Accepted Manuscript Design novel Ti-based metallic glass matrix composites with excellent dynamic plasticity Y.L. Tang, T.W. Zhang, X.H. Shi, J.W. Qiao, Z.H. Wang, H.F. Zhou, Y.C. Wu PII:
S0925-8388(18)33563-1
DOI:
10.1016/j.jallcom.2018.09.311
Reference:
JALCOM 47730
To appear in:
Journal of Alloys and Compounds
Received Date: 12 May 2018 Revised Date:
20 September 2018
Accepted Date: 24 September 2018
Please cite this article as: Y.L. Tang, T.W. Zhang, X.H. Shi, J.W. Qiao, Z.H. Wang, H.F. Zhou, Y.C. Wu, Design novel Ti-based metallic glass matrix composites with excellent dynamic plasticity, Journal of Alloys and Compounds (2018), doi: https://doi.org/10.1016/j.jallcom.2018.09.311. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Design novel Ti-based metallic glass matrix composites with excellent dynamic plasticity Y.L. Tang1,2, T.W. Zhang3, X.H. Shi1, J.W. Qiao1,2∗∗, Z.H. Wang3, H.F. Zhou1, Y.C. Wu1,** Research Center for High-entropy Alloys, College of Materials Science and
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1
Engineering, Taiyuan University of Technology, Taiyuan 030024, China
Key Laboratory of Interface Science and Engineering in Advanced Materials,
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2
Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of
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3
Technology, Taiyuan 030024, China
Abstract
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A novel light-weight and high-toughness in-situ dendrite/metallic glass matrix composites (MGMCs) with a composition of Ti58Zr12Ni6Ta13Be11 was designed.
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Quasi-static and dynamic compressive properties of MGMCs were investigated. The alloys showed excellent compressive properties of the maximum strength over 1.6
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GPa and the total strain over 10% under the quasi-static loading. Under dynamic compressive loading, the compressive strength increased up to 1.9 GPa, whereas the total strain is nearly undiminished exhibited favourable plastic deformation. Deformation mechanisms related to the improvement of strength and ductility were investigated thoroughly by focusing on how ductile dendrites affected the initiation
∗
Corresponding author. E-mail:
[email protected] (J.W. Qiao) ** corresponding author. E-mail:
[email protected] (Y.C. Wu) 1
ACCEPTED MANUSCRIPT and propagation of deformation bands, accompanied with the localization of deformed bands and effects of ω phase precipitation, shear slipping, thermo softening, and melting. A constitutive relationship is obtained by modified Johnson-Cook
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plasticity model, which is applied to model the dynamic flow stress behavior. In addition, under dynamic compression, the strain rate effect of the yielding strength exerts distinctly positive strain rate sensitivity (SRS), which can be attributed to the
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dendrite-dominated plastic deformation fracture mechanism related to the significant
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accommodation of deformed bands and dislocation in the dendrites to the macroscopic dynamic deformation at relative strain rates.
Key words: Metallic glass matrix composites; Dynamic loading; Work hardening;
1. Introduction
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Modified J-C model; Shear bands
Over recent years, bulk metallic glasses (BMGs) have drawn significantly
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technological attention for unexceptionable physical, chemical, and mechanical
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properties[1, 2]. However, it is a topic of scientific and engineering practice importance that catastrophic fracture due to rapidly shear banding is a problem that needs urgent resolution. In order to enhance macroscopic room-temperature plasticity of BMGs, a series of in-situ dendrite-reinforced metallic glass matrix composites (MGMCs) with high strength and large ductility have been successfully designed. The dual-phase microstructure with isolated dendrites, which are precipitated within the glass matrix, retards the catastrophic failure associated with unlimited propagation of 2
ACCEPTED MANUSCRIPT shear bands. As a result, enhanced global plasticity and more graceful failure come into being [3-5]. In addition, different volume fractions of B2 crystals precipitating in the glassy matrix also could exhibit not only macroscopic ductility but also high
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strength as well as work-hardening. The result is derived from the formation of multiple shear bands and martensitic transformation during deformation [6, 7].
Up to date, numerous in-situ MGMCs have been accordingly developed, and
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exhibit many exceptional mechanical performances. Representatively, in-situ Ti-based
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MGMCs are provocative of interest as engineering materials due to their low density together with high toughness. The specific strength of present composites is 2.5 ×103 N · m/kg. Although this composite is much more heavy than other reported Ti-Zr-V-Cu-Be MGMCs [8, 9], it can be compared with other light-weight crystalline
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Ti alloys [5].The investigators have explored light-weight in-situ Ti-based MGMCs with a composition of Ti58Zr16V10Cu4Be12 with an ultimate tensile strength (UTS) approaching 1970 MPa, accompanied by a fracture strain of about 14.5% [10].
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Another Ti60Zr14V12Cu4Be10 MGMCs exhibits a high fracture strength of 2,600 MPa,
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combining with a considerable plasticity of 40% at room temperature upon quasi-static compressive loading [11]. However, ductile-to-brittle transition appears for almost all these developed Ti-based MGMCs upon high-speed dynamic loading. Most of all, in practical applications, dynamic impacts widely exist in aeronautical field, automotive industry, and marine territory, and early failure often causes to a great loss in the properties and human life. Thus, the study of the dynamic deformation behaviors and mechanisms, especially for promising high-strength and 3
ACCEPTED MANUSCRIPT light-weight Ti-based MGMCs, are crucial. In order to broaden the applications of such kinds of in-situ MGMCs in the above crucial aspects, it is urgent to figure out the deformation mechanisms upon high-speed dynamic loading.
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In the present study, a novel in-situ Ti-based MGMC with a composition of Ti58Zr12Ni6Ta13Be11 in atomic percent is tentatively explored. Their mechanical properties were evaluated by conducting quasi-static and dynamic compression tests.
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Furthermore, the newly designed MGMCs exhibited excellent plasticity upon
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dynamic compression. The underlying deformation mechanisms related to improvement of strength and ductility was investigated.
2. Materials and experiments
Ti-based MGMCs with a nominal composition of Ti58Zr12Ni6Ta13Be11 (at. %)
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were explored in this study. It was referred to as Ti58. The alloys were fabricated by arc-melting the mixture of high-purity element metals, Ti, Zr, Ni, Ta, and Be with purities greater than 99.9% in a Ti-gettered high purity argon atmosphere. Due to the
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high melting point of Ta, in order to gain a homogeneous master alloy, Ta and Zr were
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preferentially melted together at least three times to ensure the chemical homogeneity. Then, the remaining elements Ti, Ni, and Be were added to the prepared solid solution to remelt, consequently receiving the homogeneous spindle. The rod like samples with 3 mm in diameter was obtained by suction the melt into the copper mould under an argon atmosphere. The structure of phases was checked by X-ray diffraction (XRD) with a monochromatic Cu-Kα radiation. The cross sections of the as-cast samples were polished, and etched using a solution of 40 mL HF, 20 mL HNO3, 40 mL HCl, 4
ACCEPTED MANUSCRIPT and 200 mL H2O for microstructure observation. The microstructures of the as-cast samples, and the lateral and fracture surfaces of the deformed samples after quasi-static and dynamic compression tests were investigated using scanning-electron
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microscopy (SEM), equipped with an energy-dispersive X-ray spectrometer (EDS). The structural characteristics of the samples before and after compression were investigated using transmission-electron microscopy (TEM) and high-resolution
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transmission electron microscopy (HRTEM) (JEOL-2010). Rod-like samples were
prepare TEM specimens.
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rubbed with the sandpaper to obtain a thickness of 20 µm and then ion-milled to
Quasi-static compression tests were carried out using an Instron 5969 testing machine at a strain rate of 5×10-4 s-1. Dynamic compression tests were
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performed with a split Hopkinson pressure bar (SHPB) apparatus at strain rates ranging from 915 to 3,650 s-1. All the tests were conducted at room temperature.
3. Results
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3.1 Microstructure of Ti58 MGMCs
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Fig. 1(a) reveals the microstructure of as-cast Ti58 composites. During cooling of the melt from high temperature, the embedded dendrites are generated by nucleation and dendritic growth, followed by the solidification of the remaining liquid alloy. It is observed that the dendrites are homogeneously distributed within the featureless and continuous glass matrix. The average volume fraction of dendrites takes a value of approximately 65% by image analysis, the spacing of the dendrite arm
is
about
1.5–2.5
µm.
Fig. 5
1(b)
and
(c)
exhibit
the
ACCEPTED MANUSCRIPT selected-area-electron-diffraction (SAED) patterns, manifested by yellow arrows in Fig. 1(a) for the matrix and dendrites, respectively. The amorphous matrix can be confirmed by ring patterns in Fig. 1(b). According to the SAED patterns of dendrites
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in Fig. 1(c), the dendrites are identified as body-centered cubic (bcc) β-Ti phase, and the diffraction patterns of hexagonal ω phases are also found, as indicated by rectangle in Fig. 1(c). The TEM analysis implies that the current composites mainly
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consist of β phases and a small amount of ω phases together with amorphous phases.
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Fig. 1(d) displays the XRD patterns of samples before and after dynamic compression. It can be found that bcc β-Ti phase diffraction peaks are superimposed on the broad diffuse scattering maxima indices. Besides, both as-cast and deformed samples have peaks of bcc β phases, which implies no phase transformation occurs for the ductile
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dendrites subjected to heavy loading. In addition, there are no hexagonal ω phase diffraction peaks on account of a small amount of ω phases in this composite.
3.2 Mechanical properties
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Fig. 2(a) exhibits true stress-strain curve of the present Ti58 MGMCs upon
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quasi-static compression at a strain rate of 5×10− 4 /s. The low-magnification image of the fractured specimen is presented in the inset of Fig. 2(a). It can be seen that the present Ti58 composites yield at ~1,235 MPa, accompanied by a significant work hardening, achieving an ultimate compressive strength of ~1,617 MPa. The total compressive plasticity of the current Ti58 MGMCs attains about 9.6%. Fig. 2(c) shows the dynamic true stress-strain curves of the present Ti58 MGMCs with varying strain rates from 915 to 3,650 /s. The corresponding strain rates are constant, taken the 6
ACCEPTED MANUSCRIPT average value, as illustrated in Fig. 2(b). What should be especially mentioned is that the dynamic samples are not broken down and do not reach the ultimate limits under the strain rate of 915/s. The inset in Fig. 2(c) shows the macroscopic feature of the
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deformed composites. As shown in the inset of c (1), it is found that deformed specimens are not broken down under the strain rate of 915 /s, on account of external loads, and the barreling can be observed here. In other words, deformed specimens
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have no time to deform entirely until there are unloaded. Therefore, only the yield
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strength is available at the strain rate of 915/s. That is, here, the yield stress can be detected rather than the plasticity. Surprisingly, a loud noise, like a firecracker, together with sparking, was detected at the moment of fracture except for deformed specimens under the strain rate of 915 /s. The other specimens are broken down into
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two or more parts /or pieces shown in inset of c (2), in agreement with the large compressive plasticity. It is noted that the yielding strengths are between 1,330 and 1,440 MPa, much higher than that upon quasi-static compression. What is more,
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compared with that of the quasi-static one, the dynamic plastic flow is still
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considerable under dynamic compression. Table 1 summarizes quasi-static and dynamic compressive results at room temperature. Table 1
Summary of yielding strength ( σ y ), ultimate strength ( σ max ), and fracture strain ( ε f ) of the Ti58 composites. Strain rate (/s)
σ y (MPa)
σ max (MPa)
ε f (%)
5×10-4
~1,235±107
~1,617±115
~9.6±0.7
7
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~1,413±112
~6.3±1.1
1,630
~1,353±103
~1,457±106
~9.6±0.5
2,870
~1,356±121
~1,443±109
~9.9±1.4
3,180
~1,436±116
~1,480±130
~10.0±1.6
3,650
~1,440±110
~1,456±126
~11.4±1.8
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3.3 Fracture behavior
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915
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SEM observations are conductive to explore the deformation mechanisms of the present composites. Exactly as shown in Fig 3(a), abundant shear bands spread over near the fracture surface, consistent with the macroscopic large plasticity. Primary shear bands mainly propagate along two directions. When the stress
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concentration surpasses the yielding stress of the glass matrix, primary shear bands nucleate at the interface in the glass matrix, which would propagate along the favorable direction. When the propagation is obstructed by the coarse and ductile
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dendrites, the shear bands either are arrested by the crystalline phases or bypass the
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barriers. Consequently, the shear bands are bent and the multiplication of shear bands prevails within glass matrix. Consequently, the interactions among shear bands will take place due to the different propagation directions of shear banding, as shown in the inset of Fig 3(a). In fact, the serious interaction among shear bands facilitates the initiation of nucleation sites for microcracks subjected to further loading. Ultimately, the specimens would have a fracture coupled with microcrack expanding. Further detailed observations show that the typical feature of the fracture surfaces is a 8
ACCEPTED MANUSCRIPT fishbone-like structure, as shown in Fig. 3(b) [12].The fracture surface upon quasi-static compression display micro-melting feature distributing on shear steps, and the high magnification of the micro-melting feature (marked in yellow arrow) is
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illustrated in the inset of Fig 3(b). Based on observations of dynamic specimens, Fig. 3(c)-(d) is outlined to illustrate the lateral surface of the deformed specimens upon dynamic compression. It
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is found that a number of deformation zones with an availability of highly localized
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shear bands perpendicular to the fracture surface, as shown in Fig. 3(c). On account of above analysis, the fractographs are consistent with the corresponding plasticity under dynamic loadings. Fig. 3(d) exhibits the fracture surface of dynamically deformed specimens for the present composite. The river-like and droplet-like patterns (marked
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in yellow arrow), characteristic of typical amorphous alloys prevails along the fracture surface, associated with the melting of shear bands and frictional sliding leading to a temperature burst sufficiently rising to prompt local melting. What is more, the
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present river-like patterns indicate the higher temperature rising than that upon
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quasi-static loading for the present Ti-based MGMCs. Fig. 4 (a) and (b) display the bright and dark fields TEM image of the
dendrites upon dynamic loading. It can be seen that abundant deformed bands marked by arrows emerge within the dendrites corresponding to obvious plastic deformation taking place under high strain rate. A more interesting thing is that the same phenomenon occurs upon quasi-static compressions (not shown in the image). Microscopically, in order to reveal whether a phase transition occurs within the 9
ACCEPTED MANUSCRIPT dendrites, SAED is employed for dendrites upon the quasi-static and dynamic compression. The results turn out that no phase transition occurs for dendrites, since corresponding SAED gives an evidence of the presence of β-Ti phases (indicated by
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the bright spots) and diffraction patterns of hexagonal ω phases (indicated by the dark
composite.
4. Discussion
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4.1 Design of in-situ Ti-based MGMCs
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spots) signed by arrows in (c) and (d), which is in accordance with the as-cast
The composition of the present composites is designed on the basis of below principles
(1) Firstly, the multicomponent alloy system with extremely large
glass-forming ability. It is well-known that low free energy, ∆G , is essential for alloy
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to restrain the nucleation and growth of crystalline phase. From equation ∆G =∆H f − T ∆S f , it is easily to obtain the low free energy ∆G for low ∆H f and
large ∆S f . ∆H f and ∆S f are enthalpy of fusion and entropy of fusion, respectively.
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Multicomponent alloy could create conditions and provide convenience for large ∆S f ,
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since ∆S f is directly proportional to the number of microcosmic states. In addition, the increasing of ∆S f could result in the increase in the degree of dense random packing which motivates the decrease of ∆H f [13]. (2) Secondly, taking a panoramic view of BMG systems, such as Ti-, Zr-, Mg-, and La-based BMGs [13-15] with high glass-forming ability, the Ti-based BMGs are selected for the present alloy on account of its relative low density and high strength compared with other BMGs. (3)Thirdly, owing to nearly zero plasticity in monolithic BMGs, the multicomponent alloy is 10
ACCEPTED MANUSCRIPT improved to induce the formation of primary dendrites by means of addition of refractory elements, which are inclined to form solid solutions in the glassy phase. According to the Ti-M binary phase diagram[16], Ta can be indefinitely melted
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together with Ti to form bcc-β-Ti solid solutions. Besides, Ta can play the part of nucleation sites for the dendritic β-phase. What is more, the equivalent Mo content is often used to evaluate the stability of the β phase [17].
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Table 2
Detected Composite
Unit
Ti
Zr
at.%
64.26±2.36
9.21±0.98
area
Ti58
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EDS-obtained composition and equivalent Mo contents in Ti58 MGMCs.
Dendrite
[Mo]eq (%) Ni
Ta
2.82±0.45 23.69±1.36 13.42±1.16
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wt.% 36.86±1.56 10.06±1.12 1.98±0.56 51.09±1.64
According to the EDS data of dendrites in Table 2, the Ti58 composite
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contains 51.1% wt. % of Ta and 2.0% wt. % of Ni in dendrites. It is noteworthy that the stability of a β-Ti alloy is strongly related to the amounts of β-stabilizing elements
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(β-stabilizers) [18]. Based on the molybdenum equivalent equation (1), Mo content ([Mo]eq ) is given by [19],
[ Mo]eq = [ Mo] + 0.22 [Ta ] + 0.28 [ Nb] + 0.67 [V ] + 2.5 [ Fe] + 1.1[ Ni ] + 1.4 [Co ] + 0.8 [Cu ]
(1)
where [i] is the amount of the element i in weight percent. We can directly calculate the [Mo]eq contents in β phases based on the EDS-obtained contents (in weight percent) of Ta and Ni listed in Table 2. The calculated [Mo]eq contents is also listed in Table 2 for comparison. Considering this equivalent equation and the amount of 11
ACCEPTED MANUSCRIPT alloying elements contained in dendrites, the β phase in the present composite seems more stable than that of the Ti48Zr27Ni6Ta5Be14 composite [20]. This indicates that the stability of the β phase is dominating so that the phase transformation in the dendrites
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is interruptive upon loading.
4.2 The deformation mechanisms upon quasi-static compression
On the basis of Fig 2(a), the present composites under quasi-static loading
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exhibit obvious work hardening. Different from the work hardening in conventional
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crystalline alloys, which is ascribed to the interaction among lattice defects, such as dislocations, deformation twins, and grain boundaries, the glassy alloys lack of crystal slip, and global strain hardening is ruled out [21]. Nevertheless, the reinforcement crystalline phases, which are precipitated within the glass matrix, have a tremendous
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impact on the deformation of the dual-phase dendrite/MGMCs. Traditionally, the plasticity in monolithic BMGs is accommodated by individual shear bands. The nucleation of shear bands is inclined to initiate at the
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weakest sites, such as casting defects, where high concentrated stresses are easily
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generated [22]. Once individual shear bands come into being, they would effortlessly propagate along the favorable direction, giving rise to catastrophic failure. Fortunately, the reinforcement phase convincingly works well to prevent the fast propagation of shear bands, which would stimulate new shear bands formed when an active shear band is well arrested. Therefore, the critical stresses to drive the formation of new shear bands would gradually increase from easy to difficult nucleation sites with the consumption of free volumes [23, 24]. Consequently, the external loading is required 12
ACCEPTED MANUSCRIPT to progressively increase to maintain successive plastic deformation, which results in so-called work hardening and definite plasticity due to the formation of multiple shear bands.
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Compared with nearly zero plasticity in monolithic BMGs, in-situ MGMCs take possession of definite plasticity upon quasi-static compressions at room temperature [5]. The result is in agreement with many shear bands on the lateral
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surface of the deformed sample upon quasi-static compression shown in Fig. 3(a). On
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one hand, the reinforcement crystalline phase prevents individual shear bands from developing into unstable cracks, which appropriately motivates multiple shear bands coming into being. As a result, the profuse shear bands within the glass matrix and the dislocations within the dendrites accommodate large plasticity. Here, the present
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in-situ Ti58 MGMCs have better plasticity than monolithic BMGs. On the other hand, the present composites exhibit restricted plasticity compared with other in-situ MGMCs [10, 11], which are principally attributed to the
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size of dendrites and the interdendrite spacing (the distance from the center of a single
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dendrite tree to the center of an adjacent one) [25]. The soft secondary phase which possesses a lower shear modulus would effectively absorb shearing energy and hinder rapid propagation of shear bands. It has been demonstrated that a small interdendrite spacing could more practically contribute to retard the propagation of shear bands. Even though the average volume fraction of dendrites takes a value of approximately 65%, the spacing of primary dendrites is about 1.5–2.5 µm, which makes a weakly negative capability to shear banding in comparison to those in-situ MGMCs upon 13
ACCEPTED MANUSCRIPT quasi-static compression [10, 11]. Qiao et al. [26] has claimed that the decrease of interdendrite spacing with the increase of the volume of dendrites has the advantage for plasticity improvement.
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The minor the spacing of primary dendrites mean major interdendrite spacing. The major interdendrite spacing leads to the possibly less lattice distortion and local amorphization in the dendrites, as well as pile-ups of dislocations close to the
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interface between the dendrites and glass matrix. Above all clearly indicate that in-situ
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MGMCs generally maintain better plasticity than monolithic BMGs, and the plastic improvement is closely related with both the volume of dendrites and the interdendrite spacing.
From Fig. 3(b), it is observed that the dominant shearing fracture is along
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the main shear stress. This demonstrates that pure shear mode is mainly dominant during compressive plastic flows, along the direction marked in Fig. 3(a). The well-organized arrangement of shear steps appears on the fracture surface. Generally,
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the normal stress, σ θ , always exerts on the fracture plane. Consequently, the fracture
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of the present MGMCs should be mainly controlled by both the normal stress, σ θ , and the shear stress, τ θ , on the shear plane. According to the shear fracture criterion, the critical shear fracture stress, τ θ ,should meet the following conditions [27, 28]:
τ θ ≥ τ 0 +µσ θ
(2)
σ θ =σ F sin 2 (θ )
(3)
τ θ =σ F sin(θ ) cos(θ )
(4)
where µ is a constant for amorphous alloys, τ 0 is regarded as the critical shear 14
ACCEPTED MANUSCRIPT fracture stress under the condition only suffering shear stress, and θ and σ F are the fracture angle and the fracture stress, respectively. A relationship between θ and σ F , is obtained by substituting Eq. (3) and Eq. (4) into Eq. (2):
τ0 sin(θ ) [ cos(θ ) − µ sin(θ ) ]
(5)
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σF ≥
Since τ 0 and µ are constants, the relationship between θ and σ F , can be obtained
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as:
(6)
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∂ (1 σ F ) 1 = [ cos 2θ − µ sin(2θ )] = 0 ∂θ 2τ 0
From Eq. (6), it can be concluded that the fracture angles strongly depend on the constant, µ . According to Zhang et al. [28], the constant, µ , can be different under diverse loading conditions. Since different effect of the normal stress on the
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fracture processes, the fracture mechanisms change under varying conditions. It was found that the fracture is mainly along primary shear bands, and the compressive fracture angle, θc , i.e., the fracture plane with respect to the loading axis,
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is 42.8°. It's worth noting that the compressive fracture angle deviates from the
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maximum shear stress plane (45°). It can be deduced that the fracture behavior of the present MGMCs under compressive loading disobeys the von Mises criterion. Zhang et.al [28] proposed that the deviation of θc from 45° can be attributed to a combined effect of the normal and shear stresses on the fracture plane.
4.3 The deformation mechanisms upon dynamic loading Commonly, there is consensus that ductile-to-brittle transition occurs upon dynamic loading with respect to upon quasi-static loading. Nonetheless, this 15
ACCEPTED MANUSCRIPT behaviour is inconspicuous for the present MGMCs. The results from SEM and TEM observation come up with a comprehensive experimental and theoretical understanding of plasticity. Here, to better understand the excellent plasticity of the
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present MGMCs, the fundamental issue is addressed by considering the ductile dendrites affected the initiation and propagation of shear bands, accompanied by the localization of deformed bands and effects of ω phase precipitation, shear slipping,
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thermo softening, and melting.
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Firstly, with regard to the metallic glass matrix, it can be seen from Fig 3 (c)-(d) that there are multiple shear bands in the case of low-level high strain rate. Surprisingly, this result provides a compelling evidence that there is relatively enough time for multiple shear bands to be generated, which is consistent with the improved
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plasticity of the present composites. Secondly, for the secondary phase, spatially heterogeneous deformed bands emerge within dendrites, as demonstrated in Fig. 4(a) and (b). The appearance of deformed bands is of great importance that leads to
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increase of the resistance to rapid propagation of shear bands. Similarly, this is a key
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point on the plasticity of the composite. Generally, the large plasticity for in-situ MGMCs is ascribed to the
twinning and phase transformation [5]. The formation of twinning and phase transformation is to accommodate plasticity. However, the present MGMCs are actually considered with excellent plasticity even if there is no twinning and phase transformation occurrence. Finally, it has been demonstrated that ω phase particles were detected in the 16
ACCEPTED MANUSCRIPT composite. Compared with the previously simplex β phase, the ω phase in composite may be an intermediate phase formed in the first stage of decomposition of the metastable β phase, which is usually ascribed to the presence of Ta. Ta element in the
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amorphous phase has a significant effect on its crystallization by promoting the formation of quasicrystals and decreasing the glass-forming ability of the glass matrix [26, 29]. Zhang et al. [30] have claimed that ω-Ti are prone to precipitate in β-Ti
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single crystals rather than transform to α-Ti by applying the negentropy model, which
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is important for designing metastable β-type MGMCs with excellent ductility. On account of the ω phase having the characteristics of brittleness as well as high hardness, ω phase may influence the mechanical properties of the composite. Specially, upon high-speed dynamic loading, it could speed the cracking.
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It can be found that the dense vein-like patterns on the fracture surface with the melting liquid under high strain rate loading, (see Fig. 3(d)), which indicates a high temperature rise endowing a viscous fluidity. Fan et al. [31] claimed that an
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increased temperature can lower the shear resistance in shear bands and thus
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facilitates the sliding to further elevate the temperature. Under the circumstance, the increased temperature will promote dislocation slip within the dendrite. Then, the hard ω phase will act as the blocks to hinder the dislocation glide either through a dislocation by-pass mechanism (Orowan-type) or particle shearing mechanism, which could strengthen the composites. In brief, the plastic flow under high temperature enhance the plasticity, and ω phase precipitation corresponds to the strength improvement upon dynamic loading. 17
ACCEPTED MANUSCRIPT In general, the constitutive response could well quantify the propensity to shear localization. Based on the Johnson-Cook (J-C) plastic model [32, 33], which is the most common phenomenological constitutive equation used to describe the plastic
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behavior of the materials, the flow stress of ductile materials can be effectively quantified as:
• T − T m r ε 1 − σ = ( A + Bε ) × 1 + C ln • T T − m r ε 0
(7)
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n p
where A, B , n, C and m are the model constants, and Tm and Tr are melting
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temperature and room temperature, respectively. In the current experiment,
Tr = 298 K . The reference strain rate, ε 0 , is simply taken as 915/s. However, a thick layer of melting liquid is found covering the vein-like pattern, as shown in Fig. 5(d). That is, the temperature rise from plastic work
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transformation is obvious under dynamic loading. Therefore, the temperature effect could not be negligent. It is acceptable that shear banding is significantly responsible
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for the temperature rise [34]. Wang et al. [35] reported that the energy transferred from testing system to shear bands concurs simultaneously with the heat diffusion
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from hot shear bands into the cold surrounding matrix. Therefore, shear banding will couple with the energy transfer. As a result, a liquid-like layer formed further demonstrated that the temperature rise, ∆T , must be higher than glass-transition temperature. During quasi-static and dynamic compression, the plastic deformation energy may be transferred to heat and led to an adiabatic temperature rise T
∆T = T − T0 = ∫ dT = T0
18
β ε σ dε p ρ C p ∫0 p
(8)
ACCEPTED MANUSCRIPT where ∆T is the temperature rise, T the current instantaneous temperature, T0 the initial temperature (298 K in this experiment), ρ is the density, and C p is the specific heat capacity. The parameter β , which is the converted fraction of the plastic
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work into heat, is often taken as 0.9 [36]. The density of the present MGMCs is taken as 6.4 × 103 kg m3 using Archimedes' Principle experimental methods, and the specific heat capacity, C p , is approximated to be 579.9 J kg ⋅ K
at room n
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temperature. C p is estimated from the rule of mixture (ROM) [37]: amix = ∑ ci ai ( ci i =1
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and ai are the atomic fraction and the parameter of the ith element, respectively, and n is the number of alloy components). A relationship between the temperature and plastic strain, at a fixed strain rate, is obtained by substituting Eq. (8) into Eq. (7):
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• −0.9 1 + C ln ε • n +1 • Bε p ε0 σ = ( A + Bε pn ) × 1 + C ln ε • exp Aε p + ρ C p (Tm − T0 ) n + 1 ε 0
(9)
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By employing the modified J-C model to fit the flow curves in Fig. 2(d) and substituting the fitting parameters into Eq. (7), the constitutive relationship for the
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present MGMCs upon dynamic compression is obtained: • −0.9 1 + 0.039ln ε • • ε0 1274ε p + 170ε 1.58 σ = (1274 + 268ε pn ) × 1 + 0.039 ln ε • exp ( p ) ρ C p (Tm − T0 ) ε 0
(10)
Fig. 5 perfectly exhibits the experimentally flow behaviors at various strain rates and those calculated by the modified J-C model under dynamic compression. It is noteworthy that the predicted flow behaviors are highly consistent with 19
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shear localization can be quantified from the constitutive relationship. Thus, the modified J-C model can macroscopically predict the constitutive relationship during high strain-rate deformation by introducing the average temperature rise.
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In addition, Fig. 5 demonstrates the rate dependency of yield stress of the
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composite, which displays an increasing tendency with the increase of strain rates. The composite undergoes different deformation mechanisms with increasing strain rates upon dynamic deformation. The present composite goes through the dendrite-dominated deformation mechanism. At higher strain rate, the multiplicity of
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dislocations will be expedited, and the addition of ω phases will retard the movement of dislocations resulting the increase of the yielding strength [38]. Besides, ex-situ MGMCs [39] present a positive strain rate sensitivity under dynamic compression.
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The forest dislocation hardening, mechanical twinning in particular for high-volume
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fractioned fiber, Wf, may lead to yield strength increasing for ex-situ MGMCs. Nonetheless, the composite in Ref. [40] is subjected to the negative strain-rate sensitivity. The changes of the yielding strength are induced by the internal thermal effect. It can be arbitrarily concluded that almost all metals and alloys take possession of a critical strain rate from positive to negative effects. Briefly, MGMCs may be subjected to either positive or negative strain rate sensitivity, which depends entirely on phases in the composites and how high of the strain rate the composites sustain. 20
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5. Conclusion To conclude, Ti-based MGMCs with a nominal composition of Ti58Zr12Ni6Ta13Be11 were designed, and their microstructures and mechanical
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properties were evaluated at both quasi-static and dynamic compression. Upon the quasi-static loading, the considerably work hardening and large plasticity were obtained owing to the abundant dislocations and profuse shear bands. However, upon
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dynamic loading, both of increased yielding strength and undiminished plasticity were
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achieved, which was superior to the previous results in a series of in-situ MGMCs. Based on the deformation mechanisms, a constitutive relationship is constructed using modified
J-C
model,
and
the
constitutive
relationship
is
as
follows
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• −0.9 1 + 0.039 ln ε • • ε0 σ = (1274 + 268ε pn ) × 1 + 0.039 ln ε • exp 1274ε p + 170ε 1.58 ( ) p ρ C p (Tm − T0 ) . ε 0
The strain rate effect of the yielding strength has an apparent positive SRS in the
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current in-situ MGMCs. The present study gives a clue to design light-weight and
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high-toughness promising MGMCs.
Acknowledgements The authors would like to acknowledge the financial support of National Natural
Science Foundation of China (Nos. 51371122 and 51801132), the Youth Natural Science Foundation of Shanxi Province, China (Nos. 2015021005 and 2014021017-3), and the project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology), and the project number is KFJJ15-19M 21
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ACCEPTED MANUSCRIPT Figure captions: FIG. 1 SEM image of the microstructure of the Ti58 MGMCs (a), and the SAED patterns for the matrix and the dendrites shown in (b) and (c), respectively, XRD pattern of the Ti58 MGMCs before and after dynamic compression (d).
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FIG. 2(a) the engineering stress-strain curves of the present composite upon quasi-static compressive loading, (a 1) the macroscopic feature for quasi-static
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samples and (b) shows the variation of strain rate with time, keeping constants during dynamic loadings for each strain rate, the engineering stress-strain curves under the
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dynamic (c) the engineering stress-strain curves of the present composite upon dynamic compressive loading, (c 1) the macroscopic feature under 915 /s strain rate, (c 2) most fractured samples shown an approximate 0.3 mm-thickness sheet formed under high strain rates.
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FIG. 3 The lateral surface of the deformed sample upon quasi-static and dynamic loadings shown in (a)-(d), (a) the detailed shear bands and deformed bands upon
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quasi-static, the fracture surface of the present composite upon quasi-static shown in (b), (c) the detailed shear bands upon dynamic loadings and the fracture surface of the
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present composite upon dynamic shown in (d). FIG. 4 TEM images of deformed microstructures in dynamic samples, (a) and (b) shown the bright and dark fields of dendrites, respectively, and abundant deformed bands within the dendrites marked by arrows, (c) and (d) shown the SAED patterns of the samples upon quasi static and dynamic samples, respectively. FIG. 5 Comparison between the experimental flow stresses and their corresponding flow behaviors by the modified Johnson-Cook (J-C) plastic model upon dynamic 25
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loadings for the Ti58 MGMCs
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