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Dynamic mechanical behavior of a Zr-based bulk metallic glass composite
Materials and Design 88 (2015) 69–74
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Dynamic mechanical behavior of a Zr-based bulk metallic glass composite Jian Kong a,⁎, Zhitao Ye a, Wen Chen b,⁎, Xueli Shao a, Kehong Wang a, Qi Zhou a a b
School of Materials Science & Engineering, Nanjing University of Science and Technology, Nanjing 210094, China Department of Mechanical Engineering & Materials Science, Yale University, New Haven, CT 06511, USA
a r t i c l e
i n f o
Article history: Received 31 July 2015 Received in revised form 25 August 2015 Accepted 26 August 2015 Available online 31 August 2015 Keywords: Metallic glass Dynamic mechanical analysis Phase transformation Mechanical properties Structural relaxation Viscoelastic properties
a b s t r a c t Dynamic mechanical analysis (DMA) was used to study the viscoelastic properties of a Zr56.2Ti13.8Nb5.0Cu6.9Ni5.6Be12.5 (LM2) bulk metallic glass (BMG) matrix composite. The temperature spectrum and the frequency spectrum were tested by three point bending. We revealed that the relaxation process of the LM2 composite is different from the single amorphous alloys. The unique superimposition of glass transition (α-relaxation) and β-phase transformation during DMA results in double peaks on the loss modulus evolution and a plateau on the storage modulus evolution. The numerical analysis of the isothermal spectrum suggests that the dynamic relaxation behavior of the LM2 composite cannot be described by a single classical relaxation model. A coupling model is instead proposed to well quantify the coupling effect of the α-relaxation and β-phase transformation in the LM2 BMG composite. Our findings provide an insight into understanding the more complex structural relaxation of BMG composite than monolithic BMGs. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Bulk metallic glasses (BMGs) are a family of amorphous materials rapidly quenched from metal alloy melts such that crystallization is suppressed. The absence of crystalline structure endows BMGs with a variety of attractive properties including high strength, high elastic limit, strong corrosion resistance, and unique processability in the supercooled liquid state [1–10]. The severe brittleness of BMGs at low temperatures, especially under un-constraint loading condition such as tension, has in the past decade limited the structural application of BMGs [1–3]. To solve this issue, the successful development of BMG composites has been recognized as a breakthrough where an effective toughening mechanism has been achieved by introducing a secondary crystalline phase within the amorphous matrix [11,12]. A thorough discussion on the mechanical behavior of BMGs and a dedicated analysis on the overall fracture process/mechanism of BMGs and their composites can be found in a recent comprehensive review by Sun and Wang [13]. The metastable nature of amorphous structure suggests the dynamic relaxation processes which correlate with the internal atomic structure and mechanical behavior of glassy materials. In polymeric materials, there are two relaxation processes: the main (α) relaxation and the secondary Johari–Goldstein (β) relaxation, the former of which
⁎ Corresponding authors. E-mail addresses: [email protected] (J. Kong), [email protected] (W. Chen).
http://dx.doi.org/10.1016/j.matdes.2015.08.132 0264-1275/© 2015 Elsevier Ltd. All rights reserved.
corresponds to the glass transition or local movements of the chain structures while the latter is often linked to the movements of the side groups. In BMGs, the non-directional atomic packing by metallic bonding results in a macroscopically homogeneous structure without any long range order. However, the microscopically short ranges orders and medium range orders have been experimentally observed [14]. Free volume model and shear transformation zone (STZ) model have been proposed to describe these nanoscale or sub-nanoscale heterogeneous structures [15,16]. The unique internal atomic organization in BMGs obviously plays a key role in determining the time-sensitive dynamic mechanical (e.g., viscoelastic or viscoplastic) behavior of BMGs. The αrelaxation has been extensively observed in various BMGs whereas a distant secondary β-relaxation is observed for some BMGs [17]. Several models such as Debye model [18], Cole–Cole model [19], Cole–Davidson model [20], Kohlrausch–Williams–Watts (KWW) model [21], and Havriliak–Negami model [22] have been employed to theoretically describe the relaxation behavior in BMGs. In comparison with the extensive investigations of monolithic BMGs, the understanding of the structural information such as the glass transition and the mechanical relaxation behavior of BMG composites is still rather limited. A particular question is how these properties evolve with the existence of the secondary crystalline phase, especially during structural service or materials processing. In this paper, the dynamic mechanical analysis (DMA) has been used to study the dynamic mechanical properties of a Zr56.2Ti13.8Nb5.0Cu6.9Ni5.6Be12.5 BMG matrix composite at different temperatures with different periodic loads. We examined the viscoelastic properties of the LM2 BMG composite, and
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particularly analyzed the influence of the secondary dendritic crystal phase on the dynamic mechanical response of the composite. From a practical viewpoint, the elastic and viscoelastic properties of BMG composites with different temperatures and dynamic loading conditions provide an insight into the processability and mechanical performance of the class of BMG composite materials. 2. Materials and methods Master ingots with nominal composition of LM2(Zr56.2Ti13.8Nb5.0 Cu6.9Ni5.6Be12.5, at.%) were prepared from a mixture of pure elements (purity ≥99.99%) by arc melting under a high purity Argon atmosphere. In order to improve the chemical homogeneity of the alloy, the ingots were remelted at least four times and subsequently cast into a copper mold to produce a rectangular feedstock with dimensions of 80 mm ∗ 50 mm ∗ 3 mm. The structure of the BMG matrix composite was detected by X-ray diffraction (XRD, Rigaku-200) with Cu target (λ = 1.5404 Å) and was observed by scanning electron microscopy (SEM, Philips Quanta-200). The characteristic temperatures of the composite were determined by differential scanning calorimetry (DSC, NETZSCH-STA4490C). The XRD, DSC, SEM results suggested that the casting samples were BMG matrix composite [23]. The glass transition onset temperature, Tg, and the crystallization onset temperature, Tx, were determined by the DSC to be 603 K and 673 K, respectively at a heating rate of 20 K/min. DMA has behaved as a toolbox for studying the mechanical properties and structural details of a wide range of materials including polymers, crystalline metals, and ceramics [24]. The dynamic mechanical behavior of a material is essentially the response of strain (or stress) to an applied periodic stress (or strain). As a periodic stress σ = σ0 cos (ωt) with a frequency ω is applied to a material, the resulting deformation is recorded as ε = ε0 cos(ωt + δ). For viscoelastic materials, the strain lags behind the stress with a phase angle δ. The ratio of stress to strain gives the modulus. For viscoelastic materials, the modulus G⁎ is a complex number due to the phase lag between the stress and strain, defined by G⁎ = σ⁎ / ε⁎ = G′ + iG″, where G′ is the storage modulus and G″ is the loss modulus. These parameters directly reflect the atomic mobility and the atomic structure that govern the viscoelastic behavior, mechanical relaxation, and the glass transition behavior of amorphous matters. In this work, DMA measurements were performed using TA DMA-Q800 by three-point bending. The samples were cut into a rectangular geometry with dimensions of 1.5 mm ∗ 3.0 mm ∗ 30 mm. To measure the temperature spectrum, a static force of 1 N was applied with a loading amplitude of 3 μm at different frequencies of 1 Hz, 5 Hz, 10 Hz, 20 Hz, and 100 Hz. The temperature was increased from room temperature (RT) to 773 K at a rate of 5 K/min. To measure the isothermal frequency spectrum, a static force of 0.1 N was applied with a loading amplitude of 3 μm with frequencies ranging from 0.01 to 100 Hz. Four different isothermal temperatures of 633 K, 643 K, 653 K, and 663 K were chosen. 3. Results and discussion 3.1. The modulus characteristics at a fixed frequency Fig. 1 shows the temperature dependence of the storage modulus (G′), the loss modulus (G″), and the internal friction (tanδ = G″/G′) of the LM2 composite at a fixed loading frequency of 1 Hz. The temperature dependence of the dynamic mechanical behavior of the LM2 composite can be divided into three stages. Stage I: At low temperatures when T b 530 K, G′ is high while G″ is very low and both are almost constant. Hence, the material is highly elastic and the viscoelastic component is negligible. As the temperature increases to ~ 600 K, G′ increases until a maximum of ~ 86 GPa and G″ also starts to increase, suggesting an increasing viscoelasticity. Stage II: G′ starts to decrease rapidly from 86 GPa to approximately 45 GPa with increasing the
Fig. 1. The temperature dependence of storage modulus (G′), loss modulus (G″), and internal friction (tanδ) of the LM2 composite under a loading condition of ω = 1 Hz, A = 3 μm, heating rate 5 K/min.
temperature from 603 K to 669 K. At the temperature region of 669 K–679 K, a plateau appears, followed by a further dramatic decrease to a minimum of 15 GPa as temperature continuously increases to 713 K. In contrast, G″ increases dramatically and decreases again after double peaks of approximately 85 GPa and 77 GPa at 662 K and 688 K, respectively (see Fig. 3(b) for the enlarged view of the second tiny peak). The internal friction (tanδ) also demonstrates double peaks at 669 K and 708 K, respectively at this stage. The overall decrease in G′ and increase in G″ at Stage II suggest an increasing viscoelastic characteristic since the material undergoes the dynamic glass transition in the supercooled liquid regime. Stage III: After 713 K, G′ increases back to the initial value of ~ 80 GPa, while G″ continuously drops to ~ 30 GPa. This is attributed to the crystallization event after 713 K, which is above the crystallization temperature of the LM2 composite [23]. Such a modulus variation at Stage III is similar to observed for monolithic BMGs at the high temperature regime where crystallization sets in [25]. The main difference between the dynamic mechanical behavior of the LM2 composite and the monolithic BMGs lies in Stage I and Stage II. In general, G′ retains almost constant below Tg for monolithic BMGs [25]. G′ for the L2 composite slightly increases from 530 K to 600 K at Stage I. We argue that this increase in G′ may result from the release of residual stresses within the composite during DMA heating. The ascast LM2 composite is composed of metallic glass matrix and supersaturated solid solution β-Zr crystals based on our previous microstructural investigation [23]. During solidification, residual compressive stresses typically form in the vicinity of the precipitated β-Zr crystals. In polymeric materials, it has been recorded that a reduction of residual stress often results in an increase in G′ and hence apparently “stiffen” the material [26]. In this regard, the heating process during DMA to some extent “anneals” the material and the residual compressive stresses during casting can be markedly released. Therefore, the subtle G′ increment in Stage I is probably originated from the residual stress release during DMA heating. At Stage II where the dynamic glass transition (α-relaxation) occurs, for monolithic BMGs, G′ often continuously decreases until a minimum whereas G″ firstly increases to and subsequently decreases continuously. In contrast, G′ demonstrates a plateau while G″ shows double peaks in the temperature regime of 669 K– 679 K. These unique modulus characteristics have not been reported previously. We attribute such characteristics to the unique β-Zr to αZr phase transformation (β-transformation) in the LM2 composite during dynamic relaxation. β-Zr is a body centered cubic (b.c.c) metastable phase at high temperatures and it tends to transform into hexagonal closest packed (h.c.p) α-Zr phase once a thermodynamic driving force
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transformation, which typically does not occur in monolithic BMGs. The β-transformation to some extent counteracts the decrease in G′ and G″ during dynamic glass transition, and the superimposition of the glass transition of the amorphous matrix and the β-transformation of the secondary crystals in turn leads to the double peaks in the G″ and tanδ curves and the plateau in the G′ curve at Stage II. In fact, the internal friction is a measure of the density of the interstitial atoms in the solid solution. The β-transformation at T = 669 K–679 K annihilates some supersaturated solid solution during heating and hence the density of the interstitial atoms decreases with the desolvation of the solid solution, which agrees well with the “valley” in tanδ.
3.2. The modulus characteristics at different frequencies
Fig. 2. The XRD patterns of the as-cast LM2 BMG composite and the as-tested after Stage II of the DMA. The phase transformation from b.c.c structured β-Zr to h.c.p structured α-Zr is detected.
is provided. For example, our previous studies have found that the phase transformation from β-Zr to α-Zr can be activated in the LM2 composite after isothermal annealing for 4 h at T = 543 K, 583 K, or 613 K [23]. Such a phase transformation in Stage II of the DMA test has been experimentally detected by XRD (Fig. 2). The phase transformation into a higher density α-Zr phase from β-Zr is associated with the elimination of twin crystals and residual compressive stresses in the β-Zr dendrites [23]. G′ and G″ are therefore enhanced due to this phase
Fig. 3 shows the frequency dependence of the dynamic mechanical response of the LM2 composite. Similar to most monolithic BMGs or polymers [17], the peak of the G′ at the onset of the glass transition of the LM2 composite gradually moves toward higher temperatures with increasing the loading frequency (Fig. 3(a)). Meanwhile, the superimposed double peaks of G″ gradually move to overall higher temperatures as well, associated with an increasingly smaller attenuation degree as the frequency increases (Fig. 3(b)). Such variations in the G′ and G″ peaks can be simply understood from the perspective of the increasing atomic mobility as increasing temperatures or decreasing frequencies. It is worth noting that the unique double peaks characteristic of G″ becomes more noticeable and the β-transformation temperature gradually decreases with increasing the frequency (Fig. 3(b)). Therefore, the increasing loading frequency may behave as a higher driving force and hence accelerate the phase transformation in the LM2 composite.
Fig. 3. The frequency dependence of storage modulus (a), loss modulus (b), and internal friction (c) of the LM2 composites under a loading amplitude of A = 3 μm and heating rate 5 K/min.
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J. Kong et al. / Materials and Design 88 (2015) 69–74 Table 2 The parameters of VFT equation and the fragility indices for different BMGs.
Vit1 [29,30] Vit4 [31] LM2 (current study) Pd40Cu30Ni10P20 [32] La55Al25Cu10Ni5Co5 [32]
B (K)
T0 (K)
f0 (Hz)
Tg (K)
m
7631 9749 15,771 4832 1270
412 352 332 431 ± 10 411 ± 10
2.97E12 1.2E13 2.3E19 1.4E13 4.0E07
623 620 603 567 453
46 37 56 64 142
the present LM2 composite (Fig. 5) further corroborates the internal structural difference of the composite. In general, the different inclination degrees reflect the different sensitivities of the reaction temperature to frequency. The higher the inclination degree, the more sensitive the effect of frequency is. 3.3. Effect of temperature on the modulus Fig. 4. Numerical analysis of VFT equation for α-relaxation and Arrhenius equation for β-transformation.
According to the relationship between viscosity (η) and temperature, Angell effectively classified the extremely complex liquids into strong liquids or fragile liquids [27]. For strong liquids, the temperature dependence of η follows the Arrhenius equation (η = η0exp (EA / RT)) whereas for fragile liquids, the temperature dependence of η follows the Vogel–Fulcher–Tammann (VFT) equation (η = η0exp[− B / (T −T0)]; f = f0exp[−B / (T − T0)]). The fragility of a liquid is essentially related to its glass transition, and it is closely linked with the non-linear relaxation, chemical structure, and atomic vibration of the liquid structure. The Arrhenius equation and VFT equation are employed herein to numerically fit the G″–T curves at different frequencies for the LM2 composite. The numerical analysis suggests that the α-relaxation behavior is well fitted with VFT equation while the β-transformation can be well described by the Arrhenius equation with the fitting parameters of f0 = 5.6 × 10−61 Hz and EA = 779.88 KJ/mol (=8.1 eV) (Fig. 4). The good fit with VFT equation for α-relaxation reveals a characteristic of a fragile liquid in the glass transition state of the LM2 composite. The parameters of VFT equation for α-relaxation and the Arrhenius equation for β-transformation are listed in Table 1. The fragility index m is defined by Angel as [28]: d logτðT Þ : m¼ d T g =T T ¼ T g
ð1Þ
Fig. 6 shows the frequency spectrum of G″ and G′ at different isothermal temperatures in the supercooled liquid region, respectively. The variational trend is consistent with the temperature spectrum obtained under a continuous load: all curves shift horizontally at different temperatures. The loss modulus (G″) spectrum appears two peaks (although the second tiny peak is not obvious) as frequency increases, corresponding to the α-relaxation and the β-phase transformation, respectively. The α-relaxation peak gradually moves toward the higher frequency with increasing the isothermal temperature, and the relaxation time (τα) at different isothermal temperatures is summarized in Table 3. In general, the dynamic relaxation process can be potentially described by various models such as Debye, Cole–Cole (C–C), Davidson–Cole (D–C), Havriliak–Negami (H–N), and Kohlrausch– Williams–Watts (KWW). Since the DMA testing results are in the form of frequency-domain, Fourier transforming was utilized to convert the above time-domain equation models into frequencydomain format. Our numerical fitting based on different models clearly reveal that the above five models cannot independently rationalize the experimental measurements. Specifically, take the results of the fitted diagrams of G″ of the frequency spectrum at 663 K for example (Fig. 7), the Debye model is based on ideal materials, and the deviation is the highest; the Davidson–Cole model fits better in the high frequency range, but there is a significant deviation in the low frequency range; Havriliak–Negami model fits not well in the entire frequency range; Cole–Cole model and KWW model fit
For the VFT-like behavior in glass-forming liquids, Eq. (1) can be simplified into: h 2 i m ¼ loge BT g = T g −T 0 :
ð2Þ
The corresponding fragility index of m = 56 for α-relaxation (glass transition) is hence calculated for the LM2 composite. This fragility index is higher than that of similar monolithic Zr-based BMG alloys such as Vit1 or Vit4 (see Table 2), which suggests that the presence of β-Zr phase varies the intrinsic structural properties of amorphous matrix. The DMA results in Table 1 and the different fitting curves of VFT parameters in the range of Tg b T b Tg + 100 K for various BMGs and Table 1 The parameters of VFT equation for α-relaxation and Arrhenius equation for βtransformation.
α-Relaxation β-Transformation
f0 (Hz)
B (K)
T0 (K)
2.3E19 5.6E−61
15,771
332
EA (KJ/mol) 779
Fig. 5. The relationship between ln(f) and 1000/T for the α-relaxation of different BMGs [29–32].
J. Kong et al. / Materials and Design 88 (2015) 69–74
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Fig. 6. The frequency dependence of the loss modulus (a) and storage modulus (b) of the LM2 composite at 633 K, 643 K, 653 K, and 663 K in the supercooled liquids.
Table 3 The relaxation time τα for the α-relaxation of the LM2 composites at different temperatures.
f0 (Hz) τ0 (s)
633 K
643 K
653 K
663 K
0.02 50
0.05 20
0.07 14.3
0.1 10
better in the low frequency, but both models significantly underpredict than the experimental results in the high frequency range. The superimposition of α-relaxation and β-phase transformation in the LM2 composite suggests that the dynamic relaxation behavior may not be described by a single model. Here, we introduce a coupling model that captures the superimposition of the two relaxation processes. Due to the relative more precise fit by the KWW model than others (Fig. 7), a modified coupling KWW model is proposed to quantitatively fit the experimental results: ϕðt Þ ¼ K expð−t=τ1 Þβ1 þ ð1−K Þ expð−t=τ 2 Þβ2
ð3Þ
where K: correlation coefficients, τ1: α-relaxation time, τ2: β-phase transformation time, β1 and β2: the non-exponentially parameters. The high consistency between the experimental observation and the coupling model indicates that the coupling KWW model can better quantify the superimposition of α-relaxation and β-phase transformation in the LM2 composite (Fig. 8). Such a coupling model is fundamentally different from the so-called “Coupling Model (CM)” proposed by Ngai et al. [33]. The concept of traditional CM is often employed to interpret the many-body nature or the heterogeneous dynamics of the
cooperative α-relaxation in glassy materials [33], whereas the current coupling KWW model seems more than a phenomenological description in elucidating the superimposition of multiple distinct relaxation processes including phase transformations in the heterogeneous BMG composite. The underlying mechanistic origin of this phenomenological description deserves further investigation. In Fig. 8, it is needed to point out that a few excess wings present in the higher frequency band, which may be attributed to the excess wings produced by β-relaxation of the amorphous matrix [31,34,35]. 4. Conclusions The DMA is utilized to examine the viscoelastic properties of the LM2 BMG composite. The LM2 composite demonstrates different dynamic mechanical behavior from monolithic BMGs resulting from distinct structural origins. Two superimposition peaks appear on the loss modulus curve of the LM2 composite, i.e. the β-transformation peak and the glass transition (α-relaxation) peak. The glass transition of the LM2 composite can be well fitted with the VFT equation while the βtransformation can be well fitted with Arrhenius equation. The studies of the isothermal frequency spectrum reveal that a single classical relaxation model cannot capture the dynamic mechanical response of the composite because of the superimposition of α-relaxation and βtransformation. We introduced a novel double KWW coupling model which better quantify the isothermal dynamic relaxation behavior of the composite. Our findings provide an insight into understanding the more complex structural relaxation of BMG composite than monolithic BMGs. More generally, the coupling effect found in the LM2 composite may offer a key guidance in thermoplastic processing of the BMG composites.
Fig. 7. Comparison of storage modulus (a) and loss modulus (b) by experimental measurements and theoretical/empirical predictions.
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Fig. 8. Comparison of loss modulus between the double KWW coupled model and experimental results at 663 K.
Author contributions J.K. and Z.Y. designed the project. J.K., Z.Y., and X.S. designed and carried out the experiments. J.K., Z.Y. and W.C. conducted the data analysis. J.K. and W.C. wrote the manuscript. All authors contributed to the discussion of the results. Acknowledgments The work is supported by the Fundamental Research Funds for the Central Universities (No. 30920130112011), and the Natural Science Foundation of Jiangsu Province of China (No. BK20131260). References [1] C.A. Schuh, T.C. Hufnagel, U. Ramamurty, Mechanical behavior of amorphous alloys, Acta Mater. 55 (2007) 4067–4109. [2] W.H. Wang, C. Dong, C. Shek, Bulk metallic glasses, Mater. Sci. Eng. R 44 (2004) 45–89. [3] W.L. Johnson, Bulk glass-forming metallic alloys: science and technology, MRS Bull. 24 (1999) 42–56. [4] J. Schroers, Processing of bulk metallic glass, Adv. Mater. 22 (2010) 1566–1597. [5] W. Chen, Z. Liu, J. Schroers, Joining of bulk metallic glasses in air, Acta Mater. 62 (2014) 49–57. [6] W. Chen, Z. Liu, H.M. Robinson, J. Schroers, Flaw tolerance vs. performance: a tradeoff in metallic glass cellular structures, Acta Mater. 73 (2014) 259–274. [7] Chen, W., Ketkaew, J., Liu, Z., Mota, R.M.O., O'Brien, K., da Silva, C.S., Schroers, J. Does the fracture toughness of bulk metallic glasses scatter? Scr. Mater. 107, 1–4 (2015) [8] S.F. Guo, H.J. Zhang, Z. Liu, W. Chen, S.F. Xie, Corrosion resistances of amorphous and crystalline Zr-based alloys in simulated seawater, Electrochem. Commun. 24 (2012) 39–42.
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Materials and Design journal homepage: www.elsevier.com/locate/jmad
Dynamic mechanical behavior of a Zr-based bulk metallic glass composite Jian Kong a,⁎, Zhitao Ye a, Wen Chen b,⁎, Xueli Shao a, Kehong Wang a, Qi Zhou a a b
School of Materials Science & Engineering, Nanjing University of Science and Technology, Nanjing 210094, China Department of Mechanical Engineering & Materials Science, Yale University, New Haven, CT 06511, USA
a r t i c l e
i n f o
Article history: Received 31 July 2015 Received in revised form 25 August 2015 Accepted 26 August 2015 Available online 31 August 2015 Keywords: Metallic glass Dynamic mechanical analysis Phase transformation Mechanical properties Structural relaxation Viscoelastic properties
a b s t r a c t Dynamic mechanical analysis (DMA) was used to study the viscoelastic properties of a Zr56.2Ti13.8Nb5.0Cu6.9Ni5.6Be12.5 (LM2) bulk metallic glass (BMG) matrix composite. The temperature spectrum and the frequency spectrum were tested by three point bending. We revealed that the relaxation process of the LM2 composite is different from the single amorphous alloys. The unique superimposition of glass transition (α-relaxation) and β-phase transformation during DMA results in double peaks on the loss modulus evolution and a plateau on the storage modulus evolution. The numerical analysis of the isothermal spectrum suggests that the dynamic relaxation behavior of the LM2 composite cannot be described by a single classical relaxation model. A coupling model is instead proposed to well quantify the coupling effect of the α-relaxation and β-phase transformation in the LM2 BMG composite. Our findings provide an insight into understanding the more complex structural relaxation of BMG composite than monolithic BMGs. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Bulk metallic glasses (BMGs) are a family of amorphous materials rapidly quenched from metal alloy melts such that crystallization is suppressed. The absence of crystalline structure endows BMGs with a variety of attractive properties including high strength, high elastic limit, strong corrosion resistance, and unique processability in the supercooled liquid state [1–10]. The severe brittleness of BMGs at low temperatures, especially under un-constraint loading condition such as tension, has in the past decade limited the structural application of BMGs [1–3]. To solve this issue, the successful development of BMG composites has been recognized as a breakthrough where an effective toughening mechanism has been achieved by introducing a secondary crystalline phase within the amorphous matrix [11,12]. A thorough discussion on the mechanical behavior of BMGs and a dedicated analysis on the overall fracture process/mechanism of BMGs and their composites can be found in a recent comprehensive review by Sun and Wang [13]. The metastable nature of amorphous structure suggests the dynamic relaxation processes which correlate with the internal atomic structure and mechanical behavior of glassy materials. In polymeric materials, there are two relaxation processes: the main (α) relaxation and the secondary Johari–Goldstein (β) relaxation, the former of which
⁎ Corresponding authors. E-mail addresses: [email protected] (J. Kong), [email protected] (W. Chen).
http://dx.doi.org/10.1016/j.matdes.2015.08.132 0264-1275/© 2015 Elsevier Ltd. All rights reserved.
corresponds to the glass transition or local movements of the chain structures while the latter is often linked to the movements of the side groups. In BMGs, the non-directional atomic packing by metallic bonding results in a macroscopically homogeneous structure without any long range order. However, the microscopically short ranges orders and medium range orders have been experimentally observed [14]. Free volume model and shear transformation zone (STZ) model have been proposed to describe these nanoscale or sub-nanoscale heterogeneous structures [15,16]. The unique internal atomic organization in BMGs obviously plays a key role in determining the time-sensitive dynamic mechanical (e.g., viscoelastic or viscoplastic) behavior of BMGs. The αrelaxation has been extensively observed in various BMGs whereas a distant secondary β-relaxation is observed for some BMGs [17]. Several models such as Debye model [18], Cole–Cole model [19], Cole–Davidson model [20], Kohlrausch–Williams–Watts (KWW) model [21], and Havriliak–Negami model [22] have been employed to theoretically describe the relaxation behavior in BMGs. In comparison with the extensive investigations of monolithic BMGs, the understanding of the structural information such as the glass transition and the mechanical relaxation behavior of BMG composites is still rather limited. A particular question is how these properties evolve with the existence of the secondary crystalline phase, especially during structural service or materials processing. In this paper, the dynamic mechanical analysis (DMA) has been used to study the dynamic mechanical properties of a Zr56.2Ti13.8Nb5.0Cu6.9Ni5.6Be12.5 BMG matrix composite at different temperatures with different periodic loads. We examined the viscoelastic properties of the LM2 BMG composite, and
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particularly analyzed the influence of the secondary dendritic crystal phase on the dynamic mechanical response of the composite. From a practical viewpoint, the elastic and viscoelastic properties of BMG composites with different temperatures and dynamic loading conditions provide an insight into the processability and mechanical performance of the class of BMG composite materials. 2. Materials and methods Master ingots with nominal composition of LM2(Zr56.2Ti13.8Nb5.0 Cu6.9Ni5.6Be12.5, at.%) were prepared from a mixture of pure elements (purity ≥99.99%) by arc melting under a high purity Argon atmosphere. In order to improve the chemical homogeneity of the alloy, the ingots were remelted at least four times and subsequently cast into a copper mold to produce a rectangular feedstock with dimensions of 80 mm ∗ 50 mm ∗ 3 mm. The structure of the BMG matrix composite was detected by X-ray diffraction (XRD, Rigaku-200) with Cu target (λ = 1.5404 Å) and was observed by scanning electron microscopy (SEM, Philips Quanta-200). The characteristic temperatures of the composite were determined by differential scanning calorimetry (DSC, NETZSCH-STA4490C). The XRD, DSC, SEM results suggested that the casting samples were BMG matrix composite [23]. The glass transition onset temperature, Tg, and the crystallization onset temperature, Tx, were determined by the DSC to be 603 K and 673 K, respectively at a heating rate of 20 K/min. DMA has behaved as a toolbox for studying the mechanical properties and structural details of a wide range of materials including polymers, crystalline metals, and ceramics [24]. The dynamic mechanical behavior of a material is essentially the response of strain (or stress) to an applied periodic stress (or strain). As a periodic stress σ = σ0 cos (ωt) with a frequency ω is applied to a material, the resulting deformation is recorded as ε = ε0 cos(ωt + δ). For viscoelastic materials, the strain lags behind the stress with a phase angle δ. The ratio of stress to strain gives the modulus. For viscoelastic materials, the modulus G⁎ is a complex number due to the phase lag between the stress and strain, defined by G⁎ = σ⁎ / ε⁎ = G′ + iG″, where G′ is the storage modulus and G″ is the loss modulus. These parameters directly reflect the atomic mobility and the atomic structure that govern the viscoelastic behavior, mechanical relaxation, and the glass transition behavior of amorphous matters. In this work, DMA measurements were performed using TA DMA-Q800 by three-point bending. The samples were cut into a rectangular geometry with dimensions of 1.5 mm ∗ 3.0 mm ∗ 30 mm. To measure the temperature spectrum, a static force of 1 N was applied with a loading amplitude of 3 μm at different frequencies of 1 Hz, 5 Hz, 10 Hz, 20 Hz, and 100 Hz. The temperature was increased from room temperature (RT) to 773 K at a rate of 5 K/min. To measure the isothermal frequency spectrum, a static force of 0.1 N was applied with a loading amplitude of 3 μm with frequencies ranging from 0.01 to 100 Hz. Four different isothermal temperatures of 633 K, 643 K, 653 K, and 663 K were chosen. 3. Results and discussion 3.1. The modulus characteristics at a fixed frequency Fig. 1 shows the temperature dependence of the storage modulus (G′), the loss modulus (G″), and the internal friction (tanδ = G″/G′) of the LM2 composite at a fixed loading frequency of 1 Hz. The temperature dependence of the dynamic mechanical behavior of the LM2 composite can be divided into three stages. Stage I: At low temperatures when T b 530 K, G′ is high while G″ is very low and both are almost constant. Hence, the material is highly elastic and the viscoelastic component is negligible. As the temperature increases to ~ 600 K, G′ increases until a maximum of ~ 86 GPa and G″ also starts to increase, suggesting an increasing viscoelasticity. Stage II: G′ starts to decrease rapidly from 86 GPa to approximately 45 GPa with increasing the
Fig. 1. The temperature dependence of storage modulus (G′), loss modulus (G″), and internal friction (tanδ) of the LM2 composite under a loading condition of ω = 1 Hz, A = 3 μm, heating rate 5 K/min.
temperature from 603 K to 669 K. At the temperature region of 669 K–679 K, a plateau appears, followed by a further dramatic decrease to a minimum of 15 GPa as temperature continuously increases to 713 K. In contrast, G″ increases dramatically and decreases again after double peaks of approximately 85 GPa and 77 GPa at 662 K and 688 K, respectively (see Fig. 3(b) for the enlarged view of the second tiny peak). The internal friction (tanδ) also demonstrates double peaks at 669 K and 708 K, respectively at this stage. The overall decrease in G′ and increase in G″ at Stage II suggest an increasing viscoelastic characteristic since the material undergoes the dynamic glass transition in the supercooled liquid regime. Stage III: After 713 K, G′ increases back to the initial value of ~ 80 GPa, while G″ continuously drops to ~ 30 GPa. This is attributed to the crystallization event after 713 K, which is above the crystallization temperature of the LM2 composite [23]. Such a modulus variation at Stage III is similar to observed for monolithic BMGs at the high temperature regime where crystallization sets in [25]. The main difference between the dynamic mechanical behavior of the LM2 composite and the monolithic BMGs lies in Stage I and Stage II. In general, G′ retains almost constant below Tg for monolithic BMGs [25]. G′ for the L2 composite slightly increases from 530 K to 600 K at Stage I. We argue that this increase in G′ may result from the release of residual stresses within the composite during DMA heating. The ascast LM2 composite is composed of metallic glass matrix and supersaturated solid solution β-Zr crystals based on our previous microstructural investigation [23]. During solidification, residual compressive stresses typically form in the vicinity of the precipitated β-Zr crystals. In polymeric materials, it has been recorded that a reduction of residual stress often results in an increase in G′ and hence apparently “stiffen” the material [26]. In this regard, the heating process during DMA to some extent “anneals” the material and the residual compressive stresses during casting can be markedly released. Therefore, the subtle G′ increment in Stage I is probably originated from the residual stress release during DMA heating. At Stage II where the dynamic glass transition (α-relaxation) occurs, for monolithic BMGs, G′ often continuously decreases until a minimum whereas G″ firstly increases to and subsequently decreases continuously. In contrast, G′ demonstrates a plateau while G″ shows double peaks in the temperature regime of 669 K– 679 K. These unique modulus characteristics have not been reported previously. We attribute such characteristics to the unique β-Zr to αZr phase transformation (β-transformation) in the LM2 composite during dynamic relaxation. β-Zr is a body centered cubic (b.c.c) metastable phase at high temperatures and it tends to transform into hexagonal closest packed (h.c.p) α-Zr phase once a thermodynamic driving force
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transformation, which typically does not occur in monolithic BMGs. The β-transformation to some extent counteracts the decrease in G′ and G″ during dynamic glass transition, and the superimposition of the glass transition of the amorphous matrix and the β-transformation of the secondary crystals in turn leads to the double peaks in the G″ and tanδ curves and the plateau in the G′ curve at Stage II. In fact, the internal friction is a measure of the density of the interstitial atoms in the solid solution. The β-transformation at T = 669 K–679 K annihilates some supersaturated solid solution during heating and hence the density of the interstitial atoms decreases with the desolvation of the solid solution, which agrees well with the “valley” in tanδ.
3.2. The modulus characteristics at different frequencies
Fig. 2. The XRD patterns of the as-cast LM2 BMG composite and the as-tested after Stage II of the DMA. The phase transformation from b.c.c structured β-Zr to h.c.p structured α-Zr is detected.
is provided. For example, our previous studies have found that the phase transformation from β-Zr to α-Zr can be activated in the LM2 composite after isothermal annealing for 4 h at T = 543 K, 583 K, or 613 K [23]. Such a phase transformation in Stage II of the DMA test has been experimentally detected by XRD (Fig. 2). The phase transformation into a higher density α-Zr phase from β-Zr is associated with the elimination of twin crystals and residual compressive stresses in the β-Zr dendrites [23]. G′ and G″ are therefore enhanced due to this phase
Fig. 3 shows the frequency dependence of the dynamic mechanical response of the LM2 composite. Similar to most monolithic BMGs or polymers [17], the peak of the G′ at the onset of the glass transition of the LM2 composite gradually moves toward higher temperatures with increasing the loading frequency (Fig. 3(a)). Meanwhile, the superimposed double peaks of G″ gradually move to overall higher temperatures as well, associated with an increasingly smaller attenuation degree as the frequency increases (Fig. 3(b)). Such variations in the G′ and G″ peaks can be simply understood from the perspective of the increasing atomic mobility as increasing temperatures or decreasing frequencies. It is worth noting that the unique double peaks characteristic of G″ becomes more noticeable and the β-transformation temperature gradually decreases with increasing the frequency (Fig. 3(b)). Therefore, the increasing loading frequency may behave as a higher driving force and hence accelerate the phase transformation in the LM2 composite.
Fig. 3. The frequency dependence of storage modulus (a), loss modulus (b), and internal friction (c) of the LM2 composites under a loading amplitude of A = 3 μm and heating rate 5 K/min.
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J. Kong et al. / Materials and Design 88 (2015) 69–74 Table 2 The parameters of VFT equation and the fragility indices for different BMGs.
Vit1 [29,30] Vit4 [31] LM2 (current study) Pd40Cu30Ni10P20 [32] La55Al25Cu10Ni5Co5 [32]
B (K)
T0 (K)
f0 (Hz)
Tg (K)
m
7631 9749 15,771 4832 1270
412 352 332 431 ± 10 411 ± 10
2.97E12 1.2E13 2.3E19 1.4E13 4.0E07
623 620 603 567 453
46 37 56 64 142
the present LM2 composite (Fig. 5) further corroborates the internal structural difference of the composite. In general, the different inclination degrees reflect the different sensitivities of the reaction temperature to frequency. The higher the inclination degree, the more sensitive the effect of frequency is. 3.3. Effect of temperature on the modulus Fig. 4. Numerical analysis of VFT equation for α-relaxation and Arrhenius equation for β-transformation.
According to the relationship between viscosity (η) and temperature, Angell effectively classified the extremely complex liquids into strong liquids or fragile liquids [27]. For strong liquids, the temperature dependence of η follows the Arrhenius equation (η = η0exp (EA / RT)) whereas for fragile liquids, the temperature dependence of η follows the Vogel–Fulcher–Tammann (VFT) equation (η = η0exp[− B / (T −T0)]; f = f0exp[−B / (T − T0)]). The fragility of a liquid is essentially related to its glass transition, and it is closely linked with the non-linear relaxation, chemical structure, and atomic vibration of the liquid structure. The Arrhenius equation and VFT equation are employed herein to numerically fit the G″–T curves at different frequencies for the LM2 composite. The numerical analysis suggests that the α-relaxation behavior is well fitted with VFT equation while the β-transformation can be well described by the Arrhenius equation with the fitting parameters of f0 = 5.6 × 10−61 Hz and EA = 779.88 KJ/mol (=8.1 eV) (Fig. 4). The good fit with VFT equation for α-relaxation reveals a characteristic of a fragile liquid in the glass transition state of the LM2 composite. The parameters of VFT equation for α-relaxation and the Arrhenius equation for β-transformation are listed in Table 1. The fragility index m is defined by Angel as [28]: d logτðT Þ : m¼ d T g =T T ¼ T g
ð1Þ
Fig. 6 shows the frequency spectrum of G″ and G′ at different isothermal temperatures in the supercooled liquid region, respectively. The variational trend is consistent with the temperature spectrum obtained under a continuous load: all curves shift horizontally at different temperatures. The loss modulus (G″) spectrum appears two peaks (although the second tiny peak is not obvious) as frequency increases, corresponding to the α-relaxation and the β-phase transformation, respectively. The α-relaxation peak gradually moves toward the higher frequency with increasing the isothermal temperature, and the relaxation time (τα) at different isothermal temperatures is summarized in Table 3. In general, the dynamic relaxation process can be potentially described by various models such as Debye, Cole–Cole (C–C), Davidson–Cole (D–C), Havriliak–Negami (H–N), and Kohlrausch– Williams–Watts (KWW). Since the DMA testing results are in the form of frequency-domain, Fourier transforming was utilized to convert the above time-domain equation models into frequencydomain format. Our numerical fitting based on different models clearly reveal that the above five models cannot independently rationalize the experimental measurements. Specifically, take the results of the fitted diagrams of G″ of the frequency spectrum at 663 K for example (Fig. 7), the Debye model is based on ideal materials, and the deviation is the highest; the Davidson–Cole model fits better in the high frequency range, but there is a significant deviation in the low frequency range; Havriliak–Negami model fits not well in the entire frequency range; Cole–Cole model and KWW model fit
For the VFT-like behavior in glass-forming liquids, Eq. (1) can be simplified into: h 2 i m ¼ loge BT g = T g −T 0 :
ð2Þ
The corresponding fragility index of m = 56 for α-relaxation (glass transition) is hence calculated for the LM2 composite. This fragility index is higher than that of similar monolithic Zr-based BMG alloys such as Vit1 or Vit4 (see Table 2), which suggests that the presence of β-Zr phase varies the intrinsic structural properties of amorphous matrix. The DMA results in Table 1 and the different fitting curves of VFT parameters in the range of Tg b T b Tg + 100 K for various BMGs and Table 1 The parameters of VFT equation for α-relaxation and Arrhenius equation for βtransformation.
α-Relaxation β-Transformation
f0 (Hz)
B (K)
T0 (K)
2.3E19 5.6E−61
15,771
332
EA (KJ/mol) 779
Fig. 5. The relationship between ln(f) and 1000/T for the α-relaxation of different BMGs [29–32].
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Fig. 6. The frequency dependence of the loss modulus (a) and storage modulus (b) of the LM2 composite at 633 K, 643 K, 653 K, and 663 K in the supercooled liquids.
Table 3 The relaxation time τα for the α-relaxation of the LM2 composites at different temperatures.
f0 (Hz) τ0 (s)
633 K
643 K
653 K
663 K
0.02 50
0.05 20
0.07 14.3
0.1 10
better in the low frequency, but both models significantly underpredict than the experimental results in the high frequency range. The superimposition of α-relaxation and β-phase transformation in the LM2 composite suggests that the dynamic relaxation behavior may not be described by a single model. Here, we introduce a coupling model that captures the superimposition of the two relaxation processes. Due to the relative more precise fit by the KWW model than others (Fig. 7), a modified coupling KWW model is proposed to quantitatively fit the experimental results: ϕðt Þ ¼ K expð−t=τ1 Þβ1 þ ð1−K Þ expð−t=τ 2 Þβ2
ð3Þ
where K: correlation coefficients, τ1: α-relaxation time, τ2: β-phase transformation time, β1 and β2: the non-exponentially parameters. The high consistency between the experimental observation and the coupling model indicates that the coupling KWW model can better quantify the superimposition of α-relaxation and β-phase transformation in the LM2 composite (Fig. 8). Such a coupling model is fundamentally different from the so-called “Coupling Model (CM)” proposed by Ngai et al. [33]. The concept of traditional CM is often employed to interpret the many-body nature or the heterogeneous dynamics of the
cooperative α-relaxation in glassy materials [33], whereas the current coupling KWW model seems more than a phenomenological description in elucidating the superimposition of multiple distinct relaxation processes including phase transformations in the heterogeneous BMG composite. The underlying mechanistic origin of this phenomenological description deserves further investigation. In Fig. 8, it is needed to point out that a few excess wings present in the higher frequency band, which may be attributed to the excess wings produced by β-relaxation of the amorphous matrix [31,34,35]. 4. Conclusions The DMA is utilized to examine the viscoelastic properties of the LM2 BMG composite. The LM2 composite demonstrates different dynamic mechanical behavior from monolithic BMGs resulting from distinct structural origins. Two superimposition peaks appear on the loss modulus curve of the LM2 composite, i.e. the β-transformation peak and the glass transition (α-relaxation) peak. The glass transition of the LM2 composite can be well fitted with the VFT equation while the βtransformation can be well fitted with Arrhenius equation. The studies of the isothermal frequency spectrum reveal that a single classical relaxation model cannot capture the dynamic mechanical response of the composite because of the superimposition of α-relaxation and βtransformation. We introduced a novel double KWW coupling model which better quantify the isothermal dynamic relaxation behavior of the composite. Our findings provide an insight into understanding the more complex structural relaxation of BMG composite than monolithic BMGs. More generally, the coupling effect found in the LM2 composite may offer a key guidance in thermoplastic processing of the BMG composites.
Fig. 7. Comparison of storage modulus (a) and loss modulus (b) by experimental measurements and theoretical/empirical predictions.
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Fig. 8. Comparison of loss modulus between the double KWW coupled model and experimental results at 663 K.
Author contributions J.K. and Z.Y. designed the project. J.K., Z.Y., and X.S. designed and carried out the experiments. J.K., Z.Y. and W.C. conducted the data analysis. J.K. and W.C. wrote the manuscript. All authors contributed to the discussion of the results. Acknowledgments The work is supported by the Fundamental Research Funds for the Central Universities (No. 30920130112011), and the Natural Science Foundation of Jiangsu Province of China (No. BK20131260). References [1] C.A. Schuh, T.C. Hufnagel, U. Ramamurty, Mechanical behavior of amorphous alloys, Acta Mater. 55 (2007) 4067–4109. [2] W.H. Wang, C. Dong, C. Shek, Bulk metallic glasses, Mater. Sci. Eng. R 44 (2004) 45–89. [3] W.L. Johnson, Bulk glass-forming metallic alloys: science and technology, MRS Bull. 24 (1999) 42–56. [4] J. Schroers, Processing of bulk metallic glass, Adv. Mater. 22 (2010) 1566–1597. [5] W. Chen, Z. Liu, J. Schroers, Joining of bulk metallic glasses in air, Acta Mater. 62 (2014) 49–57. [6] W. Chen, Z. Liu, H.M. Robinson, J. Schroers, Flaw tolerance vs. performance: a tradeoff in metallic glass cellular structures, Acta Mater. 73 (2014) 259–274. [7] Chen, W., Ketkaew, J., Liu, Z., Mota, R.M.O., O'Brien, K., da Silva, C.S., Schroers, J. Does the fracture toughness of bulk metallic glasses scatter? Scr. Mater. 107, 1–4 (2015) [8] S.F. Guo, H.J. Zhang, Z. Liu, W. Chen, S.F. Xie, Corrosion resistances of amorphous and crystalline Zr-based alloys in simulated seawater, Electrochem. Commun. 24 (2012) 39–42.
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