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Nanolaminate of metallic glass and graphene with enhanced elastic modulus, strength, and ductility in tension
Scripta Materialia 139 (2017) 63–66
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Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Nanolaminate of metallic glass and graphene with enhanced elastic modulus, strength, and ductility in tension Sun-Young Park a,b, Eun-Ji Gwak b, Ming Huang a,c, Rodney S. Ruoff a,c, Ju-Young Kim a,b,⁎ a b c
Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea School of Materials Science and Engineering, UNIST (Ulsan National University of Science and Technology), Ulsan 44919, Republic of Korea School of Natural Science, UNIST, Ulsan 44919, Republic of Korea
a r t i c l e
i n f o
Article history: Received 24 May 2017 Received in revised form 15 June 2017 Accepted 15 June 2017 Available online xxxx Keywords: Sputtering Tension test Metallic glass Multilayers thin films Graphene
a b s t r a c t We fabricate a nanolaminate by repeated co-sputter deposition of a 60 nm-thick Cu50Zr50 metallic glass layer alternating with transfer of graphene. In situ micro-tensile tests reveal that the addition of a very small fraction (0.46 vol%) of graphene in the nanolaminate improve the elastic modulus and yield strength of the nanolaminate by 9.6% and 14%, respectively, comparing with those of the 360 nm-thick monolithic Cu50Zr50 metallic glass. The nanolaminate also show enhanced tensile ductility: an ultimate tensile strength of 2.23 GPa and fracture strain of 5.39% were attained by strain-hardening after yielding at 1.98 GPa stress and 3.69% strain. © 2017 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
Metallic glasses exhibit superior strength and high elastic limits, but they generally have a lack of tensile ductility that results in sudden and catastrophic failure [1,2]. Considerable work has been aimed at improving the tensile ductility of metallic glasses [3,4], and the development of glass-matrix composites with high toughness and tensile ductility is being explored [5]. Two basic techniques are employed to attain high tensile ductility: introducing a softer secondary phase in the metallic glass matrix to induce generation of local shear banding around the secondary phase and reducing its external dimensions to suppress a propagation of shear bands or occur homogeneous flow instead, leading to enhanced strength and ductility [6–9]. Since there are limited structural applications for monolithic metallic glass with dimensions of the order of 100 nm, nanolaminates with alternating layers of metallic glass (with dimensions of 100 nm or less) and another material have been suggested as a more practical material [10,11]. Metallic glass-based nanolaminates with proper interfacial material and optimum layer thickness exhibit improved strength and ductility by utilizing sizedependent homogeneous flow of metallic glass [12,13]. Graphene is known to have an intrinsic breaking strength of 130 GPa at 25% [14] strain, which is promising for application as a corrosion barrier, lubricant material, or interfacial material in nanolaminates [15,16]. While the role of graphene as a reinforcing constituent material in metal-
⁎ Corresponding author at: Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea. E-mail address: [email protected] (J.-Y. Kim).
http://dx.doi.org/10.1016/j.scriptamat.2017.06.031 1359-6462/© 2017 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
based nanolaminates has been investigated, the strengthening effect of graphene interfacial layers with metallic glass has not been studied. We investigate a nanolaminate with alternating layers of Cu50Zr50 metallic glass and CVD-grown graphene with enhanced tensile strength and ductility. We fabricate monolithic 360 nm-thick Cu50Zr50 metallic glass and a nanolaminate consisting of 60 nm-thick Cu50Zr50 metallic glass and graphene, and conduct in situ micro-tensile testing. Compared with the 360 nm-thick monolithic metallic glass, which shows typical brittle fracture behavior, i.e., linear elastic deformation followed by catastrophic failure, the nanolaminate shows 14% higher yield strength and enhanced plasticity. Through interrupted micro-tensile testing, we investigate the strain-hardening behavior of the nanolaminate by suppressing shear-band propagation in the 60 nm-thick metallic glass layer. Fig. 1 illustrates the process used to prepare a nanolaminate with alternating layers of 60 nm-thick Cu50Zr50 metallic glass; the nanolaminate consisted of a total of five layers of graphene interleaving between a total of six layers of Cu50Zr50 metallic glass. The Cu50Zr50 metallic glass was deposited on a Si(100) substrate by co-sputtering using two separated pure Cu and Zr targets. The chemical composition of the Cu50Zr50 metallic glass was measured by energy-dispersive X-ray spectroscopy (EDS), and the existence of Cu50Zr50 in the amorphous phase was confirmed by transition electron microscopy (TEM). Graphene was synthesized on a 25 μm-thick Cu foil by CVD and transferred on Cu50Zr50 metallic glass thin film by PMMA-assisted method [17]. We measured the ratio of the intensities of the 2D and G peaks (I2D/IG) for transferred graphene on the Cu50Zr50 layer using Raman spectroscopy,
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Fig. 1. Fabrication of nanolaminate with alternating layers of Cu50Zr50 metallic glass and graphene, and sample preparation for in-situ SEM micro-tensile testing.
which confirmed most transferred area was monolayer graphene as shown in inset of Fig. 1. Freestanding film samples of the monolithic metallic glass and nanolaminate were prepared by undercutting the Si substrate by isotropic dry-etch with XeF2 gas. Dog-bone-shaped specimens with dimensions of 1 μm (gauge width) × 4 μm (gauge length) were prepared by FIB (Quanta 3D, FEI, USA) milling and then transferred onto push-topull (P-to-P) devices (Hysitron, USA) using a micromanipulator for in situ SEM micro-tensile testing. In situ SEM uniaxial micro-tensile tests were performed using a picoindenter (PI-87, Hysitron, USA). The micro-tensile tests were carried out at a constant strain rate of 1 × 10−3 s−1, and real-time movies were recorded with a field-emission SEM (FE-SEM; Quanta200, FEI, USA). The actual force exerted on each dog-gone-shaped specimen was computed by subtracting the estimated force using the stiffness of the push-to-pull devices. The initial geometry of the specimen was measured using SEM images, and the change in gauge length was measured using still images extracted from the movie, from which the true stress and strain were calculated. Fig. 2 shows typical stress–strain curves of the specimens. The monolithic metallic glass showed typical brittle fracture behavior: linear elastic deformation followed by sudden and catastrophic failure directly after yielding at a yield strength of 1.74 ± 0.03 GPa, which were measured by the 0.2%-offset method. Compared to the monolithic metallic glass, the nanolaminate of metallic glass and graphene showed a higher yield strength of 1.98 ± 0.04 GPa and enhanced ductility after yielding, leading to an ultimate tensile strength of 2.23 ± 0.06 GPa and strain of 1.7% from yielding to failure. The elastic modulus, fracture strength, and strain of graphene via computational simulation have approximate values of 1 TPa, 100 GPa, and 20% [18], respectively, even though they deviate slightly depending on the loading direction and methodology. An elastic modulus of 1 TPa and intrinsic breaking strength of 130 GPa at strain of 25% were measured through hole-nanoindentations in single-crystalline graphene [14]. More recently, a fracture strength of 98.5 GPa and elastic modulus of 979 GPa were measured for CVDgrown graphene with grain sizes of 1–5 μm, and a fracture strength of
118 GPa and elastic modulus of 1011 GPa were measured for CVDgrown graphene with grain sizes of 50–200 μm [19]. These values are in good agreement with those predicted by computational simulations of single-crystalline graphene. The CVD-grown graphene used in this study is likely to have a grain size about 10 μm [20]. It is likely that few grain boundaries were included in the five graphene layers in the nanolaminate gauge section measuring 1 μm × 4 μm. The nanolaminate specimens were under iso-strain and their fracture strain was 5.39% ± 0.32%, which is much lower than the fracture strain of graphene. Regardless of the graphene grain size, it seems reasonable to assume that as a nanolaminate constituent, graphene showed elastic behavior with an elastic modulus of 1 TPa until nanolaminate failure occurred. The elastic modulus was measured from the slope of the stress– strain curve in the linear elastic region; it had a value of 51.0 ± 2.14 GPa for monolithic metallic glass and 55.9 ± 1.68 GPa for the nanolaminate. The elastic modulus in laminated materials is generally calculated by a simple rule-of-mixture when tensile force is applied along the in-plane direction. The rule-of-mixture was applied to the six layers of 60 nm-thick metallic glass with elastic modulus 51 GPa and five layers of 0.335 nm-thick graphene with elastic modulus of 1 TPa [14], which predicted an elastic modulus of 56 GPa for the resulting nanolaminate, which is similar to the value obtained in our measurements. Despite the very low volume graphene fraction in the nanolaminate, 0.46%, the graphene layers enhanced the elastic modulus of the nanolaminate by 9.6% because of graphene's ultra-high elastic modulus. The yield strength of the nanolaminate was 14% above that of monolithic metallic glass. As with the elastic modulus, the stress applied to constituents in laminated materials can also be calculated by a simple rule-of-mixture when tensile force is applied along the in-plane direction: σnanolaminate = σMGVMG + σgrapheneVgraphene where σ is the stress, V is the volume fraction, and subscript MG indicates metallic glass. Using the measured yield strength of 1.98 GPa for the nanolaminate, the stress applied on graphene, obtained at a yield strain of 3.69% for the nanolaminate, was calculated from an elastic modulus of 1 TPa
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the negligible plasticity by shear-band propagation lead to a transition in deformation mode of monolithic metallic glass to enhanced plasticity by homogeneous flow [7,21]. While the ultimate tensile strength of monolithic metallic glass is enhanced by plastic flow on the sub100 nm scale, its yield strength is not distinctly enhanced [7,22,23]. In nanolaminates whose metallic glass layers are thinner than the critical thickness for the transition, the yield strength of the constituent metallic glass layer is similar to or slightly higher than that of a metallic glass layer that is thicker than the critical thickness. Unlike the 360 nm-thick monolithic metallic glass, the nanolaminate showed enhanced strain-hardening behavior: its ultimate tensile strength of 2.23 GPa was 12.6% higher than its yield strength of 1.98 GPa, and its fracture strain of 5.39% ± 0.32% was 46% higher than its yield strain of 3.69% ± 0.04%. Since the graphene layer exhibited parabolic nonlinear elastic deformation behavior up to strains well above the nanolaminate fracture strain, the onset of nonlinearity in the nanolaminate should most probably be attributed to a transition in deformation mode of the metallic glass layers. When designing the 60 nmthick metallic glass layers in the nanolaminate, we expected the enhanced plasticity by homogeneous flow that was observed in the monolithic metallic glass and the metallic glass layers in the nanolaminate on the sub-100 nm scale. We carried out interrupted micro-tensile testing on the nanolaminate specimens, as shown in Fig. 3. The second and third re-loading curves do not show linear elastic behavior up to the peak stress of previous steps, possibly because of graphene's nonlinear elastic behavior. However, the yield strengths in the first, second, and third loading gradually increased to 1.95 ± 0.05, 2.02 ± 0.02, and 2.11 ± 0.02 GPa, respectively, which should be attributed to strain-hardening of the nanolaminate specimens' metallic glass layers. For bulk metallic glasses, Johnson and Samwer suggested a phenomenological model for temperature-dependent plastic yielding of metallic glass, Fig. 2. (a) Typical tensile curves of 360 nm-thick monolithic metallic glass and nanolaminate with alternating layers of 60 nm-thick metallic glass and graphene. SEM images during tensile testing of (b) 360 nm-thick monolithic metallic glass and (c) the nanolaminate.
and the volume fractions mentioned above. The yield strength of metallic glass in the nanolaminate was estimated to be 1.81 GPa, which is slightly above the yield strength of the 360 nm-thick monolithic metallic glass, 1.74 GPa. By reducing the external size to the sub-100 nm scale,
γy G
2=3
¼ 0:036−0:016ðTTg Þ
where γy is the elastic strain limit in
shear, E the elastic modulus, T the temperature, and Tg the glass-transition temperature [24]. A modified Johnson–Samwer relation was suggested later,
εy E
2=3
¼ 0:026−0:012ðTTg Þ
where εy is the yield strain with
εy = γy/(1 + ν) and ν is Poisson's ratio [25]. A shear modulus of 31.3 GPa, elastic modulus of 84 GPa, Poisson's ratio of 0.35, and glasstransition temperature of 670 K were measured for Cu50Zr50 bulk metallic glass [26]. Substituting these values into the two equations, we found that homogeneous flow could occur at a uniaxial stress of 1.06 GPa from the Johnson–Samwer model and a uniaxial stress of 2.05 GPa from the modified Johnson–Samwer model. The mechanical properties and
Fig. 3. Interrupted in-situ micro-tensile testing for nanolaminate with alternating layers of 60 nm-thick metallic glass and graphene. (a) Yield strength in first, second, and third loading increases gradually, supporting that 60 nm-thick metallic glass layers are strain-hardened by homogeneous flow. (b) Homogeneous deformation is observed during interrupted microtensile testing.
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Fig. 4. Deformation map of metallic glass in nanolaminate at reduced size.
glass-transition temperature of Cu50Zr50 metallic glass could be different from those of Cu50Zr50 bulk metallic glass because our samples were prepared by co-sputtering, which could have led to different microstructural properties such as atomic packing density and homogeneity of atomic mixing. However, the original and modified Johnson– Samwer models both reveal that Cu50Zr50 metallic glass can be deformed by homogeneous flow at a yield strength that is similar to or lower than 1.74 GPa, the value for the 360 nm-thick monolithic Cu50Zr50 metallic glass. The highest strength that can be obtained for the metallic glass layer was the theoretical strength. A value of 2.83 GPa was obtained for the theoretical strength of co-sputtered Cu50Zr50 metallic glass layers in nanolaminates consisting of alternating layers of Cu50Zr50 metallic glass and nanocrystalline Cu [13]. By taking into consideration the volume fractions of the metallic glass and graphene layers, an ultimate tensile strength of 2.23 GPa for the nanolaminate would require the 60 nm-thick metallic glass layers to have a yield strength of 1.98 GPa for shear band propagation, which is much lower than the theoretical strength. The theoretical strength and the stress required for homogeneous flow are both independent of the external size of metallic glass. However, the stress required for shear-band propagation is most likely to depend on the external size of the metallic glass sample. In Griffith's theory, by setting the energy released by crack propagation proportional to the square of external sample size and setting the elastically-stored energy proportional to the cube of the external sample size, one can obtain the stress criterion between regions for brittle fracture and homogeneous deformation. By using the nanopillar diameter and effective sample radius [7,8,25,27], the stress required for shear-band propagation for metallic glass was suggested to increase with decreasing external sample size in the form of an exponential function, σ ∝ d−m where d is the external sample dimension (Fig. 4). The embryonic shear band is known to form on the scale of several atomic diameters [12,28], and the term “shear-band propagation” refers to the development from an embryonic shear band to a mature shear band, which is believed to require higher stress as the external sample size decreases. As mentioned above, the metallic glass layers in the nanolaminate in our study initiated homogeneous flow at a yield strength of 1.81 GPa for the nanolaminate, and it exhibited catastrophic failure by shear-band propagation at the ultimate tensile strength of the nanolaminate.
We designed and fabricated a nanolaminate with six 60 nm-thick layers of Cu50Zr50 metallic glass alternating with five layers of graphene. The primary goals of the design were as follows: (1) enhancing the elastic modulus and yield strength of the nanolaminate by using graphene with an ultra-high elastic modulus and elastic deformation limit as the reinforcing constituent; (2) improving the tensile ductility of the nanolaminate by inducing homogenous flow in the metallic glass layers at a reduced layer thickness. In situ micro-tensile testing revealed that (1) the elastic modulus and yield strength of the nanolaminate were higher than those of the 360 nm-thick monolithic metallic glass, which was explained by the simple rule-of-mixture, and (2) the explicit homogeneous flow in the 60 nm-thick metallic glass layers led to improved tensile ductility of the nanolaminate. This work was supported by the Institute for Basic Science (IBSR019-D1), by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science, ICT & Future Planning (MSIP) (NO. NRF-2015R1A15A1037627), and by the Global Frontier R&D Program on Center for Multiscale Energy System funded by the National Research Foundation under the Ministry of Science, ICT & Future Planning, Korea (2012M3A6A7054855). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
[20]
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Contents lists available at ScienceDirect
Scripta Materialia journal homepage: www.elsevier.com/locate/scriptamat
Nanolaminate of metallic glass and graphene with enhanced elastic modulus, strength, and ductility in tension Sun-Young Park a,b, Eun-Ji Gwak b, Ming Huang a,c, Rodney S. Ruoff a,c, Ju-Young Kim a,b,⁎ a b c
Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea School of Materials Science and Engineering, UNIST (Ulsan National University of Science and Technology), Ulsan 44919, Republic of Korea School of Natural Science, UNIST, Ulsan 44919, Republic of Korea
a r t i c l e
i n f o
Article history: Received 24 May 2017 Received in revised form 15 June 2017 Accepted 15 June 2017 Available online xxxx Keywords: Sputtering Tension test Metallic glass Multilayers thin films Graphene
a b s t r a c t We fabricate a nanolaminate by repeated co-sputter deposition of a 60 nm-thick Cu50Zr50 metallic glass layer alternating with transfer of graphene. In situ micro-tensile tests reveal that the addition of a very small fraction (0.46 vol%) of graphene in the nanolaminate improve the elastic modulus and yield strength of the nanolaminate by 9.6% and 14%, respectively, comparing with those of the 360 nm-thick monolithic Cu50Zr50 metallic glass. The nanolaminate also show enhanced tensile ductility: an ultimate tensile strength of 2.23 GPa and fracture strain of 5.39% were attained by strain-hardening after yielding at 1.98 GPa stress and 3.69% strain. © 2017 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
Metallic glasses exhibit superior strength and high elastic limits, but they generally have a lack of tensile ductility that results in sudden and catastrophic failure [1,2]. Considerable work has been aimed at improving the tensile ductility of metallic glasses [3,4], and the development of glass-matrix composites with high toughness and tensile ductility is being explored [5]. Two basic techniques are employed to attain high tensile ductility: introducing a softer secondary phase in the metallic glass matrix to induce generation of local shear banding around the secondary phase and reducing its external dimensions to suppress a propagation of shear bands or occur homogeneous flow instead, leading to enhanced strength and ductility [6–9]. Since there are limited structural applications for monolithic metallic glass with dimensions of the order of 100 nm, nanolaminates with alternating layers of metallic glass (with dimensions of 100 nm or less) and another material have been suggested as a more practical material [10,11]. Metallic glass-based nanolaminates with proper interfacial material and optimum layer thickness exhibit improved strength and ductility by utilizing sizedependent homogeneous flow of metallic glass [12,13]. Graphene is known to have an intrinsic breaking strength of 130 GPa at 25% [14] strain, which is promising for application as a corrosion barrier, lubricant material, or interfacial material in nanolaminates [15,16]. While the role of graphene as a reinforcing constituent material in metal-
⁎ Corresponding author at: Center for Multidimensional Carbon Materials (CMCM), Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea. E-mail address: [email protected] (J.-Y. Kim).
http://dx.doi.org/10.1016/j.scriptamat.2017.06.031 1359-6462/© 2017 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
based nanolaminates has been investigated, the strengthening effect of graphene interfacial layers with metallic glass has not been studied. We investigate a nanolaminate with alternating layers of Cu50Zr50 metallic glass and CVD-grown graphene with enhanced tensile strength and ductility. We fabricate monolithic 360 nm-thick Cu50Zr50 metallic glass and a nanolaminate consisting of 60 nm-thick Cu50Zr50 metallic glass and graphene, and conduct in situ micro-tensile testing. Compared with the 360 nm-thick monolithic metallic glass, which shows typical brittle fracture behavior, i.e., linear elastic deformation followed by catastrophic failure, the nanolaminate shows 14% higher yield strength and enhanced plasticity. Through interrupted micro-tensile testing, we investigate the strain-hardening behavior of the nanolaminate by suppressing shear-band propagation in the 60 nm-thick metallic glass layer. Fig. 1 illustrates the process used to prepare a nanolaminate with alternating layers of 60 nm-thick Cu50Zr50 metallic glass; the nanolaminate consisted of a total of five layers of graphene interleaving between a total of six layers of Cu50Zr50 metallic glass. The Cu50Zr50 metallic glass was deposited on a Si(100) substrate by co-sputtering using two separated pure Cu and Zr targets. The chemical composition of the Cu50Zr50 metallic glass was measured by energy-dispersive X-ray spectroscopy (EDS), and the existence of Cu50Zr50 in the amorphous phase was confirmed by transition electron microscopy (TEM). Graphene was synthesized on a 25 μm-thick Cu foil by CVD and transferred on Cu50Zr50 metallic glass thin film by PMMA-assisted method [17]. We measured the ratio of the intensities of the 2D and G peaks (I2D/IG) for transferred graphene on the Cu50Zr50 layer using Raman spectroscopy,
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Fig. 1. Fabrication of nanolaminate with alternating layers of Cu50Zr50 metallic glass and graphene, and sample preparation for in-situ SEM micro-tensile testing.
which confirmed most transferred area was monolayer graphene as shown in inset of Fig. 1. Freestanding film samples of the monolithic metallic glass and nanolaminate were prepared by undercutting the Si substrate by isotropic dry-etch with XeF2 gas. Dog-bone-shaped specimens with dimensions of 1 μm (gauge width) × 4 μm (gauge length) were prepared by FIB (Quanta 3D, FEI, USA) milling and then transferred onto push-topull (P-to-P) devices (Hysitron, USA) using a micromanipulator for in situ SEM micro-tensile testing. In situ SEM uniaxial micro-tensile tests were performed using a picoindenter (PI-87, Hysitron, USA). The micro-tensile tests were carried out at a constant strain rate of 1 × 10−3 s−1, and real-time movies were recorded with a field-emission SEM (FE-SEM; Quanta200, FEI, USA). The actual force exerted on each dog-gone-shaped specimen was computed by subtracting the estimated force using the stiffness of the push-to-pull devices. The initial geometry of the specimen was measured using SEM images, and the change in gauge length was measured using still images extracted from the movie, from which the true stress and strain were calculated. Fig. 2 shows typical stress–strain curves of the specimens. The monolithic metallic glass showed typical brittle fracture behavior: linear elastic deformation followed by sudden and catastrophic failure directly after yielding at a yield strength of 1.74 ± 0.03 GPa, which were measured by the 0.2%-offset method. Compared to the monolithic metallic glass, the nanolaminate of metallic glass and graphene showed a higher yield strength of 1.98 ± 0.04 GPa and enhanced ductility after yielding, leading to an ultimate tensile strength of 2.23 ± 0.06 GPa and strain of 1.7% from yielding to failure. The elastic modulus, fracture strength, and strain of graphene via computational simulation have approximate values of 1 TPa, 100 GPa, and 20% [18], respectively, even though they deviate slightly depending on the loading direction and methodology. An elastic modulus of 1 TPa and intrinsic breaking strength of 130 GPa at strain of 25% were measured through hole-nanoindentations in single-crystalline graphene [14]. More recently, a fracture strength of 98.5 GPa and elastic modulus of 979 GPa were measured for CVDgrown graphene with grain sizes of 1–5 μm, and a fracture strength of
118 GPa and elastic modulus of 1011 GPa were measured for CVDgrown graphene with grain sizes of 50–200 μm [19]. These values are in good agreement with those predicted by computational simulations of single-crystalline graphene. The CVD-grown graphene used in this study is likely to have a grain size about 10 μm [20]. It is likely that few grain boundaries were included in the five graphene layers in the nanolaminate gauge section measuring 1 μm × 4 μm. The nanolaminate specimens were under iso-strain and their fracture strain was 5.39% ± 0.32%, which is much lower than the fracture strain of graphene. Regardless of the graphene grain size, it seems reasonable to assume that as a nanolaminate constituent, graphene showed elastic behavior with an elastic modulus of 1 TPa until nanolaminate failure occurred. The elastic modulus was measured from the slope of the stress– strain curve in the linear elastic region; it had a value of 51.0 ± 2.14 GPa for monolithic metallic glass and 55.9 ± 1.68 GPa for the nanolaminate. The elastic modulus in laminated materials is generally calculated by a simple rule-of-mixture when tensile force is applied along the in-plane direction. The rule-of-mixture was applied to the six layers of 60 nm-thick metallic glass with elastic modulus 51 GPa and five layers of 0.335 nm-thick graphene with elastic modulus of 1 TPa [14], which predicted an elastic modulus of 56 GPa for the resulting nanolaminate, which is similar to the value obtained in our measurements. Despite the very low volume graphene fraction in the nanolaminate, 0.46%, the graphene layers enhanced the elastic modulus of the nanolaminate by 9.6% because of graphene's ultra-high elastic modulus. The yield strength of the nanolaminate was 14% above that of monolithic metallic glass. As with the elastic modulus, the stress applied to constituents in laminated materials can also be calculated by a simple rule-of-mixture when tensile force is applied along the in-plane direction: σnanolaminate = σMGVMG + σgrapheneVgraphene where σ is the stress, V is the volume fraction, and subscript MG indicates metallic glass. Using the measured yield strength of 1.98 GPa for the nanolaminate, the stress applied on graphene, obtained at a yield strain of 3.69% for the nanolaminate, was calculated from an elastic modulus of 1 TPa
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the negligible plasticity by shear-band propagation lead to a transition in deformation mode of monolithic metallic glass to enhanced plasticity by homogeneous flow [7,21]. While the ultimate tensile strength of monolithic metallic glass is enhanced by plastic flow on the sub100 nm scale, its yield strength is not distinctly enhanced [7,22,23]. In nanolaminates whose metallic glass layers are thinner than the critical thickness for the transition, the yield strength of the constituent metallic glass layer is similar to or slightly higher than that of a metallic glass layer that is thicker than the critical thickness. Unlike the 360 nm-thick monolithic metallic glass, the nanolaminate showed enhanced strain-hardening behavior: its ultimate tensile strength of 2.23 GPa was 12.6% higher than its yield strength of 1.98 GPa, and its fracture strain of 5.39% ± 0.32% was 46% higher than its yield strain of 3.69% ± 0.04%. Since the graphene layer exhibited parabolic nonlinear elastic deformation behavior up to strains well above the nanolaminate fracture strain, the onset of nonlinearity in the nanolaminate should most probably be attributed to a transition in deformation mode of the metallic glass layers. When designing the 60 nmthick metallic glass layers in the nanolaminate, we expected the enhanced plasticity by homogeneous flow that was observed in the monolithic metallic glass and the metallic glass layers in the nanolaminate on the sub-100 nm scale. We carried out interrupted micro-tensile testing on the nanolaminate specimens, as shown in Fig. 3. The second and third re-loading curves do not show linear elastic behavior up to the peak stress of previous steps, possibly because of graphene's nonlinear elastic behavior. However, the yield strengths in the first, second, and third loading gradually increased to 1.95 ± 0.05, 2.02 ± 0.02, and 2.11 ± 0.02 GPa, respectively, which should be attributed to strain-hardening of the nanolaminate specimens' metallic glass layers. For bulk metallic glasses, Johnson and Samwer suggested a phenomenological model for temperature-dependent plastic yielding of metallic glass, Fig. 2. (a) Typical tensile curves of 360 nm-thick monolithic metallic glass and nanolaminate with alternating layers of 60 nm-thick metallic glass and graphene. SEM images during tensile testing of (b) 360 nm-thick monolithic metallic glass and (c) the nanolaminate.
and the volume fractions mentioned above. The yield strength of metallic glass in the nanolaminate was estimated to be 1.81 GPa, which is slightly above the yield strength of the 360 nm-thick monolithic metallic glass, 1.74 GPa. By reducing the external size to the sub-100 nm scale,
γy G
2=3
¼ 0:036−0:016ðTTg Þ
where γy is the elastic strain limit in
shear, E the elastic modulus, T the temperature, and Tg the glass-transition temperature [24]. A modified Johnson–Samwer relation was suggested later,
εy E
2=3
¼ 0:026−0:012ðTTg Þ
where εy is the yield strain with
εy = γy/(1 + ν) and ν is Poisson's ratio [25]. A shear modulus of 31.3 GPa, elastic modulus of 84 GPa, Poisson's ratio of 0.35, and glasstransition temperature of 670 K were measured for Cu50Zr50 bulk metallic glass [26]. Substituting these values into the two equations, we found that homogeneous flow could occur at a uniaxial stress of 1.06 GPa from the Johnson–Samwer model and a uniaxial stress of 2.05 GPa from the modified Johnson–Samwer model. The mechanical properties and
Fig. 3. Interrupted in-situ micro-tensile testing for nanolaminate with alternating layers of 60 nm-thick metallic glass and graphene. (a) Yield strength in first, second, and third loading increases gradually, supporting that 60 nm-thick metallic glass layers are strain-hardened by homogeneous flow. (b) Homogeneous deformation is observed during interrupted microtensile testing.
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Fig. 4. Deformation map of metallic glass in nanolaminate at reduced size.
glass-transition temperature of Cu50Zr50 metallic glass could be different from those of Cu50Zr50 bulk metallic glass because our samples were prepared by co-sputtering, which could have led to different microstructural properties such as atomic packing density and homogeneity of atomic mixing. However, the original and modified Johnson– Samwer models both reveal that Cu50Zr50 metallic glass can be deformed by homogeneous flow at a yield strength that is similar to or lower than 1.74 GPa, the value for the 360 nm-thick monolithic Cu50Zr50 metallic glass. The highest strength that can be obtained for the metallic glass layer was the theoretical strength. A value of 2.83 GPa was obtained for the theoretical strength of co-sputtered Cu50Zr50 metallic glass layers in nanolaminates consisting of alternating layers of Cu50Zr50 metallic glass and nanocrystalline Cu [13]. By taking into consideration the volume fractions of the metallic glass and graphene layers, an ultimate tensile strength of 2.23 GPa for the nanolaminate would require the 60 nm-thick metallic glass layers to have a yield strength of 1.98 GPa for shear band propagation, which is much lower than the theoretical strength. The theoretical strength and the stress required for homogeneous flow are both independent of the external size of metallic glass. However, the stress required for shear-band propagation is most likely to depend on the external size of the metallic glass sample. In Griffith's theory, by setting the energy released by crack propagation proportional to the square of external sample size and setting the elastically-stored energy proportional to the cube of the external sample size, one can obtain the stress criterion between regions for brittle fracture and homogeneous deformation. By using the nanopillar diameter and effective sample radius [7,8,25,27], the stress required for shear-band propagation for metallic glass was suggested to increase with decreasing external sample size in the form of an exponential function, σ ∝ d−m where d is the external sample dimension (Fig. 4). The embryonic shear band is known to form on the scale of several atomic diameters [12,28], and the term “shear-band propagation” refers to the development from an embryonic shear band to a mature shear band, which is believed to require higher stress as the external sample size decreases. As mentioned above, the metallic glass layers in the nanolaminate in our study initiated homogeneous flow at a yield strength of 1.81 GPa for the nanolaminate, and it exhibited catastrophic failure by shear-band propagation at the ultimate tensile strength of the nanolaminate.
We designed and fabricated a nanolaminate with six 60 nm-thick layers of Cu50Zr50 metallic glass alternating with five layers of graphene. The primary goals of the design were as follows: (1) enhancing the elastic modulus and yield strength of the nanolaminate by using graphene with an ultra-high elastic modulus and elastic deformation limit as the reinforcing constituent; (2) improving the tensile ductility of the nanolaminate by inducing homogenous flow in the metallic glass layers at a reduced layer thickness. In situ micro-tensile testing revealed that (1) the elastic modulus and yield strength of the nanolaminate were higher than those of the 360 nm-thick monolithic metallic glass, which was explained by the simple rule-of-mixture, and (2) the explicit homogeneous flow in the 60 nm-thick metallic glass layers led to improved tensile ductility of the nanolaminate. This work was supported by the Institute for Basic Science (IBSR019-D1), by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science, ICT & Future Planning (MSIP) (NO. NRF-2015R1A15A1037627), and by the Global Frontier R&D Program on Center for Multiscale Energy System funded by the National Research Foundation under the Ministry of Science, ICT & Future Planning, Korea (2012M3A6A7054855). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
[20]
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