2011-Tensile Deformation Micro Mechanisms for Bulk Metallic Glass Matrix Composites

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Acta Materialia xxx (2011) xxxxxx www.elsevier.com/locate/actamat

Tensile deformation micromechanisms for bulk metallic glass matrix composites: From work-hardening to softeningJ.W. Qiao a,b,, A.C. Sun c, E.W. Huang d, Y. Zhang a,, P.K. Liaw e, C.P. Chuang ea

State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, Peoples Republic of China b College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, Peoples Republic of China c Department of Chemical Engineering and Materials Science, Yuan Ze University, Taoyuan 32003, Taiwan, ROC d Department of Chemical and Materials Engineering, National Central University, Jhongli 32001, Taiwan, ROC e Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN 37996-2200, USA Received 6 December 2010; received in revised form 11 March 2011; accepted 12 March 2011

Abstract A Ti-based bulk metallic glass matrix composite (BMGMC) with a homogeneous distribution of dendrites and the composition of Ti46Zr20V12Cu5Be17 is characterized by a high tensile strength of $1640 MPa and a large tensile strain of $15.5% at room temperature. The present BMGMC exhibits the largest tensile ductility and highest fracture absorption energy under the stressstrain curve of all dendrite-reinforced BMGMCs developed to date. Tensile deformation micromechanisms are explored through experimental visualization and theoretical analyses. After tension, fragmentation of the dendrites, rather than crystallization within the glass matrix and/or atom debonding near the interface of dual-phase composites, is responsible for the high tensile ductility. The subdivisions within the interior of dendrites are separated by shear bands and dense dislocation walls, and local separation of dendrites under modes I and II prevails. The multiplication of dislocations, severe lattice distortions, and even local amorphization dominate within the dendrites. Good structural coherency of the interface is demonstrated, despite being subjected to signicant plastic deformation. Theoretical analyses reveal that the constitutive relations elasticelastic, elasticplastic, and plasticplastic of dual-phase BMGMC generally correspond to the (1) elastic, (2) work-hardening, and (3) softening deformation stages, respectively. The capacity for work-hardening is highly dependent on the large plastic deformation of the dendrites and the high yield strength of the glass matrix. The present study provides a fundamental basis for designing work-hardening dual-phase BMGMCs exhibiting remarkably homogeneous deformation. Crown Copyright 2011 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved.Keywords: Metallic glasses; Composites; Plastic deformation; Work-hardening; Shear bands

1. Introduction Bulk metallic glasses (BMGs) exhibit superior performance at ambient temperature, such as high strengths, large elastic limits, and excellent corrosion and wear resistance, which renders them potential candidates as engineering structural materials [1]. However, they suer from a lack of plasticity, which leads to softening and catastrophic

Corresponding authors.

E-mail addresses: [email protected] (J.W. Qiao), drzhangy@skl. ustb.edu.cn (Y. Zhang).

failure associated with the rapid development of localized shear bands even under compression [2]. So far, macroscopic tensile ductility at room temperature has been gained only for monolithic metallic glass samples (nanopillars or thin lms) with dimensions in the nanoscale range due to homogeneous deformation rather than local shear banding [35]. For actual engineering applications millimeter scale and larger bulk samples with improved tensile ductility are needed. To circumvent the rapid propagation of shear bands within bulk samples, a series of in situ dendrite-reinforced bulk metallic glass matrix composites (BMGMCs) have been developed [610], which exhibit greater room temperature ductility compared with

1359-6454/$36.00 Crown Copyright 2011 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. doi:10.1016/j.actamat.2011.03.036

Please cite this article in press as: Qiao JW et al. Tensile deformation micromechanisms for bulk metallic glass matrix composites: From work-hardening to softening. Acta Mater (2011), doi:10.1016/j.actamat.2011.03.036

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J.W. Qiao et al. / Acta Materialia xxx (2011) xxxxxx

monolithic BMGs, macroscopically characterized by the generation of multiple shear bands. For these BMGMCs, the crystalline phase with lower shear modulus than the resulting glass is distributed within the glass matrix. Upon loading, the propagation of shear bands can be arrested by the soft crystalline phase, the length scale of which matches the plastic zone size of the glass matrix [8]. As a consequence, tensile instability can be suppressed, and the signicantly improved toughness of BMGMCs prevails. Until now studies of the deformation micromechanisms of BMGMCs have mainly focused on compressive plasticity: the severe lattice distortion and local amorphization in the dendrites, as well as the pile-up of dislocations close to the interface between the dendrites and the glass matrix upon straining, are thought to be jointly responsible for the compressive plasticity and work-hardening [10]. It should be noted that most of the developed BMGMCs exhibit softening upon tension rather than work-hardening [79], implying that the tensile deformation micromechanism may be very dierent from the corresponding compressive one. For example, pressureor normal stress-dependent yielding asymmetry has been demonstrated for monolithic BMGs [11]. However, a detailed investigation of the tensile deformation micromechanisms for BMGMCs is yet to be performed. In this study, we explore these micromechanisms, based on the analyses of microscopic images, synchrotron X-ray studies, and theoretical calculations. The present investigation provides a fundamental basis for the development of ductile composites. 2. Experimental procedures Ingots of nominal composition (at.%) Ti46Zr20V12Cu5Be17 were prepared by arc melting a mixture of Ti, Zr, V, Cu, and Be with purities greater than 99.9% (wt.%) under a Ti-gettered argon atmosphere. The liquid alloys were sucked into a cylindrical copper mold with a diameter of 5 mm and a length of about 70 mm. The microstructures of the as-cast samples, and the lateral surfaces and fracture surfaces of the samples after tensile testing were investigated by scanning electron microscopy (SEM). Cross sections of the as-cast samples were mechanically polished using 1 lm diamond paste for SEM observation. The tension sample was machined into a dumb-bell geometry, which had a nominal gage diameter of 2 mm and gage length of 6 mm. Two samples were tested under tension at a strain rate of 5 104 s1. The microstructures of the samples before and after tension testing were analyzed by transmission electron microscopy (TEM) with an energy-dispersive spectrometer (EDS), and high resolution transmission electron microscopy (HRTEM) in a JEM-2100 microscope. The specimens for TEM were prepared by mechanical grinding followed by ion milling. The Youngs moduli of the two phases were measured using an MTS Nano Indenter XP with a Berkovich diamond tip. The samples were polished prior

to the tests. The samples were indented to a depth of 300 nm in continuous stiness mode at a strain rate of 0.05 s1. The synchrotron X-ray studies were carried out in the 11ID-C beamline of the Advanced Photon Source, Argonne National Laboratory, IL. A monochromatic synchrotron high-energy X-ray beam with an energy of 115 keV penetrated specimens with a thickness of 0.6 mm and transmission diraction patterns were collected by a two-dimensional detector. 3. Results 3.1. Microstructure of the Ti46Zr20V12Cu5Be17 BMGMC Fig. 1a shows the microstructure of the as-cast Ti46Zr20V12Cu5Be17 (at.%) BMGMC. It can be seen that the crystalline phase with a dendritic morphology is uniformly distributed within a featureless glass matrix. Although there is a temperature gradient from the outer surface to the center of the rod-like sample, an inhomogeneous distribution is seldom found. The volume fraction of the dendrites is approximately 43%, by an analysis of the contrast in SEM images, with the high volume fraction of dendrites forming a network structure. The diameter of the primary dendrites is $12 lm, determined from a higher magnication of the microstructure, as displayed in Fig. 1b. To further identify the dual-phase structure, a TEM study was performed on the as-cast composites. A bright eld (BF) TEM image at low magnication is shown in

Fig. 1. (a) Low and (b) high magnication SEM images of the composites.



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Fig. 2. (a) BF TEM image of the composite at low magnication. HRTEM images of (b) the matrix and (c) the dendrites. (Insets) Corresponding SAED patterns. (d) IFFT pattern from the area of the dendrite. (Inset) Corresponding FFT pattern. (e) HRTEM image taken near the interface. IFFT patterns of (f) the dendrites and (g) the glass matrix, marked by rectangles in e, near the interface are shown in and, respectively.

Fig. 2a. The light and dark areas indicate the dendrites and the matrix, respectively, which is consistent with the SEM observations in Fig. 1. An HRTEM image of the matrix is shown in Fig. 2b. No crystallization can be detected, in agreement with the selected area electron diraction (SAED) pattern shown in the inset to Fig. 2b, containing only diuse halos typical of an amorphous structure. In contrast, clear lattice patterns dominate the interior of the dendrites, as shown in Fig. 2c. The SAED pattern, shown in the inset to Fig. 2c, with a zone axis (ZA) of

[1 1 1] indicates a body-centered cubic (bcc) structure for the dendrites with a lattice parameter a = 0.3203 nm. The TEM EDS analysis gives an average composition of the dendrites of Ti64.5Zr14.5V18.5Cu2.5 (at.%), as shown in Table 1. Under the assumption that all of Be in the alloy is partitioned into the glass matrix, it is estimated that the average composition of the matrix is Ti33Zr23 V7Cu7Be30 (at.%). The FFT pattern from the area of the dendrite is shown in the inset to Fig. 2d, with the corresponding inverse IFFT pattern displayed in Fig. 2d.


4 Table 1 The average composition of the dendrites. Element Ti(K) V(K) Cu(K) Zr(K) wt.% 56.01 17.20 2.87 23.89 at.% 64.45 18.61 2.49 14.43 Uncert. (%) 0.64 0.41 0.16 0.67


3.3. Fractographs of dual-phase BMGMCsCorrection 0.98 0.99 0.99 0.99 k factor 1.203 1.257 1.601 3.469

Obviously, lattice defects such as dislocations are rarely found, instead, a regular arrangement of the lattice patterns prevails, indicative of a lack of stress concentration within the dendrites for the as-cast composites. (The deformation behavior will be discussed later.) In order to study whether stress concentration happens near the interface between the dendrites and the glass matrix, an HRTEM image was taken near the interface, as indicated in Fig. 2e (C and A denote the crystalline and amorphous phases, respectively). Atomic bonding between the two phases was conrmed to be very good. The IFFT patterns of the dendrites and the glass matrix near the interface, marked by rectangles in Fig. 2e, are shown in Fig. 2f and g, respectively. Regular lattice patterns within the dendrites near the interface are analogous to that in the interior of the dendrites (Fig. 2c). No ordered structure is available within the matrix, consistent with that far from the interface. 3.2. Mechanical behavior of the Ti46Zr20V12Cu5Be17 BMGMC Fig. 3a shows the true stressstrain curves of the present composites upon tension. It can be seen that the results of duplicate tests are very consistent. The yield strength and the yield strain are $1420 MPa and $1.65%, respectively. After yielding the BMGMC exhibits work-hardening up to an ultrahigh tensile strength. The tensile strength and corresponding strain were $1640 MPa and $2.63%, respectively. Following this softening dominates until nal fracture at a strain of $15.5%, accompanied by continuous necking. The inset to Fig. 3a shows an area of necking at a strain of $10.0% before fracture. The tensile engineering stressstrain curves at quasi-static loading of the present composites together with a series of in situ dendritereinforced Ti- [9,12], Zr- [68,13,14], and La-based [15] BMGMCs are shown in Fig. 3b. It can clearly be seen that the present composites exhibit the largest fracture absorption energy, characterized by the greatest area under the stressstrain curve. Tensile strength is plotted against the tensile ductility at room temperature for BMGMCs in Fig. 3c. For high strength BMGMCs ductility is of the most concern. To our knowledge the present Ti-based BMGMC exhibit the largest tensile ductility among those developed. More and more ductile BMGMCs are expected to reap the benets of both the high strength and high ductility of bimodal BMGMCs, just as in ultrane grained (UFG) alloys with a bimodal distribution of grain sizes [16].

Fractographs aid in understanding the deformation and failure mechanisms of the present composites. Cup-andcone fracture prevails when tensile instability is present. Macroscopic necking can be observed in the inset to Fig. 4a, in agreement with the high tensile ductility. Profuse shear bands are distributed near the fracture surface, as shown in Fig. 4a. Primary shear bands have two main propagating directions, at an angle of about 40 with respect to the loading direction, as indicated by the lines. The detailed shear banding is presented at higher magnication in Fig. 4b, showing many microcracks (indicated by arrows) forming along the shear bands due to severe plastic deformation. Close inspection between the primary shear bands demonstrated dense secondary shear bands with a spacing of 23 lm, as shown in Fig. 4c. It is known that the improved ductility of BMGMC can be ascribed to the inhibition of the rapid propagation of shear bands by soft dendrites [17], indicated in Fig. 4d, which shows that progressing shear bands are arrested by the dendrites (indicated by the dashed lines, appearing in dark contrast), denoted by the arrows. The tips of shear bands are stopped within the dendrites as shown in Fig. 4d (denoted by short lines). Dimples are distributed over the whole fracture surface, as presented in Fig. 4e, typical of a ductile fracture mechanism. A high magnication image of the dimples reveals the nanoscaled vein patterns shown in Fig. 4f due to the instantaneous increase in temperature at nal fracture (adiabatic heating) [18]. Based on the analyses of the fractographs, macroscopically the tensile ductility can be related to the multiplication of shear bands. However, the plastic deformation behavior, including deformation of the dual-phases and interaction between the shear bands and dendrites, cannot be predicted, and the associated micromechanisms of tensile deformation are ambiguous. In the following, both experimental observations and theoretical analyses will be used to clarify the micromechanisms of tensile deformation. 4. Discussion 4.1. Tensile deformation structures of dual-phase BMGMCs based on the TEM and HRTEM analyses Fig. 5 shows detailed microscopic images of the samples after tension. A BF TEM image of the deformed sample is shown in Fig. 5a. Compared with an undeformed sample, shown in Fig. 2a, fragmentation of the dendrites is present after tension, and sharp shearing occurs within the dendrites, denoted by the arrows, without a predominant orientation. Since each individual dendrite has its own crystallographic orientation, the orientation-dependent critical shear stress is activated on dierent spatial and temporal scales. Consequently, plastic deformation of individual dendrites is harmonized, leading to random



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Fig. 3. (a) Tensile true stressstrain curves shown. (Inset) Necking at a strain of $10.0%. (b) Tensile engineering stressstrain curves for a series of BMGMCs (note that the percentage represents the volume percentage of the reinforcement phase). (c) Tensile strength plotted against the tensile ductility at room temperature for BMGMCs.

fragmentation. Fig. 5b presents an HRTEM image of the glass matrix after deformation. Only a few maze-like patterns of less than 5 nm are visible due to deformationinduced nanocrystallization [19], in agreement with the

SAED result in the inset to Fig. 5b. It is reasonable to deduce that nanocrystallization, being rare, cannot be responsible for the high ductility. In contrast, nanocrystallites are homogeneously precipitated from the glass matrix


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Fig. 4. (a) Profuse shear bands. (Inset) Macroscopic necking. (b) Detailed shear banding at higher magnication, with numerous microcracks, indicated by arrows, forming along the shear bands due to the severe plastic deformation. (c) Dense secondary shear bands with a spacing of 23 lm (d) Inhibition of the rapid propagation of shear bands by soft dendrites. (e) Dimples distributed over the whole fracture surface. (f) High magnication micrograph of the dimples revealing nanoscaled vein patterns.

of a Cu-based BMGMC, matching its high plasticity [20]. Thus, here we should focus on the dendrites and interfaces to explore the micromechanisms, ruling out a signicant ductility contribution from nanocrystallization within the glass matrix. Fig. 5c and d shows BF and dark eld (DF) images of the dendrites, respectively. Comparing the two images, three subdivisions, indicated by I, II, and III, are separated by shearing boundaries, denoted by arrows. The formation of shearing boundaries suggests that the progressing shear bands cut into the dendrites, evident in the SEM image in Fig. 4d. The dierent contrasts between these subdivisions originate from the various orientations, as they may experience varied plastic deformation. For further identication of the varied deformations, the lattice parameter a was investigated for the neighboring subdivisions I and II.

SAED patterns taken from the rectangular regions in subdivisions I and II are shown in Fig. 5c and d, respectively. The average a values obtained for subdivisions I and II were 0.3175 and 0.3221 nm, respectively. The changing tendency of the lattice parameter was consistent. For subdivision I the average lattice constant is less than that of undeformed samples, while for subdivision II the average lattice constant is larger than that of undeformed samples. So, based on the changing tendency, it can be concluded that subdivisions I and II experience dierent plastic deformations. The most heavy deformation concentrates within the thin shear bands with a thickness of about 30 nm. Fig. 5e displays the IFFT patterns within the shear bands, and it is found that dislocations, denoted by T, lattice distortions, represented by arrows, and local amorphization, represented by ellipses, are present together. Similar severe



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Fig. 5. (a) BF TEM image of the composite at low magnication. (b) HRTEM image of the glass matrix. (Inset) Corresponding SAED pattern. (c) BF and (d) DF images of deformed dendrites. (Insets) Corresponding SAED patterns of the dendrites marked by rectangles in (c) and (d). (e) IFFT image within the shear bands marked by arrows in (c) and (d). (f) BF and (g) DF images of dendrites separated by DDWs, denoted by arrows. (Inset) Higher magnication BF image of CB B, as marked in (f) and (g). (h) IFFT pattern taken from the DDW near the interface of CB A and B. (Inset) Corresponding FFT pattern. (i) BF image of a tensile-induced separation. (j) BF image of a shear-induced separation. (k) HRTEM image near the interface of the dendrites and glass matrix. (l) IFFT image in of the dendrites marked by a rectangle in k.


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plastic deformation modes have been reported in a Zrbased BMGMC [10] and a Ti-based nanostructuredendrite composite [21] upon compression. In addition to the shearing-induced separation within individual dendrites, there are many subdivisions of the dendrites separated by the dense dislocation walls (DDWs). Fig. 5f and g shows BF and DF images of the dendrites separated by DDWs, denoted by arrows, respectively. Cell blocks (CBs) form with the DDW as the boundaries due to harmonized deformation, since the number of slip systems within CBs varies. Comparing the BF and DF images, fragmentation dominates, and the varied contrasts due to the dierent CBs indicate various orientations. This is the rst time the fragmentation of dendrites in BMGMCs, divided by the DDWs, has been observed, but similar fragmentation has been reported in UFG Cu alloys [22]. Additionally, the shear steps can be observed, as shown in Fig. 5f, indicative of an interaction between the shear bands and the deformation structures. CBs A and B can be easily determined, based on the contrast in the BF and DF images. Actually, even within CB B a gradual change in contrast is still present. The higher magnication BF image of CB B shown as the inset to Fig. 5g, indicates that microbands are generated due to the local stress concentration during plastic deformation. The magnied DDW between CB A and CB B is shown in Fig. 5h. While the lattice fringes within CB B are clearly imaged, the lattice arrangement within CB A seems to be disordered. The disordered speckled pattern within CB A appears to show a lack of any lattice arrangement, which is actually caused by the dierent orientations of CB A and CB B. The FFT pattern taken from the DDW, displayed as the inset to Fig. 5h, shows extra diraction spots, indicated by arrows, agreeing with the large misorientation. Moire patterns emerge within CB B, usually caused by a mixture of translation and rotation due to local lattice superimposition [23]. The study above emphasizes the interior of the dendrites, and it is concluded that interior fragmentation results from subdivisions separated by the shear bands and DDWs. Next, observations of the fragmentation or fracture of the dendrites were carried out. Fig. 5i shows super elongation of local dendrites under mode I. Continuous necking dominates during plastic deformation, and both necking tips shrink to the nanoscale with a displacement of about 33 nm. It should be noted that for the undeformed samples, there were no sharp tips observed in BF TEM images at high magnication, as show in Fig. 2a. However, after tension sharp tips could be observed and fragmentation of the dendrites dominated. When subjected to high stresses, local fracture readily took place. Therefore, it is reasonable to deduce that local necking occurs for the dendrites upon fracture. The local tensile ductility is an indicator of the macroscopic tensile ductility. Additionally, local shearing under mode II results in the separation of adjacent portions of the dendrites, as shown in Fig. 5j. Sharp breaks in the dendrites form after shearing, and the two fracture planes are not parallel, together with a distinct distance.

Interface debonding should be investigated near the interface between the dendrite and the glass matrix, since plastic deformation could be accommodated if the spacing is generated due to the separation of the dendrite and matrix. In order to gain consistent results, many interface sites were carefully checked. Fig. 5k is a typical HRTEM image taken near the interface of a dendrite and the glass matrix, and no atomic scale segment is found, which suggests good structural coherency of the interface, and indicates that harmonized plastic deformation in the dendrites may extend into the local glass matrix. Fast atom diusion [5] or continuous cluster destructionrecreation [24] may be the fundamental deformation mechanisms of the amorphous phase in the vicinity of the interface. For the dendrite near the interface the deformation structure is clear, as shown in the IFFT pattern in Fig. 5l, which is analogous to Fig. 5e, where dislocations, lattice distortions, and local amorphizations are present. Based on the fracture study of the BMGMCs, shearing-induced subdivisions and DDW-separated CBs constitute the deformation structure within the interior of dendrites. Local separation under modes I and II prevails. 4.2. Tensile deformation structures of dual-phase BMGMCs based on synchrotron high-energy X-ray analysis To obtain complimentary information synchrotron, high-energy X-ray studies were undertaken, as synchrotron high-energy X-rays can penetrate three-dimensional bulk samples rather than planar lms. The detailed experimental set-up can be found in Li et al. [25]. Fig. 6a shows the X-ray line proles of samples before and after tension. The bcc bTi phase diraction peaks are superimposed on the broad diuse scattering maxima from the amorphous matrix, and the bcc crystal plane indices corresponding to diraction peaks are identied and marked. After tension the diffuse background scattering prole hardly changed, but the diraction peak intensity decreased remarkably with respect to the undeformed one, indicative of the dominance of decreased crystal sizes [25]. The typical diraction patterns before and after tension are exhibited in Fig. 6b and c, respectively. The sizes of micro-level dendrites are recorded as diraction spots. The discrete spots are distributed on the diraction rings for the as-cast BMGMC, since large particle sizes are present [26], as shown in Fig. 2a. Amazingly, fully continuous diraction rings form after deformation, which can be ascribed to a fragmentationinduced decrease in crystal size. It should be noted that the crystals associated with the diraction peaks in the synchrotron experiments have the same crystal orientation. The synchrotron results further provide cogent evidence of the three-dimensional fragmentation of dendrites due to the large plastic deformation. Moreover, the synchrotron results predict no deformation-induced phase transformation, which could lead to the tensile ductility [27]. The present study rules out this mechanism in the present system.



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tion. According to the stressstrain curve shown in Fig. 3a, the tension behavior of BMGMCs is characterized by three stages: (1) elastic, (2) work-hardening, and (3) softening stages, as illustrated in Fig. 7. Comparably, upon compression elastic deformation is followed by work-hardening until nal fracture, with no softening stage [6,10]. Subjected to the tensile loading, dual-phase composites experience three stages [28]. The rst is the elasticelastic stage, in which the dual phases are both elastic and the composite is also elastic. Upon straining, either the dendrites or the glass matrix will enter the plastic range, while the other will remain in the elastic range. In this stage, the composite enters the plastic range. With a further increase in stress both phases are plastic and, as a result, the composite is also plastic. Once the glass matrix becomes plastic the operation of shear bands will prevail. Only the propagation of shear bands is blocked by dendrites will accumulation of deformation result in macroscopic deformation. If the shear bands fail to sustain stable extension, plastic instability commences. When both phases are elastic, provided that the Poisson ratios of both phases are equal (since most BMG have an average Poisson ratio of about 0.3 [2], similar to that of crystalline phases), the Youngs modulus of the composite Ec can be estimated according to Hashin and Shtrikman [29]: fv Ed Em Ec Em 1 1 1 fv bEd Em Em where Em and Ed are the Youngs moduli of the glass matrix and the dendrites, respectively, fv is the volume fraction of dendrites with a value of 0.43, b is the material constant 2 calculated by b 15 45mmm , and mm is the Poisson ratio of the 1m glass matrix with a value of about 0.3 [2]. Em and Ed were measured as 120.5 3.1, and 108.6 5.0 GPa, respectively, from the nanoindentation results. The Ec was calculated as 115.2 GPa. A simple rule of mixtures (ROM) is employed as a rst-order approximation: Ec Ed fv Em 1 fv 2 Ec = 115.4 GPa, according to ROM. The two results of Eqs. (1) and (2) are very consistent, and the calculated Ec values are close to the value of 98.5 GPa obtained from the stressstrain curve in Fig. 3a. Generally, the yield strength of the composite is between those of the secondary phase and the matrix [30]. Upon straining, to determine which one will rst yield, a criterion and the eective tensile yield stress, ry, of the composite are proposed [30]: if rym/cm 6 ryd/cd, the glass matrix yields rst, and ry = rym/cm; if rym/cm P ryd/cd, the dendrites yield rst, and ry = ryd/cd. Here, rym and ryd are the yield stresses of the glass matrix and the dendrites, respectively, and cm and cd are the average stressconcentration factors of the glass matrix and the dendrites, respectively. It has been demonstrated that there is little dierence between cm and cd (cm % cd % 1) [28], and bcc Ti alloys have a lower yield stress than Ti-based BMGs

Fig. 6. (a) Synchrotron X-ray line proles of samples before and after tension tests. (b and c) Typical diraction patterns (b) before and (c) after tension tests.

4.3. Three stage deformation mechanisms of dual-phase BMGMCs In parallel with the demonstration of the above detailed deformation mechanisms through experimental visualization, it is of importance to provide a theoretical founda-


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Fig. 7. True stressstrain curve illustrating the (1) elastic, (2) work-hardening, and (3) softening stages, respectively, and the possible tensile deformation micromechanisms for each of the three stages.

[3133]. Consequently, the dendrites rst yield, and the plastic-tensile strain, ep, of the composite is given by [30]: ep fv cd ep d ep d 3 where is the plastic tensile strain of the dendrites. Meanwhile, the constitutive equation in the elasticplastic stage is [30]: p 1 1 f v ep p r p 3rd 3Em 1 b 4 fv 3c d 3 where r and rd are the tensile stresses of the composite and the dendrites, respectively. Combining Eqs. (3) and (4) one obtains the solution of the constitutive equation in the elasticplastic stage: r % rd 18; 545ep MPa d 5 For bcc Ti alloys, rd will increase with increasing ep , d because work-hardening after yielding dominates for crystalline alloys [31,32]. Therefore, in the elasticplastic stage the tensile stress r of the composite is enhanced

with increasing ep , and the composite exhibits workd hardening upon straining. From Eq. (5) r increases remarkably by more than 185 MPa with respect to the work-hardening of dendrites after yielding when the strain increases from 1.65% to 2.63%, in reasonably good agreement with the value of $220 MPa obtained from the stressstrain curve in Fig. 3a. It should be noted that usually the tensile strength of bcc Ti alloys [31,32] is lower than the yield strength of Ti-based BMGs [33]. Thus, necking and/or fracture of dendrites within the glass matrix may occur when the tensile stress approaches the tensile strength of dendrites, as shown in Fig. 5i and j. Once the tensile stress approaches the yield strength of the glass matrix, both phases enter a plasticplastic stage. The tensile stress of the composite is [30]: p 1 ep r p 3rym 3Em 1 b p 3c m 3

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Eq. (6) can be simplied as: r % rym 32; 535e MPap

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Under the assumption of rym = 1640 MPa (the deformation of dendrites may result in early yielding of the glass matrix, since the stress concentration at the interface could provide a channel for the initiation of shear bands.) and rd = 900 MPa [31], combining Eqs. (5) and (7) the critical plastic strain of the composite at the beginning of the plasticplastic stage is $0.98%, which is consistent with 2.63% (the strain corresponding to the maximum stress) 1.65% (the yield strain) =0.98% from the stressstrain curve in Fig. 3a. This close equivalency suggests that the capacity for work-hardening is controlled by the plastic strain of the dendrites and the yield strength of the glass matrix. When yielding, the glass matrix usually exhibits softening [34], i.e., rym decreases with strain, accompanied by the occurrence of shear bands. From Eqs. (6) and (7) the tensile stress of the composite decreases in the plasticplastic stage, as illustrated in Fig. 7. In this stage deformation is characterized by an interaction between the deformation structure (dendrites) and the shear bands, evident in Fig. 4ad and 5d and j. Additionally, severe plastic deformation continues in order to harmonize necking, characterized by the formation of CBs separated by DDWs. It should be noted that the formation of CBs can also happen during stage (2), as illustrated in Fig. 7, since it is associated with the harmonization of deformation, and the DDWs act as geometrically necessary boundaries. Based on the above theoretical analyses, the elastic elastic, elasticplastic, and plasticplastic stages of the dual-phase BMGMCs generally correspond to deformation stages (1), (2), and (3), respectively. Homogeneous elongation occurs in stage (2), followed by local plastic deformation in stage (3), accompanied by continuous necking, as illustrated in Fig. 7, with the proposed deformation mechanisms for each stage. Homogeneous deformation is a requirement for use as engineering materials, since inhomogeneous deformation may lead to early failure during service. Therefore, work-hardening is appreciated for structural applications. The large plastic deformation of dendrites facilitates work-hardening when the composite yields. Moreover, the high yield strength of the glass matrix controls the tensile strength of the composite, as an indicator of the capacity for work-hardening. 5. Conclusions In conclusion, the Ti46Zr20V12Cu5Be17 BMCMC with a homogeneous distribution of dendrites within the glass matrix exhibits a high tensile strength of $1640 MPa and a large tensile strain of $15.5% at room temperature, which is the largest tensile ductility observed in the BMGMCs developed so far. The tensile deformation micromechanisms from work-hardening to softening for BMGMCs are revealed and characterized by experimen-

tal visualization and theoretical calculations. The fragmentation of dendrites prevails as the deformation mechanism, shown by the electron microscopy images and synchrotron X-ray measurements. The subdivisions within the interior of dendrites are separated by shear bands and dense dislocation walls, and local separation between dendrites under modes I and II prevails. Theoretical calculations reveal that the constitutive relations: the elasticelastic, elasticplastic, and plasticplastic stages of the dual-phase BMGMCs generally correspond to the (1) elastic, (2) work-hardening, and (3) softening deformation stages, respectively. As engineering materials, work-hardening, which is controlled by the plastic deformation of dendrites, associated with homogeneous deformation, is appreciated. The tensile strength of the composites depends on the yield strength of the glass matrix. Thus, the present studies indicate that the large plastic deformation of the secondary crystalline phases and the high yield strength of the glass matrix are necessary to obtain work-hardening, which provides a guide to design ductile BMGMCs exhibiting remarkably homogeneous deformation. Before closing it is worth presenting the important implications of the current work. The present study provides a fundamental understanding of the tensile deformation micromechanisms of in situ dendrite-reinforced BMGMCs with signicant ductility. With the aid of the microscopic images and synchrotron X-ray measurements the fragmentation of dendrites has been demonstrated, which is responsible for the tensile ductility during plastic deformation, irrespective of the stage, i.e. work-hardening or softening. Based on the experimental visualizations and theoretical calculations, the capacity for homogeneous deformation is highly dependent on both the plastic deformation of dendrites and the yield strength of the glass matrix. The present ndings are very important for the development of work-hardening dual-phase BMGMCs.

Acknowledgements The authors thank Prof. W.H. Wang for enlightening discussions. We gratefully acknowledge the assistance of Dr. Y. Ren for help with the synchrotron X-ray measurements, Dr. G.Y. Wang for help with the set-up of the testing machine, and Mr. J.T. Zhang for help with the preparation of the composites. Y. Zhang would like to acknowledge support by the National Basic Research Program of China (the 973 Program) under Contract no. 2007CB613903. P.K. Liaw is very grateful for support by the National Science Foundation Programs DMR0231320, DMR-0421219, DMR-0909037, and CMMI0900271 with Drs. C. Huber, C. Bouldin, D. Finotello, A. Ardell, and C.V. Cooper as program directors. E.W. Huang appreciates support by the National Science Council Program NSC99-2218-E-008-009.


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2011-Tensile Deformation Micro Mechanisms for Bulk Metallic Glass Matrix Composites

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