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Deformation-induced nanocrystallization and its influence on work hardening in a bulk amorphous matrix composite
Acta Materialia 52 (2004) 1525–1533 www.actamat-journals.com
Deformation-induced nanocrystallization and its influence on work hardening in a bulk amorphous matrix composite Jae-Chul Lee
b
a,*
, Yu-Chan Kim b, Jae-Pyoung Ahn b, Hyoung-Seop Kim c, Sung-Hak Lee d, Byeong-Joo Lee d
a Division of Materials Science and Engineering, Korea University, Seoul 136-701, South Korea Advanced Metals Research Center, Korea Institute of Science and Technology (KIST), P.O. Box 131, Cheongryang, Seoul 130-650, South Korea c Department of Metallurgical Engineering, Chungnam National University, Daejeon 305-764, South Korea d Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang 790-784, South Korea
Received 6 October 2003; received in revised form 28 October 2003; accepted 28 November 2003
Abstract With the development of various processes to produce bulk amorphous composites with enhanced plasticity, investigations of the mechanical behaviors of the amorphous alloys in the plastic regime have now become feasible. In addition to dramatically enhanced plasticity, some bulk amorphous composites have exhibited a work hardening behavior during plastic deformation. Considering that most strengthening mechanisms, such as solid solution hardening, martensitic hardening, etc., operative in crystalline metals are associated with dislocations, the work hardening behavior observed from amorphous composites, where dislocations do not exist, is of a special scientific interest. We have observed that quasistatic compression imposed to the amorphous composite induces the homogeneous precipitation of nanocrystallites from the amorphous matrix of the composite, which, in turn, leads to strengthening the amorphous composite. The strengthening mechanism of the amorphous matrix composite is investigated as well. Ó 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Deformation-induced crystallites; Amorphous composite; Shear bands; Phase mixture hardening model
1. Introduction Extensive researches have been carried out to develop various bulk amorphous materials due to their superior mechanical properties suitable for structural applications. The mechanical properties of the amorphous materials can further be improved by promoting the homogeneous precipitation of nanocrystallites within the amorphous matrix. Since amorphous alloys are not in thermodynamic equilibrium, phase transformation from the amorphous to the more stable crystalline phase can take place with the supply of external energy. Temperature and de-
*
Corresponding author. Tel.: +82-2-3290-3283; fax: +82-2-928-3584. E-mail address: [email protected] (J.-C. Lee).
formation (or stress) are the two most significant categories of driving forces affecting this transformation. Thermal annealing has been typically used to produce thermally induced nanocrystallites that are homogeneously distributed in the amorphous matrix [1,2]. Mechanical deformation can also lead to the formation of nanocrystallites from amorphous phases; bending of the Al-based amorphous ribbons at room temperature induces the formation of Al nanocrystallites near shear bands [3–5]. Nanoindentations on the Zr-based amorphous alloy confirmed the formation of nanocrystallites beneath the indents [6]. Ball milling of some Al-based amorphous ribbons has been found to induce nanocrystallites [7]. However, the mechanism for the formation of Ôdeformation-induced nanocrystallitesÕ is not yet understood; it is not clear whether the deformation energy directly results in the formation of nanocrystallites or is first converted into thermal energy, which,
1359-6454/$30.00 Ó 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2003.11.034
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in turn, results in nanocrystallites formation. Bruck et al. [8] argued that the temperature rise during mechanical deformation plays a significant role for nanocrystallization. Meanwhile, several studies have confirmed that nanocrystallization in the amorphous alloys could take place without any heating effect [5,6,9]. Jiang et al. [5], based on the TEM observations of nanocrystallites formed in the vicinity of the deformed regions, claimed that stress-enhanced diffusion during dynamic loading plays a potential role for nanocrystallites formation. Since mechanical deformation strongly induces nanocrystallite formation, and thermal energy induces a uniformly distributed nanocrystallite formation, the simultaneous application of both mechanical deformation and thermal energy causes an abundant and homogeneous formation of nanocrystallites. Kim et al. [10] have observed the homogeneous precipitation of nanocrystallites from the fractured Zr-based amorphous alloy tested under tension at elevated temperatures. Deformation-induced crystallization at elevated temperature was also observed to take place in a Cu-based amorphous alloy during deforming in the supercooled liquid region [11]. Unlike the uniformly precipitated nanocrystallites induced by thermal annealing, the deformation-induced nanocrystallites observed from the earlier studies were viewed only from a very localized area, such as regions near shear bands of the bent specimens or beneath the indent of the indented specimens. Such features are thought to be due to the loading methods and loading time employed in the studies. Under these experimental conditions, higher stress (or deformation) will concentrate only at regions near the propagating shear bands or beneath the indents with a duration of at most 10 s. As a result, atoms located at regions away from the bands or the indents, where the stress level is not as high, do not have chances to be supplied with sufficient energy enough to transform into more stable phases. If loading is quasistatic to allow more time for atoms to be rearranged, homogeneous precipitation of nanocrystallites may take place in amorphous alloys even at room temperature. Therefore, it is of interest to examine whether a homogeneous precipitation of nanocrystallites occurs under quasistatic loading at room temperature and to study its effect on the mechanical properties of the amorphous alloy. To our knowledge, no information is currently available on the formation of nanocrystallites during quasistatic deformation at room temperature. Understanding of the formation mechanism of nanocrystallites in the amorphous alloy subjected to quasistatic deformation is important not only to better design amorphous alloys, but also to develop various post-treatment processes suitable for improving the mechanical properties of amorphous alloys.
2. Experimental procedures The chemical composition of the bulk amorphous composite used in this study was (Cu60 Zr30 Ti10 )0:95 Ta5 (in atomic percent). The alloy was prepared by arc melting the high purity Ti (99.9%), Cu (99.9%), Zr (99.9%), and Ta (99.9%) under a purified argon atmosphere; Master alloy ingots for casting were prepared by first melting Zr and Ta together. This binary alloy was then melted with Cu, Zr, and Ti. The ingot was remelted several times to ensure microstructural homogeneity and then cast into a copper mold to produce a 40-mm long cylindrical rod with a diameter of 1 mm. To compare the thermal properties of the (Cu60 Zr30 Ti10 )0:95 Ta5 composite with the Cu60 Zr30 Ti10 alloy, the Cu60 Zr30 Ti10 alloy ribbons were prepared by ejecting the melt through a nozzle with an over-pressure of 50 kPa onto a Cu wheel rotating with a tangential speed of 40 m/s. Samples for compression tests were cut from the cast rod. Room temperature uniaxial compression tests were conducted on 2-mm long sections under a strain rate of 104 /s. The thermal properties of the monolithic amorphous alloy and the amorphous matrix composite were examined using differential scanning calorimetry (DSC) at a constant heating rate of 10 K/min in a flowing argon atmosphere. Variations in the hardness of the phases within the composite were measured as a function of the plastic strain using an ultra-micro-Vickers hardness tester under a 10 g load. At least three measurements were made along the specimenÕs long axis at positions evenly spaced by 90 lm. The structures of the specimens were analyzed by X-ray diffraction (XRD) with Cu Ka radiation. Samples for transmission electron microcopy (TEM) were perforated by chemical jet thinning using a solution of 10% perchlolic acid in ethanol at a temperature )40 °C. The chemical reaction product covering the disc was removed by subsequent ion milling for about 1–2 min. 1 Detailed structures were examined with high-resolution transmission electron microscopy (HRTEM) coupled with electron energy loss spectroscopy (EELS).
1 Nanocrystallites were observed to form in the Cu60 Zr30 Ti10 amorphous alloy when specimens are prepared by ion milling. Therefore, chemical jet thinning is preferred to avoid crystallization. Subsequent ion milling is normally adopted to remove the chemical reaction product formed at the surface of the chemically perforated disc. However, during the subsequent ion milling, nanocrystallization may take place. Therefore, special caution has to be made to prevent nanocrystallization during ion milling. To our experience, the chemically thinned specimen has to be cleaned by ion milling (argon ions, 6 kV, h ¼ 11:5° within less than 1–2 min. Beyond 3 min, Cu begins to segregate to form Cu-rich nanocrystallites. After 6–7 min, the microstructure became almost identical to that shown in Fig. 6(a).
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Fig. 1. (a) SEM micrograph of the (Cu60 Zr30 Ti10 )95 Ta5 composite, showing the presence of the Ta-rich particles (white) in the amorphous matrix (black), (b) TEM bright field image and SADP of the matrix, showing the matrix being an amorphous state and (c) TEM bright field image and SADP of the Ta-rich phase, showing the Ta-rich phase being a crystalline phase with bcc structure.
3. Results 3.1. Mechanical properties Fig. 1(a) is the microstructure of the as-cast (Cu60 Zr30 Ti10 )0:95 Ta5 amorphous matrix composite (hereinafter composite), showing the composite structure consisting of uniformly dispersed crystalline particles (white phase) in the amorphous matrix (dark area). Fig. 1(b) is the TEM bright field image and the corresponding selected area diffraction pattern (SADP) recorded from the matrix of the composite, showing the typical characteristics of an amorphous phase. Fig. 1(c) is the bright field image and corresponding SADP recorded from the crystalline particle. Although exact chemical composition of the crystalline particles is not known, based on XRD and SADP of TEM, they were identified as a bcc phase with a lattice constant of 3.25 Considering that the lattice constant of Ta being A. the particles are thought to be a Ta-rich solid 3.3206 A, solution containing Ti and Zr. According to the image analysis, the average size and the volume fraction of these particles are 10 lm and 8.0%, respectively. Fig. 2 shows the DSC traces obtained from the meltspun Cu60 Zr30 Ti10 specimen and the injection-cast (Cu60 Zr30 Ti10 )0:95 Ta5 composite specimen. The DSC
trace obtained from the melt spun Cu60 Zr30 Ti10 specimen exhibits one endothermic event, i.e., characteristics of the glass transition to a supercooled liquid state, followed by a couple of exothermic reactions associated with consecutive crystallization of the supercooled liquid. The glass transition and the crystallization temperature were 456 and 478 °C, respectively. It is noted that the glass transition and the crystallization onset temperature for the (Cu60 Zr30 Ti10 )0:95 Ta5 composite
Fig. 2. The DSC trace obtained from the as-cast (Cu60 Zr30 Ti10 )95 Ta5 composite sample with a diameter of 1 mm superposed with that of the melt-spun Cu60 Zr30 Ti10 alloy.
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Table 1 Various thermal properties obtained from DSC traces corresponding to the melt-spun Cu60 Zr30 Ti10 specimen and the injection-cast (Cu60 Zr30 Ti10 )0:95 Ta5 composite specimen Composition
Synthesis methods
Tg (°C)
Tx1 (°C), DH1 (J/g)
Tx2 (°C), DH2 (J/g)
Tx3 (°C), DH3 (J/g)
Cu60 Zr30 Ti10 (Cu60 Zr30 Ti10 )0:95 Ta5
Melt spinning Injection casting
456 460
478, )31.2 482, )28.2
532, )29.8 539, )24.5
628, )2.8 636, )3.1
were almost identical to those of the melt-spun Cu60 Zr30 Ti10 specimen within the measurement accuracy. However, the amount of the exothermic heat for the first crystallization peak decreased from 31.2 to 28.2 J/g. Less heat measured from the composite is considered to be due to the presence of the Ta-rich particles, which, upon heating, do not involve in crystallization. Therefore, it is regarded that the chemical composition of the matrix of the (Cu60 Zr30 Ti10 )0:95 Ta5 composite is nearly the same as that of the Cu60 Zr30 Ti10 alloy. Various thermal properties corresponding to the meltspun Cu60 Zr30 Ti10 specimen and the injection-cast (Cu60 Zr30 Ti10 )0:95 Ta5 composite specimen are summarized in Table 1. Fig. 3 is the engineering stress–strain curves corresponding to the Cu60 Zr30 Ti10 alloy and the (Cu60 Zr30 Ti10 )0:95 Ta5 composite measured under quasistatic (104 /s) compression. In each case, the samples were tested to failure. The two materials exhibited elasticity up to the strain of 2%, followed by plastic deformation. The Cu60 Zr30 Ti10 alloy exhibits yielding with the ultimate strength of 2106 MPa and a mean fracture strain of 3.5%, while the (Cu60 Zr30 Ti10 )0:95 Ta5 composite demonstrates the ultimate strength of 2332 MPa with a dramatically enhanced fracture strain of 15.3%. The yield strength (1930 MPa) of the (Cu60 Zr30 Ti10 )0:95 Ta5 composite is slightly lower than that (1983 MPa) of the monolithic Cu60 Zr30 Ti10 amorphous alloy due to the presence of the ductile crystalline Ta-rich phase. However, the (Cu60 Zr30
Ti10 )0:95 Ta5 composite showed work hardening associated with the enhanced plasticity, resulting in the higher fracture strength. It is well known that bulk amorphous metals fail by the formation of shear bands upon loading. Considering that the plastic deformation achieved by bulk amorphous metals is virtually confined at narrow regions near shear bands, the two specimens considered in this study should differ both in the number density and the shape of shear bands. Presented in Fig. 4 are the SEM micrographs recorded from the side surfaces of the fractured Cu60 Zr30 Ti10 and (Cu60 Zr30 Ti10 )0:95 Ta5 specimens, showing completely different patterns of shear bands. Observation of the monolithic Cu60 Zr30 Ti10 sample showed that only a few long and clean-cut shear bands were developed, while a number of shear bands have formed over the entire length of the (Cu60 Zr30 Ti10 )0:95 Ta5 composite sample. In addition, as compared to long and clan-cut shear bands observed from the
Fig. 3. Uniaxial compressive stress–strain curves measured form the Cu60 Zr30 Ti10 monolithic amorphous alloy and the (Cu60 Zr30 Ti10 )95 Ta5 composite. Significantly enhanced plasticity and the work hardening behavior were noted in the composite.
Fig. 4. SEM micrographs showing differences in the shear band formation in terms of the number density, length, and general shape observed from (a) the Cu60 Zr30 Ti10 monolithic amorphous alloy and (b) the (Cu60 Zr30 Ti10 )95 Ta5 composite.
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Cu60 Zr30 Ti10 amorphous alloy, shear bands observed from the composite sample are characterized as short and winding. The major shear bands are oriented at an approximately angle of 48° with respect to compression, which is similar to the direction of the maximum shear stress, i.e., 45°. Although the enhanced plasticity observed from the composite allows us to explore the mechanical behaviors in the plastic regime, detailed mechanisms for the enhanced plasticity will not be treated further in this study and only the strengthening mechanism of the amorphous composite will be discussed. With this regard, it is still questionable if the plastic flow in Fig. 3 is accompanied by the work hardening. This questionnaire arises because calculations to construct the stress–strain curves in Fig. 3 neither compensated changes in the specimenÕs cross-sectional area associated with the formation of shear steps and cracks, nor took the instantaneous changes of the specimenÕs cross-section during testing into account. As such, one may consider that the increasing tendency in the stress in Fig. 3 could contain a certain degree of unintended artifact caused by the measurement technique. To confirm the work hardening behavior in Fig. 3, a tapered-cylindrical rod for the compression test was machined such that the crosssectional area of one end of the rod is smaller than the other as shown by the inset of Fig. 5. Such a geometry of the test specimen facilitates plastic deformation in a progressive and controlled manner upon compression, enabling introduction of different amount of strains into the specimen. Prior to compression, the side surface of the specimen was polished to mirror image so that micro-indentation can be made directly on the matrix and the Ta-rich particle at evenly spaced positions along the specimenÕs long axis. Fig. 5 shows the variations in the hardness of the matrix and the Ta-rich particle measured as a function of the strain subjected to the composite specimen. The
Fig. 5. Microhardness of the amorphous matrix and the Ta-rich phase measured as a function of the plastic strain subjected to the (Cu60 Zr30 Ti10 )95 Ta5 composite.
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hardness of the amorphous matrix was observed to increase linearly with increasing strain, while the hardness of the Ta-rich particle did not vary. This experimental result obtained from micro-indentation again confirmed the work hardening behavior observed from the quasistatic compression test. Work hardening behaviors similar to that observed from the present study can also be found from the other amorphous composites [12–15]. Work hardening is thought to take place in some monolithic amorphous alloys [16].
3.2. Microstructures In general, work hardening observed from the crystalline metals is associated with dislocations. Considering that dislocations neither exist, nor are mobile within the amorphous materials, the work hardening behavior shown by the (Cu60 Zr30 Ti10 )0:95 Ta5 composite is quite unique and unusual. Since the hardness of the Ta-rich particles did not vary significantly even after compression, actual strengthening of 400 MPa associated with the plastic deformation of the composite in Fig. 3 cannot be explained based on the strengthening of the Ta-rich particles. This initiated us to probe detailed microstructural changes in the matrix of the deformed composite. Fig. 6(a) is the TEM bright field image recorded from the matrix of the deformed composite, showing the presence of gray spots with an average size of 10 nm embedded in the amorphous matrix. The diffraction ring in the SADP pattern in Fig. 6(a) confirms that the image contrast is resulted by the presence of nanocrystallites. The HRTEM image of the gray spots shows lattice fringes as in Fig. 6(b), further validating the crystalline state of the gray spots. Careful observations of the nanocrystallites confirmed that the nanocrystallites are free from dislocations. Therefore, they can be regarded as a perfect crystal having a theoretical strength. Details regarding the effect of the nanocrystallites on the strength of the composite are discussed in proceeding section. Quantitative analyses on the chemical composition of the nanocrystallites and the remaining amorphous matrix were made using EELS. As can be seen from the jump ratio image in Fig. 7, Cu enrichment was noted from the nanocrystallites, while Cu depletion was observed from the amorphous matrix. Although the measured chemical composition does not represent the exact composition of the nanocrystallites and the remaining amorphous matrix, the average Cu content of the nanocrystallites is approximately 75%, while that in the amorphous matrix is approximately 50%. Such a result is in a relatively good agreement with that obtained by Jiang et al. [17]. However, considering the size of the nanocrystallites being smaller than the thickness of the
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Fig. 6. (a) TEM bright field image and the corresponding SADP recorded from the deformed composite, showing the presence of nanocrystallites with an average size of 10 nm embedded in the amorphous matrix, (b) HRTEM image of (a) showing the presence of the lattice fringe.
the strength of the amorphous composite is discussed in Section 4. Judging from the diffraction ring of the SADP as indicated by the arrow in Fig. 6(a), the degree of crystallinity of the deformed composite appears to be considerable. However, it is very difficult to determine the true volume fraction of the nanocrystallites directly from the TEM images, since nanocrystallites observed from TEM are viewed in superposition. On the other hand, DSC has been widely employed to estimate the volume fraction of a crystalline phase; assuming that the amount of the heat flow associated with crystallization is inversely proportional to the volume fraction of a crystalline phase in an amorphous matrix, the volume fractions of the crystalline phase can be estimated by comparing the amount of the heat flow obtained from the deformed composite with that of the as-cast composite. Shown in Fig. 8 are the DSC curves recorded from the as-cast and the deformed composite specimen, showing dissimilar thermal behaviors. When comparing the DSC trace recorded from the deformed composite specimen with that of the as-cast one, less heat associated with the first crystallization as well as the disappearance of the glass transition temperature were noted from the deformed composite specimen. These features obtained from the deformed composite provide direct evidence that homogeneous precipitation of nanocrystallites has taken place to some extent during quasistatic compression. According to the measurement of the exothermic heat corresponding to the first crystallization recorded from the two specimens, it was noticed that the amount of the heat associated with the crystallization in the deformed composite is 10% smaller than that of the as-cast composite, indicating that the crystallization has proceeded by 10 vol% during quasistatic compression.
Fig. 7. Jump ratio image obtained by EELS, showing Cu enrichment noted from the nanocrystallites.
TEM specimen, it is possible that the actual Cu contents in the nanocrystallites could be even higher than the measured value. The effect of the solvent enrichment on
Fig. 8. DSC curves obtained from the as-cast and the deformed specimen.
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4. Discussion The effect of the deformation-induced nanocrystallization on the work hardening behavior was studied based on the experimental observations. The strengthening mechanism was theoretically investigated using the phase mixture model. 4.1. Transformation-based strengthening The deformation-induced phase transformations have been known to take place in various materials such as ceramics, polymers, and metals, which have different bonding structures. In some cases, these phase transformations have been successfully applied to commercialization. Crystallization of some commonly used polymers during shaping has long been known as the result of the deformation subjected to the workpiece [18]. Toughened ZrO2 probably is one of the best examples, which utilize deformation-induced phase transformation for toughening the ceramics; under tensile loading, the phase transformation from the tetragonal to the monoclinic phase takes place [19]. This phase transformation is accompanied with the volume expansion, which, in turn, impedes the crack propagation by closing the crack tip. Strengthening of the TRIP steel is another example utilizing the phase transformation (from the austenite to the martensite phase) during tensile loading [20]. However, the strengthening mechanism of the TRIP steel still lies in the conventional dislocation-based model, which cannot be applicable for predicting the strength of the amorphous composite. Therefore, construction of an appropriate model explaining the work hardening behavior observed from the amorphous metal, where dislocations do not exist, is of an academic interest. In general, the hardness of nanocrystallites is higher than that of amorphous phases. This is because the size of the nanocrystallites is so small that both dislocations and other types of defects can neither form, nor be active within the nanocrystallites. Therefore, they can be regarded as a perfect crystal having a theoretical shear strength of s G=2pp[21], ffiffiffi where G is the shear modulus. Assuming that r 3s and the shear modulus of Cu ranges from 37 to 45 GPa depending on microstructures. 2 the normal strength of the Cu-rich nanocrystallites is expected to be 10–12 GPa. Considering that the normal strength of the Cu-based amorphous alloys is 2 GPa, nanocrystallites can serve as a reinforcing phase. In addition, in contrast to the localized distri-
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bution of the nanocrystallites generated under dynamic loading, the nanocrystallites precipitated due to quasistatic compression were observed to disperse uniformly throughout the amorphous matrix. Such observations can explain the work hardening behavior of the amorphous composite. 4.2. Phase mechanism
mixture
model
for
the
strengthening
In order to analyze the strengthening behavior of amorphous composites during deformation, the phase mixture model [22–25] was considered. The phase mixture model has been successfully applied to quantitatively describe not only the strengthening behavior but also the ductile–brittle transition behavior of various amorphous nanocomposites. In the phase mixture model of devitrified amorphous nanocomposites, key points in dealing with the phase mixture model are to consider the two strengthening mechanisms; composite particle hardening and matrix solution hardening. Fig. 9 shows a schematic diagram of the phase mixture model in the partially devitrified amorphous nanocomposites by precipitation in the amorphous matrix. Here, the Ta-rich particles are not shown because they do not contribute the hardening of the composites, as already seen in Fig. 5. As the deformation-induced nanocrystallization proceeds, solute elements rejected from the Cu-rich nanocrystallites are distributed in the remaining amorphous matrix, leading to a change in the solute concentration there (i.e., solute enrichment). It would not be necessary to consider dislocation motion especially in the case of amorphous and nanocrystalline materials, since there are hardly any dislocations. Therefore, the rule of mixtures, Eq. (1), based on the volume fraction of each phase is eligible to describe the effective strength of the mixture. Indeed, the rule of mixtures based on the volume fraction of each phase agrees well with the results of the finite element analysis of the unit cell model [25], since there is no
2
Measurements of the YoungÕs modulus and the shear modulus of Cu having different microstructures were carried out using the standard sonic resonance test method designated by ASTM C848-78.
Fig. 9. (a) Schematic model of particles embedded in amorphous matrix and (b) schematic solute concentration profile.
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special interaction between the particles and the matrix except the force and energy balances. The necessary parameters for the analysis are the mechanical strengths and the volume fraction of each phase. The rule of mixtures for the tensile strength, r, of the (Cu60 Zr30 Ti10 )0:95 Ta5 composite is represented by Eq. (1), r ¼ Vam ram þ VTa rTa þ VCu rCu ;
ð1Þ
where V is the volume fraction of each phase and the subscripts am, Ta, and Cu represent the amorphous matrix, Ta-rich particles, and the Cu-rich nanocrystallites, respectively. The phase mixture model can be used to predict the overall strength of the amorphous matrix composite. Assuming that the volume fraction and the strength of the Ta-rich particles being 9.2% and 600–700 MPa, the strength of the composite calculated from the phase mixture model was predicted as 2600 MPa. Considering that the predicted strength is the upper bound value, the prediction agrees reasonably well with the measured strength, 2332 MPa. Fig. 10 shows the schematic plot for the contributions of the strengthening of the residual amorphous matrix due to solute enrichment, Ta-rich particles, and Cu-rich nanocrystallites to the total strengthening of the (Cu60 Zr30 Ti10 )0:95 Ta5 composite. Since VTa and rTa are constant during the deformation as can be seen in microstructure and particle hardness measurement in Fig. 5, Ta-rich particles do not contribute to the strengthening of the amorphous composite. Although the hardness increase of the amorphous matrix alone by solute enrichment is high, as is usually found in the Albased and Zr-based amorphous alloys [24], its volume fraction decreases and the overall contribution by solute enrichment DðVam ram ) is not considered to be significant. Here, D means changes in values during crystallization. Since the defect-free nanocrystallites have higher strength (10 GPa) than the amorphous matrix (2 GPa), the Cu-rich nanocrystallites precipitated during deformation play a major contribution to the total strengthening. That is, the strengthening due to the deformation-induced nanocrystallites, Dr, is as follows:
Fig. 10. Schematic plot of the strength of (Cu60 Zr30 Ti10 )95 Ta5 as a function of the volume fraction of the Cu-rich nanocrystallite.
Dr ¼ DðVam ram Þ þ DðVTa rTa Þ þ DðVCu DrCu Þ DðVCu rCu Þ:
ð2Þ
Therefore, the amount of strengthening in the stress– strain curve (Fig. 3) is comparable to the hardness increase in the matrix containing the Cu-rich nanocrystallites (Fig. 5). The more detail numerical analysis is to be performed in the future.
5. Conclusion The present work confirmed that work hardening does indeed take place in a bulk amorphous composite during quasistatic compression. Unlike most strengthening mechanisms operative in polycrystalline materials, the work hardening observed from the amorphous alloy is due to the formation of homogeneously distributed nanocrystallites that have precipitated in the amorphous matrix of the amorphous composite imposed to quasistatic compression. Nanocrystallites precipitated in the matrix during quasistatic deformation were observed to be a Cu-rich perfect crystal, which is free from dislocations and, therefore, can serve as the reinforcement. The phase mixture model has been successfully applied to quantitatively describe the strengthening behavior and to predict the strength of the amorphous composite.
Acknowledgements The authors are grateful for the financial support from the Korea Institute of Science and Technology (KIST) and the Ministry of Science and Technology of Korea through the program for Nanostructured Materials Technology Development.
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Deformation-induced nanocrystallization and its influence on work hardening in a bulk amorphous matrix composite Jae-Chul Lee
b
a,*
, Yu-Chan Kim b, Jae-Pyoung Ahn b, Hyoung-Seop Kim c, Sung-Hak Lee d, Byeong-Joo Lee d
a Division of Materials Science and Engineering, Korea University, Seoul 136-701, South Korea Advanced Metals Research Center, Korea Institute of Science and Technology (KIST), P.O. Box 131, Cheongryang, Seoul 130-650, South Korea c Department of Metallurgical Engineering, Chungnam National University, Daejeon 305-764, South Korea d Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang 790-784, South Korea
Received 6 October 2003; received in revised form 28 October 2003; accepted 28 November 2003
Abstract With the development of various processes to produce bulk amorphous composites with enhanced plasticity, investigations of the mechanical behaviors of the amorphous alloys in the plastic regime have now become feasible. In addition to dramatically enhanced plasticity, some bulk amorphous composites have exhibited a work hardening behavior during plastic deformation. Considering that most strengthening mechanisms, such as solid solution hardening, martensitic hardening, etc., operative in crystalline metals are associated with dislocations, the work hardening behavior observed from amorphous composites, where dislocations do not exist, is of a special scientific interest. We have observed that quasistatic compression imposed to the amorphous composite induces the homogeneous precipitation of nanocrystallites from the amorphous matrix of the composite, which, in turn, leads to strengthening the amorphous composite. The strengthening mechanism of the amorphous matrix composite is investigated as well. Ó 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Deformation-induced crystallites; Amorphous composite; Shear bands; Phase mixture hardening model
1. Introduction Extensive researches have been carried out to develop various bulk amorphous materials due to their superior mechanical properties suitable for structural applications. The mechanical properties of the amorphous materials can further be improved by promoting the homogeneous precipitation of nanocrystallites within the amorphous matrix. Since amorphous alloys are not in thermodynamic equilibrium, phase transformation from the amorphous to the more stable crystalline phase can take place with the supply of external energy. Temperature and de-
*
Corresponding author. Tel.: +82-2-3290-3283; fax: +82-2-928-3584. E-mail address: [email protected] (J.-C. Lee).
formation (or stress) are the two most significant categories of driving forces affecting this transformation. Thermal annealing has been typically used to produce thermally induced nanocrystallites that are homogeneously distributed in the amorphous matrix [1,2]. Mechanical deformation can also lead to the formation of nanocrystallites from amorphous phases; bending of the Al-based amorphous ribbons at room temperature induces the formation of Al nanocrystallites near shear bands [3–5]. Nanoindentations on the Zr-based amorphous alloy confirmed the formation of nanocrystallites beneath the indents [6]. Ball milling of some Al-based amorphous ribbons has been found to induce nanocrystallites [7]. However, the mechanism for the formation of Ôdeformation-induced nanocrystallitesÕ is not yet understood; it is not clear whether the deformation energy directly results in the formation of nanocrystallites or is first converted into thermal energy, which,
1359-6454/$30.00 Ó 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2003.11.034
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in turn, results in nanocrystallites formation. Bruck et al. [8] argued that the temperature rise during mechanical deformation plays a significant role for nanocrystallization. Meanwhile, several studies have confirmed that nanocrystallization in the amorphous alloys could take place without any heating effect [5,6,9]. Jiang et al. [5], based on the TEM observations of nanocrystallites formed in the vicinity of the deformed regions, claimed that stress-enhanced diffusion during dynamic loading plays a potential role for nanocrystallites formation. Since mechanical deformation strongly induces nanocrystallite formation, and thermal energy induces a uniformly distributed nanocrystallite formation, the simultaneous application of both mechanical deformation and thermal energy causes an abundant and homogeneous formation of nanocrystallites. Kim et al. [10] have observed the homogeneous precipitation of nanocrystallites from the fractured Zr-based amorphous alloy tested under tension at elevated temperatures. Deformation-induced crystallization at elevated temperature was also observed to take place in a Cu-based amorphous alloy during deforming in the supercooled liquid region [11]. Unlike the uniformly precipitated nanocrystallites induced by thermal annealing, the deformation-induced nanocrystallites observed from the earlier studies were viewed only from a very localized area, such as regions near shear bands of the bent specimens or beneath the indent of the indented specimens. Such features are thought to be due to the loading methods and loading time employed in the studies. Under these experimental conditions, higher stress (or deformation) will concentrate only at regions near the propagating shear bands or beneath the indents with a duration of at most 10 s. As a result, atoms located at regions away from the bands or the indents, where the stress level is not as high, do not have chances to be supplied with sufficient energy enough to transform into more stable phases. If loading is quasistatic to allow more time for atoms to be rearranged, homogeneous precipitation of nanocrystallites may take place in amorphous alloys even at room temperature. Therefore, it is of interest to examine whether a homogeneous precipitation of nanocrystallites occurs under quasistatic loading at room temperature and to study its effect on the mechanical properties of the amorphous alloy. To our knowledge, no information is currently available on the formation of nanocrystallites during quasistatic deformation at room temperature. Understanding of the formation mechanism of nanocrystallites in the amorphous alloy subjected to quasistatic deformation is important not only to better design amorphous alloys, but also to develop various post-treatment processes suitable for improving the mechanical properties of amorphous alloys.
2. Experimental procedures The chemical composition of the bulk amorphous composite used in this study was (Cu60 Zr30 Ti10 )0:95 Ta5 (in atomic percent). The alloy was prepared by arc melting the high purity Ti (99.9%), Cu (99.9%), Zr (99.9%), and Ta (99.9%) under a purified argon atmosphere; Master alloy ingots for casting were prepared by first melting Zr and Ta together. This binary alloy was then melted with Cu, Zr, and Ti. The ingot was remelted several times to ensure microstructural homogeneity and then cast into a copper mold to produce a 40-mm long cylindrical rod with a diameter of 1 mm. To compare the thermal properties of the (Cu60 Zr30 Ti10 )0:95 Ta5 composite with the Cu60 Zr30 Ti10 alloy, the Cu60 Zr30 Ti10 alloy ribbons were prepared by ejecting the melt through a nozzle with an over-pressure of 50 kPa onto a Cu wheel rotating with a tangential speed of 40 m/s. Samples for compression tests were cut from the cast rod. Room temperature uniaxial compression tests were conducted on 2-mm long sections under a strain rate of 104 /s. The thermal properties of the monolithic amorphous alloy and the amorphous matrix composite were examined using differential scanning calorimetry (DSC) at a constant heating rate of 10 K/min in a flowing argon atmosphere. Variations in the hardness of the phases within the composite were measured as a function of the plastic strain using an ultra-micro-Vickers hardness tester under a 10 g load. At least three measurements were made along the specimenÕs long axis at positions evenly spaced by 90 lm. The structures of the specimens were analyzed by X-ray diffraction (XRD) with Cu Ka radiation. Samples for transmission electron microcopy (TEM) were perforated by chemical jet thinning using a solution of 10% perchlolic acid in ethanol at a temperature )40 °C. The chemical reaction product covering the disc was removed by subsequent ion milling for about 1–2 min. 1 Detailed structures were examined with high-resolution transmission electron microscopy (HRTEM) coupled with electron energy loss spectroscopy (EELS).
1 Nanocrystallites were observed to form in the Cu60 Zr30 Ti10 amorphous alloy when specimens are prepared by ion milling. Therefore, chemical jet thinning is preferred to avoid crystallization. Subsequent ion milling is normally adopted to remove the chemical reaction product formed at the surface of the chemically perforated disc. However, during the subsequent ion milling, nanocrystallization may take place. Therefore, special caution has to be made to prevent nanocrystallization during ion milling. To our experience, the chemically thinned specimen has to be cleaned by ion milling (argon ions, 6 kV, h ¼ 11:5° within less than 1–2 min. Beyond 3 min, Cu begins to segregate to form Cu-rich nanocrystallites. After 6–7 min, the microstructure became almost identical to that shown in Fig. 6(a).
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Fig. 1. (a) SEM micrograph of the (Cu60 Zr30 Ti10 )95 Ta5 composite, showing the presence of the Ta-rich particles (white) in the amorphous matrix (black), (b) TEM bright field image and SADP of the matrix, showing the matrix being an amorphous state and (c) TEM bright field image and SADP of the Ta-rich phase, showing the Ta-rich phase being a crystalline phase with bcc structure.
3. Results 3.1. Mechanical properties Fig. 1(a) is the microstructure of the as-cast (Cu60 Zr30 Ti10 )0:95 Ta5 amorphous matrix composite (hereinafter composite), showing the composite structure consisting of uniformly dispersed crystalline particles (white phase) in the amorphous matrix (dark area). Fig. 1(b) is the TEM bright field image and the corresponding selected area diffraction pattern (SADP) recorded from the matrix of the composite, showing the typical characteristics of an amorphous phase. Fig. 1(c) is the bright field image and corresponding SADP recorded from the crystalline particle. Although exact chemical composition of the crystalline particles is not known, based on XRD and SADP of TEM, they were identified as a bcc phase with a lattice constant of 3.25 Considering that the lattice constant of Ta being A. the particles are thought to be a Ta-rich solid 3.3206 A, solution containing Ti and Zr. According to the image analysis, the average size and the volume fraction of these particles are 10 lm and 8.0%, respectively. Fig. 2 shows the DSC traces obtained from the meltspun Cu60 Zr30 Ti10 specimen and the injection-cast (Cu60 Zr30 Ti10 )0:95 Ta5 composite specimen. The DSC
trace obtained from the melt spun Cu60 Zr30 Ti10 specimen exhibits one endothermic event, i.e., characteristics of the glass transition to a supercooled liquid state, followed by a couple of exothermic reactions associated with consecutive crystallization of the supercooled liquid. The glass transition and the crystallization temperature were 456 and 478 °C, respectively. It is noted that the glass transition and the crystallization onset temperature for the (Cu60 Zr30 Ti10 )0:95 Ta5 composite
Fig. 2. The DSC trace obtained from the as-cast (Cu60 Zr30 Ti10 )95 Ta5 composite sample with a diameter of 1 mm superposed with that of the melt-spun Cu60 Zr30 Ti10 alloy.
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Table 1 Various thermal properties obtained from DSC traces corresponding to the melt-spun Cu60 Zr30 Ti10 specimen and the injection-cast (Cu60 Zr30 Ti10 )0:95 Ta5 composite specimen Composition
Synthesis methods
Tg (°C)
Tx1 (°C), DH1 (J/g)
Tx2 (°C), DH2 (J/g)
Tx3 (°C), DH3 (J/g)
Cu60 Zr30 Ti10 (Cu60 Zr30 Ti10 )0:95 Ta5
Melt spinning Injection casting
456 460
478, )31.2 482, )28.2
532, )29.8 539, )24.5
628, )2.8 636, )3.1
were almost identical to those of the melt-spun Cu60 Zr30 Ti10 specimen within the measurement accuracy. However, the amount of the exothermic heat for the first crystallization peak decreased from 31.2 to 28.2 J/g. Less heat measured from the composite is considered to be due to the presence of the Ta-rich particles, which, upon heating, do not involve in crystallization. Therefore, it is regarded that the chemical composition of the matrix of the (Cu60 Zr30 Ti10 )0:95 Ta5 composite is nearly the same as that of the Cu60 Zr30 Ti10 alloy. Various thermal properties corresponding to the meltspun Cu60 Zr30 Ti10 specimen and the injection-cast (Cu60 Zr30 Ti10 )0:95 Ta5 composite specimen are summarized in Table 1. Fig. 3 is the engineering stress–strain curves corresponding to the Cu60 Zr30 Ti10 alloy and the (Cu60 Zr30 Ti10 )0:95 Ta5 composite measured under quasistatic (104 /s) compression. In each case, the samples were tested to failure. The two materials exhibited elasticity up to the strain of 2%, followed by plastic deformation. The Cu60 Zr30 Ti10 alloy exhibits yielding with the ultimate strength of 2106 MPa and a mean fracture strain of 3.5%, while the (Cu60 Zr30 Ti10 )0:95 Ta5 composite demonstrates the ultimate strength of 2332 MPa with a dramatically enhanced fracture strain of 15.3%. The yield strength (1930 MPa) of the (Cu60 Zr30 Ti10 )0:95 Ta5 composite is slightly lower than that (1983 MPa) of the monolithic Cu60 Zr30 Ti10 amorphous alloy due to the presence of the ductile crystalline Ta-rich phase. However, the (Cu60 Zr30
Ti10 )0:95 Ta5 composite showed work hardening associated with the enhanced plasticity, resulting in the higher fracture strength. It is well known that bulk amorphous metals fail by the formation of shear bands upon loading. Considering that the plastic deformation achieved by bulk amorphous metals is virtually confined at narrow regions near shear bands, the two specimens considered in this study should differ both in the number density and the shape of shear bands. Presented in Fig. 4 are the SEM micrographs recorded from the side surfaces of the fractured Cu60 Zr30 Ti10 and (Cu60 Zr30 Ti10 )0:95 Ta5 specimens, showing completely different patterns of shear bands. Observation of the monolithic Cu60 Zr30 Ti10 sample showed that only a few long and clean-cut shear bands were developed, while a number of shear bands have formed over the entire length of the (Cu60 Zr30 Ti10 )0:95 Ta5 composite sample. In addition, as compared to long and clan-cut shear bands observed from the
Fig. 3. Uniaxial compressive stress–strain curves measured form the Cu60 Zr30 Ti10 monolithic amorphous alloy and the (Cu60 Zr30 Ti10 )95 Ta5 composite. Significantly enhanced plasticity and the work hardening behavior were noted in the composite.
Fig. 4. SEM micrographs showing differences in the shear band formation in terms of the number density, length, and general shape observed from (a) the Cu60 Zr30 Ti10 monolithic amorphous alloy and (b) the (Cu60 Zr30 Ti10 )95 Ta5 composite.
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Cu60 Zr30 Ti10 amorphous alloy, shear bands observed from the composite sample are characterized as short and winding. The major shear bands are oriented at an approximately angle of 48° with respect to compression, which is similar to the direction of the maximum shear stress, i.e., 45°. Although the enhanced plasticity observed from the composite allows us to explore the mechanical behaviors in the plastic regime, detailed mechanisms for the enhanced plasticity will not be treated further in this study and only the strengthening mechanism of the amorphous composite will be discussed. With this regard, it is still questionable if the plastic flow in Fig. 3 is accompanied by the work hardening. This questionnaire arises because calculations to construct the stress–strain curves in Fig. 3 neither compensated changes in the specimenÕs cross-sectional area associated with the formation of shear steps and cracks, nor took the instantaneous changes of the specimenÕs cross-section during testing into account. As such, one may consider that the increasing tendency in the stress in Fig. 3 could contain a certain degree of unintended artifact caused by the measurement technique. To confirm the work hardening behavior in Fig. 3, a tapered-cylindrical rod for the compression test was machined such that the crosssectional area of one end of the rod is smaller than the other as shown by the inset of Fig. 5. Such a geometry of the test specimen facilitates plastic deformation in a progressive and controlled manner upon compression, enabling introduction of different amount of strains into the specimen. Prior to compression, the side surface of the specimen was polished to mirror image so that micro-indentation can be made directly on the matrix and the Ta-rich particle at evenly spaced positions along the specimenÕs long axis. Fig. 5 shows the variations in the hardness of the matrix and the Ta-rich particle measured as a function of the strain subjected to the composite specimen. The
Fig. 5. Microhardness of the amorphous matrix and the Ta-rich phase measured as a function of the plastic strain subjected to the (Cu60 Zr30 Ti10 )95 Ta5 composite.
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hardness of the amorphous matrix was observed to increase linearly with increasing strain, while the hardness of the Ta-rich particle did not vary. This experimental result obtained from micro-indentation again confirmed the work hardening behavior observed from the quasistatic compression test. Work hardening behaviors similar to that observed from the present study can also be found from the other amorphous composites [12–15]. Work hardening is thought to take place in some monolithic amorphous alloys [16].
3.2. Microstructures In general, work hardening observed from the crystalline metals is associated with dislocations. Considering that dislocations neither exist, nor are mobile within the amorphous materials, the work hardening behavior shown by the (Cu60 Zr30 Ti10 )0:95 Ta5 composite is quite unique and unusual. Since the hardness of the Ta-rich particles did not vary significantly even after compression, actual strengthening of 400 MPa associated with the plastic deformation of the composite in Fig. 3 cannot be explained based on the strengthening of the Ta-rich particles. This initiated us to probe detailed microstructural changes in the matrix of the deformed composite. Fig. 6(a) is the TEM bright field image recorded from the matrix of the deformed composite, showing the presence of gray spots with an average size of 10 nm embedded in the amorphous matrix. The diffraction ring in the SADP pattern in Fig. 6(a) confirms that the image contrast is resulted by the presence of nanocrystallites. The HRTEM image of the gray spots shows lattice fringes as in Fig. 6(b), further validating the crystalline state of the gray spots. Careful observations of the nanocrystallites confirmed that the nanocrystallites are free from dislocations. Therefore, they can be regarded as a perfect crystal having a theoretical strength. Details regarding the effect of the nanocrystallites on the strength of the composite are discussed in proceeding section. Quantitative analyses on the chemical composition of the nanocrystallites and the remaining amorphous matrix were made using EELS. As can be seen from the jump ratio image in Fig. 7, Cu enrichment was noted from the nanocrystallites, while Cu depletion was observed from the amorphous matrix. Although the measured chemical composition does not represent the exact composition of the nanocrystallites and the remaining amorphous matrix, the average Cu content of the nanocrystallites is approximately 75%, while that in the amorphous matrix is approximately 50%. Such a result is in a relatively good agreement with that obtained by Jiang et al. [17]. However, considering the size of the nanocrystallites being smaller than the thickness of the
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Fig. 6. (a) TEM bright field image and the corresponding SADP recorded from the deformed composite, showing the presence of nanocrystallites with an average size of 10 nm embedded in the amorphous matrix, (b) HRTEM image of (a) showing the presence of the lattice fringe.
the strength of the amorphous composite is discussed in Section 4. Judging from the diffraction ring of the SADP as indicated by the arrow in Fig. 6(a), the degree of crystallinity of the deformed composite appears to be considerable. However, it is very difficult to determine the true volume fraction of the nanocrystallites directly from the TEM images, since nanocrystallites observed from TEM are viewed in superposition. On the other hand, DSC has been widely employed to estimate the volume fraction of a crystalline phase; assuming that the amount of the heat flow associated with crystallization is inversely proportional to the volume fraction of a crystalline phase in an amorphous matrix, the volume fractions of the crystalline phase can be estimated by comparing the amount of the heat flow obtained from the deformed composite with that of the as-cast composite. Shown in Fig. 8 are the DSC curves recorded from the as-cast and the deformed composite specimen, showing dissimilar thermal behaviors. When comparing the DSC trace recorded from the deformed composite specimen with that of the as-cast one, less heat associated with the first crystallization as well as the disappearance of the glass transition temperature were noted from the deformed composite specimen. These features obtained from the deformed composite provide direct evidence that homogeneous precipitation of nanocrystallites has taken place to some extent during quasistatic compression. According to the measurement of the exothermic heat corresponding to the first crystallization recorded from the two specimens, it was noticed that the amount of the heat associated with the crystallization in the deformed composite is 10% smaller than that of the as-cast composite, indicating that the crystallization has proceeded by 10 vol% during quasistatic compression.
Fig. 7. Jump ratio image obtained by EELS, showing Cu enrichment noted from the nanocrystallites.
TEM specimen, it is possible that the actual Cu contents in the nanocrystallites could be even higher than the measured value. The effect of the solvent enrichment on
Fig. 8. DSC curves obtained from the as-cast and the deformed specimen.
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4. Discussion The effect of the deformation-induced nanocrystallization on the work hardening behavior was studied based on the experimental observations. The strengthening mechanism was theoretically investigated using the phase mixture model. 4.1. Transformation-based strengthening The deformation-induced phase transformations have been known to take place in various materials such as ceramics, polymers, and metals, which have different bonding structures. In some cases, these phase transformations have been successfully applied to commercialization. Crystallization of some commonly used polymers during shaping has long been known as the result of the deformation subjected to the workpiece [18]. Toughened ZrO2 probably is one of the best examples, which utilize deformation-induced phase transformation for toughening the ceramics; under tensile loading, the phase transformation from the tetragonal to the monoclinic phase takes place [19]. This phase transformation is accompanied with the volume expansion, which, in turn, impedes the crack propagation by closing the crack tip. Strengthening of the TRIP steel is another example utilizing the phase transformation (from the austenite to the martensite phase) during tensile loading [20]. However, the strengthening mechanism of the TRIP steel still lies in the conventional dislocation-based model, which cannot be applicable for predicting the strength of the amorphous composite. Therefore, construction of an appropriate model explaining the work hardening behavior observed from the amorphous metal, where dislocations do not exist, is of an academic interest. In general, the hardness of nanocrystallites is higher than that of amorphous phases. This is because the size of the nanocrystallites is so small that both dislocations and other types of defects can neither form, nor be active within the nanocrystallites. Therefore, they can be regarded as a perfect crystal having a theoretical shear strength of s G=2pp[21], ffiffiffi where G is the shear modulus. Assuming that r 3s and the shear modulus of Cu ranges from 37 to 45 GPa depending on microstructures. 2 the normal strength of the Cu-rich nanocrystallites is expected to be 10–12 GPa. Considering that the normal strength of the Cu-based amorphous alloys is 2 GPa, nanocrystallites can serve as a reinforcing phase. In addition, in contrast to the localized distri-
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bution of the nanocrystallites generated under dynamic loading, the nanocrystallites precipitated due to quasistatic compression were observed to disperse uniformly throughout the amorphous matrix. Such observations can explain the work hardening behavior of the amorphous composite. 4.2. Phase mechanism
mixture
model
for
the
strengthening
In order to analyze the strengthening behavior of amorphous composites during deformation, the phase mixture model [22–25] was considered. The phase mixture model has been successfully applied to quantitatively describe not only the strengthening behavior but also the ductile–brittle transition behavior of various amorphous nanocomposites. In the phase mixture model of devitrified amorphous nanocomposites, key points in dealing with the phase mixture model are to consider the two strengthening mechanisms; composite particle hardening and matrix solution hardening. Fig. 9 shows a schematic diagram of the phase mixture model in the partially devitrified amorphous nanocomposites by precipitation in the amorphous matrix. Here, the Ta-rich particles are not shown because they do not contribute the hardening of the composites, as already seen in Fig. 5. As the deformation-induced nanocrystallization proceeds, solute elements rejected from the Cu-rich nanocrystallites are distributed in the remaining amorphous matrix, leading to a change in the solute concentration there (i.e., solute enrichment). It would not be necessary to consider dislocation motion especially in the case of amorphous and nanocrystalline materials, since there are hardly any dislocations. Therefore, the rule of mixtures, Eq. (1), based on the volume fraction of each phase is eligible to describe the effective strength of the mixture. Indeed, the rule of mixtures based on the volume fraction of each phase agrees well with the results of the finite element analysis of the unit cell model [25], since there is no
2
Measurements of the YoungÕs modulus and the shear modulus of Cu having different microstructures were carried out using the standard sonic resonance test method designated by ASTM C848-78.
Fig. 9. (a) Schematic model of particles embedded in amorphous matrix and (b) schematic solute concentration profile.
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special interaction between the particles and the matrix except the force and energy balances. The necessary parameters for the analysis are the mechanical strengths and the volume fraction of each phase. The rule of mixtures for the tensile strength, r, of the (Cu60 Zr30 Ti10 )0:95 Ta5 composite is represented by Eq. (1), r ¼ Vam ram þ VTa rTa þ VCu rCu ;
ð1Þ
where V is the volume fraction of each phase and the subscripts am, Ta, and Cu represent the amorphous matrix, Ta-rich particles, and the Cu-rich nanocrystallites, respectively. The phase mixture model can be used to predict the overall strength of the amorphous matrix composite. Assuming that the volume fraction and the strength of the Ta-rich particles being 9.2% and 600–700 MPa, the strength of the composite calculated from the phase mixture model was predicted as 2600 MPa. Considering that the predicted strength is the upper bound value, the prediction agrees reasonably well with the measured strength, 2332 MPa. Fig. 10 shows the schematic plot for the contributions of the strengthening of the residual amorphous matrix due to solute enrichment, Ta-rich particles, and Cu-rich nanocrystallites to the total strengthening of the (Cu60 Zr30 Ti10 )0:95 Ta5 composite. Since VTa and rTa are constant during the deformation as can be seen in microstructure and particle hardness measurement in Fig. 5, Ta-rich particles do not contribute to the strengthening of the amorphous composite. Although the hardness increase of the amorphous matrix alone by solute enrichment is high, as is usually found in the Albased and Zr-based amorphous alloys [24], its volume fraction decreases and the overall contribution by solute enrichment DðVam ram ) is not considered to be significant. Here, D means changes in values during crystallization. Since the defect-free nanocrystallites have higher strength (10 GPa) than the amorphous matrix (2 GPa), the Cu-rich nanocrystallites precipitated during deformation play a major contribution to the total strengthening. That is, the strengthening due to the deformation-induced nanocrystallites, Dr, is as follows:
Fig. 10. Schematic plot of the strength of (Cu60 Zr30 Ti10 )95 Ta5 as a function of the volume fraction of the Cu-rich nanocrystallite.
Dr ¼ DðVam ram Þ þ DðVTa rTa Þ þ DðVCu DrCu Þ DðVCu rCu Þ:
ð2Þ
Therefore, the amount of strengthening in the stress– strain curve (Fig. 3) is comparable to the hardness increase in the matrix containing the Cu-rich nanocrystallites (Fig. 5). The more detail numerical analysis is to be performed in the future.
5. Conclusion The present work confirmed that work hardening does indeed take place in a bulk amorphous composite during quasistatic compression. Unlike most strengthening mechanisms operative in polycrystalline materials, the work hardening observed from the amorphous alloy is due to the formation of homogeneously distributed nanocrystallites that have precipitated in the amorphous matrix of the amorphous composite imposed to quasistatic compression. Nanocrystallites precipitated in the matrix during quasistatic deformation were observed to be a Cu-rich perfect crystal, which is free from dislocations and, therefore, can serve as the reinforcement. The phase mixture model has been successfully applied to quantitatively describe the strengthening behavior and to predict the strength of the amorphous composite.
Acknowledgements The authors are grateful for the financial support from the Korea Institute of Science and Technology (KIST) and the Ministry of Science and Technology of Korea through the program for Nanostructured Materials Technology Development.
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