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Plasticity criterion for bulk amorphous alloys
Materials Science and Engineering A 477 (2008) 344–349
Plasticity criterion for bulk amorphous alloys Seok-Woo Lee, Sang-Chul Lee, Jae-Chul Lee ∗ Department of Materials Science and Engineering, Korea University, Anamdong, Seoul 136-701, Republic of Korea Received 15 February 2007; received in revised form 10 May 2007; accepted 11 May 2007
Abstract A plasticity criterion (p-parameter), which enables the prediction of the plasticity of monolithic bulk amorphous alloys, is proposed. This criterion, which is defined as |λ − 0.18|Tx /Tx , takes into account the local packing state and structural stability characterized by the thermal properties of amorphous alloys. Bulk amorphous alloys with large p-values have more loosely packed and mechanically less stable microstructures, so that local structural evolution including nanocrystallization is promoted during the process of loading, leading to enhanced. The proposed criterion can be used as a means for predicting the plasticity of monolithic bulk amorphous alloys, which are devoid of a minor element with positive mixing enthalpy. © 2007 Published by Elsevier B.V. Keywords: Bulk amorphous alloy; Plasticity; Nanocrystallization
1. Introduction The plasticity shown by crystalline metals can be described on the basis of their dislocation motion [1]. In bulk amorphous alloys, however, where conventional dislocation-based plasticity is not permitted due to the absence of long range atomic periodicity, it is not easy to characterize the mechanism underlying the plasticity exhibited by these alloys [2]. It is known that the plastic deformation of amorphous alloys is mostly caused by the formation of the shear band. As a result, the degree of global plasticity in amorphous alloys is predominantly dependent on the total number density of the shear bands generated during the process of deformation [3]. However, it is unclear why amorphous alloys exhibit different strains prior to fracture or how amorphous alloys with enhanced plasticity can be designed from a microstructural perspective. Recently, Lee et al. reported that the formation of multiple shear bands in monolithic amorphous alloys is directly related to the microstructural changes driven by the deformation imposed on the sample, which is known as deformation-induced nanocrystallization [4]. Saida et al. claimed that the dynamic precipitation of nanocrystallites during deformation can act as a barrier to the propagation of shear bands, thereby leading to the formation of multiple shear bands [5]. Lately, Kumar et al. [6], Chen et al. [7] and Lee et al. [8] reported the experimen∗
Corresponding author. Tel.: +82 2 3290 3283. E-mail address: [email protected] (J.-C. Lee).
0921-5093/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.msea.2007.05.036
tal evidences which validated the intimate relationship between deformation-induced nanocrystallization and plasticity. These recent results indicate that multiple shear bands can be formed in bulk amorphous alloys with structures in which deformation facilitates nanocrystallization, causing them to have enhanced plasticity. Therefore, if the structural features which can influence the nanocrystallization process could be quantified, the degree of plastic deformation in amorphous alloys could be predicted. In this paper, we propose a parameter which can be used to assess the degree of plasticity in bulk amorphous alloys, by combining both the structural and thermodynamic factors characterizing their microstructural features related to deformation-induced nanocrystallization. 2. Results and discussion 2.1. Formulation of the p-criterion Earlier studies suggested that nanocrystallization behavior during deformation plays a significant role in the generation of multiple shear bands in bulk amorphous alloys [4–8]. Therefore, to enhance their plasticity, it is necessary to design amorphous alloys with loosely packed structures containing abundant free volumes, i.e. open space. This is because, during the process of loading, atomic diffusion is promoted in alloys in which the constituent atoms are loosely packed, and this in turn promotes the formation of excess free volume and nanocrystallites. Therefore,
S.-W. Lee et al. / Materials Science and Engineering A 477 (2008) 344–349
it is necessary to evaluate the packing state of the constituent atoms in amorphous alloys, in order to examine the facility with which deformation-induced nanocrystallization takes place. The packing state of the constituent atoms in bulk amorphous alloys can usually be described by the dense random packing model [9]. The principle behind this model is to find the optimum atomic size ratio and the composition satisfying the densest state of atomic packing. The λ-parameter, as defined by Eq. (1), is probably the most widely accepted parameter which enables the evaluation of the packing state of the constituent atoms in amorphous alloys [10]: 3 n−1 rB λ= − 1 CB , (1) rA B=1
where rA and rB are the atomic radii of the solvent and solute, respectively, and CB (in atomic percent) is the solute concentration of element B. Although Eq. (1) was first used by Egami [9] in order to explain the glass formation phenomena of binary alloy systems, Yan et al. [10] expanded Eq. (1) for the application to multicomponent systems. According to Yan’s empirical results, multi-component bulk amorphous alloys with λ ≈ 0.18 have densely packed structures, while alloys with λ-values which deviate from 0.18 are likely to be loosely packed. Since the λparameter can be used as a measure of the efficiency of atomic packing, it has often been used to evaluate the glass forming ability (GFA) [11]. The λ-parameter could also be used as a means to evaluate the plasticity of amorphous alloys. This is because the plasticity of amorphous alloys is closely related to the packing state, which largely influences the degree of nanocrystallization of amorphous alloys during deformation. Amorphous alloys with large |λ − 0.18|-values would be expected to be more loosely packed, thus making them more susceptible to undergo nanocrystallization when subjected to a sufficiently high deformation level. As a result, the plasticity of amorphous alloys is thought to be proportional to the magnitude of the |λ − 0.18|-value. The onset crystallization temperature (Tx ) also provides an important structural information related to the easiness of crystallization. It is known that the degree of atomic dilatation increases with increasing temperature due to the increasing magnitude of atomic vibration. Beyond the onset crystallization temperature, the atomic vibration becomes vigorous enough to force atoms change their positions into lattice sites, causing crystallization. This crystallization process occurs more readily in bulk amorphous alloys with low crystallization temperatures. This is because, from the thermodynamics viewpoint, amorphous alloys with low crystallization temperatures can be regarded as having less stable microstructures. Therefore, application of mechanical energy in the form of deformation can also promote crystallization in a manner similar to thermally induced nanocrystallization. That is, deformation-induced phase transformation from an amorphous phase to a more stable crystalline phase may take place more readily in alloys with low crystallization temperatures. As such, the plasticity is considered to be inversely proportional to the magnitude of the onset crystallization temperature.
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The magnitude of the supercooled liquid region (Tx = Tx − Tg , where Tg is the glass transition temperature) has long been used as a parameter for judging the liquid stability of amorphous alloys. In general, bulk amorphous alloys with a large supercooled liquid region are known to have high liquid stability. This implies that alloys with a large supercooled liquid region can sustain liquid structures over a wide temperature range above the glass transition temperature. Therefore, in the as-cast condition, bulk amorphous alloys with a large supercooled liquid region have an amorphous structure close to that of a liquid, while those with a small supercooled liquid region tend to have an amorphous structure which closely resembles a crystalline one. Among these two amorphous structures, it is more likely for the former to have a larger initial free volume in the as-cast condition, in which case mechanically driven diffusion could take place more easily in this type of alloy due to its loosely packed structure, thereby promoting deformation-induced nanocrystallization. Therefore, the plasticity of an amorphous alloy is considered to be proportional to the magnitude of the supercooled liquid region. To summarize, |λ − 0.18|, Tx , and Tx are considered to be the three important parameters affecting the plasticity of bulk amorphous alloys. To examine whether these parameters have a linear relationship with the plasticity, plots of each factor versus the plasticity were made based on data obtained from the authors’ previous experiments on the Cu-based amorphous alloys [8] and are shown in Fig. 1. In general, the resultant plots showed that |λ − 0.18| and Tx exhibit reasonably good proportionality with the plastic strains as in Fig. 1(a and b), while Tx exhibits inverse proportionality with data scattering as in Fig. 1(c). However, the value of Tx /Tx , which reflects the mechanical stability1 as defined in a combined form of two thermal properties, i.e. Tx and Tx , exhibits a good proportionality as shown in Fig. 1(d). Thus, the suggested three parameters can be reduced into two parts, which reflect the atomic packing state (|λ − 0.18|) and mechanical stability characterized by the thermal properties (Tx /Tx ). Although these two parts show a reasonably good proportionality with the plastic strains, they also exhibit considerable data scatterings as shown in Fig. 1(a and d). These scatterings can be reduced by taking into consideration both parts simultaneously. For this reason, we formulate the plasticity criterion (p) for bulk amorphous alloys as defined by: p = |λ − 0.18|
Tx . Tx
(2)
1 Here, the concept of stability could be confusing because the mechanical stability is quite different from the thermal stability. In fact, bulk amorphous alloys with large Tx are known to be thermally stable, but this does not necessarily warrant their mechanical stability under the application of the mechanical force. As already discussed, it is more probable that alloys with large Tx have the open structures close to that of a liquid phase. That is, because those alloys possess structures close to the liquid phase, they could be mechanically less stable. This is because the local rearrangement of the constituent atoms can take place with ease due to structural openness when stress ‘greater than the yield strength’ is applied.
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Fig. 2. A plot showing the relationship between the p-parameter and the plasticity of bulk amorphous alloys. The data denoted by the dark solid circles were obtained in the current study, while the data denoted by the open symbols were obtained from the literature.
(or rearrangement) of the constituent atoms under local shear stress as discussed earlier. Therefore, the physics underlying the proposed criterion is that bulk amorphous alloys with larger pvalues are more loosely packed (i.e. larger |λ − 0.18|-value) and mechanically less stable as quantified by their thermal properties (i.e. larger Tx /Tx ) with the result that deformation can facilitate nanocrystallization, which in turn leads to enhanced plasticity. 2.2. Validation of the p-criterion
Fig. 1. Plots showing the relationship between the plasticity and various parameters measured from the Cu-based amorphous alloys reported in Ref. [8]. (a) |λ − 0.18|, (b) Tx , (c) Tx , and (d) Tx /Tx .
As can be seen from Eq. (2), the p-parameter is dependent on the factors related to the atomic packing state (|λ − 0.18|) and thermal characteristics (Tx /Tx ). Since these factors are intimately related to the structural openness, they can be used as a means for judging the facility of local atomic movement
The proposed plasticity criterion was tested for the Cu-based amorphous alloys. A total of 15 samples in the form of 1 mm in diameter and 2 mm long cylindrical cast rods were prepared and tested under uniaxial compression applied using a screwdriven type mechanical test machine at an initial strain rate of ∼10−4 s−1 . The corresponding p-values were calculated using the λ-values and the characteristic temperatures, as listed in Table 1, determined from the thermograms obtained using differential scanning calorimetry conducted at a heating rate of 40 ◦ C/min. As shown in Fig. 2, there exists a linear relationship between the p-value and the corresponding plastic strain in the Cu-based amorphous alloys. We also calculated the p-values for monolithic Cu [8,11,12], Co [13], Pd [14], Zr [8,15–22], Fe [23–25] Mg [26,27], and Ni-based [28,29] alloys, in order to evaluate the validity of the proposed criterion in other previously reported amorphous alloy systems in Table 1. Experimental conditions used to collected all data in Table 1 were similar, i.e. the strain rate of 0.5–1 × 10−4 s−1 and the heating rate of 30–40 ◦ C/min, which would minimize possible data scatterings, especially plastic strains [30], caused by the experimental conditions. Although these alloys were synthesized using different equipment and cast into different sizes, a linear relationship between the pvalues and the corresponding plasticity was still found to exist as can be seen from Fig. 2, indicating that the proposed criterion is valid for other amorphous alloy systems. However, as indicated by the arrows in Fig. 2, there are some alloys for
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Table 1 Various parameters measured from different families of amorphous alloys Base
Alloys
λ
Tx
Tx
εp
Ref.
Cu
Cu66 Zr34 Cu64 Zr36 Cu62 Zr38 Cu54 Zr46 Cu52 Zr48 Cu50 Zr50 Cu60 Zr30 Ti10 Cu60 Zr22 Ti18 Cu60 Zr20 Hf10 Ti10 Cu50 Zr41 Ti9 Cu54 Zr22 Ti18 Ni6 Cu43 Zr43 Al7 Be7 Cu43 Zr43 Al7 Ag7 Cu47.5 Zr47.5 Al5 Cu50 Zr43 Al7 Cu47 Ti33 Zr7 Nb4 Ni8 Si1 Cu47 Ti33 Zr11 Ni8 Si1 Cu50 Ni8 Zr17 Hf1 Ti22 Nb2
0.330 0.350 0.369 0.447 0.466 0.486 0.341 0.303 0.322 0.443 0.307 0.468 0.477 0.446 0.482 0.256 0.279 0.297
782 773 777 731 726 718 754 780 766 704 769 795 794 760 792 736 757 744
24 39 45 37 42 41 25 59 45 33 57 115 72 67 61 23 37 52
0.6 0.1 3.0 2.3 2.8 4.1 1.8 2.5 2.0 2.5 3.5 6.5 5.5 4.5 6.6 4.2 1.5 1.7
[8] [8] [8] [8] [8] [8] [8] [8] [8] [8] [8] [8] [8] [8] [8] [11] [11] [12]
Co43 Fe20 Ta5.5 B31.5
0.258
982
72
0
[13]
Pd
Pd40 Ni40 P20
0.211
670
81
2.3
[14]
Zr
Zr52 Cu48 Zr63 Al10 Ni10 Cu14 Nb3 Zr41.2 Ti13.8 Cu12.5 Ni10 Be22.5 Zr55 Al10 Cu30 Ni5 Zr57 Ti5 Cu20 Ni8 Al10 Zr59 Ta5 Cu18 Ni8 Al10 Zr49.7 Cu34.4 Al8.9 Be7 Zr60 Cu20 Pd10 Al10 Zr65 Al7.5 Ni10 Pd17.5
0.505 0.159 0.294 0.203 0.182 0.174 0.241 0.164 0.139
716 738 725 765 703 770 792 758 705
40 95 80 82 52 97 111 65 80
3 0.75 2 1 0.02 6.8 3 1.9 1.2
[8] [15] [16] [17] [18] [19] [20] [21] [22]
Fe
Fe65.5 Cr4 Mo4 Ga4 P12 C5 B5.5 Fe77 Ga3 P9.5 C4 B4 Si2.5 (Fe75 B15 Si10 )0.96 Nb4 Fe74 Nb6 Y3 B17
0.152 0.112 0.143 0.214
806 885 800 879
61 50 50 48
0.19 0.35 0.45 0
[23] [24] [24] [25]
Mg
Mg65 Cu7.5 Ni7.5 Zn5 Ag5 Y10 Mg65 Cu20 Ni5 Gd10 Mg65 Cu25 Gd10
0.149 0.155 0.153
463 480 483
41 61 67
0 0.15 0
[26] [27] [27]
Ni
Ni59 Zr20 Ti16 Si2 Sn3 Ni59 Zr20 Ti16 Si2 Sn3 Ni59 Zr16 Ti13 Si2 Sn3 Nb7
0.334 0.364 0.336
876 877 885
46 56 40
2.2 2 6.5
[28] [28] [29]
Co
εp is the plastic strain, which deviated from the linearity of the flow curves (usually ∼2%).
which the data points are scattered. A common feature of these alloys is that some of the alloying elements, such as Ta, Nb, Ag and Be, have either positive mixing enthalpies or large differences in the mixing enthalpy with their major constituent elements. It is generally accepted that amorphous alloys, which have positive mixing enthalpies among their constituent elements, contain atomic-scale chemical inhomogeneities and/or localized fluctuations in their free volume distribution [31]. Upon compression, these chemical and spatial disturbances act as the initiation site for shear band formation and, therefore, can promote the formation of multiple shear bands, leading to large plastic strains prior to fracture. Accordingly, the addition of alloying elements having a positive mixing enthalpy with the constituent atoms can provide a useful method of enhancing the
Fig. 3. The activation energy vs. plasticity relationship for various Cu-based amorphous alloys. The solid circles denote the mean plasticity, while the vertical lines indicate the total range of the measurements recorded during 7–40 tests per specimen.
plasticity of bulk amorphous alloys. However, in this study, the effect of the mixing enthalpy on the plasticity was not taken into consideration. As such, further studies are needed to determine the important role played by the positive mixing enthalpy on the plasticity. Experiments were extended to correlate the p-criterion with the plasticity associated with the deformation-induced nanocrystallization in the Cu-based amorphous alloys. Based on the fact that the crystallization rate depends on the activation energy for crystallization, the authors found that dynamic structural changes including nanocrystallization are promoted in bulk amorphous alloys with low activation energy for crystallization (or loosely packed structures) [8]. This is because, with the supply of mechanical energy, the atoms can change their position with ease in amorphous alloys with low activation energy. Therefore, excess free volume can be nucleated in many localized regions during the process of deformation. Several recent experimental works [31,32] confirmed that excess free volume indeed formed in alloys with enhanced plasticity during deformation, of which formation mechanisms are theoretically explored based on 3D molecular dynamics simulations [33]. The formation of excess free volume would further reduce the activation energy for crystallization. It was found that the activation energy for crystallization is a major parameter that influences the rate of the phase transformation from an amorphous to a crystalline phase [34]. This means that as the activation energy becomes lower, the corresponding transformation rate becomes faster, suggesting that the supply of the mechanical energy can promote the uniform precipitation of nanocrystallites. Under this condition, shear bands are initiated by the local coalescence of free volume or at the crystalline/amorphous interfaces, which in turn can lead to the formation of multiple shear bands. Simultaneously formed shear bands interact with each other and can disturb their further propagation, resulting in large plastic strains [16]. Therefore, the plasticity of amorphous alloys is related to the activation energy of the overall crystallization process as shown in Fig. 3 [8].
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the deformation imposed to the sample, and the activation energy for crystallization is low. Thus, the p-parameter can be used as a criterion which is worthwhile for designing monolithic bulk amorphous alloys with enhanced plasticity. However, in order to derive the more reliable plasticity criterion, the structural feature caused by a minor element with the positive mixing enthalpy is to be incorporated. Acknowledgement This research was supported by grants from the Basic Research Program (R01-2004-000-10891-0) of the Ministry of Science and Technology, Korea. References Fig. 4. A plot showing the relationship between the p-parameter and the activation energy for crystallization in bulk amorphous alloys.
It should be noted here that the activation energies for the overall crystallization were calculated using the non-isothermal Kissinger analysis by varying the heating rates, while Tx /Tx values were obtained at a constant heating rate. Despite the changes in the heating rate, the activation energy calculated based on the non-isothermal Kissinger analysis is nearly independent of the heating rate [35]. In the meantime when calculating the p-value, the values of Tx and Tx increases with increasing heating rate. However, their ratio, i.e. Tx /Tx was observed to be nearly the same regardless of the heating rate. Therefore, both the activation energy and the p-value are independent of the heating rate, providing the basis of using these parameters as the plasticity criterion. The facility of crystallization can also be evaluated from the microstructural viewpoint. Alloys with a loosely packed structure inherently contain many free volumes. Therefore, under uniaxial compression, the atoms can change their position easily, which may result in deformation-induced nanocrystallization. As a result, it can be regarded that amorphous alloys with low activation energies for crystallization correspond to those with loosely packed structure or large p-values. Indeed, as shown in Fig. 4, there exists a reasonably good inverse proportionality between the p-value and the activation energy for crystallization. Therefore, as with other widely accepted parameters such as G/B ratio [36] and v-value [37] used to predict the plasticity, the p-parameter and the activation energy for crystallization can be used as a reliable criterion that enables the plasticity to be predicted, as well as facilitating the design of bulk amorphous alloys with enhanced plasticity. 3. Conclusion We proposed a plasticity criterion, |λ − 0.18|Tx /Tx to correlate with the plasticity of bulk amorphous alloys in Cu-, Fe-, Zr-, Mg-, Co-, Ni-, and Pd-based systems. The results show that bulk amorphous alloys with large p-values exhibit large plasticity. It is because large p-values indicate that bulk amorphous alloys have loosely packed structures, of which evolution is susceptible to
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Plasticity criterion for bulk amorphous alloys Seok-Woo Lee, Sang-Chul Lee, Jae-Chul Lee ∗ Department of Materials Science and Engineering, Korea University, Anamdong, Seoul 136-701, Republic of Korea Received 15 February 2007; received in revised form 10 May 2007; accepted 11 May 2007
Abstract A plasticity criterion (p-parameter), which enables the prediction of the plasticity of monolithic bulk amorphous alloys, is proposed. This criterion, which is defined as |λ − 0.18|Tx /Tx , takes into account the local packing state and structural stability characterized by the thermal properties of amorphous alloys. Bulk amorphous alloys with large p-values have more loosely packed and mechanically less stable microstructures, so that local structural evolution including nanocrystallization is promoted during the process of loading, leading to enhanced. The proposed criterion can be used as a means for predicting the plasticity of monolithic bulk amorphous alloys, which are devoid of a minor element with positive mixing enthalpy. © 2007 Published by Elsevier B.V. Keywords: Bulk amorphous alloy; Plasticity; Nanocrystallization
1. Introduction The plasticity shown by crystalline metals can be described on the basis of their dislocation motion [1]. In bulk amorphous alloys, however, where conventional dislocation-based plasticity is not permitted due to the absence of long range atomic periodicity, it is not easy to characterize the mechanism underlying the plasticity exhibited by these alloys [2]. It is known that the plastic deformation of amorphous alloys is mostly caused by the formation of the shear band. As a result, the degree of global plasticity in amorphous alloys is predominantly dependent on the total number density of the shear bands generated during the process of deformation [3]. However, it is unclear why amorphous alloys exhibit different strains prior to fracture or how amorphous alloys with enhanced plasticity can be designed from a microstructural perspective. Recently, Lee et al. reported that the formation of multiple shear bands in monolithic amorphous alloys is directly related to the microstructural changes driven by the deformation imposed on the sample, which is known as deformation-induced nanocrystallization [4]. Saida et al. claimed that the dynamic precipitation of nanocrystallites during deformation can act as a barrier to the propagation of shear bands, thereby leading to the formation of multiple shear bands [5]. Lately, Kumar et al. [6], Chen et al. [7] and Lee et al. [8] reported the experimen∗
Corresponding author. Tel.: +82 2 3290 3283. E-mail address: [email protected] (J.-C. Lee).
0921-5093/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.msea.2007.05.036
tal evidences which validated the intimate relationship between deformation-induced nanocrystallization and plasticity. These recent results indicate that multiple shear bands can be formed in bulk amorphous alloys with structures in which deformation facilitates nanocrystallization, causing them to have enhanced plasticity. Therefore, if the structural features which can influence the nanocrystallization process could be quantified, the degree of plastic deformation in amorphous alloys could be predicted. In this paper, we propose a parameter which can be used to assess the degree of plasticity in bulk amorphous alloys, by combining both the structural and thermodynamic factors characterizing their microstructural features related to deformation-induced nanocrystallization. 2. Results and discussion 2.1. Formulation of the p-criterion Earlier studies suggested that nanocrystallization behavior during deformation plays a significant role in the generation of multiple shear bands in bulk amorphous alloys [4–8]. Therefore, to enhance their plasticity, it is necessary to design amorphous alloys with loosely packed structures containing abundant free volumes, i.e. open space. This is because, during the process of loading, atomic diffusion is promoted in alloys in which the constituent atoms are loosely packed, and this in turn promotes the formation of excess free volume and nanocrystallites. Therefore,
S.-W. Lee et al. / Materials Science and Engineering A 477 (2008) 344–349
it is necessary to evaluate the packing state of the constituent atoms in amorphous alloys, in order to examine the facility with which deformation-induced nanocrystallization takes place. The packing state of the constituent atoms in bulk amorphous alloys can usually be described by the dense random packing model [9]. The principle behind this model is to find the optimum atomic size ratio and the composition satisfying the densest state of atomic packing. The λ-parameter, as defined by Eq. (1), is probably the most widely accepted parameter which enables the evaluation of the packing state of the constituent atoms in amorphous alloys [10]: 3 n−1 rB λ= − 1 CB , (1) rA B=1
where rA and rB are the atomic radii of the solvent and solute, respectively, and CB (in atomic percent) is the solute concentration of element B. Although Eq. (1) was first used by Egami [9] in order to explain the glass formation phenomena of binary alloy systems, Yan et al. [10] expanded Eq. (1) for the application to multicomponent systems. According to Yan’s empirical results, multi-component bulk amorphous alloys with λ ≈ 0.18 have densely packed structures, while alloys with λ-values which deviate from 0.18 are likely to be loosely packed. Since the λparameter can be used as a measure of the efficiency of atomic packing, it has often been used to evaluate the glass forming ability (GFA) [11]. The λ-parameter could also be used as a means to evaluate the plasticity of amorphous alloys. This is because the plasticity of amorphous alloys is closely related to the packing state, which largely influences the degree of nanocrystallization of amorphous alloys during deformation. Amorphous alloys with large |λ − 0.18|-values would be expected to be more loosely packed, thus making them more susceptible to undergo nanocrystallization when subjected to a sufficiently high deformation level. As a result, the plasticity of amorphous alloys is thought to be proportional to the magnitude of the |λ − 0.18|-value. The onset crystallization temperature (Tx ) also provides an important structural information related to the easiness of crystallization. It is known that the degree of atomic dilatation increases with increasing temperature due to the increasing magnitude of atomic vibration. Beyond the onset crystallization temperature, the atomic vibration becomes vigorous enough to force atoms change their positions into lattice sites, causing crystallization. This crystallization process occurs more readily in bulk amorphous alloys with low crystallization temperatures. This is because, from the thermodynamics viewpoint, amorphous alloys with low crystallization temperatures can be regarded as having less stable microstructures. Therefore, application of mechanical energy in the form of deformation can also promote crystallization in a manner similar to thermally induced nanocrystallization. That is, deformation-induced phase transformation from an amorphous phase to a more stable crystalline phase may take place more readily in alloys with low crystallization temperatures. As such, the plasticity is considered to be inversely proportional to the magnitude of the onset crystallization temperature.
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The magnitude of the supercooled liquid region (Tx = Tx − Tg , where Tg is the glass transition temperature) has long been used as a parameter for judging the liquid stability of amorphous alloys. In general, bulk amorphous alloys with a large supercooled liquid region are known to have high liquid stability. This implies that alloys with a large supercooled liquid region can sustain liquid structures over a wide temperature range above the glass transition temperature. Therefore, in the as-cast condition, bulk amorphous alloys with a large supercooled liquid region have an amorphous structure close to that of a liquid, while those with a small supercooled liquid region tend to have an amorphous structure which closely resembles a crystalline one. Among these two amorphous structures, it is more likely for the former to have a larger initial free volume in the as-cast condition, in which case mechanically driven diffusion could take place more easily in this type of alloy due to its loosely packed structure, thereby promoting deformation-induced nanocrystallization. Therefore, the plasticity of an amorphous alloy is considered to be proportional to the magnitude of the supercooled liquid region. To summarize, |λ − 0.18|, Tx , and Tx are considered to be the three important parameters affecting the plasticity of bulk amorphous alloys. To examine whether these parameters have a linear relationship with the plasticity, plots of each factor versus the plasticity were made based on data obtained from the authors’ previous experiments on the Cu-based amorphous alloys [8] and are shown in Fig. 1. In general, the resultant plots showed that |λ − 0.18| and Tx exhibit reasonably good proportionality with the plastic strains as in Fig. 1(a and b), while Tx exhibits inverse proportionality with data scattering as in Fig. 1(c). However, the value of Tx /Tx , which reflects the mechanical stability1 as defined in a combined form of two thermal properties, i.e. Tx and Tx , exhibits a good proportionality as shown in Fig. 1(d). Thus, the suggested three parameters can be reduced into two parts, which reflect the atomic packing state (|λ − 0.18|) and mechanical stability characterized by the thermal properties (Tx /Tx ). Although these two parts show a reasonably good proportionality with the plastic strains, they also exhibit considerable data scatterings as shown in Fig. 1(a and d). These scatterings can be reduced by taking into consideration both parts simultaneously. For this reason, we formulate the plasticity criterion (p) for bulk amorphous alloys as defined by: p = |λ − 0.18|
Tx . Tx
(2)
1 Here, the concept of stability could be confusing because the mechanical stability is quite different from the thermal stability. In fact, bulk amorphous alloys with large Tx are known to be thermally stable, but this does not necessarily warrant their mechanical stability under the application of the mechanical force. As already discussed, it is more probable that alloys with large Tx have the open structures close to that of a liquid phase. That is, because those alloys possess structures close to the liquid phase, they could be mechanically less stable. This is because the local rearrangement of the constituent atoms can take place with ease due to structural openness when stress ‘greater than the yield strength’ is applied.
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Fig. 2. A plot showing the relationship between the p-parameter and the plasticity of bulk amorphous alloys. The data denoted by the dark solid circles were obtained in the current study, while the data denoted by the open symbols were obtained from the literature.
(or rearrangement) of the constituent atoms under local shear stress as discussed earlier. Therefore, the physics underlying the proposed criterion is that bulk amorphous alloys with larger pvalues are more loosely packed (i.e. larger |λ − 0.18|-value) and mechanically less stable as quantified by their thermal properties (i.e. larger Tx /Tx ) with the result that deformation can facilitate nanocrystallization, which in turn leads to enhanced plasticity. 2.2. Validation of the p-criterion
Fig. 1. Plots showing the relationship between the plasticity and various parameters measured from the Cu-based amorphous alloys reported in Ref. [8]. (a) |λ − 0.18|, (b) Tx , (c) Tx , and (d) Tx /Tx .
As can be seen from Eq. (2), the p-parameter is dependent on the factors related to the atomic packing state (|λ − 0.18|) and thermal characteristics (Tx /Tx ). Since these factors are intimately related to the structural openness, they can be used as a means for judging the facility of local atomic movement
The proposed plasticity criterion was tested for the Cu-based amorphous alloys. A total of 15 samples in the form of 1 mm in diameter and 2 mm long cylindrical cast rods were prepared and tested under uniaxial compression applied using a screwdriven type mechanical test machine at an initial strain rate of ∼10−4 s−1 . The corresponding p-values were calculated using the λ-values and the characteristic temperatures, as listed in Table 1, determined from the thermograms obtained using differential scanning calorimetry conducted at a heating rate of 40 ◦ C/min. As shown in Fig. 2, there exists a linear relationship between the p-value and the corresponding plastic strain in the Cu-based amorphous alloys. We also calculated the p-values for monolithic Cu [8,11,12], Co [13], Pd [14], Zr [8,15–22], Fe [23–25] Mg [26,27], and Ni-based [28,29] alloys, in order to evaluate the validity of the proposed criterion in other previously reported amorphous alloy systems in Table 1. Experimental conditions used to collected all data in Table 1 were similar, i.e. the strain rate of 0.5–1 × 10−4 s−1 and the heating rate of 30–40 ◦ C/min, which would minimize possible data scatterings, especially plastic strains [30], caused by the experimental conditions. Although these alloys were synthesized using different equipment and cast into different sizes, a linear relationship between the pvalues and the corresponding plasticity was still found to exist as can be seen from Fig. 2, indicating that the proposed criterion is valid for other amorphous alloy systems. However, as indicated by the arrows in Fig. 2, there are some alloys for
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Table 1 Various parameters measured from different families of amorphous alloys Base
Alloys
λ
Tx
Tx
εp
Ref.
Cu
Cu66 Zr34 Cu64 Zr36 Cu62 Zr38 Cu54 Zr46 Cu52 Zr48 Cu50 Zr50 Cu60 Zr30 Ti10 Cu60 Zr22 Ti18 Cu60 Zr20 Hf10 Ti10 Cu50 Zr41 Ti9 Cu54 Zr22 Ti18 Ni6 Cu43 Zr43 Al7 Be7 Cu43 Zr43 Al7 Ag7 Cu47.5 Zr47.5 Al5 Cu50 Zr43 Al7 Cu47 Ti33 Zr7 Nb4 Ni8 Si1 Cu47 Ti33 Zr11 Ni8 Si1 Cu50 Ni8 Zr17 Hf1 Ti22 Nb2
0.330 0.350 0.369 0.447 0.466 0.486 0.341 0.303 0.322 0.443 0.307 0.468 0.477 0.446 0.482 0.256 0.279 0.297
782 773 777 731 726 718 754 780 766 704 769 795 794 760 792 736 757 744
24 39 45 37 42 41 25 59 45 33 57 115 72 67 61 23 37 52
0.6 0.1 3.0 2.3 2.8 4.1 1.8 2.5 2.0 2.5 3.5 6.5 5.5 4.5 6.6 4.2 1.5 1.7
[8] [8] [8] [8] [8] [8] [8] [8] [8] [8] [8] [8] [8] [8] [8] [11] [11] [12]
Co43 Fe20 Ta5.5 B31.5
0.258
982
72
0
[13]
Pd
Pd40 Ni40 P20
0.211
670
81
2.3
[14]
Zr
Zr52 Cu48 Zr63 Al10 Ni10 Cu14 Nb3 Zr41.2 Ti13.8 Cu12.5 Ni10 Be22.5 Zr55 Al10 Cu30 Ni5 Zr57 Ti5 Cu20 Ni8 Al10 Zr59 Ta5 Cu18 Ni8 Al10 Zr49.7 Cu34.4 Al8.9 Be7 Zr60 Cu20 Pd10 Al10 Zr65 Al7.5 Ni10 Pd17.5
0.505 0.159 0.294 0.203 0.182 0.174 0.241 0.164 0.139
716 738 725 765 703 770 792 758 705
40 95 80 82 52 97 111 65 80
3 0.75 2 1 0.02 6.8 3 1.9 1.2
[8] [15] [16] [17] [18] [19] [20] [21] [22]
Fe
Fe65.5 Cr4 Mo4 Ga4 P12 C5 B5.5 Fe77 Ga3 P9.5 C4 B4 Si2.5 (Fe75 B15 Si10 )0.96 Nb4 Fe74 Nb6 Y3 B17
0.152 0.112 0.143 0.214
806 885 800 879
61 50 50 48
0.19 0.35 0.45 0
[23] [24] [24] [25]
Mg
Mg65 Cu7.5 Ni7.5 Zn5 Ag5 Y10 Mg65 Cu20 Ni5 Gd10 Mg65 Cu25 Gd10
0.149 0.155 0.153
463 480 483
41 61 67
0 0.15 0
[26] [27] [27]
Ni
Ni59 Zr20 Ti16 Si2 Sn3 Ni59 Zr20 Ti16 Si2 Sn3 Ni59 Zr16 Ti13 Si2 Sn3 Nb7
0.334 0.364 0.336
876 877 885
46 56 40
2.2 2 6.5
[28] [28] [29]
Co
εp is the plastic strain, which deviated from the linearity of the flow curves (usually ∼2%).
which the data points are scattered. A common feature of these alloys is that some of the alloying elements, such as Ta, Nb, Ag and Be, have either positive mixing enthalpies or large differences in the mixing enthalpy with their major constituent elements. It is generally accepted that amorphous alloys, which have positive mixing enthalpies among their constituent elements, contain atomic-scale chemical inhomogeneities and/or localized fluctuations in their free volume distribution [31]. Upon compression, these chemical and spatial disturbances act as the initiation site for shear band formation and, therefore, can promote the formation of multiple shear bands, leading to large plastic strains prior to fracture. Accordingly, the addition of alloying elements having a positive mixing enthalpy with the constituent atoms can provide a useful method of enhancing the
Fig. 3. The activation energy vs. plasticity relationship for various Cu-based amorphous alloys. The solid circles denote the mean plasticity, while the vertical lines indicate the total range of the measurements recorded during 7–40 tests per specimen.
plasticity of bulk amorphous alloys. However, in this study, the effect of the mixing enthalpy on the plasticity was not taken into consideration. As such, further studies are needed to determine the important role played by the positive mixing enthalpy on the plasticity. Experiments were extended to correlate the p-criterion with the plasticity associated with the deformation-induced nanocrystallization in the Cu-based amorphous alloys. Based on the fact that the crystallization rate depends on the activation energy for crystallization, the authors found that dynamic structural changes including nanocrystallization are promoted in bulk amorphous alloys with low activation energy for crystallization (or loosely packed structures) [8]. This is because, with the supply of mechanical energy, the atoms can change their position with ease in amorphous alloys with low activation energy. Therefore, excess free volume can be nucleated in many localized regions during the process of deformation. Several recent experimental works [31,32] confirmed that excess free volume indeed formed in alloys with enhanced plasticity during deformation, of which formation mechanisms are theoretically explored based on 3D molecular dynamics simulations [33]. The formation of excess free volume would further reduce the activation energy for crystallization. It was found that the activation energy for crystallization is a major parameter that influences the rate of the phase transformation from an amorphous to a crystalline phase [34]. This means that as the activation energy becomes lower, the corresponding transformation rate becomes faster, suggesting that the supply of the mechanical energy can promote the uniform precipitation of nanocrystallites. Under this condition, shear bands are initiated by the local coalescence of free volume or at the crystalline/amorphous interfaces, which in turn can lead to the formation of multiple shear bands. Simultaneously formed shear bands interact with each other and can disturb their further propagation, resulting in large plastic strains [16]. Therefore, the plasticity of amorphous alloys is related to the activation energy of the overall crystallization process as shown in Fig. 3 [8].
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the deformation imposed to the sample, and the activation energy for crystallization is low. Thus, the p-parameter can be used as a criterion which is worthwhile for designing monolithic bulk amorphous alloys with enhanced plasticity. However, in order to derive the more reliable plasticity criterion, the structural feature caused by a minor element with the positive mixing enthalpy is to be incorporated. Acknowledgement This research was supported by grants from the Basic Research Program (R01-2004-000-10891-0) of the Ministry of Science and Technology, Korea. References Fig. 4. A plot showing the relationship between the p-parameter and the activation energy for crystallization in bulk amorphous alloys.
It should be noted here that the activation energies for the overall crystallization were calculated using the non-isothermal Kissinger analysis by varying the heating rates, while Tx /Tx values were obtained at a constant heating rate. Despite the changes in the heating rate, the activation energy calculated based on the non-isothermal Kissinger analysis is nearly independent of the heating rate [35]. In the meantime when calculating the p-value, the values of Tx and Tx increases with increasing heating rate. However, their ratio, i.e. Tx /Tx was observed to be nearly the same regardless of the heating rate. Therefore, both the activation energy and the p-value are independent of the heating rate, providing the basis of using these parameters as the plasticity criterion. The facility of crystallization can also be evaluated from the microstructural viewpoint. Alloys with a loosely packed structure inherently contain many free volumes. Therefore, under uniaxial compression, the atoms can change their position easily, which may result in deformation-induced nanocrystallization. As a result, it can be regarded that amorphous alloys with low activation energies for crystallization correspond to those with loosely packed structure or large p-values. Indeed, as shown in Fig. 4, there exists a reasonably good inverse proportionality between the p-value and the activation energy for crystallization. Therefore, as with other widely accepted parameters such as G/B ratio [36] and v-value [37] used to predict the plasticity, the p-parameter and the activation energy for crystallization can be used as a reliable criterion that enables the plasticity to be predicted, as well as facilitating the design of bulk amorphous alloys with enhanced plasticity. 3. Conclusion We proposed a plasticity criterion, |λ − 0.18|Tx /Tx to correlate with the plasticity of bulk amorphous alloys in Cu-, Fe-, Zr-, Mg-, Co-, Ni-, and Pd-based systems. The results show that bulk amorphous alloys with large p-values exhibit large plasticity. It is because large p-values indicate that bulk amorphous alloys have loosely packed structures, of which evolution is susceptible to
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