wt.%Zn alloys indicating SRS values of 0.03 and 0.22 respectively (adopted from [30])

Nanocrystalline and Ultrafine-Grained Al–Mg Alloys

Kapoor et al. [40] have studied Al–1.5wt%Mg alloy obtained from equal channel angular pressing (ECAP) technique which resulted in ufg material with an average grain size of ~280 nm. They observed increased SRS for ufg alloy when compared to coarse grained alloy. They attributed the increase in SRS value to lower activation volume values observed. They suggested that grain refinement results in lower activation energy for diffusion leading to grain boundary deformation mechanisms. Investigations by Ahn et al. [41] on Al–Mg alloy (Al 5083 alloy containing Mn and Cr) revealed negative SRS for nc powder obtained from cryomilling and the forged ufg plate. Cryomilling was used to synthesize nc Al 5083 alloy powder which resulted in nc structure (50 nm in size). The nc powder also showed high thermal stability. Quasi-isostatic forging was used to consolidate the powder which resulted in a bulk sample of 250 nm grain size. Mechanical properties were measured by performing nanoindentation at different loading rates. The nc powder as well as the forged plate showed negative SRS, whereas, conventional coarse grained (132 μm) alloy was strain rate insensitive. In general, negative SRS is observed in materials which exhibit dynamic strain ageing [42] during tensile tests. The interstitial atoms might be pinning the moving dislocations, resulting in negative SRS values. The authors suggested that the nanoindentation at higher loading rates might be triggering the motion of dislocations by unlocking them from the interstitial solute atoms.

Nanocrystalline Cu–Al Alloy

Recent studies on the SRS and activation volume of nc Cu–11.1at.%Al alloy produced by ECAP showed lower SRS (0.0187) for nc Cu–Al alloy when compared to that of nc pure Cu (0.0264) [43]. Strain rate jump tests were employed to measure SRS. The alloy exhibited low values of stacking fault energy and activation volume. The Cu–Al alloy formed a solid solution and nano twins were observed in nano meter sized grains. The lower SRS value obtained was attributed partly to the lower stacking fault energy and it was further attributed to the grain boundary mediated deformation processes and twinning.

Nanocrystalline Al–Fe Alloy

The SRS of Al–1.71at.%Fe alloy fabricated by electron beam deposition was found to be weakly positive [44]. The alloy consisted of nano sub-grain structure (<100 nm) within a polycrystalline matrix of Al solid-solution having high-angle grain boundaries. The authors have suggested that the dominant deformation mechanisms in this alloy are very different.

Studies on SRS, activation volume and plastic deformation mechanisms play an important role in tailoring nc materials with high strength along with reasonable ductility and toughness values. As nc Al and its alloys have a potential for structural applications, investigations carried out on these alloys have been reviewed in this paper. The comparison of SRS values of various alloys is shown in Fig. 9a. Face centered cubic Pb addition lead to increased SRS of nc Al, whereas bcc W addition resulted in decreased SRS. Conventional Al–Pb is an immiscible system and no solid solution was formed even under non equilibrium processing conditions. When both the alloying elements Pb and W are added simultaneously to nc Al, there was an enhancement of SRS for in situ consolidated nc Al–Pb–W alloy. The Al–Pb–W alloy also did not show formation of any solid solution. Lead and tungsten particles were dispersed in the nc Al matrix. Ultrafine-grained Al–Zn alloy showed high SRS (0.22) with high ductility at room temperature. High ductility was attributed to the deformation mechanisms involving grain boundaries such as grain boundary sliding, occurring due to the presence of Zn atom segregates at Al grain boundaries. Nanocrystalline Cu–Al alloy showed lower SRS when compared to that of nc pure Cu. The SRS of Al–1.71at.%Fe alloy processed by electron beam deposition was found to be weakly positive. This alloy consisted of nano sub-grain structure (<100 nm) with in a polycrystalline matrix of Al solid-solution with high-angle grain boundaries. The activation volume values for most of these nc alloys were found to be much lower when compared to those of coarse grained materials as shown in Fig. 9b.
Fig. 9

a Strain rate sensitivity and b activation volume values of various nc Al and Al alloys which include some of our earlier work and the literature data

Hence, it may be stated that in multi-phase nc Al alloys, the crystal structure, grain size and size distribution of individual phases greatly influence the plastic deformation mechanisms which influence the strain rate sensitive characteristics. The nature of the matrix and the dispersed phases (solid solution/intermetallic/metallic) of the nc alloy also influences its strain rate sensitive characteristics. Majorly interfaces (grain boundaries/triple junctions/quadruple junctions/particle-matrix boundaries, twin boundaries etc.) mediated processes are expected to be operative in these alloys.

Summary and Conclusions

The structure and the nature of the second phase added seem to be greatly influencing the strain rate sensitive characteristics in nc Al based alloys. When fcc Pb is a added to nc Al, the SRS increased and when bcc W is added the overall SRS decreased. When both the alloying additions Pb and W are added to nc Al, there was an enhancement of SRS in case of in situ consolidated nc Al–Pb–W alloy. At room temperature, ufg Al–Zn alloy showed high SRS of 0.22 and high ductility with elongations of ~150%. The negative SRS obtained in nc and ufg Al–Mg alloy was attributed to the presence of solute atoms acting as barriers for the movement of dislocations. Nanocrystalline Cu–Al alloy showed lower SRS when compared to that of nc pure Cu. The SRS of Al–1.71at.%Fe alloy processed by electron beam deposition was found to be weakly positive. This alloy consisted of nano sub-grain structure (<100 nm) with in a polycrystalline matrix of Al solid-solution with high-angle grain boundaries. Investigations carried out on SRS, activation volume and plastic deformation mechanisms of various nc multi-phase Al alloys revealed that these alloys can be tailored to have high strength along with reasonable ductility and toughness values by manipulating the second phase additions.


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Copyright information

© The Minerals, Metals & Materials Society 2017

Authors and Affiliations

  • Sreedevi Varam
    • 1
    • 3
  • K. Bhanu Sankara Rao
    • 2
  • Koteswararao V. Rajulapati
    • 1
    Email author
  1. 1.School of Engineering Sciences and TechnologyUniversity of HyderabadHyderabadIndia
  2. 2.Ministry of Steel (Government of India) ChairMahatma Gandhi Institute of TechnologyHyderabadIndia
  3. 3.Department of Metallurgical and Materials EngineeringMahatma Gandhi Institute of TechnologyHyderabadIndia

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